%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM563+1 : 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 0.77s 0.84s
% Output : Refutation 2.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 12
% Syntax : Number of formulae : 106 ( 18 unt; 0 def)
% Number of atoms : 422 ( 89 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 552 ( 236 ~; 222 |; 71 &)
% ( 12 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 159 ( 144 !; 15 ?)
% 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(f23,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(f42,axiom,
! [X0] :
( aSet0(X0)
=> ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
fof(f57,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElementOf0(X1,szNzAzT0) )
=> ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(f69,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( aElementOf0(X1,szDzozmdt0(X0))
=> aElementOf0(sdtlpdtrp0(X0,X1),sdtlcdtrc0(X0,szDzozmdt0(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgRng) ).
fof(f73,axiom,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3291) ).
fof(f75,axiom,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(f76,axiom,
( aFunction0(xc)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& 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] :
( aSubsetOf0(X1,xS)
& isCountable0(X1)
& ! [X2] :
( 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] :
( aSubsetOf0(X1,xS)
& isCountable0(X1)
& ! [X2] :
( aElementOf0(X2,slbdtsldtrb0(X1,xK))
=> sdtlpdtrp0(xc,X2) = X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f78]) ).
fof(f92,plain,
( ! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( ~ aSubsetOf0(X1,xS)
| ~ isCountable0(X1)
| ? [X2] :
( sdtlpdtrp0(xc,X2) != X0
& aElementOf0(X2,slbdtsldtrb0(X1,xK)) ) ) )
& xK = sz00 ),
inference(ennf_transformation,[],[f79]) ).
fof(f101,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f113,plain,
! [X0,X1] :
( ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f114,plain,
! [X0,X1] :
( ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f113]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( aElementOf0(sdtlpdtrp0(X0,X1),sdtlcdtrc0(X0,szDzozmdt0(X0)))
| ~ aElementOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f128,plain,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f133,plain,
! [X0] :
( ( sbrdtbr0(X0) = sz00
<=> X0 = slcrc0 )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f149,plain,
( ! [X0] :
( ~ aElementOf0(X0,xT)
| ! [X1] :
( ~ aSubsetOf0(X1,xS)
| ~ isCountable0(X1)
| ( sdtlpdtrp0(xc,sK2(X0,X1)) != X0
& aElementOf0(sK2(X0,X1),slbdtsldtrb0(X1,xK)) ) ) )
& xK = sz00 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f92]) ).
fof(f150,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,[],[f102]) ).
fof(f151,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,[],[f150]) ).
fof(f152,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,[],[f151]) ).
fof(f153,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK3(X0,X1),X0)
& aElementOf0(sK3(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f152]) ).
fof(f155,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1 )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(nnf_transformation,[],[f114]) ).
fof(f156,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1 )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f155]) ).
fof(f157,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1 )
& ( ( aSubsetOf0(X4,X0)
& sbrdtbr0(X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(rectify,[],[f156]) ).
fof(f158,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ( ( ~ aSubsetOf0(sK5(X0,X1,X2),X0)
| sbrdtbr0(sK5(X0,X1,X2)) != X1
| ~ aElementOf0(sK5(X0,X1,X2),X2) )
& ( ( aSubsetOf0(sK5(X0,X1,X2),X0)
& sbrdtbr0(sK5(X0,X1,X2)) = X1 )
| aElementOf0(sK5(X0,X1,X2),X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1 )
& ( ( aSubsetOf0(X4,X0)
& sbrdtbr0(X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f157]) ).
fof(f165,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f128]) ).
fof(f166,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f165]) ).
fof(f167,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f166]) ).
fof(f168,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| aElementOf0(sK12(X0),X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X1,sK12(X0))],[f167]) ).
fof(f170,plain,
! [X0] :
( ( ( sbrdtbr0(X0) = sz00
| slcrc0 != X0 )
& ( X0 = slcrc0
| sz00 != sbrdtbr0(X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f133]) ).
fof(f174,plain,
aSet0(xT),
inference(cnf_transformation,[],[f73]) ).
fof(f176,plain,
isCountable0(xS),
inference(cnf_transformation,[],[f75]) ).
fof(f177,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f75]) ).
fof(f178,plain,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(cnf_transformation,[],[f76]) ).
fof(f179,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(cnf_transformation,[],[f76]) ).
