%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM580+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 : n006.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 1.00s 0.65s
% Output : Refutation 1.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 92 ( 17 unt; 5 def)
% Number of atoms : 496 ( 69 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 577 ( 173 ~; 156 |; 199 &)
% ( 18 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 4 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-2 aty)
% Number of variables : 104 ( 0 sgn 101 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f41,axiom,
! [X0] :
( aSet0(X0)
=> ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardNum) ).
fof(f43,axiom,
! [X0] :
( ( aSet0(X0)
& isFinite0(X0) )
=> ! [X1] :
( aElement0(X1)
=> ( ~ aElementOf0(X1,X0)
=> sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardCons) ).
fof(f80,axiom,
( aElementOf0(xk,szNzAzT0)
& szszuzczcdt0(xk) = xK ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3533) ).
fof(f81,axiom,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,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)) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).
fof(f82,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(f85,axiom,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3989) ).
fof(f86,axiom,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X0)
& aElementOf0(X0,sdtlpdtrp0(xN,xi))
& X0 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
& aSet0(xQ)
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3989_02) ).
fof(f87,conjecture,
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) ) )
=> ( ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xQ)
| X0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
=> sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f88,negated_conjecture,
~ ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) ) )
=> ( ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X0] :
( aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X0)
& ( aElementOf0(X0,xQ)
| X0 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
=> sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ) ),
inference(negated_conjecture,[status(cth)],[f87]) ).
fof(f98,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,X0)) )
=> ( 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(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
=> aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) ),
inference(rectify,[],[f81]) ).
fof(f100,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
& 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))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 ) )
& aSet0(xQ)
& ! [X2] :
( aElementOf0(X2,xQ)
=> aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
inference(rectify,[],[f86]) ).
fof(f101,plain,
~ ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) ) )
=> ( ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 ) ) ) )
=> sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ) ),
inference(rectify,[],[f88]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f151,plain,
! [X0] :
( ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f153,plain,
! [X0] :
( ! [X1] :
( sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| aElementOf0(X1,X0)
| ~ aElement0(X1) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f154,plain,
! [X0] :
( ! [X1] :
( sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| aElementOf0(X1,X0)
| ~ aElement0(X1) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(flattening,[],[f153]) ).
fof(f206,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( 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(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f98]) ).
fof(f207,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( 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(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f206]) ).
fof(f208,plain,
! [X0] :
( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f213,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& 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))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 ) )
& aSet0(xQ)
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X2,xQ) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
inference(ennf_transformation,[],[f100]) ).
fof(f214,plain,
( xK != sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) ) ),
inference(ennf_transformation,[],[f101]) ).
fof(f215,plain,
( xK != sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 ) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) ) ),
inference(flattening,[],[f214]) ).
fof(f227,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 ) )
| ~ sP8(X0) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f228,definition,
! [X0] :
( ( 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))))
& sP8(X0)
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ sP9(X0) ),
introduced(definition,[new_symbols(definition,[sP9])],[predicate_definition_introduction]) ).
fof(f229,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( sP9(X0)
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ? [X1] :
( ~ aElementOf0(X1,szNzAzT0)
& aElementOf0(X1,sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(definition_folding,[],[f207,f228,f227]) ).
fof(f252,plain,
! [X0] :
( ( ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ isFinite0(X0) )
& ( isFinite0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f151]) ).
fof(f305,plain,
! [X0] :
( ( 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))))
& sP8(X0)
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ sP9(X0) ),
inference(nnf_transformation,[],[f228]) ).
fof(f306,plain,
! [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))))
& sP8(X0)
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ sP9(X0) ),
inference(rectify,[],[f305]) ).
fof(f307,plain,
! [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)))) ) )
| ~ sP8(X0) ),
inference(nnf_transformation,[],[f227]) ).
fof(f308,plain,
! [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)))) ) )
| ~ sP8(X0) ),
inference(flattening,[],[f307]) ).
fof(f309,plain,
! [X0] :
( ! [X1] :
( ( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aElement0(X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| szmzizndt0(sdtlpdtrp0(xN,X0)) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,X0))
& szmzizndt0(sdtlpdtrp0(xN,X0)) != X1 )
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ) )
| ~ sP8(X0) ),
inference(rectify,[],[f308]) ).
fof(f310,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( sP9(X0)
| ( ( ~ aSet0(sdtlpdtrp0(xN,X0))
| ( ~ aElementOf0(sK39(X0),szNzAzT0)
& aElementOf0(sK39(X0),sdtlpdtrp0(xN,X0)) ) )
& ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) )
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(X1,sK39(X0))],[f229]) ).
fof(f313,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& 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))
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 )
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(xQ)
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X2,xQ) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
inference(nnf_transformation,[],[f213]) ).
fof(f314,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) )
& 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))
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 )
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aSet0(xQ)
& ! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X2,xQ) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
inference(flattening,[],[f313]) ).
fof(f315,plain,
( xK != sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( ( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X1)
| ( ~ aElementOf0(X1,xQ)
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 ) )
| ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) ) ),
inference(nnf_transformation,[],[f215]) ).
