%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM588+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 : n026.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 12:24:55 PM UTC 2026
% Result : Theorem 0.16s 0.50s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% 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 : 403 ( 90 ~; 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/sandbox2/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(f104,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(f221,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,[],[f104]) ).
fof(f222,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,[],[f221]) ).
fof(f358,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,[],[f222]) ).
fof(f359,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,[],[f358]) ).
fof(f360,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,[],[f359]) ).
fof(f361,plain,
( ~ aElementOf0(sK56,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
& aElementOf0(sK56,sK55)
& ~ aSubsetOf0(sK55,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
& ~ aElementOf0(sK55,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))),xk))
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
& ! [X4] :
( ( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
| ~ aElement0(X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,sK53))
| szmzizndt0(sdtlpdtrp0(xN,sK53)) = X4 )
& ( ( aElement0(X4)
& aElementOf0(X4,sdtlpdtrp0(xN,sK53))
& szmzizndt0(sdtlpdtrp0(xN,sK53)) != X4 )
| ~ aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK53)),sdtlpdtrp0(xN,sK53))
& ! [X5] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK53)),X5)
| ~ aElementOf0(X5,sdtlpdtrp0(xN,sK53)) )
& aSet0(sK55)
& ! [X6] :
( aElementOf0(X6,sK54)
| ~ aElementOf0(X6,sK55) )
& aSubsetOf0(sK55,sK54)
& xk = sbrdtbr0(sK55)
& aElementOf0(sK55,slbdtsldtrb0(sK54,xk))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK53)),sdtlpdtrp0(xN,sK53))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,sK53)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,sK53)) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
& ! [X8] :
( ( aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
| ~ aElement0(X8)
| ~ aElementOf0(X8,sdtlpdtrp0(xN,sK53))
| szmzizndt0(sdtlpdtrp0(xN,sK53)) = X8 )
& ( ( aElement0(X8)
& aElementOf0(X8,sdtlpdtrp0(xN,sK53))
& szmzizndt0(sdtlpdtrp0(xN,sK53)) != X8 )
| ~ aElementOf0(X8,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))) ) )
& aSet0(sK54)
& ! [X9] :
( aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
| ~ aElementOf0(X9,sK54) )
& aSubsetOf0(sK54,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
& isCountable0(sK54)
& aElementOf0(sK53,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56)],[f360]) ).
fof(f664,plain,
! [X9] :
( aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53))))
| ~ aElementOf0(X9,sK54) ),
inference(cnf_transformation,[],[f361]) ).
fof(f676,plain,
! [X6] :
( ~ aElementOf0(X6,sK55)
| aElementOf0(X6,sK54) ),
inference(cnf_transformation,[],[f361]) ).
fof(f687,plain,
aElementOf0(sK56,sK55),
inference(cnf_transformation,[],[f361]) ).
fof(f688,plain,
~ aElementOf0(sK56,sdtmndt0(sdtlpdtrp0(xN,sK53),szmzizndt0(sdtlpdtrp0(xN,sK53)))),
inference(cnf_transformation,[],[f361]) ).
fof(f756,plain,
aElementOf0(sK56,sK54),
inference(resolution,[],[f676,f687]) ).
fof(f758,plain,
~ aElementOf0(sK56,sK54),
inference(resolution,[],[f664,f688]) ).
fof(f759,plain,
$false,
inference(forward_subsumption_resolution,[],[f758,f756]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM588+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n026.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 20:40:57 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.16/0.50 % (3189289)Will run a generic schedule for satisfiability detection.
% 0.16/0.50 % (3189294)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=645689608_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.50 % (3189295)% WARNING: option uhcvi not known.
% 0.16/0.50 % (3189295)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3379643045:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.50 % (3189296)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2658214241:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.50 % (3189297)dis+10_1_sil=32000:sp=arity:random_seed=1018892882:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.50 % (3189298)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=440932712:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.50 % (3189299)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1563606416:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.50 % (3189300)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2603340416:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.50 % (3189297) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3189289-3189297"...
% 0.16/0.50 % (3189297)...printing done.
% 0.16/0.50 % (3189297)Refutation found. Thanks to Tanya!
% 0.16/0.50 % SZS status Theorem for theBenchmark
% 0.16/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.50 % (3189297)------------------------------
% 0.16/0.50 % (3189297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.50 % (3189297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.50 % (3189297)CaDiCaL version: 2.1.3
% 0.16/0.50 % (3189297)Termination reason: Refutation
% 0.16/0.50 % (3189297)Time elapsed: 0.011 s
% 0.16/0.50 % (3189297)Peak memory usage: 12 MB
% 0.16/0.50 % (3189297)Instructions burned: 19 (million)
% 0.16/0.50 % (3189289)Success in time 0.065 s
% 0.16/0.50 % Vampire exiting
%------------------------------------------------------------------------------