%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM586+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 0.55s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 13 unt; 2 def)
% Number of atoms : 318 ( 63 equ)
% Maximal formula atoms : 47 ( 8 avg)
% Number of connectives : 357 ( 78 ~; 69 |; 155 &)
% ( 19 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 68 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f86,axiom,
( aFunction0(xC)
& szDzozmdt0(xC) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aFunction0(sdtlpdtrp0(xC,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)) ) )
& ! [X1] :
( ( aElementOf0(X1,szDzozmdt0(sdtlpdtrp0(xC,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))))
& sbrdtbr0(X1) = xk ) )
& ( ( ( ( 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)))) )
& sbrdtbr0(X1) = xk )
=> aElementOf0(X1,szDzozmdt0(sdtlpdtrp0(xC,X0))) ) )
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& ! [X1] :
( ( aSet0(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)) ) ) )
=> ( ( ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| aSubsetOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& sbrdtbr0(X1) = xk )
| aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) ) ) ) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& ! [X2] :
( aElementOf0(X2,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X2)
& ( aElementOf0(X2,X1)
| X2 = szmzizndt0(sdtlpdtrp0(xN,X0)) ) ) )
& sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4151) ).
fof(f87,axiom,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4200) ).
fof(f88,axiom,
( ? [X0] :
( aElementOf0(X0,szDzozmdt0(sdtlpdtrp0(xC,xi)))
& sdtlpdtrp0(sdtlpdtrp0(xC,xi),X0) = xx )
& aElementOf0(xx,sdtlcdtrc0(sdtlpdtrp0(xC,xi),szDzozmdt0(sdtlpdtrp0(xC,xi)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4200_02) ).
fof(f89,conjecture,
? [X0] :
( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) ) )
=> ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& X1 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
=> ( ( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& sbrdtbr0(X0) = xk )
| aElementOf0(X0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ) ) )
& sdtlpdtrp0(sdtlpdtrp0(xC,xi),X0) = xx ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f90,negated_conjecture,
~ ? [X0] :
( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) ) )
=> ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& X1 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
=> ( ( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& sbrdtbr0(X0) = xk )
| aElementOf0(X0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ) ) )
& sdtlpdtrp0(sdtlpdtrp0(xC,xi),X0) = xx ),
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f96,plain,
( aFunction0(xC)
& szDzozmdt0(xC) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aFunction0(sdtlpdtrp0(xC,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))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X2 ) )
& ! [X3] :
( ( aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0)))
=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
=> aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sbrdtbr0(X3) = xk ) )
& ( ( ( ( aSet0(X3)
& ! [X5] :
( aElementOf0(X5,X3)
=> aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
| aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& sbrdtbr0(X3) = xk )
=> aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0))) ) )
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& ! [X6] :
( ( aSet0(X6)
& ( ( 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,X6)
=> aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| aSubsetOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& xk = sbrdtbr0(X6) )
| aElementOf0(X6,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) ) ) ) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X10] :
( aElementOf0(X10,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X10) )
& ! [X11] :
( aElementOf0(X11,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X11)
& ( aElementOf0(X11,X6)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X11 ) ) )
& sdtlpdtrp0(sdtlpdtrp0(xC,X0),X6) = sdtlpdtrp0(xc,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ) ),
inference(rectify,[],[f86]) ).
fof(f97,plain,
~ ? [X0] :
( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) ) )
=> ( ( 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))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X2 ) ) )
=> ( ( ( ( aSet0(X0)
& ! [X3] :
( aElementOf0(X3,X0)
=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& sbrdtbr0(X0) = xk )
| aElementOf0(X0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ) ) )
& sdtlpdtrp0(sdtlpdtrp0(xC,xi),X0) = xx ),
inference(rectify,[],[f90]) ).
fof(f222,plain,
( aFunction0(xC)
& szDzozmdt0(xC) = szNzAzT0
& ! [X0] :
( ( aFunction0(sdtlpdtrp0(xC,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))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X2 ) )
& ! [X3] :
( ( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,X3) )
& aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sbrdtbr0(X3) = xk )
| ~ aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0))) )
& ( aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| ( ( ~ aSet0(X3)
| ? [X5] :
( ~ aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X5,X3) ) )
& ~ aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| sbrdtbr0(X3) != xk ) )
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& ! [X6] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X10] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X10)
| ~ aElementOf0(X10,sdtlpdtrp0(xN,X0)) )
& ! [X11] :
( aElementOf0(X11,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X11)
& ( aElementOf0(X11,X6)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X11 ) ) )
& sdtlpdtrp0(sdtlpdtrp0(xC,X0),X6) = sdtlpdtrp0(xc,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| ~ aSet0(X6)
| ( ( ( ? [X9] :
( ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X9,X6) )
& ~ aSubsetOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| xk != sbrdtbr0(X6) )
& ~ aElementOf0(X6,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)) ) ) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f96]) ).
