%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM563+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 12:15:45 PM UTC 2026
% Result : Theorem 0.65s 0.79s
% Output : Refutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 9
% Syntax : Number of formulae : 101 ( 16 unt; 1 def)
% Number of atoms : 533 ( 100 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 660 ( 228 ~; 203 |; 192 &)
% ( 10 <=>; 27 =>; 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 : 18 ( 18 usr; 7 con; 0-2 aty)
% Number of variables : 194 ( 163 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ~ ? [X1] : aElementOf0(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
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(f12,axiom,
! [X0] :
( aSet0(X0)
=> aSubsetOf0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
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,conjecture,
( xK = sz00
=> ? [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(f79,negated_conjecture,
~ ( xK = sz00
=> ? [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)],[f78]) ).
fof(f80,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(f82,plain,
~ ( xK = sz00
=> ? [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,[],[f79]) ).
fof(f93,plain,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
inference(ennf_transformation,[],[f75]) ).
fof(f94,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,[],[f80]) ).
fof(f95,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,[],[f94]) ).
fof(f98,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)) ) ) )
& xK = sz00 ),
inference(ennf_transformation,[],[f82]) ).
fof(f99,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)) ) ) )
& xK = sz00 ),
inference(flattening,[],[f98]) ).
fof(f108,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f133,plain,
! [X0] :
( ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f146,plain,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f160,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)) )
| ~ sP4(X0,X1) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f161,plain,
( ! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( ( ( ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X1) ) )
& ~ aSubsetOf0(X1,xS) )
| ~ isCountable0(X1)
| sP4(X0,X1) ) )
& xK = sz00 ),
inference(definition_folding,[],[f99,f160]) ).
fof(f162,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,[],[f95]) ).
fof(f163,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,[],[f162]) ).
fof(f164,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(sK5(X0),xS)
& aElementOf0(sK5(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(sK6(X3),szDzozmdt0(xc))
& sdtlpdtrp0(xc,sK6(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,[sK5,sK6]),skolemize(X2,sK5(X0)),skolemize(X5,sK6(X3))],[f163]) ).
fof(f178,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)) )
| ~ sP4(X0,X1) ),
inference(nnf_transformation,[],[f160]) ).
fof(f179,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)) )
| ~ sP4(X0,X1) ),
inference(rectify,[],[f178]) ).
fof(f180,plain,
! [X0,X1] :
( ( sdtlpdtrp0(xc,sK15(X0,X1)) != X0
& aSet0(sK15(X0,X1))
& ! [X3] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,sK15(X0,X1)) )
& aSubsetOf0(sK15(X0,X1),X1)
& xK = sbrdtbr0(sK15(X0,X1))
& aElementOf0(sK15(X0,X1),slbdtsldtrb0(X1,xK)) )
| ~ sP4(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X2,sK15(X0,X1))],[f179]) ).
fof(f181,plain,
( ! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( ( ( ~ aSet0(X1)
| ( ~ aElementOf0(sK16(X1),xS)
& aElementOf0(sK16(X1),X1) ) )
& ~ aSubsetOf0(X1,xS) )
| ~ isCountable0(X1)
| sP4(X0,X1) ) )
& xK = sz00 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X2,sK16(X1))],[f161]) ).
fof(f182,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,[],[f109]) ).
fof(f183,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,[],[f182]) ).
fof(f184,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,[],[f183]) ).
fof(f185,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK17(X0,X1),X0)
& aElementOf0(sK17(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X2,sK17(X0,X1))],[f184]) ).
fof(f198,plain,
! [X0] :
( ( ( sbrdtbr0(X0) = sz00
| slcrc0 != X0 )
& ( X0 = slcrc0
| sz00 != sbrdtbr0(X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f133]) ).
fof(f200,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f146]) ).
fof(f201,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f200]) ).
fof(f202,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f201]) ).
fof(f203,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| aElementOf0(sK27(X0),X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(X1,sK27(X0))],[f202]) ).
fof(f206,plain,
aSet0(xT),
inference(cnf_transformation,[],[f73]) ).
fof(f208,plain,
isCountable0(xS),
inference(cnf_transformation,[],[f93]) ).
fof(f211,plain,
aSet0(xS),
inference(cnf_transformation,[],[f93]) ).
fof(f212,plain,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(cnf_transformation,[],[f164]) ).
fof(f216,plain,
! [X3,X4] :
( aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ aElementOf0(X4,szDzozmdt0(xc))
| sdtlpdtrp0(xc,X4) != X3 ),
inference(cnf_transformation,[],[f164]) ).
fof(f218,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(cnf_transformation,[],[f164]) ).
