%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM566+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 12:15:46 PM UTC 2026
% Result : Theorem 0.66s 0.80s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 71 ( 14 unt; 1 def)
% Number of atoms : 448 ( 73 equ)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 552 ( 175 ~; 154 |; 190 &)
% ( 8 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-2 aty)
% Number of variables : 158 ( 129 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(f42,axiom,
! [X0] :
( aSet0(X0)
=> ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
fof(f73,axiom,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3291) ).
fof(f75,axiom,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(f76,axiom,
( aFunction0(xc)
& ! [X0] :
( ( aElementOf0(X0,szDzozmdt0(xc))
=> ( 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,szDzozmdt0(xc)) ) )
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ! [X0] :
( aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [X1] :
( aElementOf0(X1,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X1) = X0 ) )
& ! [X0] :
( aElementOf0(X0,sdtlcdtrc0(xc,szDzozmdt0(xc)))
=> aElementOf0(X0,xT) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).
fof(f78,axiom,
xK = sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).
fof(f79,axiom,
( aSet0(slcrc0)
& ~ ? [X0] : aElementOf0(X0,slcrc0)
& ! [X0] :
( aElementOf0(X0,slcrc0)
=> aElementOf0(X0,xS) )
& aSubsetOf0(slcrc0,xS)
& aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3476) ).
fof(f81,conjecture,
? [X0] :
( aElementOf0(X0,xT)
& ? [X1] :
( ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) ) )
| aSubsetOf0(X1,xS) )
& isCountable0(X1)
& ! [X2] :
( ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSubsetOf0(X2,X1)
& sbrdtbr0(X2) = xK
& aElementOf0(X2,slbdtsldtrb0(X1,xK)) )
=> sdtlpdtrp0(xc,X2) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f82,negated_conjecture,
~ ? [X0] :
( aElementOf0(X0,xT)
& ? [X1] :
( ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) ) )
| aSubsetOf0(X1,xS) )
& isCountable0(X1)
& ! [X2] :
( ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) )
& aSubsetOf0(X2,X1)
& sbrdtbr0(X2) = xK
& aElementOf0(X2,slbdtsldtrb0(X1,xK)) )
=> sdtlpdtrp0(xc,X2) = X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f81]) ).
fof(f83,plain,
( aFunction0(xc)
& ! [X0] :
( ( aElementOf0(X0,szDzozmdt0(xc))
=> ( 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,szDzozmdt0(xc)) ) )
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ! [X3] :
( aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [X4] :
( aElementOf0(X4,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X4) = X3 ) )
& ! [X5] :
( aElementOf0(X5,sdtlcdtrc0(xc,szDzozmdt0(xc)))
=> aElementOf0(X5,xT) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
inference(rectify,[],[f76]) ).
fof(f85,plain,
( aSet0(slcrc0)
& ~ ? [X0] : aElementOf0(X0,slcrc0)
& ! [X1] :
( aElementOf0(X1,slcrc0)
=> aElementOf0(X1,xS) )
& aSubsetOf0(slcrc0,xS)
& aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)) ),
inference(rectify,[],[f79]) ).
fof(f87,plain,
~ ? [X0] :
( aElementOf0(X0,xT)
& ? [X1] :
( ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xS) ) )
| aSubsetOf0(X1,xS) )
& isCountable0(X1)
& ! [X3] :
( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
=> aElementOf0(X4,X1) )
& aSubsetOf0(X3,X1)
& sbrdtbr0(X3) = xK
& aElementOf0(X3,slbdtsldtrb0(X1,xK)) )
=> sdtlpdtrp0(xc,X3) = X0 ) ) ),
inference(rectify,[],[f82]) ).
fof(f98,plain,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
inference(ennf_transformation,[],[f75]) ).
fof(f99,plain,
( aFunction0(xc)
& ! [X0] :
( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xK )
| ~ aElementOf0(X0,szDzozmdt0(xc)) )
& ( aElementOf0(X0,szDzozmdt0(xc))
| ( ( ~ aSet0(X0)
| ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sbrdtbr0(X0) != xK ) )
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ! [X3] :
( aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [X4] :
( aElementOf0(X4,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X4) = X3 ) )
& ! [X5] :
( aElementOf0(X5,xT)
| ~ aElementOf0(X5,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
inference(ennf_transformation,[],[f83]) ).