fof(f223,plain,
( aFunction0(xC)
& szDzozmdt0(xC) = szNzAzT0
& ! [X0] :
( ( aFunction0(sdtlpdtrp0(xC,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))))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X2)
& aElementOf0(X2,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X2 ) )
& ! [X3] :
( ( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,X3) )
& aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sbrdtbr0(X3) = xk )
| ~ aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0))) )
& ( aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| ( ( ~ aSet0(X3)
| ? [X5] :
( ~ aElementOf0(X5,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X5,X3) ) )
& ~ aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| sbrdtbr0(X3) != xk ) )
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& ! [X6] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
& ! [X10] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X10)
| ~ aElementOf0(X10,sdtlpdtrp0(xN,X0)) )
& ! [X11] :
( aElementOf0(X11,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0))))
<=> ( aElement0(X11)
& ( aElementOf0(X11,X6)
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X11 ) ) )
& sdtlpdtrp0(sdtlpdtrp0(xC,X0),X6) = sdtlpdtrp0(xc,sdtpldt0(X6,szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| ~ aSet0(X6)
| ( ( ( ? [X9] :
( ~ aElementOf0(X9,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& aElementOf0(X9,X6) )
& ~ aSubsetOf0(X6,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
| xk != sbrdtbr0(X6) )
& ~ aElementOf0(X6,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)) ) ) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f222]) ).
fof(f224,plain,
! [X0] :
( ( ( ( ( ~ aSet0(X0)
| ? [X3] :
( ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(X3,X0) ) )
& ~ aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| sbrdtbr0(X0) != xk )
& ~ aElementOf0(X0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& 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))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X2 ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi)) ) )
| sdtlpdtrp0(sdtlpdtrp0(xC,xi),X0) != xx ),
inference(ennf_transformation,[],[f97]) ).
fof(f225,plain,
! [X0] :
( ( ( ( ( ~ aSet0(X0)
| ? [X3] :
( ~ aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(X3,X0) ) )
& ~ aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
| sbrdtbr0(X0) != xk )
& ~ aElementOf0(X0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk))
& 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))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X2 ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi)) ) )
| sdtlpdtrp0(sdtlpdtrp0(xC,xi),X0) != xx ),
inference(flattening,[],[f224]) ).
fof(f620,plain,
! [X3,X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| sbrdtbr0(X3) = xk ),
inference(cnf_transformation,[],[f223]) ).
fof(f621,plain,
! [X3,X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
inference(cnf_transformation,[],[f223]) ).
fof(f641,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f87]) ).
fof(f642,plain,
xx = sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK43),
inference(cnf_transformation,[],[f88]) ).
fof(f643,plain,
aElementOf0(sK43,szDzozmdt0(sdtlpdtrp0(xC,xi))),
inference(cnf_transformation,[],[f88]) ).
fof(f651,plain,
! [X0] :
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),X0) != xx
| sbrdtbr0(X0) != xk
| ~ aSubsetOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(cnf_transformation,[],[f225]) ).
fof(f1056,plain,
! [X3,X0] :
( aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| aElementOf0(X0,szNzAzT0) ),
inference(consistent_polarity_flipping,[],[f621]) ).
fof(f1057,plain,
! [X3,X0] :
( aElementOf0(X3,szDzozmdt0(sdtlpdtrp0(xC,X0)))
| aElementOf0(X0,szNzAzT0)
| sbrdtbr0(X3) = xk ),
inference(consistent_polarity_flipping,[],[f620]) ).
fof(f1108,plain,
~ aElementOf0(xi,szNzAzT0),
inference(consistent_polarity_flipping,[],[f641]) ).
fof(f1110,plain,
~ aElementOf0(sK43,szDzozmdt0(sdtlpdtrp0(xC,xi))),
inference(consistent_polarity_flipping,[],[f643]) ).
fof(f1257,plain,
( xx != xx
| xk != sbrdtbr0(sK43)
| ~ aSubsetOf0(sK43,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(superposition,[],[f651,f642]) ).
fof(f1262,plain,
( xk != sbrdtbr0(sK43)
| ~ aSubsetOf0(sK43,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(trivial_inequality_removal,[],[f1257]) ).
fof(f1273,definition,
( spl45_28
<=> xk = sbrdtbr0(sK43) ),
introduced(definition,[new_symbols(definition,[spl45_28])],[avatar_definition]) ).
fof(f1278,definition,
( spl45_29
<=> aSubsetOf0(sK43,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
introduced(definition,[new_symbols(definition,[spl45_29])],[avatar_definition]) ).
fof(f1280,plain,
( ~ aSubsetOf0(sK43,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| spl45_29 ),
inference(avatar_component_clause,[],[f1278]) ).
fof(f1281,plain,
( ~ spl45_29
| ~ spl45_28 ),
inference(avatar_split_clause,[],[f1262,f1273,f1278]) ).
fof(f1890,plain,
( aElementOf0(xi,szNzAzT0)
| xk = sbrdtbr0(sK43) ),
inference(resolution,[],[f1057,f1110]) ).
