%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM578+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 : n018.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 12:15:50 PM UTC 2026
% Result : Theorem 1.76s 1.13s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 8 unt; 3 def)
% Number of atoms : 272 ( 37 equ)
% Maximal formula atoms : 29 ( 7 avg)
% Number of connectives : 327 ( 91 ~; 72 |; 124 &)
% ( 6 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 79 ( 76 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f84,axiom,
( aElementOf0(xi,szNzAzT0)
& aElementOf0(xj,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3856) ).
fof(f85,axiom,
( xi != xj
=> ( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ) ),
file('/export/starexec/sandbox/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/sandbox/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(f91,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(f109,plain,
( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| xi = xj ),
inference(ennf_transformation,[],[f85]) ).
fof(f110,plain,
( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| xi = xj ),
inference(flattening,[],[f109]) ).
fof(f111,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,[],[f91]) ).
fof(f112,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,[],[f111]) ).
fof(f191,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 ) )
| ~ sP6(X0) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f192,definition,
! [X0,X1] :
( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X0))
| ? [X6] :
( ~ sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X6)
& aElementOf0(X6,sdtlpdtrp0(xN,X0)) )
| ~ sP7(X0,X1) ),
introduced(definition,[new_symbols(definition,[sP7])],[predicate_definition_introduction]) ).
fof(f193,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))))
& sP6(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))))
& sP7(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)) ) )
| ~ sP8(X0,X1) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f194,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] :
( sP8(X0,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X0),X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ) ),
inference(definition_folding,[],[f112,f193,f192,f191]) ).
fof(f220,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))))
& sP6(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))))
& sP7(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)) ) )
| ~ sP8(X0,X1) ),
inference(nnf_transformation,[],[f193]) ).
fof(f221,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))))
& sP6(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))))
& sP7(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)) ) )
| ~ sP8(X0,X1) ),
inference(rectify,[],[f220]) ).
fof(f228,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] :
( sP8(X2,X3)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X3)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X3,szNzAzT0) ) ),
inference(rectify,[],[f194]) ).
fof(f343,plain,
aElementOf0(xj,szNzAzT0),
inference(cnf_transformation,[],[f84]) ).
fof(f344,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f84]) ).
fof(f345,plain,
( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| xi = xj ),
inference(cnf_transformation,[],[f110]) ).
fof(f348,plain,
! [X0,X1] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f221]) ).
fof(f362,plain,
! [X2,X3] :
( ~ sdtlseqdt0(szszuzczcdt0(X2),X3)
| sP8(X2,X3)
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X3,szNzAzT0) ),
inference(cnf_transformation,[],[f228]) ).
fof(f363,plain,
xi != xj,
inference(cnf_transformation,[],[f228]) ).
fof(f364,plain,
szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)),
inference(cnf_transformation,[],[f228]) ).
fof(f680,plain,
( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ),
inference(forward_subsumption_resolution,[],[f345,f363]) ).
fof(f681,plain,
( sdtlseqdt0(szszuzczcdt0(xi),xj)
| sP8(xj,xi)
| ~ aElementOf0(xj,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(resolution,[],[f680,f362]) ).
fof(f682,plain,
( sdtlseqdt0(szszuzczcdt0(xi),xj)
| sP8(xj,xi)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f681,f343]) ).
fof(f683,plain,
( sdtlseqdt0(szszuzczcdt0(xi),xj)
| sP8(xj,xi) ),
inference(forward_subsumption_resolution,[],[f682,f344]) ).
fof(f685,plain,
( sP8(xj,xi)
| sP8(xi,xj)
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0) ),
inference(resolution,[],[f683,f362]) ).
fof(f686,plain,
( sP8(xj,xi)
| sP8(xi,xj)
| ~ aElementOf0(xj,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f685,f344]) ).
fof(f687,plain,
( sP8(xj,xi)
| sP8(xi,xj) ),
inference(forward_subsumption_resolution,[],[f686,f343]) ).
fof(f819,plain,
! [X0] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,xj))
| ~ sP8(xi,X0) ),
inference(superposition,[],[f348,f364]) ).
fof(f821,plain,
! [X0] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,xj))
| ~ sP8(X0,xi) ),
inference(superposition,[],[f348,f364]) ).
fof(f829,plain,
~ sP8(xi,xj),
inference(equality_resolution,[],[f819]) ).
fof(f877,plain,
~ sP8(xj,xi),
inference(equality_resolution,[],[f821]) ).
fof(f897,plain,
sP8(xi,xj),
inference(resolution,[],[f877,f687]) ).
fof(f898,plain,
$false,
inference(forward_subsumption_resolution,[],[f897,f829]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM578+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 20:37:09 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 1.76/1.13 % (2704262)Detected formulas, will run a generic FOF schedule.
% 1.76/1.13 % (2704271)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3802365713:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.76/1.13 % (2704271)First to succeed.
% 1.76/1.13 % (2704271)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2704262"
% 1.76/1.13 % (2704270)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3745388706:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.76/1.13 % (2704269)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=67073688:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.76/1.13 % (2704268)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=4202410854:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.76/1.13 % (2704267)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=1675976426:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.76/1.13 % (2704272)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=320041348:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.76/1.13 % (2704273)dis-21_1_sil=8000:lcm=predicate:random_seed=4103636185: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)
% 1.76/1.13 % (2704270)Also succeeded, but the first one will report.
% 1.76/1.13 % (2704273)Instruction limit reached!
% 1.76/1.13 % (2704273)------------------------------
% 1.76/1.13 % (2704273)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.76/1.13 % (2704273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.76/1.13 % (2704273)CaDiCaL version: 2.1.3
% 1.76/1.13 % (2704273)Termination reason: Instruction limit
% 1.76/1.13 % (2704273)Termination phase: Saturation
% 1.76/1.13 % (2704273)Time elapsed: 0.077 s
% 1.76/1.13 % (2704273)Peak memory usage: 91 MB
% 1.76/1.13 % (2704273)Instructions burned: 130 (million)
% 1.76/1.13 % (2704272)Instruction limit reached!
% 1.76/1.13 % (2704272)------------------------------
% 1.76/1.13 % (2704272)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.76/1.13 % (2704272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.76/1.13 % (2704272)CaDiCaL version: 2.1.3
% 1.76/1.13 % (2704272)Termination reason: Instruction limit
% 1.76/1.13 % (2704272)Termination phase: Saturation
% 1.76/1.13 % (2704272)Time elapsed: 0.108 s
% 1.76/1.13 % (2704272)Peak memory usage: 90 MB
% 1.76/1.13 % (2704272)Instructions burned: 139 (million)
% 1.76/1.13 % (2704271)Refutation found. Thanks to Tanya!
% 1.76/1.13 % SZS status Theorem for theBenchmark
% 1.76/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 2.66/1.32 % (2704271)------------------------------
% 2.66/1.32 % (2704271)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.66/1.32 % (2704271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/1.32 % (2704271)CaDiCaL version: 2.1.3
% 2.66/1.32 % (2704271)Termination reason: Refutation
% 2.66/1.32 % (2704271)Time elapsed: 0.010 s
% 2.66/1.32 % (2704271)Peak memory usage: 89 MB
% 2.66/1.32 % (2704271)Instructions burned: 27 (million)
% 2.66/1.32 % (2704271)------------------------------
% 2.66/1.32 % (2704271)------------------------------
% 2.66/1.32 % (2704262)Success in time 0.293 s
% 2.66/1.32 % Vampire exiting
%------------------------------------------------------------------------------