fof(f100,plain,
( aFunction0(xc)
& ! [X0] :
( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xK )
| ~ aElementOf0(X0,szDzozmdt0(xc)) )
& ( aElementOf0(X0,szDzozmdt0(xc))
| ( ( ~ aSet0(X0)
| ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sbrdtbr0(X0) != xK ) )
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ! [X3] :
( aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> ? [X4] :
( aElementOf0(X4,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X4) = X3 ) )
& ! [X5] :
( aElementOf0(X5,xT)
| ~ aElementOf0(X5,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
inference(flattening,[],[f99]) ).
fof(f103,plain,
( aSet0(slcrc0)
& ! [X0] : ~ aElementOf0(X0,slcrc0)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,slcrc0) )
& aSubsetOf0(slcrc0,xS)
& aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)) ),
inference(ennf_transformation,[],[f85]) ).
fof(f105,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( ( ( ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X1) ) )
& ~ aSubsetOf0(X1,xS) )
| ~ isCountable0(X1)
| ? [X3] :
( sdtlpdtrp0(xc,X3) != X0
& aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X1)
| ~ aElementOf0(X4,X3) )
& aSubsetOf0(X3,X1)
& sbrdtbr0(X3) = xK
& aElementOf0(X3,slbdtsldtrb0(X1,xK)) ) ) ),
inference(ennf_transformation,[],[f87]) ).
fof(f106,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( ( ( ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X1) ) )
& ~ aSubsetOf0(X1,xS) )
| ~ isCountable0(X1)
| ? [X3] :
( sdtlpdtrp0(xc,X3) != X0
& aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X1)
| ~ aElementOf0(X4,X3) )
& aSubsetOf0(X3,X1)
& sbrdtbr0(X3) = xK
& aElementOf0(X3,slbdtsldtrb0(X1,xK)) ) ) ),
inference(flattening,[],[f105]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f142,plain,
! [X0] :
( ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f169,definition,
! [X0,X1] :
( ? [X3] :
( sdtlpdtrp0(xc,X3) != X0
& aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X1)
| ~ aElementOf0(X4,X3) )
& aSubsetOf0(X3,X1)
& sbrdtbr0(X3) = xK
& aElementOf0(X3,slbdtsldtrb0(X1,xK)) )
| ~ sP5(X0,X1) ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f170,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( ( ( ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X1) ) )
& ~ aSubsetOf0(X1,xS) )
| ~ isCountable0(X1)
| sP5(X0,X1) ) ),
inference(definition_folding,[],[f106,f169]) ).
fof(f171,plain,
( aFunction0(xc)
& ! [X0] :
( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xK )
| ~ aElementOf0(X0,szDzozmdt0(xc)) )
& ( aElementOf0(X0,szDzozmdt0(xc))
| ( ( ~ aSet0(X0)
| ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sbrdtbr0(X0) != xK ) )
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ! [X3] :
( ( aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ! [X4] :
( ~ aElementOf0(X4,szDzozmdt0(xc))
| sdtlpdtrp0(xc,X4) != X3 ) )
& ( ? [X4] :
( aElementOf0(X4,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X4) = X3 )
| ~ aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc))) ) )
& ! [X5] :
( aElementOf0(X5,xT)
| ~ aElementOf0(X5,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
inference(nnf_transformation,[],[f100]) ).
fof(f172,plain,
( aFunction0(xc)
& ! [X0] :
( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xK )
| ~ aElementOf0(X0,szDzozmdt0(xc)) )
& ( aElementOf0(X0,szDzozmdt0(xc))
| ( ( ~ aSet0(X0)
| ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sbrdtbr0(X0) != xK ) )
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ! [X3] :
( ( aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ! [X4] :
( ~ aElementOf0(X4,szDzozmdt0(xc))
| sdtlpdtrp0(xc,X4) != X3 ) )
& ( ? [X5] :
( aElementOf0(X5,szDzozmdt0(xc))
& sdtlpdtrp0(xc,X5) = X3 )
| ~ aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc))) ) )
& ! [X6] :
( aElementOf0(X6,xT)
| ~ aElementOf0(X6,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
inference(rectify,[],[f171]) ).
