%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM558+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 : 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 12:15:44 PM UTC 2026
% Result : Theorem 2.83s 1.24s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 15 unt; 2 def)
% Number of atoms : 390 ( 62 equ)
% Maximal formula atoms : 43 ( 8 avg)
% Number of connectives : 475 ( 132 ~; 112 |; 194 &)
% ( 6 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn 71 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f62,axiom,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(f63,axiom,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [X0] :
( ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xk ) )
& ( ( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) ) )
| aSubsetOf0(X0,xS) )
& sbrdtbr0(X0) = xk )
=> aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X0] :
( ( aElementOf0(X0,slbdtsldtrb0(xT,xk))
=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xT) )
& aSubsetOf0(X0,xT)
& sbrdtbr0(X0) = xk ) )
& ( ( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xT) ) )
| aSubsetOf0(X0,xT) )
& sbrdtbr0(X0) = xk )
=> aElementOf0(X0,slbdtsldtrb0(xT,xk)) ) )
& ! [X0] :
( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> aElementOf0(X0,slbdtsldtrb0(xT,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ~ ( ! [X0] :
( ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xk ) )
& ( ( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) ) )
| aSubsetOf0(X0,xS) )
& sbrdtbr0(X0) = xk )
=> aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
=> ( ~ ? [X0] : aElementOf0(X0,slbdtsldtrb0(xS,xk))
| slbdtsldtrb0(xS,xk) = slcrc0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2227) ).
fof(f64,axiom,
aElementOf0(xx,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2256) ).
fof(f70,axiom,
( aSet0(sdtmndt0(xQ,xy))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xQ,xy))
<=> ( aElement0(X0)
& aElementOf0(X0,xQ)
& X0 != xy ) )
& aSet0(xP)
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( aElement0(X0)
& ( aElementOf0(X0,sdtmndt0(xQ,xy))
| X0 = xx ) ) )
& xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2357) ).
fof(f71,axiom,
( ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xS) )
& aSubsetOf0(xP,xS)
& sbrdtbr0(xP) = xk
& aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2378) ).
fof(f72,conjecture,
aElementOf0(xx,xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f73,negated_conjecture,
~ aElementOf0(xx,xT),
inference(negated_conjecture,[status(cth)],[f72]) ).
fof(f80,plain,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [X0] :
( ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xk ) )
& ( ( ( ( aSet0(X0)
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(X2,xS) ) )
| aSubsetOf0(X0,xS) )
& sbrdtbr0(X0) = xk )
=> aElementOf0(X0,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X3] :
( ( aElementOf0(X3,slbdtsldtrb0(xT,xk))
=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
=> aElementOf0(X4,xT) )
& aSubsetOf0(X3,xT)
& sbrdtbr0(X3) = xk ) )
& ( ( ( ( aSet0(X3)
& ! [X5] :
( aElementOf0(X5,X3)
=> aElementOf0(X5,xT) ) )
| aSubsetOf0(X3,xT) )
& sbrdtbr0(X3) = xk )
=> aElementOf0(X3,slbdtsldtrb0(xT,xk)) ) )
& ! [X6] :
( aElementOf0(X6,slbdtsldtrb0(xS,xk))
=> aElementOf0(X6,slbdtsldtrb0(xT,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ~ ( ! [X7] :
( ( aElementOf0(X7,slbdtsldtrb0(xS,xk))
=> ( aSet0(X7)
& ! [X8] :
( aElementOf0(X8,X7)
=> aElementOf0(X8,xS) )
& aSubsetOf0(X7,xS)
& xk = sbrdtbr0(X7) ) )
& ( ( ( ( aSet0(X7)
& ! [X9] :
( aElementOf0(X9,X7)
=> aElementOf0(X9,xS) ) )
| aSubsetOf0(X7,xS) )
& xk = sbrdtbr0(X7) )
=> aElementOf0(X7,slbdtsldtrb0(xS,xk)) ) )
=> ( ~ ? [X10] : aElementOf0(X10,slbdtsldtrb0(xS,xk))
| slbdtsldtrb0(xS,xk) = slcrc0 ) ) ),
inference(rectify,[],[f63]) ).
