%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM578+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 : n019.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 12:24:53 PM UTC 2026
% Result : Theorem 0.16s 0.49s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 12 unt; 5 def)
% Number of atoms : 292 ( 37 equ)
% Maximal formula atoms : 29 ( 6 avg)
% Number of connectives : 351 ( 107 ~; 78 |; 124 &)
% ( 8 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 76 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f84,axiom,
( aElementOf0(xi,szNzAzT0)
& aElementOf0(xj,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3856) ).
fof(f85,axiom,
( xi != xj
=> ( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3856_02) ).
fof(f86,conjecture,
( ! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(X0),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,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ~ ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X2) ) )
=> ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X2) ) )
| szmzizndt0(sdtlpdtrp0(xN,X1)) = szmzizndt0(sdtlpdtrp0(xN,X0)) ) ) ) ) )
=> ( xi != xj
=> ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xj))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f87,negated_conjecture,
~ ( ! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(X0),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,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ~ ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X2) ) )
=> ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X0))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X2) ) )
| szmzizndt0(sdtlpdtrp0(xN,X1)) = szmzizndt0(sdtlpdtrp0(xN,X0)) ) ) ) ) )
=> ( xi != xj
=> ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xj))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) ) ) ),
inference(negated_conjecture,[status(cth)],[f86]) ).
fof(f98,plain,
~ ( ! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(X0),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 ) )
& ! [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,X1))
=> aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ~ ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& ! [X5] :
( aElementOf0(X5,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X5) ) )
=> ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X0))
& ! [X6] :
( aElementOf0(X6,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X6) ) )
| szmzizndt0(sdtlpdtrp0(xN,X1)) = szmzizndt0(sdtlpdtrp0(xN,X0)) ) ) ) ) )
=> ( xi != xj
=> ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X7] :
( aElementOf0(X7,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X7) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
& ! [X8] :
( aElementOf0(X8,sdtlpdtrp0(xN,xj))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X8) )
& szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)) ) ) ),
inference(rectify,[],[f87]) ).
fof(f208,plain,
( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| xi = xj ),
inference(ennf_transformation,[],[f85]) ).
fof(f209,plain,
( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| xi = xj ),
inference(flattening,[],[f208]) ).
fof(f210,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
& ! [X8] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X8)
| ~ aElementOf0(X8,sdtlpdtrp0(xN,xj)) )
& szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj))
& xi != xj
& ! [X0,X1] :
( ( 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 ) )
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X1)) )
& aSubsetOf0(sdtlpdtrp0(xN,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X0))
| ? [X6] :
( ~ sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X6)
& aElementOf0(X6,sdtlpdtrp0(xN,X0)) ) )
& szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& ! [X5] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X5)
| ~ aElementOf0(X5,sdtlpdtrp0(xN,X1)) ) )
| ~ sdtlseqdt0(szszuzczcdt0(X0),X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ) ),
inference(ennf_transformation,[],[f98]) ).
fof(f211,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
& ! [X8] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X8)
| ~ aElementOf0(X8,sdtlpdtrp0(xN,xj)) )
& szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj))
& xi != xj
& ! [X0,X1] :
( ( 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 ) )
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X1)) )
& aSubsetOf0(sdtlpdtrp0(xN,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X0))
| ? [X6] :
( ~ sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X6)
& aElementOf0(X6,sdtlpdtrp0(xN,X0)) ) )
& szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& ! [X5] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X5)
| ~ aElementOf0(X5,sdtlpdtrp0(xN,X1)) ) )
| ~ sdtlseqdt0(szszuzczcdt0(X0),X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ) ),
inference(flattening,[],[f210]) ).
fof(f226,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 ) )
| ~ sP10(X0) ),
introduced(definition,[new_symbols(definition,[sP10])],[predicate_definition_introduction]) ).