fof(f219,plain,
! [X0] :
( sbrdtbr0(X0) != xK
| ~ aSubsetOf0(X0,xS)
| aElementOf0(X0,szDzozmdt0(xc)) ),
inference(cnf_transformation,[],[f164]) ).
fof(f258,plain,
! [X0,X1] :
( aElementOf0(sK15(X0,X1),slbdtsldtrb0(X1,xK))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f180]) ).
fof(f259,plain,
! [X0,X1] :
( xK = sbrdtbr0(sK15(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f180]) ).
fof(f262,plain,
! [X0,X1] :
( aSet0(sK15(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f180]) ).
fof(f263,plain,
! [X0,X1] :
( sdtlpdtrp0(xc,sK15(X0,X1)) != X0
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f180]) ).
fof(f264,plain,
sz00 = xK,
inference(cnf_transformation,[],[f181]) ).
fof(f265,plain,
! [X0,X1] :
( sP4(X0,X1)
| ~ aSubsetOf0(X1,xS)
| ~ isCountable0(X1)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f181]) ).
fof(f266,plain,
! [X0,X1] :
( aElementOf0(sK16(X1),X1)
| ~ aSet0(X1)
| ~ aElementOf0(X0,xT)
| ~ isCountable0(X1)
| sP4(X0,X1) ),
inference(cnf_transformation,[],[f181]) ).
fof(f267,plain,
! [X0,X1] :
( ~ aElementOf0(sK16(X1),xS)
| ~ aSet0(X1)
| ~ aElementOf0(X0,xT)
| ~ isCountable0(X1)
| sP4(X0,X1) ),
inference(cnf_transformation,[],[f181]) ).
fof(f274,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f275,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f185]) ).
fof(f277,plain,
! [X0,X1] :
( aElementOf0(sK17(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f185]) ).
fof(f312,plain,
! [X0] :
( slcrc0 = X0
| sz00 != sbrdtbr0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f313,plain,
! [X0] :
( sz00 = sbrdtbr0(X0)
| slcrc0 != X0
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f327,plain,
! [X0] :
( aSet0(X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f203]) ).
fof(f328,plain,
! [X0] :
( aElementOf0(sK27(X0),X0)
| ~ aSet0(X0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f203]) ).
fof(f337,plain,
! [X0] :
( sbrdtbr0(X0) = xK
| slcrc0 != X0
| ~ aSet0(X0) ),
inference(definition_unfolding,[],[f313,f264]) ).
fof(f338,plain,
! [X0] :
( sbrdtbr0(X0) != xK
| slcrc0 = X0
| ~ aSet0(X0) ),
inference(definition_unfolding,[],[f312,f264]) ).
fof(f345,plain,
! [X4] :
( aElementOf0(sdtlpdtrp0(xc,X4),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ aElementOf0(X4,szDzozmdt0(xc)) ),
inference(equality_resolution,[],[f216]) ).
fof(f360,plain,
( xK = sbrdtbr0(slcrc0)
| ~ aSet0(slcrc0) ),
inference(equality_resolution,[],[f337]) ).
fof(f362,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f327]) ).
fof(f369,plain,
! [X0,X1] :
( ~ aSet0(xS)
| ~ aElementOf0(X0,xT)
| ~ isCountable0(xS)
| sP4(X0,xS)
| ~ aSet0(xS)
| ~ aElementOf0(X1,xT)
| ~ isCountable0(xS)
| sP4(X1,xS) ),
inference(resolution,[],[f267,f266]) ).
fof(f370,plain,
! [X0,X1] :
( sP4(X1,xS)
| ~ aElementOf0(X0,xT)
| ~ isCountable0(xS)
| sP4(X0,xS)
| ~ aElementOf0(X1,xT)
| ~ aSet0(xS) ),
inference(duplicate_literal_removal,[],[f369]) ).
fof(f432,plain,
! [X0,X1] :
( xK != xK
| slcrc0 = sK15(X0,X1)
| ~ aSet0(sK15(X0,X1))
| ~ sP4(X0,X1) ),
inference(superposition,[],[f338,f259]) ).
fof(f433,plain,
! [X0,X1] :
( slcrc0 = sK15(X0,X1)
| ~ aSet0(sK15(X0,X1))
| ~ sP4(X0,X1) ),
inference(trivial_inequality_removal,[],[f432]) ).
fof(f434,plain,
! [X0,X1] :
( slcrc0 = sK15(X0,X1)
| ~ sP4(X0,X1) ),
inference(forward_subsumption_resolution,[],[f433,f262]) ).
