%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM592+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 12:24:56 PM UTC 2026
% Result : Theorem 0.16s 0.52s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 59 ( 12 unt; 3 def)
% Number of atoms : 388 ( 60 equ)
% Maximal formula atoms : 21 ( 6 avg)
% Number of connectives : 467 ( 138 ~; 115 |; 178 &)
% ( 10 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 3 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 96 ( 0 sgn 79 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f91,axiom,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aSet0(xY)
& ! [X0] :
( aElementOf0(X0,xY)
<=> ( aElement0(X0)
& aElementOf0(X0,sdtlpdtrp0(xN,xi))
& X0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& xd = sdtlpdtrp0(xC,xi) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4448_02) ).
fof(f93,axiom,
( aElementOf0(xu,xT)
& aSet0(xX)
& ! [X0] :
( aElementOf0(X0,xX)
=> aElementOf0(X0,xY) )
& aSubsetOf0(xX,xY)
& isCountable0(xX)
& ! [X0] :
( ( aSet0(X0)
& ( ( ( ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xX) )
| aSubsetOf0(X0,xX) )
& sbrdtbr0(X0) = xk )
| aElementOf0(X0,slbdtsldtrb0(xX,xk)) ) )
=> sdtlpdtrp0(xd,X0) = xu ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4545) ).
fof(f94,conjecture,
? [X0] :
( aElementOf0(X0,xT)
& ? [X1] :
( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2) ) )
=> ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,xi))
& X2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
=> ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
& isCountable0(X1)
& ! [X2] :
( ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSubsetOf0(X2,X1)
& sbrdtbr0(X2) = xk
& aElementOf0(X2,slbdtsldtrb0(X1,xk)) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,xi),X2) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f95,negated_conjecture,
~ ? [X0] :
( aElementOf0(X0,xT)
& ? [X1] :
( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2) ) )
=> ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,xi))
& X2 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
=> ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
& isCountable0(X1)
& ! [X2] :
( ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSubsetOf0(X2,X1)
& sbrdtbr0(X2) = xk
& aElementOf0(X2,slbdtsldtrb0(X1,xk)) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,xi),X2) = X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f111,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aSet0(xY)
& ! [X1] :
( aElementOf0(X1,xY)
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 ) )
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& xd = sdtlpdtrp0(xC,xi) ),
inference(rectify,[],[f91]) ).
fof(f113,plain,
( aElementOf0(xu,xT)
& aSet0(xX)
& ! [X0] :
( aElementOf0(X0,xX)
=> aElementOf0(X0,xY) )
& aSubsetOf0(xX,xY)
& isCountable0(xX)
& ! [X1] :
( ( aSet0(X1)
& ( ( ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xX) )
| aSubsetOf0(X1,xX) )
& sbrdtbr0(X1) = xk )
| aElementOf0(X1,slbdtsldtrb0(xX,xk)) ) )
=> sdtlpdtrp0(xd,X1) = xu ) ),
inference(rectify,[],[f93]) ).
fof(f114,plain,
~ ? [X0] :
( aElementOf0(X0,xT)
& ? [X1] :
( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2) ) )
=> ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X3 ) ) )
=> ( ( aSet0(X1)
& ! [X4] :
( aElementOf0(X4,X1)
=> aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
& isCountable0(X1)
& ! [X5] :
( ( aSet0(X5)
& ! [X6] :
( aElementOf0(X6,X5)
=> aElementOf0(X6,X1) )
& aSubsetOf0(X5,X1)
& sbrdtbr0(X5) = xk
& aElementOf0(X5,slbdtsldtrb0(X1,xk)) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,xi),X5) = X0 ) ) ),
inference(rectify,[],[f95]) ).
fof(f233,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& aSet0(xY)
& ! [X1] :
( aElementOf0(X1,xY)
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 ) )
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& xd = sdtlpdtrp0(xC,xi) ),
inference(ennf_transformation,[],[f111]) ).
fof(f236,plain,
( aElementOf0(xu,xT)
& aSet0(xX)
& ! [X0] :
( aElementOf0(X0,xY)
| ~ aElementOf0(X0,xX) )
& aSubsetOf0(xX,xY)
& isCountable0(xX)
& ! [X1] :
( sdtlpdtrp0(xd,X1) = xu
| ~ aSet0(X1)
| ( ( ( ? [X2] :
( ~ aElementOf0(X2,xX)
& aElementOf0(X2,X1) )
& ~ aSubsetOf0(X1,xX) )
| sbrdtbr0(X1) != xk )
& ~ aElementOf0(X1,slbdtsldtrb0(xX,xk)) ) ) ),
inference(ennf_transformation,[],[f113]) ).