fof(f227,definition,
! [X0,X1] :
( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X0))
| ? [X6] :
( ~ sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X6)
& aElementOf0(X6,sdtlpdtrp0(xN,X0)) )
| ~ sP11(X0,X1) ),
introduced(definition,[new_symbols(definition,[sP11])],[predicate_definition_introduction]) ).
fof(f228,definition,
! [X0,X1] :
( ( 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))))
& sP10(X0)
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X1)) )
& aSubsetOf0(sdtlpdtrp0(xN,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sP11(X0,X1)
& szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& ! [X5] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X5)
| ~ aElementOf0(X5,sdtlpdtrp0(xN,X1)) ) )
| ~ sP12(X0,X1) ),
introduced(definition,[new_symbols(definition,[sP12])],[predicate_definition_introduction]) ).
fof(f229,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X7] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X7)
| ~ aElementOf0(X7,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
& ! [X8] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X8)
| ~ aElementOf0(X8,sdtlpdtrp0(xN,xj)) )
& szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj))
& xi != xj
& ! [X0,X1] :
( sP12(X0,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X0),X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ) ),
inference(definition_folding,[],[f211,f228,f227,f226]) ).
fof(f311,plain,
! [X0,X1] :
( ( 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))))
& sP10(X0)
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X1)) )
& aSubsetOf0(sdtlpdtrp0(xN,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sP11(X0,X1)
& szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& ! [X5] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X5)
| ~ aElementOf0(X5,sdtlpdtrp0(xN,X1)) ) )
| ~ sP12(X0,X1) ),
inference(nnf_transformation,[],[f228]) ).
fof(f312,plain,
! [X0,X1] :
( ( 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))))
& sP10(X0)
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X1)) )
& aSubsetOf0(sdtlpdtrp0(xN,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& sP11(X0,X1)
& szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& ! [X4] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X4)
| ~ aElementOf0(X4,sdtlpdtrp0(xN,X1)) ) )
| ~ sP12(X0,X1) ),
inference(rectify,[],[f311]) ).
fof(f319,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xj))
& ! [X1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xj)) )
& szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj))
& xi != xj
& ! [X2,X3] :
( sP12(X2,X3)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X3)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X3,szNzAzT0) ) ),
inference(rectify,[],[f229]) ).
fof(f544,plain,
aElementOf0(xj,szNzAzT0),
inference(cnf_transformation,[],[f84]) ).
fof(f545,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f84]) ).
fof(f546,plain,
( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| xi = xj ),
inference(cnf_transformation,[],[f209]) ).
fof(f549,plain,
! [X0,X1] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f312]) ).
fof(f563,plain,
! [X2,X3] :
( ~ sdtlseqdt0(szszuzczcdt0(X2),X3)
| sP12(X2,X3)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X3,szNzAzT0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f564,plain,
xi != xj,
inference(cnf_transformation,[],[f319]) ).
fof(f565,plain,
szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)),
inference(cnf_transformation,[],[f319]) ).
fof(f615,plain,
( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ),
inference(global_subsumption,[],[f546,f564]) ).
fof(f687,plain,
! [X0] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ sP12(xj,X0) ),
inference(superposition,[],[f549,f565]) ).
fof(f688,plain,
! [X0] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ sP12(X0,xj) ),
inference(superposition,[],[f549,f565]) ).
fof(f789,definition,
( spl44_31
<=> sdtlseqdt0(szszuzczcdt0(xi),xj) ),
introduced(definition,[new_symbols(definition,[spl44_31])],[avatar_definition]) ).
fof(f791,plain,
( sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ spl44_31 ),
inference(avatar_component_clause,[],[f789]) ).
fof(f793,definition,
( spl44_32
<=> sdtlseqdt0(szszuzczcdt0(xj),xi) ),
introduced(definition,[new_symbols(definition,[spl44_32])],[avatar_definition]) ).
fof(f795,plain,
( sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ spl44_32 ),
inference(avatar_component_clause,[],[f793]) ).