fof(f173,plain,
( aFunction0(xc)
& ! [X0] :
( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,X0) )
& aSubsetOf0(X0,xS)
& sbrdtbr0(X0) = xK )
| ~ aElementOf0(X0,szDzozmdt0(xc)) )
& ( aElementOf0(X0,szDzozmdt0(xc))
| ( ( ~ aSet0(X0)
| ( ~ aElementOf0(sK6(X0),xS)
& aElementOf0(sK6(X0),X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sbrdtbr0(X0) != xK ) )
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
& ! [X3] :
( ( aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ! [X4] :
( ~ aElementOf0(X4,szDzozmdt0(xc))
| sdtlpdtrp0(xc,X4) != X3 ) )
& ( ( aElementOf0(sK7(X3),szDzozmdt0(xc))
& sdtlpdtrp0(xc,sK7(X3)) = X3 )
| ~ aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc))) ) )
& ! [X6] :
( aElementOf0(X6,xT)
| ~ aElementOf0(X6,sdtlcdtrc0(xc,szDzozmdt0(xc))) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X2,sK6(X0)),skolemize(X5,sK7(X3))],[f172]) ).
fof(f190,plain,
! [X0,X1] :
( ? [X3] :
( sdtlpdtrp0(xc,X3) != X0
& aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X1)
| ~ aElementOf0(X4,X3) )
& aSubsetOf0(X3,X1)
& sbrdtbr0(X3) = xK
& aElementOf0(X3,slbdtsldtrb0(X1,xK)) )
| ~ sP5(X0,X1) ),
inference(nnf_transformation,[],[f169]) ).
fof(f191,plain,
! [X0,X1] :
( ? [X2] :
( sdtlpdtrp0(xc,X2) != X0
& aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,X2) )
& aSubsetOf0(X2,X1)
& sbrdtbr0(X2) = xK
& aElementOf0(X2,slbdtsldtrb0(X1,xK)) )
| ~ sP5(X0,X1) ),
inference(rectify,[],[f190]) ).
fof(f192,plain,
! [X0,X1] :
( ( sdtlpdtrp0(xc,sK17(X0,X1)) != X0
& aSet0(sK17(X0,X1))
& ! [X3] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,sK17(X0,X1)) )
& aSubsetOf0(sK17(X0,X1),X1)
& xK = sbrdtbr0(sK17(X0,X1))
& aElementOf0(sK17(X0,X1),slbdtsldtrb0(X1,xK)) )
| ~ sP5(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X2,sK17(X0,X1))],[f191]) ).
fof(f193,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( ( ( ~ aSet0(X1)
| ( ~ aElementOf0(sK18(X1),xS)
& aElementOf0(sK18(X1),X1) ) )
& ~ aSubsetOf0(X1,xS) )
| ~ isCountable0(X1)
| sP5(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X2,sK18(X1))],[f170]) ).
fof(f194,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f195,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f194]) ).
fof(f196,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f195]) ).
fof(f197,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK19(X0,X1),X0)
& aElementOf0(sK19(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X2,sK19(X0,X1))],[f196]) ).
fof(f210,plain,
! [X0] :
( ( ( sbrdtbr0(X0) = sz00
| slcrc0 != X0 )
& ( X0 = slcrc0
| sz00 != sbrdtbr0(X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f142]) ).
fof(f218,plain,
aSet0(xT),
inference(cnf_transformation,[],[f73]) ).
fof(f220,plain,
isCountable0(xS),
inference(cnf_transformation,[],[f98]) ).
fof(f223,plain,
aSet0(xS),
inference(cnf_transformation,[],[f98]) ).
fof(f224,plain,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(cnf_transformation,[],[f173]) ).
fof(f228,plain,
! [X3,X4] :
( aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ aElementOf0(X4,szDzozmdt0(xc))
| sdtlpdtrp0(xc,X4) != X3 ),
inference(cnf_transformation,[],[f173]) ).
fof(f230,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(cnf_transformation,[],[f173]) ).
fof(f270,plain,
sz00 = xK,
inference(cnf_transformation,[],[f78]) ).
fof(f271,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(cnf_transformation,[],[f103]) ).
fof(f284,plain,
! [X0,X1] :
( xK = sbrdtbr0(sK17(X0,X1))
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f192]) ).
fof(f287,plain,
! [X0,X1] :
( aSet0(sK17(X0,X1))
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f192]) ).
fof(f288,plain,
! [X0,X1] :
( sdtlpdtrp0(xc,sK17(X0,X1)) != X0
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f192]) ).
fof(f290,plain,
! [X0,X1] :
( aElementOf0(sK18(X1),X1)
| ~ aSet0(X1)
| ~ aElementOf0(X0,xT)
| ~ isCountable0(X1)
| sP5(X0,X1) ),
inference(cnf_transformation,[],[f193]) ).