fof(f81,plain,
( aSet0(sdtmndt0(xQ,xy))
& ! [X0] :
( aElementOf0(X0,sdtmndt0(xQ,xy))
<=> ( aElement0(X0)
& aElementOf0(X0,xQ)
& X0 != xy ) )
& aSet0(xP)
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( aElement0(X1)
& ( aElementOf0(X1,sdtmndt0(xQ,xy))
| xx = X1 ) ) )
& xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ),
inference(rectify,[],[f70]) ).
fof(f82,plain,
~ aElementOf0(xx,xT),
inference(flattening,[],[f73]) ).
fof(f84,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f165,plain,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [X0] :
( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xk )
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ( ( ~ aSet0(X0)
| ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sbrdtbr0(X0) != xk ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X3] :
( ( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,xT)
| ~ aElementOf0(X4,X3) )
& aSubsetOf0(X3,xT)
& sbrdtbr0(X3) = xk )
| ~ aElementOf0(X3,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(X3,slbdtsldtrb0(xT,xk))
| ( ( ~ aSet0(X3)
| ? [X5] :
( ~ aElementOf0(X5,xT)
& aElementOf0(X5,X3) ) )
& ~ aSubsetOf0(X3,xT) )
| sbrdtbr0(X3) != xk ) )
& ! [X6] :
( aElementOf0(X6,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X6,slbdtsldtrb0(xS,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ? [X10] : aElementOf0(X10,slbdtsldtrb0(xS,xk))
& slcrc0 != slbdtsldtrb0(xS,xk)
& ! [X7] :
( ( ( aSet0(X7)
& ! [X8] :
( aElementOf0(X8,xS)
| ~ aElementOf0(X8,X7) )
& aSubsetOf0(X7,xS)
& xk = sbrdtbr0(X7) )
| ~ aElementOf0(X7,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X7,slbdtsldtrb0(xS,xk))
| ( ( ~ aSet0(X7)
| ? [X9] :
( ~ aElementOf0(X9,xS)
& aElementOf0(X9,X7) ) )
& ~ aSubsetOf0(X7,xS) )
| xk != sbrdtbr0(X7) ) ) ),
inference(ennf_transformation,[],[f80]) ).
fof(f166,plain,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [X0] :
( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xk )
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ( ( ~ aSet0(X0)
| ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sbrdtbr0(X0) != xk ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X3] :
( ( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,xT)
| ~ aElementOf0(X4,X3) )
& aSubsetOf0(X3,xT)
& sbrdtbr0(X3) = xk )
| ~ aElementOf0(X3,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(X3,slbdtsldtrb0(xT,xk))
| ( ( ~ aSet0(X3)
| ? [X5] :
( ~ aElementOf0(X5,xT)
& aElementOf0(X5,X3) ) )
& ~ aSubsetOf0(X3,xT) )
| sbrdtbr0(X3) != xk ) )
& ! [X6] :
( aElementOf0(X6,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X6,slbdtsldtrb0(xS,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ? [X10] : aElementOf0(X10,slbdtsldtrb0(xS,xk))
& slcrc0 != slbdtsldtrb0(xS,xk)
& ! [X7] :
( ( ( aSet0(X7)
& ! [X8] :
( aElementOf0(X8,xS)
| ~ aElementOf0(X8,X7) )
& aSubsetOf0(X7,xS)
& xk = sbrdtbr0(X7) )
| ~ aElementOf0(X7,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X7,slbdtsldtrb0(xS,xk))
| ( ( ~ aSet0(X7)
| ? [X9] :
( ~ aElementOf0(X9,xS)
& aElementOf0(X9,X7) ) )
& ~ aSubsetOf0(X7,xS) )
| xk != sbrdtbr0(X7) ) ) ),
inference(flattening,[],[f165]) ).
fof(f168,plain,
( ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xP) )
& aSubsetOf0(xP,xS)
& sbrdtbr0(xP) = xk
& aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
inference(ennf_transformation,[],[f71]) ).