fof(f237,plain,
( aElementOf0(xu,xT)
& aSet0(xX)
& ! [X0] :
( aElementOf0(X0,xY)
| ~ aElementOf0(X0,xX) )
& aSubsetOf0(xX,xY)
& isCountable0(xX)
& ! [X1] :
( sdtlpdtrp0(xd,X1) = xu
| ~ aSet0(X1)
| ( ( ( ? [X2] :
( ~ aElementOf0(X2,xX)
& aElementOf0(X2,X1) )
& ~ aSubsetOf0(X1,xX) )
| sbrdtbr0(X1) != xk )
& ~ aElementOf0(X1,slbdtsldtrb0(xX,xk)) ) ) ),
inference(flattening,[],[f236]) ).
fof(f238,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( ( ( ~ aSet0(X1)
| ? [X4] :
( ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(X4,X1) ) )
& ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X3 ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,xi)) ) )
| ~ isCountable0(X1)
| ? [X5] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X5) != X0
& aSet0(X5)
& ! [X6] :
( aElementOf0(X6,X1)
| ~ aElementOf0(X6,X5) )
& aSubsetOf0(X5,X1)
& sbrdtbr0(X5) = xk
& aElementOf0(X5,slbdtsldtrb0(X1,xk)) ) ) ),
inference(ennf_transformation,[],[f114]) ).
fof(f239,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( ( ( ~ aSet0(X1)
| ? [X4] :
( ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(X4,X1) ) )
& ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X3 ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,xi)) ) )
| ~ isCountable0(X1)
| ? [X5] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X5) != X0
& aSet0(X5)
& ! [X6] :
( aElementOf0(X6,X1)
| ~ aElementOf0(X6,X5) )
& aSubsetOf0(X5,X1)
& sbrdtbr0(X5) = xk
& aElementOf0(X5,slbdtsldtrb0(X1,xk)) ) ) ),
inference(flattening,[],[f238]) ).
fof(f269,definition,
( ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X3 ) )
| ~ sP22 ),
introduced(definition,[new_symbols(definition,[sP22])],[predicate_definition_introduction]) ).
fof(f270,definition,
! [X1] :
( ( ( ~ aSet0(X1)
| ? [X4] :
( ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(X4,X1) ) )
& ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sP22
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,xi)) ) )
| ~ sP23(X1) ),
introduced(definition,[new_symbols(definition,[sP23])],[predicate_definition_introduction]) ).
fof(f271,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( sP23(X1)
| ~ isCountable0(X1)
| ? [X5] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X5) != X0
& aSet0(X5)
& ! [X6] :
( aElementOf0(X6,X1)
| ~ aElementOf0(X6,X5) )
& aSubsetOf0(X5,X1)
& sbrdtbr0(X5) = xk
& aElementOf0(X5,slbdtsldtrb0(X1,xk)) ) ) ),
inference(definition_folding,[],[f239,f270,f269]) ).
fof(f396,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& aSet0(xY)
& ! [X1] :
( ( aElementOf0(X1,xY)
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi))
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 )
| ~ aElementOf0(X1,xY) ) )
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& xd = sdtlpdtrp0(xC,xi) ),
inference(nnf_transformation,[],[f233]) ).
fof(f397,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& aSet0(xY)
& ! [X1] :
( ( aElementOf0(X1,xY)
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi))
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 )
| ~ aElementOf0(X1,xY) ) )
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& xd = sdtlpdtrp0(xC,xi) ),
inference(flattening,[],[f396]) ).
fof(f401,plain,
( aElementOf0(xu,xT)
& aSet0(xX)
& ! [X0] :
( aElementOf0(X0,xY)
| ~ aElementOf0(X0,xX) )
& aSubsetOf0(xX,xY)
& isCountable0(xX)
& ! [X1] :
( sdtlpdtrp0(xd,X1) = xu
| ~ aSet0(X1)
| ( ( ( ~ aElementOf0(sK63(X1),xX)
& aElementOf0(sK63(X1),X1)
& ~ aSubsetOf0(X1,xX) )
| sbrdtbr0(X1) != xk )
& ~ aElementOf0(X1,slbdtsldtrb0(xX,xk)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(X2,sK63(X1))],[f237]) ).
fof(f402,plain,
! [X1] :
( ( ( ~ aSet0(X1)
| ? [X4] :
( ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(X4,X1) ) )
& ~ aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sP22
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,xi)) ) )
| ~ sP23(X1) ),
inference(nnf_transformation,[],[f270]) ).
fof(f403,plain,
! [X0] :
( ( ( ~ aSet0(X0)
| ? [X1] :
( ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(X1,X0) ) )
& ~ aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sP22
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,xi)) ) )
| ~ sP23(X0) ),
inference(rectify,[],[f402]) ).