fof(f291,plain,
! [X0,X1] :
( ~ aElementOf0(sK18(X1),xS)
| ~ aSet0(X1)
| ~ aElementOf0(X0,xT)
| ~ isCountable0(X1)
| sP5(X0,X1) ),
inference(cnf_transformation,[],[f193]) ).
fof(f300,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f197]) ).
fof(f337,plain,
! [X0] :
( slcrc0 = X0
| sz00 != sbrdtbr0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f210]) ).
fof(f359,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)),
inference(definition_unfolding,[],[f271,f270]) ).
fof(f367,plain,
! [X0] :
( sbrdtbr0(X0) != xK
| slcrc0 = X0
| ~ aSet0(X0) ),
inference(definition_unfolding,[],[f337,f270]) ).
fof(f374,plain,
! [X4] :
( aElementOf0(sdtlpdtrp0(xc,X4),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ aElementOf0(X4,szDzozmdt0(xc)) ),
inference(equality_resolution,[],[f228]) ).
fof(f393,plain,
! [X0,X1] :
( ~ aSet0(xS)
| ~ aElementOf0(X0,xT)
| ~ isCountable0(xS)
| sP5(X0,xS)
| ~ aSet0(xS)
| ~ aElementOf0(X1,xT)
| ~ isCountable0(xS)
| sP5(X1,xS) ),
inference(resolution,[],[f291,f290]) ).
fof(f394,plain,
! [X0,X1] :
( sP5(X1,xS)
| ~ aElementOf0(X0,xT)
| ~ isCountable0(xS)
| sP5(X0,xS)
| ~ aElementOf0(X1,xT)
| ~ aSet0(xS) ),
inference(duplicate_literal_removal,[],[f393]) ).
fof(f398,plain,
aElementOf0(slcrc0,szDzozmdt0(xc)),
inference(superposition,[],[f359,f230]) ).
fof(f451,plain,
! [X0,X1] :
( xK != xK
| slcrc0 = sK17(X0,X1)
| ~ aSet0(sK17(X0,X1))
| ~ sP5(X0,X1) ),
inference(superposition,[],[f367,f284]) ).
fof(f457,plain,
! [X0,X1] :
( slcrc0 = sK17(X0,X1)
| ~ aSet0(sK17(X0,X1))
| ~ sP5(X0,X1) ),
inference(trivial_inequality_removal,[],[f451]) ).
fof(f460,plain,
! [X0,X1] :
( slcrc0 = sK17(X0,X1)
| ~ sP5(X0,X1) ),
inference(forward_subsumption_resolution,[],[f457,f287]) ).
fof(f509,plain,
! [X0,X1] :
( sdtlpdtrp0(xc,slcrc0) != X0
| ~ sP5(X0,X1)
| ~ sP5(X0,X1) ),
inference(superposition,[],[f288,f460]) ).
fof(f511,plain,
! [X0,X1] :
( sdtlpdtrp0(xc,slcrc0) != X0
| ~ sP5(X0,X1) ),
inference(duplicate_literal_removal,[],[f509]) ).
fof(f513,plain,
! [X0] : ~ sP5(sdtlpdtrp0(xc,slcrc0),X0),
inference(equality_resolution,[],[f511]) ).
fof(f520,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ~ isCountable0(xS)
| sP5(X0,xS)
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ~ aSet0(xS) ),
inference(resolution,[],[f513,f394]) ).
fof(f523,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| sP5(X0,xS)
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ~ aSet0(xS) ),
inference(forward_subsumption_resolution,[],[f520,f220]) ).
fof(f528,plain,
! [X0] :
( ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| sP5(X0,xS)
| ~ aElementOf0(X0,xT) ),
inference(forward_subsumption_resolution,[],[f523,f223]) ).
fof(f535,plain,
( ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| sP5(sdtlpdtrp0(xc,slcrc0),xS) ),
inference(factoring,[],[f528]) ).
fof(f537,plain,
~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT),
inference(forward_subsumption_resolution,[],[f535,f513]) ).
fof(f596,plain,
! [X0] :
( ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),X0)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[],[f300,f537]) ).
fof(f607,plain,
! [X0] :
( ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),X0)
| ~ aSubsetOf0(X0,xT) ),
inference(forward_subsumption_resolution,[],[f596,f218]) ).
fof(f663,plain,
( ~ aElementOf0(slcrc0,szDzozmdt0(xc))
| ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
inference(resolution,[],[f374,f607]) ).
fof(f673,plain,
~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(forward_subsumption_resolution,[],[f663,f398]) ).
fof(f676,plain,
$false,
inference(forward_subsumption_resolution,[],[f673,f224]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM566+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sun Sep 27 20:31:05 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.66/0.80 % (2711608)Detected formulas, will run a generic FOF schedule.
