%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM588+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 : n013.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 12:15:53 PM UTC 2026
% Result : Theorem 0.86s 1.14s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 5 unt; 0 def)
% Number of atoms : 329 ( 35 equ)
% Maximal formula atoms : 40 ( 20 avg)
% Number of connectives : 404 ( 91 ~; 64 |; 209 &)
% ( 10 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 14 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 88 ( 68 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f88,conjecture,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( 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))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& X2 != szmzizndt0(sdtlpdtrp0(xN,X0)) ) )
& aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(X1) )
=> ! [X2] :
( ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSubsetOf0(X2,X1)
& sbrdtbr0(X2) = xk
& aElementOf0(X2,slbdtsldtrb0(X1,xk)) )
=> ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3) ) )
=> ( ( 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))
& X3 != szmzizndt0(sdtlpdtrp0(xN,X0)) ) ) )
=> ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f89,negated_conjecture,
~ ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( 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))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& X2 != szmzizndt0(sdtlpdtrp0(xN,X0)) ) )
& aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(X1) )
=> ! [X2] :
( ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSubsetOf0(X2,X1)
& sbrdtbr0(X2) = xk
& aElementOf0(X2,slbdtsldtrb0(X1,xk)) )
=> ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X3) ) )
=> ( ( 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))
& X3 != szmzizndt0(sdtlpdtrp0(xN,X0)) ) ) )
=> ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f97,plain,
~ ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( 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(X1)
& ! [X4] :
( aElementOf0(X4,X1)
=> aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(X1) )
=> ! [X5] :
( ( aSet0(X5)
& ! [X6] :
( aElementOf0(X6,X5)
=> aElementOf0(X6,X1) )
& aSubsetOf0(X5,X1)
& sbrdtbr0(X5) = xk
& aElementOf0(X5,slbdtsldtrb0(X1,xk)) )
=> ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X7] :
( aElementOf0(X7,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7) ) )
=> ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X8] :
( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X8)
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X8 ) ) )
=> ( ! [X9] :
( aElementOf0(X9,X5)
=> aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) ) ) ) ) ) ),
inference(rectify,[],[f89]) ).
fof(f122,plain,
? [X0] :
( ? [X1] :
( ? [X5] :
( ? [X9] :
( ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X9,X5) )
& ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X8] :
( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X8)
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X8 ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) )
& aSet0(X5)
& ! [X6] :
( aElementOf0(X6,X1)
| ~ aElementOf0(X6,X5) )
& aSubsetOf0(X5,X1)
& sbrdtbr0(X5) = xk
& aElementOf0(X5,slbdtsldtrb0(X1,xk)) )
& 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(X1)
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,X1) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(X1) )
& aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f123,plain,
? [X0] :
( ? [X1] :
( ? [X5] :
( ? [X9] :
( ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X9,X5) )
& ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X8] :
( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X8)
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X8 ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) )
& aSet0(X5)
& ! [X6] :
( aElementOf0(X6,X1)
| ~ aElementOf0(X6,X5) )
& aSubsetOf0(X5,X1)
& sbrdtbr0(X5) = xk
& aElementOf0(X5,slbdtsldtrb0(X1,xk)) )
& 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(X1)
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,X1) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(X1) )
& aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f122]) ).
fof(f281,plain,
? [X0] :
( ? [X1] :
( ? [X5] :
( ? [X9] :
( ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X9,X5) )
& ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X8] :
( ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X8)
| ~ aElementOf0(X8,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X8 )
& ( ( aElement0(X8)
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X8 )
| ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) )
& aSet0(X5)
& ! [X6] :
( aElementOf0(X6,X1)
| ~ aElementOf0(X6,X5) )
& aSubsetOf0(X5,X1)
& sbrdtbr0(X5) = xk
& aElementOf0(X5,slbdtsldtrb0(X1,xk)) )
& 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 )
& ( ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aSet0(X1)
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,X1) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(X1) )
& aElementOf0(X0,szNzAzT0) ),
inference(nnf_transformation,[],[f123]) ).
