%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM566+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 12:24:50 PM UTC 2026
% Result : Theorem 0.17s 0.55s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 89 ( 14 unt; 5 def)
% Number of atoms : 469 ( 73 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 553 ( 173 ~; 146 |; 200 &)
% ( 7 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 4 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-2 aty)
% Number of variables : 135 ( 0 sgn 104 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] :
( aSet0(X0)
=> aSubsetOf0(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubRefl) ).
fof(f75,axiom,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',m__3453) ).
fof(f78,axiom,
xK = sz00,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',m__3476) ).
fof(f80,axiom,
! [X0] :
( ( ( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) ) )
| aSubsetOf0(X0,xS) )
& sbrdtbr0(X0) = sz00 )
| aElementOf0(X0,slbdtsldtrb0(xS,sz00)) )
=> ( aSet0(slcrc0)
& ~ ? [X1] : aElementOf0(X1,slcrc0)
& sdtlpdtrp0(xc,X0) = sdtlpdtrp0(xc,slcrc0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3507) ).
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/sandbox/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(f90,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(f92,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(f93,plain,
! [X0] :
( ( ( ( ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> aElementOf0(X1,xS) ) )
| aSubsetOf0(X0,xS) )
& sbrdtbr0(X0) = sz00 )
| aElementOf0(X0,slbdtsldtrb0(xS,sz00)) )
=> ( aSet0(slcrc0)
& ~ ? [X2] : aElementOf0(X2,slcrc0)
& sdtlpdtrp0(xc,X0) = sdtlpdtrp0(xc,slcrc0) ) ),
inference(rectify,[],[f80]) ).
fof(f94,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(f104,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f194,plain,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
inference(ennf_transformation,[],[f75]) ).
fof(f195,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,[],[f90]) ).
fof(f196,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,[],[f195]) ).
fof(f199,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,[],[f92]) ).
fof(f200,plain,
! [X0] :
( ( aSet0(slcrc0)
& ! [X2] : ~ aElementOf0(X2,slcrc0)
& sdtlpdtrp0(xc,X0) = sdtlpdtrp0(xc,slcrc0) )
| ( ( ( ( ~ aSet0(X0)
| ? [X1] :
( ~ aElementOf0(X1,xS)
& aElementOf0(X1,X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sz00 != sbrdtbr0(X0) )
& ~ aElementOf0(X0,slbdtsldtrb0(xS,sz00)) ) ),
inference(ennf_transformation,[],[f93]) ).
fof(f201,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,[],[f94]) ).
fof(f202,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,[],[f201]) ).
fof(f214,definition,
! [X0] :
( ( ( ( ( ~ aSet0(X0)
| ? [X1] :
( ~ aElementOf0(X1,xS)
& aElementOf0(X1,X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sz00 != sbrdtbr0(X0) )
& ~ aElementOf0(X0,slbdtsldtrb0(xS,sz00)) )
| ~ sP8(X0) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f215,plain,
! [X0] :
( ( aSet0(slcrc0)
& ! [X2] : ~ aElementOf0(X2,slcrc0)
& sdtlpdtrp0(xc,X0) = sdtlpdtrp0(xc,slcrc0) )
| sP8(X0) ),
inference(definition_folding,[],[f200,f214]) ).
fof(f216,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)) )
| ~ sP9(X0,X1) ),
introduced(definition,[new_symbols(definition,[sP9])],[predicate_definition_introduction]) ).
fof(f217,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( ( ( ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,xS)
& aElementOf0(X2,X1) ) )
& ~ aSubsetOf0(X1,xS) )
| ~ isCountable0(X1)
| sP9(X0,X1) ) ),
inference(definition_folding,[],[f202,f216]) ).
fof(f277,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,[],[f196]) ).
fof(f278,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,[],[f277]) ).
fof(f279,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(sK29(X0),xS)
& aElementOf0(sK29(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(sK30(X3),szDzozmdt0(xc))
& sdtlpdtrp0(xc,sK30(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,[sK29,sK30]),skolemize(X2,sK29(X0)),skolemize(X5,sK30(X3))],[f278]) ).
fof(f293,plain,
! [X0] :
( ( ( ( ( ~ aSet0(X0)
| ? [X1] :
( ~ aElementOf0(X1,xS)
& aElementOf0(X1,X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sz00 != sbrdtbr0(X0) )
& ~ aElementOf0(X0,slbdtsldtrb0(xS,sz00)) )
| ~ sP8(X0) ),
inference(nnf_transformation,[],[f214]) ).