fof(f180,plain,
aFunction0(xc),
inference(cnf_transformation,[],[f76]) ).
fof(f185,plain,
sz00 = xK,
inference(cnf_transformation,[],[f149]) ).
fof(f186,plain,
! [X0,X1] :
( aElementOf0(sK2(X0,X1),slbdtsldtrb0(X1,xK))
| ~ aSubsetOf0(X1,xS)
| ~ isCountable0(X1)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f149]) ).
fof(f187,plain,
! [X0,X1] :
( sdtlpdtrp0(xc,sK2(X0,X1)) != X0
| ~ aSubsetOf0(X1,xS)
| ~ isCountable0(X1)
| ~ aElementOf0(X0,xT) ),
inference(cnf_transformation,[],[f149]) ).
fof(f190,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f194,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f195,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f196,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f197,plain,
! [X0,X1] :
( aElementOf0(sK3(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f206,plain,
! [X2,X0,X1,X4] :
( sbrdtbr0(X4) = X1
| ~ aElementOf0(X4,X2)
| slbdtsldtrb0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f207,plain,
! [X2,X0,X1,X4] :
( aSubsetOf0(X4,X0)
| ~ aElementOf0(X4,X2)
| slbdtsldtrb0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f208,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1
| slbdtsldtrb0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f218,plain,
! [X0,X1] :
( aElementOf0(sdtlpdtrp0(X0,X1),sdtlcdtrc0(X0,szDzozmdt0(X0)))
| ~ aElementOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f233,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f24]) ).
fof(f236,plain,
! [X2,X0] :
( ~ aElementOf0(X2,X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f168]) ).
fof(f237,plain,
! [X0] :
( aSet0(X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f168]) ).
fof(f242,plain,
! [X0] :
( slcrc0 = X0
| sz00 != sbrdtbr0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f243,plain,
! [X0] :
( sz00 = sbrdtbr0(X0)
| slcrc0 != X0
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f262,plain,
aElementOf0(xK,szNzAzT0),
inference(definition_unfolding,[],[f233,f185]) ).
fof(f263,plain,
! [X0] :
( sbrdtbr0(X0) = xK
| slcrc0 != X0
| ~ aSet0(X0) ),
inference(definition_unfolding,[],[f243,f185]) ).
fof(f264,plain,
! [X0] :
( sbrdtbr0(X0) != xK
| slcrc0 = X0
| ~ aSet0(X0) ),
inference(definition_unfolding,[],[f242,f185]) ).
fof(f266,plain,
! [X2,X0,X4] :
( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| slbdtsldtrb0(X0,sbrdtbr0(X4)) != X2
| ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X4),szNzAzT0) ),
inference(equality_resolution,[],[f208]) ).
fof(f267,plain,
! [X0,X4] :
( aElementOf0(X4,slbdtsldtrb0(X0,sbrdtbr0(X4)))
| ~ aSubsetOf0(X4,X0)
| ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X4),szNzAzT0) ),
inference(equality_resolution,[],[f266]) ).
fof(f268,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| aSubsetOf0(X4,X0)
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(equality_resolution,[],[f207]) ).
fof(f269,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| sbrdtbr0(X4) = X1
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(equality_resolution,[],[f206]) ).
fof(f276,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f237]) ).
fof(f277,plain,
! [X2] : ~ aElementOf0(X2,slcrc0),
inference(equality_resolution,[],[f236]) ).
fof(f278,plain,
( xK = sbrdtbr0(slcrc0)
| ~ aSet0(slcrc0) ),
inference(equality_resolution,[],[f263]) ).
fof(f287,plain,
! [X0] :
( aElementOf0(sK2(X0,xS),szDzozmdt0(xc))
| ~ aSubsetOf0(xS,xS)
| ~ isCountable0(xS)
| ~ aElementOf0(X0,xT) ),
inference(superposition,[],[f186,f179]) ).
fof(f288,plain,
! [X0] :
( aElementOf0(sK2(X0,xS),szDzozmdt0(xc))
| ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(X0,xT) ),
inference(forward_subsumption_resolution,[],[f287,f176]) ).
fof(f295,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f196,f177]) ).
fof(f300,plain,
aSet0(xS),
inference(forward_subsumption_resolution,[],[f295,f190]) ).
fof(f339,plain,
! [X0] :
( ~ aSet0(slcrc0)
| aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ),
inference(resolution,[],[f197,f277]) ).