% 0.66/0.80 % (2711615)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=3302009519:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.66/0.80 % (2711613)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=626333199:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.66/0.80 % (2711614)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=898359472:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.66/0.80 % (2711616)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1800312663:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.66/0.80 % (2711618)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1264034167:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.66/0.80 % (2711617)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3204365285:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.66/0.80 % (2711619)dis-21_1_sil=8000:lcm=predicate:random_seed=3806859001: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)
% 0.66/0.80 % (2711617)First to succeed.
% 0.66/0.80 % (2711617)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2711608"
% 0.66/0.80 % (2711619)Instruction limit reached!
% 0.66/0.80 % (2711619)------------------------------
% 0.66/0.80 % (2711619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.66/0.80 % (2711619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.80 % (2711619)CaDiCaL version: 2.1.3
% 0.66/0.80 % (2711619)Termination reason: Instruction limit
% 0.66/0.80 % (2711619)Termination phase: Saturation
% 0.66/0.80 % (2711619)Time elapsed: 0.034 s
% 0.66/0.80 % (2711619)Peak memory usage: 89 MB
% 0.66/0.80 % (2711619)Instructions burned: 130 (million)
% 0.66/0.80 % (2711616)Instruction limit reached!
% 0.66/0.80 % (2711616)------------------------------
% 0.66/0.80 % (2711616)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.66/0.80 % (2711616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.80 % (2711616)CaDiCaL version: 2.1.3
% 0.66/0.80 % (2711616)Termination reason: Instruction limit
% 0.66/0.80 % (2711616)Termination phase: Saturation
% 0.66/0.80 % (2711616)Time elapsed: 0.040 s
% 0.66/0.80 % (2711616)Peak memory usage: 90 MB
% 0.66/0.80 % (2711616)Instructions burned: 111 (million)
% 0.66/0.80 % (2711618)Instruction limit reached!
% 0.66/0.80 % (2711618)------------------------------
% 0.66/0.80 % (2711618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.66/0.80 % (2711618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.80 % (2711618)CaDiCaL version: 2.1.3
% 0.66/0.80 % (2711618)Termination reason: Instruction limit
% 0.66/0.80 % (2711618)Termination phase: Saturation
% 0.66/0.80 % (2711618)Time elapsed: 0.055 s
% 0.66/0.80 % (2711618)Peak memory usage: 90 MB
% 0.66/0.80 % (2711618)Instructions burned: 139 (million)
% 0.66/0.80 % (2711627)lrs+10_1_sil=8000:sp=occurrence:random_seed=1327157900:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.66/0.80 % (2711628)lrs+10_1_sil=32000:urr=on:br=off:random_seed=770629543:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 0.66/0.80 % (2711629)lrs+1011_1_sil=32000:sp=occurrence:random_seed=325650308:i=325:sd=1:ss=axioms:sgt=32_2998 on theBenchmark for (2998ds/325Mi)
% 0.66/0.80 % (2711628)Also succeeded, but the first one will report.
% 0.66/0.80 % (2711617)Refutation found. Thanks to Tanya!
% 0.66/0.80 % SZS status Theorem for theBenchmark
% 0.66/0.80 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.90 % (2711617)------------------------------
% 0.07/0.90 % (2711617)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.07/0.90 % (2711617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.90 % (2711617)CaDiCaL version: 2.1.3
% 0.07/0.90 % (2711617)Termination reason: Refutation
% 0.07/0.90 % (2711617)Time elapsed: 0.007 s
% 0.07/0.90 % (2711617)Peak memory usage: 88 MB
% 0.07/0.90 % (2711617)Instructions burned: 20 (million)
% 0.07/0.90 % (2711617)------------------------------
% 0.07/0.90 % (2711617)------------------------------
% 0.07/0.90 % (2711608)Success in time 0.271 s
% 0.07/0.90 % Vampire exiting
%------------------------------------------------------------------------------