fof(f294,plain,
! [X0] :
( ( ( ( ( ~ aSet0(X0)
| ( ~ aElementOf0(sK39(X0),xS)
& aElementOf0(sK39(X0),X0) ) )
& ~ aSubsetOf0(X0,xS) )
| sz00 != sbrdtbr0(X0) )
& ~ aElementOf0(X0,slbdtsldtrb0(xS,sz00)) )
| ~ sP8(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(X1,sK39(X0))],[f293]) ).
fof(f295,plain,
! [X0] :
( ( aSet0(slcrc0)
& ! [X1] : ~ aElementOf0(X1,slcrc0)
& sdtlpdtrp0(xc,X0) = sdtlpdtrp0(xc,slcrc0) )
| sP8(X0) ),
inference(rectify,[],[f215]) ).
fof(f296,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)) )
| ~ sP9(X0,X1) ),
inference(nnf_transformation,[],[f216]) ).
fof(f297,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)) )
| ~ sP9(X0,X1) ),
inference(rectify,[],[f296]) ).
fof(f298,plain,
! [X0,X1] :
( ( sdtlpdtrp0(xc,sK40(X0,X1)) != X0
& aSet0(sK40(X0,X1))
& ! [X3] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,sK40(X0,X1)) )
& aSubsetOf0(sK40(X0,X1),X1)
& xK = sbrdtbr0(sK40(X0,X1))
& aElementOf0(sK40(X0,X1),slbdtsldtrb0(X1,xK)) )
| ~ sP9(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(X2,sK40(X0,X1))],[f297]) ).
fof(f299,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( ( ( ~ aSet0(X1)
| ( ~ aElementOf0(sK41(X1),xS)
& aElementOf0(sK41(X1),X1) ) )
& ~ aSubsetOf0(X1,xS) )
| ~ isCountable0(X1)
| sP9(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(X2,sK41(X1))],[f217]) ).
fof(f312,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f446,plain,
isCountable0(xS),
inference(cnf_transformation,[],[f194]) ).
fof(f449,plain,
aSet0(xS),
inference(cnf_transformation,[],[f194]) ).
fof(f451,plain,
! [X6] :
( ~ aElementOf0(X6,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(X6,xT) ),
inference(cnf_transformation,[],[f279]) ).
fof(f454,plain,
! [X3,X4] :
( aElementOf0(X3,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ aElementOf0(X4,szDzozmdt0(xc))
| sdtlpdtrp0(xc,X4) != X3 ),
inference(cnf_transformation,[],[f279]) ).
fof(f456,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(cnf_transformation,[],[f279]) ).
fof(f496,plain,
sz00 = xK,
inference(cnf_transformation,[],[f78]) ).
fof(f497,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(cnf_transformation,[],[f199]) ).
fof(f503,plain,
! [X0] :
( ~ aSubsetOf0(X0,xS)
| sz00 != sbrdtbr0(X0)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f294]) ).
fof(f506,plain,
! [X0] :
( sP8(X0)
| sdtlpdtrp0(xc,X0) = sdtlpdtrp0(xc,slcrc0) ),
inference(cnf_transformation,[],[f295]) ).
fof(f510,plain,
! [X0,X1] :
( ~ sP9(X0,X1)
| xK = sbrdtbr0(sK40(X0,X1)) ),
inference(cnf_transformation,[],[f298]) ).
fof(f511,plain,
! [X0,X1] :
( aSubsetOf0(sK40(X0,X1),X1)
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f298]) ).
fof(f514,plain,
! [X0,X1] :
( sdtlpdtrp0(xc,sK40(X0,X1)) != X0
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f298]) ).
fof(f515,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,xS)
| ~ aElementOf0(X0,xT)
| ~ isCountable0(X1)
| sP9(X0,X1) ),
inference(cnf_transformation,[],[f299]) ).
fof(f529,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xS,xK)),
inference(definition_unfolding,[],[f497,f496]) ).
fof(f532,plain,
! [X0] :
( sbrdtbr0(X0) != xK
| ~ aSubsetOf0(X0,xS)
| ~ sP8(X0) ),
inference(definition_unfolding,[],[f503,f496]) ).
fof(f571,plain,
! [X4] :
( aElementOf0(sdtlpdtrp0(xc,X4),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ aElementOf0(X4,szDzozmdt0(xc)) ),
inference(equality_resolution,[],[f454]) ).
fof(f670,plain,
! [X0] :
( ~ aSet0(xS)
| ~ aElementOf0(X0,xT)
| ~ isCountable0(xS)
| sP9(X0,xS) ),
inference(resolution,[],[f312,f515]) ).
fof(f689,plain,
aElementOf0(slcrc0,szDzozmdt0(xc)),
inference(superposition,[],[f529,f456]) ).