fof(f316,plain,
( xK != sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( ( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X1)
| ( ~ aElementOf0(X1,xQ)
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X1 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X1 ) )
| ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X0] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xi)) ) ),
inference(flattening,[],[f315]) ).
fof(f317,plain,
( xK != sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X0] :
( ( aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElement0(X0)
| ( ~ aElementOf0(X0,xQ)
& szmzizndt0(sdtlpdtrp0(xN,xi)) != X0 ) )
& ( ( aElement0(X0)
& ( aElementOf0(X0,xQ)
| szmzizndt0(sdtlpdtrp0(xN,xi)) = X0 ) )
| ~ aElementOf0(X0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi)) ) ),
inference(rectify,[],[f316]) ).
fof(f318,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f383,plain,
! [X0] :
( ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f252]) ).
fof(f387,plain,
! [X0,X1] :
( aElementOf0(X1,X0)
| sbrdtbr0(sdtpldt0(X0,X1)) = szszuzczcdt0(sbrdtbr0(X0))
| ~ aElement0(X1)
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f516,plain,
xK = szszuzczcdt0(xk),
inference(cnf_transformation,[],[f80]) ).
fof(f517,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f80]) ).
fof(f522,plain,
! [X0] :
( ~ sP9(X0)
| sP8(X0) ),
inference(cnf_transformation,[],[f306]) ).
fof(f526,plain,
! [X0,X1] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) != X1
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f530,plain,
! [X0] :
( sP9(X0)
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f536,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f537,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f539,plain,
! [X0] :
( aSet0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f547,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f85]) ).
fof(f549,plain,
xk = sbrdtbr0(xQ),
inference(cnf_transformation,[],[f314]) ).
fof(f551,plain,
! [X2] :
( aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X2,xQ) ),
inference(cnf_transformation,[],[f314]) ).
fof(f552,plain,
aSet0(xQ),
inference(cnf_transformation,[],[f314]) ).
fof(f561,plain,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)),
inference(cnf_transformation,[],[f317]) ).
fof(f567,plain,
xK != sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(cnf_transformation,[],[f317]) ).
fof(f610,plain,
! [X0] :
( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP8(X0) ),
inference(equality_resolution,[],[f526]) ).
fof(f615,definition,
( spl41_1
<=> aElement0(szmzizndt0(sdtlpdtrp0(xN,xi))) ),
introduced(definition,[new_symbols(definition,[spl41_1])],[avatar_definition]) ).
fof(f616,plain,
( aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ spl41_1 ),
inference(avatar_component_clause,[],[f615]) ).
fof(f672,plain,
( aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ aSet0(sdtlpdtrp0(xN,xi)) ),
inference(resolution,[],[f318,f561]) ).
fof(f683,definition,
( spl41_6
<=> aSet0(sdtlpdtrp0(xN,xi)) ),
introduced(definition,[new_symbols(definition,[spl41_6])],[avatar_definition]) ).
fof(f685,plain,
( ~ aSet0(sdtlpdtrp0(xN,xi))
| spl41_6 ),
inference(avatar_component_clause,[],[f683]) ).
fof(f686,plain,
( ~ spl41_6
| spl41_1 ),
inference(avatar_split_clause,[],[f672,f615,f683]) ).
fof(f740,plain,
( ~ aElementOf0(xk,szNzAzT0)
| isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(superposition,[],[f383,f549]) ).
fof(f742,plain,
( isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(forward_subsumption_resolution,[],[f740,f517]) ).
fof(f743,plain,
isFinite0(xQ),
inference(forward_subsumption_resolution,[],[f742,f552]) ).
fof(f1435,definition,
( spl41_77
<=> sP9(xi) ),
introduced(definition,[new_symbols(definition,[spl41_77])],[avatar_definition]) ).
fof(f1436,plain,
( sP9(xi)
| ~ spl41_77 ),
inference(avatar_component_clause,[],[f1435]) ).
fof(f1711,plain,
( ~ aElementOf0(xi,szNzAzT0)
| spl41_6 ),
inference(resolution,[],[f685,f539]) ).
fof(f1712,plain,
( $false
| spl41_6 ),
inference(forward_subsumption_resolution,[],[f1711,f547]) ).
fof(f1713,plain,
spl41_6,
inference(avatar_contradiction_clause,[],[f1712]) ).
fof(f2115,plain,
! [X0] :
( sP9(X0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f530,f537]) ).
fof(f2116,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sP9(X0) ),
inference(forward_subsumption_resolution,[],[f2115,f536]) ).
fof(f2189,plain,
sP9(xi),
inference(resolution,[],[f2116,f547]) ).
fof(f2200,plain,
spl41_77,
inference(avatar_split_clause,[],[f2189,f1435]) ).
fof(f2225,plain,
( sP8(xi)
| ~ spl41_77 ),
inference(resolution,[],[f1436,f522]) ).
fof(f2852,plain,
( ~ sP8(xi)
| ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ) ),
inference(resolution,[],[f610,f551]) ).
fof(f2860,plain,
( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xQ)
| ~ spl41_77 ),
inference(forward_subsumption_resolution,[],[f2852,f2225]) ).