fof(f1894,plain,
xk = sbrdtbr0(sK43),
inference(forward_subsumption_resolution,[],[f1890,f1108]) ).
fof(f1897,plain,
spl45_28,
inference(avatar_split_clause,[],[f1894,f1273]) ).
fof(f3597,plain,
( aElementOf0(sK43,szDzozmdt0(sdtlpdtrp0(xC,xi)))
| aElementOf0(xi,szNzAzT0)
| spl45_29 ),
inference(resolution,[],[f1280,f1056]) ).
fof(f3598,plain,
( aElementOf0(xi,szNzAzT0)
| spl45_29 ),
inference(forward_subsumption_resolution,[],[f3597,f1110]) ).
fof(f3599,plain,
( $false
| spl45_29 ),
inference(forward_subsumption_resolution,[],[f3598,f1108]) ).
fof(f3600,plain,
spl45_29,
inference(avatar_contradiction_clause,[],[f3599]) ).
cnf(s36,plain,
( ~ spl45_28
| ~ spl45_29 ),
inference(sat_conversion,[],[f1281]) ).
cnf(s82,plain,
spl45_28,
inference(sat_conversion,[],[f1897]) ).
cnf(s188,plain,
spl45_29,
inference(sat_conversion,[],[f3600]) ).
cnf(s207,plain,
$false,
inference(rat,[],[s36,s188,s82]) ).
fof(f3601,plain,
$false,
inference(avatar_sat_refutation,[],[s207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM586+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n001.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 20:44:01 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.55 % (3933134)Will run a generic schedule for satisfiability detection.
% 0.16/0.55 % (3933141)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1008706074:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.55 % (3933140)% WARNING: option uhcvi not known.
% 0.16/0.55 % (3933139)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=976917526_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.55 % (3933140)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2470484638:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.55 % (3933142)dis+10_1_sil=32000:sp=arity:random_seed=1677859249:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.55 % (3933143)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1716118788:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.55 % (3933145)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1105490708:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.55 % (3933144)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=902021474:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.55 % TRYING [1]
% 0.16/0.55 % TRYING [2]
% 0.16/0.55 % TRYING [3]
% 0.16/0.55 % (3933143)Instruction limit reached!
% 0.16/0.55 % (3933143)------------------------------
% 0.16/0.55 % (3933143)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.55 % (3933143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.55 % (3933143)CaDiCaL version: 2.1.3
% 0.16/0.55 % (3933143)Termination reason: Instruction limit
% 0.16/0.55 % (3933143)Termination phase: Saturation
% 0.16/0.55 % (3933143)Time elapsed: 0.069 s
% 0.16/0.55 % (3933143)Peak memory usage: 13 MB
% 0.16/0.55 % (3933143)Instructions burned: 121 (million)
% 0.16/0.55 % (3933142)Instruction limit reached!
% 0.16/0.55 % (3933142)------------------------------
% 0.16/0.55 % (3933142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.55 % (3933142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.55 % (3933142)CaDiCaL version: 2.1.3
% 0.16/0.55 % (3933142)Termination reason: Instruction limit
% 0.16/0.55 % (3933142)Termination phase: Saturation
% 0.16/0.55 % (3933142)Time elapsed: 0.070 s
% 0.16/0.55 % (3933142)Peak memory usage: 13 MB
% 0.16/0.55 % (3933142)Instructions burned: 103 (million)
% 0.16/0.55 % (3933140) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3933134-3933140"...
% 0.16/0.55 % (3933140)...printing done.
% 0.16/0.55 % (3933144)Instruction limit reached!
% 0.16/0.55 % (3933144)------------------------------
% 0.16/0.55 % (3933144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.55 % (3933144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.55 % (3933144)CaDiCaL version: 2.1.3
% 0.16/0.55 % (3933144)Termination reason: Instruction limit
% 0.16/0.55 % (3933144)Termination phase: Saturation
% 0.16/0.55 % (3933144)Time elapsed: 0.082 s
% 0.16/0.55 % (3933144)Peak memory usage: 13 MB
% 0.16/0.55 % (3933144)Instructions burned: 131 (million)
% 0.16/0.55 % (3933140)Refutation found. Thanks to Tanya!
% 0.16/0.55 % SZS status Theorem for theBenchmark
% 0.16/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.55 % (3933140)------------------------------
% 0.16/0.55 % (3933140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.55 % (3933140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.55 % (3933140)CaDiCaL version: 2.1.3
% 0.16/0.55 % (3933140)Termination reason: Refutation
% 0.16/0.55 % (3933140)Time elapsed: 0.081 s
% 0.16/0.55 % (3933140)Peak memory usage: 14 MB
% 0.16/0.55 % (3933140)Instructions burned: 118 (million)
% 0.16/0.55 % (3933134)Success in time 0.123 s
% 0.16/0.55 % Vampire exiting
%------------------------------------------------------------------------------