fof(f1768,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| ~ isCountable0(xS)
| sP9(X0,xS) ),
inference(forward_subsumption_resolution,[],[f670,f449]) ).
fof(f1774,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| sP9(X0,xS) ),
inference(forward_subsumption_resolution,[],[f1768,f446]) ).
fof(f3305,definition,
( spl42_133
<=> aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
introduced(definition,[new_symbols(definition,[spl42_133])],[avatar_definition]) ).
fof(f3306,plain,
( ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| spl42_133 ),
inference(avatar_component_clause,[],[f3305]) ).
fof(f3307,plain,
( aElementOf0(sdtlpdtrp0(xc,slcrc0),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ spl42_133 ),
inference(avatar_component_clause,[],[f3305]) ).
fof(f3502,plain,
( aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ~ spl42_133 ),
inference(resolution,[],[f3307,f451]) ).
fof(f3505,plain,
( sP9(sdtlpdtrp0(xc,slcrc0),xS)
| ~ spl42_133 ),
inference(resolution,[],[f3502,f1774]) ).
fof(f3507,plain,
( xK = sbrdtbr0(sK40(sdtlpdtrp0(xc,slcrc0),xS))
| ~ spl42_133 ),
inference(resolution,[],[f3505,f510]) ).
fof(f3515,plain,
( xK != xK
| ~ aSubsetOf0(sK40(sdtlpdtrp0(xc,slcrc0),xS),xS)
| ~ sP8(sK40(sdtlpdtrp0(xc,slcrc0),xS))
| ~ spl42_133 ),
inference(superposition,[],[f532,f3507]) ).
fof(f3519,plain,
( ~ aSubsetOf0(sK40(sdtlpdtrp0(xc,slcrc0),xS),xS)
| ~ sP8(sK40(sdtlpdtrp0(xc,slcrc0),xS))
| ~ spl42_133 ),
inference(trivial_inequality_removal,[],[f3515]) ).
fof(f3526,definition,
( spl42_147
<=> sP8(sK40(sdtlpdtrp0(xc,slcrc0),xS)) ),
introduced(definition,[new_symbols(definition,[spl42_147])],[avatar_definition]) ).
fof(f3528,plain,
( ~ sP8(sK40(sdtlpdtrp0(xc,slcrc0),xS))
| spl42_147 ),
inference(avatar_component_clause,[],[f3526]) ).
fof(f3530,definition,
( spl42_148
<=> aSubsetOf0(sK40(sdtlpdtrp0(xc,slcrc0),xS),xS) ),
introduced(definition,[new_symbols(definition,[spl42_148])],[avatar_definition]) ).
fof(f3532,plain,
( ~ aSubsetOf0(sK40(sdtlpdtrp0(xc,slcrc0),xS),xS)
| spl42_148 ),
inference(avatar_component_clause,[],[f3530]) ).
fof(f3533,plain,
( ~ spl42_147
| ~ spl42_148
| ~ spl42_133 ),
inference(avatar_split_clause,[],[f3519,f3305,f3530,f3526]) ).
fof(f3534,plain,
( sdtlpdtrp0(xc,slcrc0) = sdtlpdtrp0(xc,sK40(sdtlpdtrp0(xc,slcrc0),xS))
| spl42_147 ),
inference(resolution,[],[f3528,f506]) ).
fof(f3536,plain,
( sdtlpdtrp0(xc,slcrc0) != sdtlpdtrp0(xc,slcrc0)
| ~ sP9(sdtlpdtrp0(xc,slcrc0),xS)
| spl42_147 ),
inference(superposition,[],[f514,f3534]) ).
fof(f3538,plain,
( ~ sP9(sdtlpdtrp0(xc,slcrc0),xS)
| spl42_147 ),
inference(trivial_inequality_removal,[],[f3536]) ).
fof(f3539,plain,
( $false
| ~ spl42_133
| spl42_147 ),
inference(forward_subsumption_resolution,[],[f3538,f3505]) ).
fof(f3540,plain,
( ~ spl42_133
| spl42_147 ),
inference(avatar_contradiction_clause,[],[f3539]) ).
fof(f3542,plain,
( ~ aElementOf0(slcrc0,szDzozmdt0(xc))
| spl42_133 ),
inference(resolution,[],[f3306,f571]) ).
fof(f3543,plain,
( $false
| spl42_133 ),
inference(forward_subsumption_resolution,[],[f3542,f689]) ).
fof(f3544,plain,
spl42_133,
inference(avatar_contradiction_clause,[],[f3543]) ).
fof(f3545,plain,
( ~ sP9(sdtlpdtrp0(xc,slcrc0),xS)
| spl42_148 ),
inference(resolution,[],[f3532,f511]) ).