fof(f482,plain,
! [X0,X1] :
( aElementOf0(slcrc0,slbdtsldtrb0(X1,xK))
| ~ sP4(X0,X1)
| ~ sP4(X0,X1) ),
inference(superposition,[],[f258,f434]) ).
fof(f484,plain,
! [X0,X1] :
( aElementOf0(slcrc0,slbdtsldtrb0(X1,xK))
| ~ sP4(X0,X1) ),
inference(duplicate_literal_removal,[],[f482]) ).
fof(f485,plain,
! [X0] :
( aElementOf0(slcrc0,szDzozmdt0(xc))
| ~ sP4(X0,xS) ),
inference(superposition,[],[f484,f218]) ).
fof(f486,plain,
! [X0,X1] :
( sdtlpdtrp0(xc,slcrc0) != X0
| ~ sP4(X0,X1)
| ~ sP4(X0,X1) ),
inference(superposition,[],[f263,f434]) ).
fof(f487,plain,
! [X0,X1] :
( sdtlpdtrp0(xc,slcrc0) != X0
| ~ sP4(X0,X1) ),
inference(duplicate_literal_removal,[],[f486]) ).
fof(f492,plain,
! [X0] : ~ sP4(sdtlpdtrp0(xc,slcrc0),X0),
inference(equality_resolution,[],[f487]) ).
fof(f501,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ~ isCountable0(xS)
| sP4(X0,xS)
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ~ aSet0(xS) ),
inference(resolution,[],[f492,f370]) ).
fof(f502,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| sP4(X0,xS)
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ~ aSet0(xS) ),
inference(forward_subsumption_resolution,[],[f501,f208]) ).
fof(f509,plain,
! [X0] :
( ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| sP4(X0,xS)
| ~ aElementOf0(X0,xT) ),
inference(forward_subsumption_resolution,[],[f502,f211]) ).
fof(f516,plain,
( ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| sP4(sdtlpdtrp0(xc,slcrc0),xS) ),
inference(factoring,[],[f509]) ).
fof(f517,plain,
~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT),
inference(forward_subsumption_resolution,[],[f516,f492]) ).
fof(f519,plain,
( xK != xK
| ~ aSubsetOf0(slcrc0,xS)
| aElementOf0(slcrc0,szDzozmdt0(xc))
| ~ aSet0(slcrc0) ),
inference(superposition,[],[f219,f360]) ).
fof(f524,plain,
( ~ aSubsetOf0(slcrc0,xS)
| aElementOf0(slcrc0,szDzozmdt0(xc))
| ~ aSet0(slcrc0) ),
inference(trivial_inequality_removal,[],[f519]) ).
fof(f526,plain,
( aElementOf0(slcrc0,szDzozmdt0(xc))
| ~ aSubsetOf0(slcrc0,xS) ),
inference(forward_subsumption_resolution,[],[f524,f362]) ).
fof(f555,plain,
! [X0] :
( ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),X0)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[],[f275,f517]) ).
fof(f564,plain,
! [X0] :
( ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),X0)
| ~ aSubsetOf0(X0,xT) ),
inference(forward_subsumption_resolution,[],[f555,f206]) ).
fof(f599,plain,
( ~ aElementOf0(slcrc0,szDzozmdt0(xc))
| ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
inference(resolution,[],[f345,f564]) ).
fof(f603,plain,
~ aElementOf0(slcrc0,szDzozmdt0(xc)),
inference(forward_subsumption_resolution,[],[f599,f212]) ).
fof(f604,plain,
~ aSubsetOf0(slcrc0,xS),
inference(resolution,[],[f603,f526]) ).
fof(f605,plain,
! [X0] : ~ sP4(X0,xS),
inference(resolution,[],[f603,f485]) ).
fof(f615,plain,
! [X0] :
( ~ aSubsetOf0(xS,xS)
| ~ isCountable0(xS)
| ~ aElementOf0(X0,xT) ),
inference(resolution,[],[f605,f265]) ).
fof(f616,plain,
! [X0] :
( ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(X0,xT) ),
inference(forward_subsumption_resolution,[],[f615,f208]) ).
fof(f646,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ~ aSet0(xS) ),
inference(resolution,[],[f616,f274]) ).
fof(f647,plain,
! [X0] : ~ aElementOf0(X0,xT),
inference(forward_subsumption_resolution,[],[f646,f211]) ).
fof(f650,plain,
( ~ aSet0(xT)
| slcrc0 = xT ),
inference(resolution,[],[f647,f328]) ).
fof(f652,plain,
! [X0] :
( ~ aSet0(xT)
| aSubsetOf0(xT,X0)
| ~ aSet0(X0) ),
inference(resolution,[],[f647,f277]) ).