fof(f282,plain,
? [X0] :
( ? [X1] :
( ? [X5] :
( ? [X9] :
( ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X9,X5) )
& ~ aSubsetOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ~ aElementOf0(X5,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X8] :
( ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X8)
| ~ aElementOf0(X8,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X8 )
& ( ( aElement0(X8)
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X8 )
| ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) )
& aSet0(X5)
& ! [X6] :
( aElementOf0(X6,X1)
| ~ aElementOf0(X6,X5) )
& aSubsetOf0(X5,X1)
& sbrdtbr0(X5) = xk
& aElementOf0(X5,slbdtsldtrb0(X1,xk)) )
& 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 )
& ( ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X3 )
| ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aSet0(X1)
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,X1) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(X1) )
& aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f281]) ).
fof(f283,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X3,X2) )
& ~ aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ~ aElementOf0(X2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( ( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X4 )
& ( ( aElement0(X4)
& aElementOf0(X4,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X4 )
| ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X5] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X5)
| ~ aElementOf0(X5,sdtlpdtrp0(xN,X0)) )
& aSet0(X2)
& ! [X6] :
( aElementOf0(X6,X1)
| ~ aElementOf0(X6,X2) )
& aSubsetOf0(X2,X1)
& sbrdtbr0(X2) = xk
& aElementOf0(X2,slbdtsldtrb0(X1,xk)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,X0)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X8] :
( ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X8)
| ~ aElementOf0(X8,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X8 )
& ( ( aElement0(X8)
& aElementOf0(X8,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X8 )
| ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
& aSet0(X1)
& ! [X9] :
( aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X9,X1) )
& aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(X1) )
& aElementOf0(X0,szNzAzT0) ),
inference(rectify,[],[f282]) ).
fof(f284,plain,
( ~ aElementOf0(sK37,sdtmndt0(sdtlpdtrp0(xN,sK34),szmzizndt0(sdtlpdtrp0(xN,sK34))))
& aElementOf0(sK37,sK36)
& ~ aSubsetOf0(sK36,sdtmndt0(sdtlpdtrp0(xN,sK34),szmzizndt0(sdtlpdtrp0(xN,sK34))))
& ~ aElementOf0(sK36,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK34),szmzizndt0(sdtlpdtrp0(xN,sK34))),xk))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK34),szmzizndt0(sdtlpdtrp0(xN,sK34))))
& ! [X4] :
( ( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK34),szmzizndt0(sdtlpdtrp0(xN,sK34))))
| ~ aElement0(X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,sK34))
| szmzizndt0(sdtlpdtrp0(xN,sK34)) = X4 )
& ( ( aElement0(X4)
& aElementOf0(X4,sdtlpdtrp0(xN,sK34))
& szmzizndt0(sdtlpdtrp0(xN,sK34)) != X4 )
| ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK34),szmzizndt0(sdtlpdtrp0(xN,sK34)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK34)),sdtlpdtrp0(xN,sK34))
& ! [X5] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK34)),X5)
| ~ aElementOf0(X5,sdtlpdtrp0(xN,sK34)) )
& aSet0(sK36)
& ! [X6] :
( aElementOf0(X6,sK35)
| ~ aElementOf0(X6,sK36) )
& aSubsetOf0(sK36,sK35)
& xk = sbrdtbr0(sK36)
& aElementOf0(sK36,slbdtsldtrb0(sK35,xk))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK34)),sdtlpdtrp0(xN,sK34))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK34)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,sK34)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK34),szmzizndt0(sdtlpdtrp0(xN,sK34))))
& ! [X8] :
( ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK34),szmzizndt0(sdtlpdtrp0(xN,sK34))))
| ~ aElement0(X8)
| ~ aElementOf0(X8,sdtlpdtrp0(xN,sK34))
| szmzizndt0(sdtlpdtrp0(xN,sK34)) = X8 )
& ( ( aElement0(X8)
& aElementOf0(X8,sdtlpdtrp0(xN,sK34))
& szmzizndt0(sdtlpdtrp0(xN,sK34)) != X8 )
| ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK34),szmzizndt0(sdtlpdtrp0(xN,sK34)))) ) )
& aSet0(sK35)
& ! [X9] :
( aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,sK34),szmzizndt0(sdtlpdtrp0(xN,sK34))))
| ~ aElementOf0(X9,sK35) )
& aSubsetOf0(sK35,sdtmndt0(sdtlpdtrp0(xN,sK34),szmzizndt0(sdtlpdtrp0(xN,sK34))))
& isCountable0(sK35)
& aElementOf0(sK34,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34,sK35,sK36,sK37]),skolemize(X0,sK34),skolemize(X1,sK35),skolemize(X2,sK36),skolemize(X3,sK37)],[f283]) ).