fof(f404,plain,
! [X0] :
( ( ( ~ aSet0(X0)
| ( ~ aElementOf0(sK64(X0),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(sK64(X0),X0) ) )
& ~ aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sP22
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X2] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X2)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,xi)) ) )
| ~ sP23(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(X1,sK64(X0))],[f403]) ).
fof(f408,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( sP23(X1)
| ~ isCountable0(X1)
| ? [X2] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X2) != X0
& aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,X2) )
& aSubsetOf0(X2,X1)
& sbrdtbr0(X2) = xk
& aElementOf0(X2,slbdtsldtrb0(X1,xk)) ) ) ),
inference(rectify,[],[f271]) ).
fof(f409,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( sP23(X1)
| ~ isCountable0(X1)
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK65(X0,X1)) != X0
& aSet0(sK65(X0,X1))
& ! [X3] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,sK65(X0,X1)) )
& aSubsetOf0(sK65(X0,X1),X1)
& xk = sbrdtbr0(sK65(X0,X1))
& aElementOf0(sK65(X0,X1),slbdtsldtrb0(X1,xk)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(X2,sK65(X0,X1))],[f408]) ).
fof(f737,plain,
xd = sdtlpdtrp0(xC,xi),
inference(cnf_transformation,[],[f397]) ).
fof(f738,plain,
xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),
inference(cnf_transformation,[],[f397]) ).
fof(f761,plain,
! [X1] :
( ~ aElementOf0(X1,slbdtsldtrb0(xX,xk))
| ~ aSet0(X1)
| sdtlpdtrp0(xd,X1) = xu ),
inference(cnf_transformation,[],[f401]) ).
fof(f765,plain,
isCountable0(xX),
inference(cnf_transformation,[],[f401]) ).
fof(f766,plain,
aSubsetOf0(xX,xY),
inference(cnf_transformation,[],[f401]) ).
fof(f769,plain,
aElementOf0(xu,xT),
inference(cnf_transformation,[],[f401]) ).
fof(f774,plain,
! [X0] :
( ~ aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ sP23(X0) ),
inference(cnf_transformation,[],[f404]) ).
fof(f781,plain,
! [X0,X1] :
( aElementOf0(sK65(X0,X1),slbdtsldtrb0(X1,xk))
| sP23(X1)
| ~ isCountable0(X1)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f409]) ).
fof(f785,plain,
! [X0,X1] :
( aSet0(sK65(X0,X1))
| sP23(X1)
| ~ isCountable0(X1)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f409]) ).
fof(f786,plain,
! [X0,X1] :
( ~ aElementOf0(X0,xT)
| sP23(X1)
| ~ isCountable0(X1)
| sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK65(X0,X1)) != X0 ),
inference(cnf_transformation,[],[f409]) ).
fof(f1140,plain,
! [X0] :
( ~ aSubsetOf0(X0,xY)
| ~ sP23(X0) ),
inference(superposition,[],[f774,f738]) ).
fof(f1439,plain,
~ sP23(xX),
inference(resolution,[],[f1140,f766]) ).
fof(f2208,plain,
! [X0,X1] :
( sdtlpdtrp0(xd,sK65(X0,X1)) != X0
| ~ aElementOf0(X0,xT)
| sP23(X1)
| ~ isCountable0(X1) ),
inference(forward_demodulation,[],[f786,f737]) ).
fof(f2519,plain,
! [X0] :
( ~ aSet0(sK65(X0,xX))
| xu = sdtlpdtrp0(xd,sK65(X0,xX))
| sP23(xX)
| ~ isCountable0(xX)
| ~ aElementOf0(X0,xT) ),
inference(resolution,[],[f761,f781]) ).
fof(f2521,plain,
! [X0] :
( ~ aSet0(sK65(X0,xX))
| xu = sdtlpdtrp0(xd,sK65(X0,xX))
| ~ isCountable0(xX)
| ~ aElementOf0(X0,xT) ),
inference(forward_subsumption_resolution,[],[f2519,f1439]) ).
fof(f2522,plain,
! [X0] :
( ~ aSet0(sK65(X0,xX))
| xu = sdtlpdtrp0(xd,sK65(X0,xX))
| ~ aElementOf0(X0,xT) ),
inference(forward_subsumption_resolution,[],[f2521,f765]) ).
fof(f2575,definition,
( spl66_138
<=> aSet0(sK65(xu,xX)) ),
introduced(definition,[new_symbols(definition,[spl66_138])],[avatar_definition]) ).
fof(f2576,plain,
( aSet0(sK65(xu,xX))
| ~ spl66_138 ),
inference(avatar_component_clause,[],[f2575]) ).
fof(f2577,plain,
( ~ aSet0(sK65(xu,xX))
| spl66_138 ),
inference(avatar_component_clause,[],[f2575]) ).
fof(f2587,plain,
( xu = sdtlpdtrp0(xd,sK65(xu,xX))
| ~ aElementOf0(xu,xT)
| ~ spl66_138 ),
inference(resolution,[],[f2576,f2522]) ).