fof(f653,plain,
! [X0] :
( aSubsetOf0(xT,X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[],[f652,f206]) ).
fof(f655,plain,
slcrc0 = xT,
inference(forward_subsumption_resolution,[],[f650,f206]) ).
fof(f688,plain,
! [X0] :
( aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ),
inference(forward_demodulation,[],[f653,f655]) ).
fof(f690,plain,
~ aSet0(xS),
inference(resolution,[],[f688,f604]) ).
fof(f698,plain,
$false,
inference(forward_subsumption_resolution,[],[f690,f211]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM563+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 27 20:30:34 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.32 Running first-order theorem proving
% 0.07/0.32 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
% 0.65/0.79 % (2710773)Detected formulas, will run a generic FOF schedule.
% 0.65/0.79 % (2710783)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1660221224:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.65/0.79 % (2710781)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2286925223:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.65/0.79 % (2710784)dis-21_1_sil=8000:lcm=predicate:random_seed=3376776542: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)
% 0.65/0.79 % (2710778)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=4247565517:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.65/0.79 % (2710779)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=1342866346:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.65/0.79 % (2710780)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=685902621:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.65/0.79 % (2710782)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=214778818:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.65/0.79 % (2710782)First to succeed.
% 0.65/0.79 % (2710782)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2710773"
% 0.65/0.79 % (2710784)Instruction limit reached!
% 0.65/0.79 % (2710784)------------------------------
% 0.65/0.79 % (2710784)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.65/0.79 % (2710784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.79 % (2710784)CaDiCaL version: 2.1.3
% 0.65/0.79 % (2710784)Termination reason: Instruction limit
% 0.65/0.79 % (2710784)Termination phase: Saturation
% 0.65/0.79 % (2710784)Time elapsed: 0.038 s
% 0.65/0.79 % (2710784)Peak memory usage: 89 MB
% 0.65/0.79 % (2710784)Instructions burned: 132 (million)
% 0.65/0.79 % (2710781)Instruction limit reached!
% 0.65/0.79 % (2710781)------------------------------
% 0.65/0.79 % (2710781)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.65/0.79 % (2710781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.79 % (2710781)CaDiCaL version: 2.1.3
% 0.65/0.79 % (2710781)Termination reason: Instruction limit
% 0.65/0.79 % (2710781)Termination phase: Saturation
% 0.65/0.79 % (2710781)Time elapsed: 0.039 s
% 0.65/0.79 % (2710781)Peak memory usage: 89 MB
% 0.65/0.79 % (2710781)Instructions burned: 110 (million)
% 0.65/0.79 % (2710783)Instruction limit reached!
% 0.65/0.79 % (2710783)------------------------------
% 0.65/0.79 % (2710783)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.65/0.79 % (2710783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.79 % (2710783)CaDiCaL version: 2.1.3
% 0.65/0.79 % (2710783)Termination reason: Instruction limit
% 0.65/0.79 % (2710783)Termination phase: Saturation
% 0.65/0.79 % (2710783)Time elapsed: 0.056 s
% 0.65/0.79 % (2710783)Peak memory usage: 90 MB
% 0.65/0.79 % (2710783)Instructions burned: 141 (million)
% 0.65/0.79 % (2710792)lrs+10_1_sil=8000:sp=occurrence:random_seed=1105267406:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.65/0.79 % (2710793)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1574345238:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 0.65/0.79 % (2710794)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2769912461:i=325:sd=1:ss=axioms:sgt=32_2998 on theBenchmark for (2998ds/325Mi)
% 0.65/0.79 % (2710782)Refutation found. Thanks to Tanya!
% 0.65/0.79 % SZS status Theorem for theBenchmark
% 0.65/0.79 % SZS output start Proof for theBenchmark
% See solution above
% 2.04/0.89 % (2710782)------------------------------
% 2.04/0.89 % (2710782)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.04/0.89 % (2710782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.04/0.89 % (2710782)CaDiCaL version: 2.1.3
% 2.04/0.89 % (2710782)Termination reason: Refutation
% 2.04/0.89 % (2710782)Time elapsed: 0.008 s
% 2.04/0.89 % (2710782)Peak memory usage: 88 MB
% 2.04/0.89 % (2710782)Instructions burned: 22 (million)
% 2.04/0.89 % (2710782)------------------------------
% 2.04/0.89 % (2710782)------------------------------
% 2.04/0.89 % (2710773)Success in time 0.266 s
% 2.04/0.89 % Vampire exiting
%------------------------------------------------------------------------------