fof(f220,plain,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [X0] :
( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xk )
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ( ( ~ aSet0(X0)
| ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sbrdtbr0(X0) != xk ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X3] :
( ( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,xT)
| ~ aElementOf0(X4,X3) )
& aSubsetOf0(X3,xT)
& sbrdtbr0(X3) = xk )
| ~ aElementOf0(X3,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(X3,slbdtsldtrb0(xT,xk))
| ( ( ~ aSet0(X3)
| ? [X5] :
( ~ aElementOf0(X5,xT)
& aElementOf0(X5,X3) ) )
& ~ aSubsetOf0(X3,xT) )
| sbrdtbr0(X3) != xk ) )
& ! [X6] :
( aElementOf0(X6,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X6,slbdtsldtrb0(xS,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ? [X7] : aElementOf0(X7,slbdtsldtrb0(xS,xk))
& slcrc0 != slbdtsldtrb0(xS,xk)
& ! [X8] :
( ( ( aSet0(X8)
& ! [X9] :
( aElementOf0(X9,xS)
| ~ aElementOf0(X9,X8) )
& aSubsetOf0(X8,xS)
& xk = sbrdtbr0(X8) )
| ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
| ( ( ~ aSet0(X8)
| ? [X10] :
( ~ aElementOf0(X10,xS)
& aElementOf0(X10,X8) ) )
& ~ aSubsetOf0(X8,xS) )
| xk != sbrdtbr0(X8) ) ) ),
inference(rectify,[],[f166]) ).
fof(f221,plain,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [X0] :
( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xk )
| ~ aElementOf0(X0,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ( ( ~ aSet0(X0)
| ( ~ aElementOf0(sK15(X0),xS)
& aElementOf0(sK15(X0),X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sbrdtbr0(X0) != xk ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [X3] :
( ( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,xT)
| ~ aElementOf0(X4,X3) )
& aSubsetOf0(X3,xT)
& sbrdtbr0(X3) = xk )
| ~ aElementOf0(X3,slbdtsldtrb0(xT,xk)) )
& ( aElementOf0(X3,slbdtsldtrb0(xT,xk))
| ( ( ~ aSet0(X3)
| ( ~ aElementOf0(sK16(X3),xT)
& aElementOf0(sK16(X3),X3) ) )
& ~ aSubsetOf0(X3,xT) )
| sbrdtbr0(X3) != xk ) )
& ! [X6] :
( aElementOf0(X6,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X6,slbdtsldtrb0(xS,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& aElementOf0(sK17,slbdtsldtrb0(xS,xk))
& slcrc0 != slbdtsldtrb0(xS,xk)
& ! [X8] :
( ( ( aSet0(X8)
& ! [X9] :
( aElementOf0(X9,xS)
| ~ aElementOf0(X9,X8) )
& aSubsetOf0(X8,xS)
& xk = sbrdtbr0(X8) )
| ~ aElementOf0(X8,slbdtsldtrb0(xS,xk)) )
& ( aElementOf0(X8,slbdtsldtrb0(xS,xk))
| ( ( ~ aSet0(X8)
| ( ~ aElementOf0(sK18(X8),xS)
& aElementOf0(sK18(X8),X8) ) )
& ~ aSubsetOf0(X8,xS) )
| xk != sbrdtbr0(X8) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17,sK18]),skolemize(X2,sK15(X0)),skolemize(X5,sK16(X3)),skolemize(X7,sK17),skolemize(X10,sK18(X8))],[f220]) ).
fof(f222,plain,
( aSet0(sdtmndt0(xQ,xy))
& ! [X0] :
( ( aElementOf0(X0,sdtmndt0(xQ,xy))
| ~ aElement0(X0)
| ~ aElementOf0(X0,xQ)
| xy = X0 )
& ( ( aElement0(X0)
& aElementOf0(X0,xQ)
& X0 != xy )
| ~ aElementOf0(X0,sdtmndt0(xQ,xy)) ) )
& aSet0(xP)
& ! [X1] :
( ( aElementOf0(X1,xP)
| ~ aElement0(X1)
| ( ~ aElementOf0(X1,sdtmndt0(xQ,xy))
& xx != X1 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,sdtmndt0(xQ,xy))
| xx = X1 ) )
| ~ aElementOf0(X1,xP) ) )
& xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ),
inference(nnf_transformation,[],[f81]) ).