fof(f796,plain,
( spl44_31
| spl44_32 ),
inference(avatar_split_clause,[],[f615,f793,f789]) ).
fof(f810,plain,
~ sP12(xj,xi),
inference(equality_resolution,[],[f687]) ).
fof(f821,plain,
~ sP12(xi,xj),
inference(equality_resolution,[],[f688]) ).
fof(f884,plain,
( sP12(xj,xi)
| ~ aElementOf0(xj,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0)
| ~ spl44_32 ),
inference(resolution,[],[f795,f563]) ).
fof(f889,plain,
( sP12(xj,xi)
| ~ aElementOf0(xi,szNzAzT0)
| ~ spl44_32 ),
inference(forward_subsumption_resolution,[],[f884,f544]) ).
fof(f890,plain,
( sP12(xj,xi)
| ~ spl44_32 ),
inference(forward_subsumption_resolution,[],[f889,f545]) ).
fof(f891,plain,
( $false
| ~ spl44_32 ),
inference(global_subsumption,[],[f890,f810]) ).
fof(f892,plain,
~ spl44_32,
inference(avatar_contradiction_clause,[],[f891]) ).
fof(f893,plain,
( sP12(xi,xj)
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0)
| ~ spl44_31 ),
inference(resolution,[],[f791,f563]) ).
fof(f894,plain,
( ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0)
| ~ spl44_31 ),
inference(forward_subsumption_resolution,[],[f893,f821]) ).
fof(f895,plain,
( ~ aElementOf0(xj,szNzAzT0)
| ~ spl44_31 ),
inference(forward_subsumption_resolution,[],[f894,f545]) ).
fof(f896,plain,
( $false
| ~ spl44_31 ),
inference(forward_subsumption_resolution,[],[f895,f544]) ).
fof(f897,plain,
~ spl44_31,
inference(avatar_contradiction_clause,[],[f896]) ).
cnf(s437,plain,
( spl44_31
| spl44_32 ),
inference(sat_conversion,[],[f796]) ).
cnf(s510,plain,
~ spl44_32,
inference(sat_conversion,[],[f892]) ).
cnf(s517,plain,
~ spl44_31,
inference(sat_conversion,[],[f897]) ).
cnf(s518,plain,
$false,
inference(rat,[],[s437,s510,s517]) ).
fof(f898,plain,
$false,
inference(avatar_sat_refutation,[],[s518]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM578+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 % Computer : n019.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 20:35:34 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 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
% 0.16/0.49 % (3386900)Will run a generic schedule for satisfiability detection.
% 0.16/0.49 % (3386910)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2745202206:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.49 % (3386906)% WARNING: option uhcvi not known.
% 0.16/0.49 % (3386905)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3530541277_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.49 % (3386909)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2633377107:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.49 % (3386906)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3366154190:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.49 % (3386907)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2588067895:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.49 % (3386908)dis+10_1_sil=32000:sp=arity:random_seed=1709039198:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.49 % (3386911)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4097739801:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.49 % (3386907) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3386900-3386907"...
% 0.16/0.49 % (3386909) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3386900-3386909"...
% 0.16/0.49 % (3386907)...printing done.
% 0.16/0.49 % (3386907)Refutation found. Thanks to Tanya!
% 0.16/0.49 % SZS status Theorem for theBenchmark
% 0.16/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.49 % (3386907)------------------------------
% 0.16/0.49 % (3386907)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.49 % (3386907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.49 % (3386907)CaDiCaL version: 2.1.3
% 0.16/0.49 % (3386907)Termination reason: Refutation
% 0.16/0.49 % (3386907)Time elapsed: 0.019 s
% 0.16/0.49 % (3386907)Peak memory usage: 13 MB
% 0.16/0.49 % (3386907)Instructions burned: 27 (million)
% 0.16/0.49 % (3386900)Success in time 0.056 s
% 0.16/0.49 % Vampire exiting
%------------------------------------------------------------------------------