fof(f483,plain,
! [X9] :
( aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,sK34),szmzizndt0(sdtlpdtrp0(xN,sK34))))
| ~ aElementOf0(X9,sK35) ),
inference(cnf_transformation,[],[f284]) ).
fof(f495,plain,
! [X6] :
( aElementOf0(X6,sK35)
| ~ aElementOf0(X6,sK36) ),
inference(cnf_transformation,[],[f284]) ).
fof(f506,plain,
aElementOf0(sK37,sK36),
inference(cnf_transformation,[],[f284]) ).
fof(f507,plain,
~ aElementOf0(sK37,sdtmndt0(sdtlpdtrp0(xN,sK34),szmzizndt0(sdtlpdtrp0(xN,sK34)))),
inference(cnf_transformation,[],[f284]) ).
fof(f649,plain,
~ aElementOf0(sK37,sK35),
inference(resolution,[],[f483,f507]) ).
fof(f651,plain,
~ aElementOf0(sK37,sK36),
inference(resolution,[],[f649,f495]) ).
fof(f652,plain,
$false,
inference(forward_subsumption_resolution,[],[f651,f506]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM588+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 20:37:37 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.86/1.14 % (529882)Detected formulas, will run a generic FOF schedule.
% 0.86/1.14 % (529891)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2974271531:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.86/1.14 % (529891)First to succeed.
% 0.86/1.14 % (529891)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-529882"
% 0.86/1.14 % (529889)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=627945961:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.86/1.14 % (529890)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3736958473:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.86/1.14 % (529887)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=2415586385:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.86/1.14 % (529888)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=705212825:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.86/1.14 % (529892)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=298721384:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.86/1.14 % (529893)dis-21_1_sil=8000:lcm=predicate:random_seed=2566245139: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)
% 0.86/1.14 % (529892)Also succeeded, but the first one will report.
% 0.86/1.14 % (529893)Also succeeded, but the first one will report.
% 0.86/1.14 % (529890)Also succeeded, but the first one will report.
% 0.86/1.14 % (529891)Refutation found. Thanks to Tanya!
% 0.86/1.14 % SZS status Theorem for theBenchmark
% 0.86/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.34 % (529891)------------------------------
% 2.56/1.34 % (529891)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.34 % (529891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.34 % (529891)CaDiCaL version: 2.1.3
% 2.56/1.34 % (529891)Termination reason: Refutation
% 2.56/1.34 % (529891)Time elapsed: 0.005 s
% 2.56/1.34 % (529891)Peak memory usage: 88 MB
% 2.56/1.34 % (529891)Instructions burned: 16 (million)
% 2.56/1.34 % (529891)------------------------------
% 2.56/1.34 % (529891)------------------------------
% 2.56/1.34 % (529882)Success in time 0.278 s
% 2.56/1.34 % Vampire exiting
%------------------------------------------------------------------------------