fof(f223,plain,
( aSet0(sdtmndt0(xQ,xy))
& ! [X0] :
( ( aElementOf0(X0,sdtmndt0(xQ,xy))
| ~ aElement0(X0)
| ~ aElementOf0(X0,xQ)
| xy = X0 )
& ( ( aElement0(X0)
& aElementOf0(X0,xQ)
& X0 != xy )
| ~ aElementOf0(X0,sdtmndt0(xQ,xy)) ) )
& aSet0(xP)
& ! [X1] :
( ( aElementOf0(X1,xP)
| ~ aElement0(X1)
| ( ~ aElementOf0(X1,sdtmndt0(xQ,xy))
& xx != X1 ) )
& ( ( aElement0(X1)
& ( aElementOf0(X1,sdtmndt0(xQ,xy))
| xx = X1 ) )
| ~ aElementOf0(X1,xP) ) )
& xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ),
inference(flattening,[],[f222]) ).
fof(f224,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f336,plain,
aSet0(xS),
inference(cnf_transformation,[],[f62]) ).
fof(f347,plain,
! [X6] :
( aElementOf0(X6,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X6,slbdtsldtrb0(xS,xk)) ),
inference(cnf_transformation,[],[f221]) ).
fof(f353,plain,
! [X3,X4] :
( aElementOf0(X4,xT)
| ~ aElementOf0(X4,X3)
| ~ aElementOf0(X3,slbdtsldtrb0(xT,xk)) ),
inference(cnf_transformation,[],[f221]) ).
fof(f364,plain,
aElementOf0(xx,xS),
inference(cnf_transformation,[],[f64]) ).
fof(f380,plain,
! [X1] :
( aElementOf0(X1,xP)
| ~ aElement0(X1)
| xx != X1 ),
inference(cnf_transformation,[],[f223]) ).
fof(f388,plain,
aElementOf0(xP,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f168]) ).
fof(f392,plain,
~ aElementOf0(xx,xT),
inference(cnf_transformation,[],[f82]) ).
fof(f416,plain,
( aElementOf0(xx,xP)
| ~ aElement0(xx) ),
inference(equality_resolution,[],[f380]) ).
fof(f419,definition,
( spl19_1
<=> aElement0(xx) ),
introduced(definition,[new_symbols(definition,[spl19_1])],[avatar_definition]) ).
fof(f421,plain,
( ~ aElement0(xx)
| spl19_1 ),
inference(avatar_component_clause,[],[f419]) ).
fof(f423,definition,
( spl19_2
<=> aElementOf0(xx,xP) ),
introduced(definition,[new_symbols(definition,[spl19_2])],[avatar_definition]) ).
fof(f425,plain,
( aElementOf0(xx,xP)
| ~ spl19_2 ),
inference(avatar_component_clause,[],[f423]) ).
fof(f426,plain,
( ~ spl19_1
| spl19_2 ),
inference(avatar_split_clause,[],[f416,f423,f419]) ).
fof(f452,plain,
( ! [X0] :
( ~ aElementOf0(xx,X0)
| ~ aSet0(X0) )
| spl19_1 ),
inference(resolution,[],[f224,f421]) ).
fof(f453,plain,
( ~ aSet0(xS)
| spl19_1 ),
inference(resolution,[],[f452,f364]) ).
fof(f457,plain,
( $false
| spl19_1 ),
inference(forward_subsumption_resolution,[],[f453,f336]) ).
fof(f458,plain,
spl19_1,
inference(avatar_contradiction_clause,[],[f457]) ).
fof(f582,plain,
! [X0] :
( ~ aElementOf0(X0,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(xx,X0) ),
inference(resolution,[],[f353,f392]) ).
fof(f583,plain,
! [X0] :
( ~ aElementOf0(X0,slbdtsldtrb0(xS,xk))
| ~ aElementOf0(xx,X0) ),
inference(resolution,[],[f582,f347]) ).
fof(f594,plain,
~ aElementOf0(xx,xP),
inference(resolution,[],[f583,f388]) ).
fof(f598,plain,
( $false
| ~ spl19_2 ),
inference(forward_subsumption_resolution,[],[f594,f425]) ).
fof(f599,plain,
~ spl19_2,
inference(avatar_contradiction_clause,[],[f598]) ).
cnf(s1,plain,
( ~ spl19_1
| spl19_2 ),
inference(sat_conversion,[],[f426]) ).
cnf(s5,plain,
spl19_1,
inference(sat_conversion,[],[f458]) ).
cnf(s21,plain,
~ spl19_2,
inference(sat_conversion,[],[f599]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s1,s21,s5]) ).
fof(f601,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM558+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 20:29:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 2.83/1.24 % (3383602)Detected formulas, will run a generic FOF schedule.