fof(f3149,plain,
( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = szszuzczcdt0(sbrdtbr0(xQ))
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,xi)))
| ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ~ spl41_77 ),
inference(resolution,[],[f387,f2860]) ).
fof(f3158,plain,
( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = szszuzczcdt0(sbrdtbr0(xQ))
| ~ aSet0(xQ)
| ~ isFinite0(xQ)
| ~ spl41_1
| ~ spl41_77 ),
inference(forward_subsumption_resolution,[],[f3149,f616]) ).
fof(f3182,plain,
( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = szszuzczcdt0(sbrdtbr0(xQ))
| ~ isFinite0(xQ)
| ~ spl41_1
| ~ spl41_77 ),
inference(forward_subsumption_resolution,[],[f3158,f552]) ).
fof(f3220,plain,
( sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = szszuzczcdt0(sbrdtbr0(xQ))
| ~ spl41_1
| ~ spl41_77 ),
inference(forward_subsumption_resolution,[],[f3182,f743]) ).
fof(f3227,plain,
( szszuzczcdt0(xk) = sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ spl41_1
| ~ spl41_77 ),
inference(forward_demodulation,[],[f3220,f549]) ).
fof(f3228,plain,
( xK = sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ spl41_1
| ~ spl41_77 ),
inference(forward_demodulation,[],[f3227,f516]) ).
fof(f3229,plain,
( $false
| ~ spl41_1
| ~ spl41_77 ),
inference(forward_subsumption_resolution,[],[f3228,f567]) ).
fof(f3230,plain,
( ~ spl41_1
| ~ spl41_77 ),
inference(avatar_contradiction_clause,[],[f3229]) ).
cnf(s6,plain,
( spl41_1
| ~ spl41_6 ),
inference(sat_conversion,[],[f686]) ).
cnf(s90,plain,
spl41_6,
inference(sat_conversion,[],[f1713]) ).
cnf(s130,plain,
spl41_77,
inference(sat_conversion,[],[f2200]) ).
cnf(s202,plain,
( ~ spl41_1
| ~ spl41_77 ),
inference(sat_conversion,[],[f3230]) ).
cnf(s208,plain,
~ spl41_1,
inference(rat,[],[s202,s130]) ).
cnf(s246,plain,
$false,
inference(rat,[],[s6,s90,s208]) ).
fof(f3231,plain,
$false,
inference(avatar_sat_refutation,[],[s246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM580+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.17/0.45 % Computer : n006.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Sun Sep 27 20:35:10 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.21/0.50 Running first-order model finding
% 0.21/0.50 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
% 1.00/0.65 % (3292737)Will run a generic schedule for satisfiability detection.
% 1.00/0.65 % (3292746)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3023132362:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.00/0.65 % (3292743)% WARNING: option uhcvi not known.
% 1.00/0.65 % (3292744)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2842300727:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.00/0.65 % (3292742)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=442682691_2999 on theBenchmark for (2999ds/0Mi)
% 1.00/0.65 % (3292748)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3808302104:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.00/0.65 % (3292743)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3621356547:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.00/0.65 % (3292745)dis+10_1_sil=32000:sp=arity:random_seed=228856615:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.00/0.65 % (3292747)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1916743905:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.00/0.65 % TRYING [1]
% 1.00/0.65 % TRYING [2]
% 1.00/0.65 % (3292746)Instruction limit reached!
% 1.00/0.65 % (3292746)------------------------------
% 1.00/0.65 % (3292746)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.00/0.65 % (3292746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.00/0.65 % (3292746)CaDiCaL version: 2.1.3
% 1.00/0.65 % (3292746)Termination reason: Instruction limit
% 1.00/0.65 % (3292746)Termination phase: Saturation
% 1.00/0.65 % (3292746)Time elapsed: 0.061 s
% 1.00/0.65 % (3292746)Peak memory usage: 13 MB
% 1.00/0.65 % (3292746)Instructions burned: 116 (million)
% 1.00/0.65 % TRYING [3]
% 1.00/0.65 % (3292756)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=221718140:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.00/0.65 % (3292745) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3292737-3292745"...
% 1.00/0.65 % (3292745)...printing done.
% 1.00/0.65 % TRYING [1]
% 1.00/0.65 % (3292745)Refutation found. Thanks to Tanya!
% 1.00/0.65 % SZS status Theorem for theBenchmark
% 1.00/0.65 % SZS output start Proof for theBenchmark
% See solution above
% 1.00/0.65 % (3292745)------------------------------
% 1.00/0.65 % (3292745)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.00/0.65 % (3292745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.00/0.65 % (3292745)CaDiCaL version: 2.1.3
% 1.00/0.65 % (3292745)Termination reason: Refutation
% 1.00/0.65 % (3292745)Time elapsed: 0.093 s
% 1.00/0.65 % (3292745)Peak memory usage: 14 MB
% 1.00/0.65 % (3292745)Instructions burned: 85 (million)
% 1.00/0.65 % (3292737)Success in time 0.137 s
% 1.00/0.65 % Vampire exiting
%------------------------------------------------------------------------------