fof(f2588,plain,
( xu = sdtlpdtrp0(xd,sK65(xu,xX))
| ~ spl66_138 ),
inference(forward_subsumption_resolution,[],[f2587,f769]) ).
fof(f2589,plain,
( xu != xu
| ~ aElementOf0(xu,xT)
| sP23(xX)
| ~ isCountable0(xX)
| ~ spl66_138 ),
inference(superposition,[],[f2208,f2588]) ).
fof(f2590,plain,
( ~ aElementOf0(xu,xT)
| sP23(xX)
| ~ isCountable0(xX)
| ~ spl66_138 ),
inference(trivial_inequality_removal,[],[f2589]) ).
fof(f2591,plain,
( sP23(xX)
| ~ isCountable0(xX)
| ~ spl66_138 ),
inference(forward_subsumption_resolution,[],[f2590,f769]) ).
fof(f2592,plain,
( ~ isCountable0(xX)
| ~ spl66_138 ),
inference(forward_subsumption_resolution,[],[f2591,f1439]) ).
fof(f2593,plain,
( $false
| ~ spl66_138 ),
inference(forward_subsumption_resolution,[],[f2592,f765]) ).
fof(f2594,plain,
~ spl66_138,
inference(avatar_contradiction_clause,[],[f2593]) ).
fof(f2628,plain,
( sP23(xX)
| ~ isCountable0(xX)
| ~ aElementOf0(xu,xT)
| spl66_138 ),
inference(resolution,[],[f785,f2577]) ).
fof(f2630,plain,
( ~ isCountable0(xX)
| ~ aElementOf0(xu,xT)
| spl66_138 ),
inference(forward_subsumption_resolution,[],[f2628,f1439]) ).
fof(f2632,plain,
( ~ aElementOf0(xu,xT)
| spl66_138 ),
inference(forward_subsumption_resolution,[],[f2630,f765]) ).
fof(f2634,plain,
( $false
| spl66_138 ),
inference(forward_subsumption_resolution,[],[f2632,f769]) ).
fof(f2635,plain,
spl66_138,
inference(avatar_contradiction_clause,[],[f2634]) ).
cnf(s1602,plain,
~ spl66_138,
inference(sat_conversion,[],[f2594]) ).
cnf(s1644,plain,
spl66_138,
inference(sat_conversion,[],[f2635]) ).
cnf(s1646,plain,
$false,
inference(rat,[],[s1602,s1644]) ).
fof(f2636,plain,
$false,
inference(avatar_sat_refutation,[],[s1646]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM592+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n017.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 20:35:06 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.52 % (2922011)Will run a generic schedule for satisfiability detection.
% 0.16/0.52 % (2922019)dis+10_1_sil=32000:sp=arity:random_seed=1770403084:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.52 % (2922017)% WARNING: option uhcvi not known.
% 0.16/0.52 % (2922017)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2994165819:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.52 % (2922016)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1629118604_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.52 % (2922018)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2040248153:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.52 % (2922020)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1264976952:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.52 % (2922021)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3049538722:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.52 % (2922022)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=690440040:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.52 % (2922019)Instruction limit reached!
% 0.16/0.52 % (2922019)------------------------------
% 0.16/0.52 % (2922019)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (2922019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (2922019)CaDiCaL version: 2.1.3
% 0.16/0.52 % (2922019)Termination reason: Instruction limit
% 0.16/0.52 % (2922019)Termination phase: Saturation
% 0.16/0.52 % (2922019)Time elapsed: 0.040 s
% 0.16/0.52 % (2922019)Peak memory usage: 13 MB
% 0.16/0.52 % (2922019)Instructions burned: 104 (million)
% 0.16/0.52 % (2922030)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2023702585:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.16/0.52 % TRYING [1]
% 0.16/0.52 % TRYING [2]
% 0.16/0.52 % (2922018) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2922011-2922018"...
% 0.16/0.52 % (2922018)...printing done.
% 0.16/0.52 % (2922018)Refutation found. Thanks to Tanya!
% 0.16/0.52 % SZS status Theorem for theBenchmark
% 0.16/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.52 % (2922018)------------------------------
% 0.16/0.52 % (2922018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (2922018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (2922018)CaDiCaL version: 2.1.3
% 0.16/0.52 % (2922018)Termination reason: Refutation
% 0.16/0.52 % (2922018)Time elapsed: 0.060 s
% 0.16/0.52 % (2922018)Peak memory usage: 14 MB
% 0.16/0.52 % (2922018)Instructions burned: 84 (million)
% 0.16/0.52 % (2922011)Success in time 0.1 s
% 0.16/0.52 % Vampire exiting
%------------------------------------------------------------------------------