% 2.83/1.24 % (3383610)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=998836115:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.83/1.24 % (3383610)Instruction limit reached!
% 2.83/1.24 % (3383610)------------------------------
% 2.83/1.24 % (3383610)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.24 % (3383610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.24 % (3383610)CaDiCaL version: 2.1.3
% 2.83/1.24 % (3383610)Termination reason: Instruction limit
% 2.83/1.24 % (3383610)Termination phase: Saturation
% 2.83/1.24 % (3383610)Time elapsed: 0.040 s
% 2.83/1.24 % (3383610)Peak memory usage: 90 MB
% 2.83/1.24 % (3383610)Instructions burned: 109 (million)
% 2.83/1.24 % (3383612)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=593010588:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.83/1.24 % (3383607)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=1430305646:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.83/1.24 % (3383608)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=911571920:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.83/1.24 % (3383609)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=2313610221:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.83/1.24 % (3383611)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=197554798:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.83/1.24 % (3383613)dis-21_1_sil=8000:lcm=predicate:random_seed=4103664052: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)
% 2.83/1.24 % (3383612)First to succeed.
% 2.83/1.24 % (3383612)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3383602"
% 2.83/1.24 % (3383611)Also succeeded, but the first one will report.
% 2.83/1.24 % (3383613)Instruction limit reached!
% 2.83/1.24 % (3383613)------------------------------
% 2.83/1.24 % (3383613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.24 % (3383613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.24 % (3383613)CaDiCaL version: 2.1.3
% 2.83/1.24 % (3383613)Termination reason: Instruction limit
% 2.83/1.24 % (3383613)Termination phase: Saturation
% 2.83/1.24 % (3383613)Time elapsed: 0.062 s
% 2.83/1.24 % (3383613)Peak memory usage: 88 MB
% 2.83/1.24 % (3383613)Instructions burned: 130 (million)
% 2.83/1.24 % (3383619)lrs+10_1_sil=8000:sp=occurrence:random_seed=4236510330:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.83/1.24 % (3383619)Instruction limit reached!
% 2.83/1.24 % (3383619)------------------------------
% 2.83/1.24 % (3383619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.24 % (3383619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.24 % (3383619)CaDiCaL version: 2.1.3
% 2.83/1.24 % (3383619)Termination reason: Instruction limit
% 2.83/1.24 % (3383619)Termination phase: Saturation
% 2.83/1.24 % (3383619)Time elapsed: 0.097 s
% 2.83/1.24 % (3383619)Peak memory usage: 92 MB
% 2.83/1.24 % (3383619)Instructions burned: 286 (million)
% 2.83/1.24 % (3383622)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2111096624:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.83/1.24 % (3383622)Refutation not found, incomplete strategy
% 2.83/1.24 % (3383622)------------------------------
% 2.83/1.24 % (3383622)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.24 % (3383622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.24 % (3383622)CaDiCaL version: 2.1.3
% 2.83/1.24 % (3383622)Termination reason: Refutation not found, incomplete strategy
% 2.83/1.24 % (3383622)Time elapsed: 0.004 s
% 2.83/1.24 % (3383622)Peak memory usage: 89 MB
% 2.83/1.24 % (3383622)Instructions burned: 5 (million)
% 2.83/1.24 % (3383612)Refutation found. Thanks to Tanya!
% 2.83/1.24 % SZS status Theorem for theBenchmark
% 2.83/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.44 % (3383612)------------------------------
% 3.51/1.44 % (3383612)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.44 % (3383612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.44 % (3383612)CaDiCaL version: 2.1.3
% 3.51/1.44 % (3383612)Termination reason: Refutation
% 3.51/1.44 % (3383612)Time elapsed: 0.012 s
% 3.51/1.44 % (3383612)Peak memory usage: 90 MB
% 3.51/1.44 % (3383612)Instructions burned: 16 (million)
% 3.51/1.44 % (3383612)------------------------------
% 3.51/1.44 % (3383612)------------------------------
% 3.51/1.44 % (3383602)Success in time 0.414 s
% 3.51/1.44 % Vampire exiting
%------------------------------------------------------------------------------