fof(f3548,plain,
( aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ~ spl42_133 ),
inference(resolution,[],[f3307,f451]) ).
fof(f3551,plain,
( sP9(sdtlpdtrp0(xc,slcrc0),xS)
| ~ spl42_133 ),
inference(resolution,[],[f3548,f1774]) ).
fof(f3553,plain,
( $false
| ~ spl42_133
| spl42_148 ),
inference(forward_subsumption_resolution,[],[f3551,f3545]) ).
fof(f3554,plain,
( ~ spl42_133
| spl42_148 ),
inference(avatar_contradiction_clause,[],[f3553]) ).
cnf(s1857,plain,
( ~ spl42_133
| ~ spl42_147
| ~ spl42_148 ),
inference(sat_conversion,[],[f3533]) ).
cnf(s1863,plain,
( ~ spl42_133
| spl42_147 ),
inference(sat_conversion,[],[f3540]) ).
cnf(s1875,plain,
spl42_133,
inference(sat_conversion,[],[f3544]) ).
cnf(s1886,plain,
( ~ spl42_133
| spl42_148 ),
inference(sat_conversion,[],[f3554]) ).
cnf(s1888,plain,
spl42_148,
inference(rat,[],[s1886,s1875]) ).
cnf(s1889,plain,
spl42_147,
inference(rat,[],[s1863,s1875]) ).
cnf(s1890,plain,
$false,
inference(rat,[],[s1857,s1888,s1889,s1875]) ).
fof(f3555,plain,
$false,
inference(avatar_sat_refutation,[],[s1890]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM566+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n017.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 20:26:51 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.55 % (2916051)Will run a generic schedule for satisfiability detection.
% 0.17/0.55 % (2916060)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2509675444:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.55 % (2916057)% WARNING: option uhcvi not known.
% 0.17/0.55 % (2916057)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3972715815:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.55 % (2916056)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3458766473_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.55 % (2916058)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2892176761:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.55 % (2916059)dis+10_1_sil=32000:sp=arity:random_seed=154626998:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.55 % (2916061)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=279611675:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.55 % (2916062)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1798090869:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.55 % TRYING [1]
% 0.17/0.55 % TRYING [2]
% 0.17/0.55 % TRYING [3]
% 0.17/0.55 % (2916060)Instruction limit reached!
% 0.17/0.55 % (2916060)------------------------------
% 0.17/0.55 % (2916060)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.55 % (2916060)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.55 % (2916060)CaDiCaL version: 2.1.3
% 0.17/0.55 % (2916060)Termination reason: Instruction limit
% 0.17/0.55 % (2916060)Termination phase: Saturation
% 0.17/0.55 % (2916060)Time elapsed: 0.041 s
% 0.17/0.55 % (2916060)Peak memory usage: 13 MB
% 0.17/0.55 % (2916060)Instructions burned: 117 (million)
% 0.17/0.55 % (2916070)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2277571773:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.17/0.55 % TRYING [1]
% 0.17/0.55 % TRYING [2]
% 0.17/0.55 % TRYING [3]
% 0.17/0.55 % TRYING [4]
% 0.17/0.55 % (2916059)Instruction limit reached!
% 0.17/0.55 % (2916059)------------------------------
% 0.17/0.55 % (2916059)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.55 % (2916059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.55 % (2916059)CaDiCaL version: 2.1.3
% 0.17/0.55 % (2916059)Termination reason: Instruction limit
% 0.17/0.55 % (2916059)Termination phase: Saturation
% 0.17/0.55 % (2916059)Time elapsed: 0.069 s
% 0.17/0.55 % (2916059)Peak memory usage: 13 MB
% 0.17/0.55 % (2916059)Instructions burned: 103 (million)
% 0.17/0.55 % TRYING [4]
% 0.17/0.55 % (2916058) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2916051-2916058"...
% 0.17/0.55 % (2916058)...printing done.
% 0.17/0.55 % (2916058)Refutation found. Thanks to Tanya!
% 0.17/0.55 % SZS status Theorem for theBenchmark
% 0.17/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.55 % (2916058)------------------------------
% 0.17/0.55 % (2916058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.55 % (2916058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.55 % (2916058)CaDiCaL version: 2.1.3
% 0.17/0.55 % (2916058)Termination reason: Refutation
% 0.17/0.55 % (2916058)Time elapsed: 0.076 s
% 0.17/0.55 % (2916058)Peak memory usage: 14 MB
% 0.17/0.55 % (2916058)Instructions burned: 104 (million)
% 0.17/0.55 % (2916051)Success in time 0.116 s
% 0.17/0.55 % Vampire exiting
%------------------------------------------------------------------------------