%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM558+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 : n003.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 12:24:48 PM UTC 2026
% Result : Theorem 0.13s 0.45s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 15 unt; 2 def)
% Number of atoms : 389 ( 62 equ)
% Maximal formula atoms : 43 ( 8 avg)
% Number of connectives : 470 ( 128 ~; 111 |; 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 : 83 ( 0 sgn 69 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f62,axiom,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',m__2227) ).
fof(f64,axiom,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',m__2378) ).
fof(f72,conjecture,
aElementOf0(xx,xT),
file('/export/starexec/sandbox2/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] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f336,plain,
aSet0(xS),
inference(cnf_transformation,[],[f62]) ).
fof(f347,plain,
! [X6] :
( ~ aElementOf0(X6,slbdtsldtrb0(xS,xk))
| aElementOf0(X6,slbdtsldtrb0(xT,xk)) ),
inference(cnf_transformation,[],[f221]) ).
fof(f353,plain,
! [X3,X4] :
( ~ aElementOf0(X3,slbdtsldtrb0(xT,xk))
| ~ aElementOf0(X4,X3)
| aElementOf0(X4,xT) ),
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(f694,plain,
aElementOf0(xP,slbdtsldtrb0(xT,xk)),
inference(resolution,[],[f347,f388]) ).
fof(f723,plain,
! [X0] :
( ~ aElementOf0(X0,xP)
| aElementOf0(X0,xT) ),
inference(resolution,[],[f353,f694]) ).
fof(f754,definition,
( spl19_38
<=> aElement0(xx) ),
introduced(definition,[new_symbols(definition,[spl19_38])],[avatar_definition]) ).
fof(f756,plain,
( ~ aElement0(xx)
| spl19_38 ),
inference(avatar_component_clause,[],[f754]) ).
fof(f758,definition,
( spl19_39
<=> aElementOf0(xx,xP) ),
introduced(definition,[new_symbols(definition,[spl19_39])],[avatar_definition]) ).
fof(f760,plain,
( aElementOf0(xx,xP)
| ~ spl19_39 ),
inference(avatar_component_clause,[],[f758]) ).
fof(f761,plain,
( ~ spl19_38
| spl19_39 ),
inference(avatar_split_clause,[],[f416,f758,f754]) ).
fof(f770,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[],[f224,f364]) ).
fof(f785,plain,
( ~ aSet0(xS)
| spl19_38 ),
inference(forward_subsumption_resolution,[],[f770,f756]) ).
fof(f789,plain,
( $false
| spl19_38 ),
inference(forward_subsumption_resolution,[],[f785,f336]) ).
fof(f790,plain,
spl19_38,
inference(avatar_contradiction_clause,[],[f789]) ).
fof(f793,plain,
( aElementOf0(xx,xT)
| ~ spl19_39 ),
inference(resolution,[],[f760,f723]) ).
fof(f796,plain,
( $false
| ~ spl19_39 ),
inference(forward_subsumption_resolution,[],[f793,f392]) ).
fof(f797,plain,
~ spl19_39,
inference(avatar_contradiction_clause,[],[f796]) ).
cnf(s492,plain,
( ~ spl19_38
| spl19_39 ),
inference(sat_conversion,[],[f761]) ).
cnf(s505,plain,
spl19_38,
inference(sat_conversion,[],[f790]) ).
cnf(s522,plain,
~ spl19_39,
inference(sat_conversion,[],[f797]) ).
cnf(s523,plain,
$false,
inference(rat,[],[s492,s522,s505]) ).
fof(f798,plain,
$false,
inference(avatar_sat_refutation,[],[s523]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM558+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 20:30:57 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 Running first-order model finding
% 0.13/0.39 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
% 0.13/0.45 % (897614)Will run a generic schedule for satisfiability detection.
% 0.13/0.45 % (897624)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3154421949:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.45 % (897620)% WARNING: option uhcvi not known.
% 0.13/0.45 % (897619)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=610743382_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.45 % (897625)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3122173520:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.45 % (897620)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1626234753:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.45 % (897621)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=918997166:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.45 % (897622)dis+10_1_sil=32000:sp=arity:random_seed=1445204437:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.45 % (897623)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=54360357:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.45 % TRYING [1]
% 0.13/0.45 % TRYING [2]
% 0.13/0.45 % (897621) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-897614-897621"...
% 0.13/0.45 % TRYING [3]
% 0.13/0.45 % (897621)...printing done.
% 0.13/0.45 % (897621)Refutation found. Thanks to Tanya!
% 0.13/0.45 % SZS status Theorem for theBenchmark
% 0.13/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.46 % (897621)------------------------------
% 0.13/0.46 % (897621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.46 % (897621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.46 % (897621)CaDiCaL version: 2.1.3
% 0.13/0.46 % (897621)Termination reason: Refutation
% 0.13/0.46 % (897621)Time elapsed: 0.016 s
% 0.13/0.46 % (897621)Peak memory usage: 13 MB
% 0.13/0.46 % (897621)Instructions burned: 21 (million)
% 0.13/0.46 % (897614)Success in time 0.053 s
% 0.13/0.46 % Vampire exiting
%------------------------------------------------------------------------------