fof(f340,plain,
! [X0] :
( aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[],[f339,f276]) ).
fof(f409,plain,
! [X0] :
( ~ aElementOf0(X0,szDzozmdt0(xc))
| aSubsetOf0(X0,xS)
| ~ aSet0(xS)
| ~ aElementOf0(xK,szNzAzT0) ),
inference(superposition,[],[f268,f179]) ).
fof(f410,plain,
! [X0] :
( ~ aElementOf0(X0,szDzozmdt0(xc))
| aSubsetOf0(X0,xS)
| ~ aElementOf0(xK,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f409,f300]) ).
fof(f415,plain,
! [X0] :
( ~ aElementOf0(X0,szDzozmdt0(xc))
| aSubsetOf0(X0,xS) ),
inference(forward_subsumption_resolution,[],[f410,f262]) ).
fof(f416,plain,
! [X0] :
( aSubsetOf0(sK2(X0,xS),xS)
| ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(X0,xT) ),
inference(resolution,[],[f415,f288]) ).
fof(f435,plain,
! [X0] :
( ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(X0,xT)
| aSet0(sK2(X0,xS))
| ~ aSet0(xS) ),
inference(resolution,[],[f416,f196]) ).
fof(f436,plain,
! [X0] :
( ~ aElementOf0(X0,xT)
| aSet0(sK2(X0,xS))
| ~ aSet0(xS) ),
inference(forward_subsumption_resolution,[],[f435,f194]) ).
fof(f437,plain,
! [X0] :
( aSet0(sK2(X0,xS))
| ~ aElementOf0(X0,xT) ),
inference(forward_subsumption_resolution,[],[f436,f300]) ).
fof(f464,plain,
! [X0] :
( ~ aElementOf0(X0,szDzozmdt0(xc))
| sbrdtbr0(X0) = xK
| ~ aSet0(xS)
| ~ aElementOf0(xK,szNzAzT0) ),
inference(superposition,[],[f269,f179]) ).
fof(f465,plain,
! [X0] :
( ~ aElementOf0(X0,szDzozmdt0(xc))
| sbrdtbr0(X0) = xK
| ~ aElementOf0(xK,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f464,f300]) ).
fof(f470,plain,
! [X0] :
( ~ aElementOf0(X0,szDzozmdt0(xc))
| sbrdtbr0(X0) = xK ),
inference(forward_subsumption_resolution,[],[f465,f262]) ).
fof(f471,plain,
! [X0] :
( xK = sbrdtbr0(sK2(X0,xS))
| ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(X0,xT) ),
inference(resolution,[],[f470,f288]) ).
fof(f568,plain,
! [X0] :
( aElementOf0(slcrc0,slbdtsldtrb0(X0,xK))
| ~ aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0)
| ~ aElementOf0(xK,szNzAzT0)
| ~ aSet0(slcrc0) ),
inference(superposition,[],[f267,f278]) ).
fof(f575,plain,
! [X0] :
( aElementOf0(slcrc0,slbdtsldtrb0(X0,xK))
| ~ aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0)
| ~ aSet0(slcrc0) ),
inference(forward_subsumption_resolution,[],[f568,f262]) ).
fof(f577,plain,
! [X0] :
( aElementOf0(slcrc0,slbdtsldtrb0(X0,xK))
| ~ aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[],[f575,f276]) ).
fof(f578,plain,
! [X0] :
( aElementOf0(slcrc0,slbdtsldtrb0(X0,xK))
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[],[f577,f340]) ).
fof(f581,plain,
( aElementOf0(slcrc0,szDzozmdt0(xc))
| ~ aSet0(xS) ),
inference(superposition,[],[f578,f179]) ).
fof(f584,plain,
aElementOf0(slcrc0,szDzozmdt0(xc)),
inference(forward_subsumption_resolution,[],[f581,f300]) ).
fof(f715,plain,
! [X0] :
( xK != xK
| slcrc0 = sK2(X0,xS)
| ~ aSet0(sK2(X0,xS))
| ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(X0,xT) ),
inference(superposition,[],[f264,f471]) ).
fof(f720,plain,
! [X0] :
( slcrc0 = sK2(X0,xS)
| ~ aSet0(sK2(X0,xS))
| ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(X0,xT) ),
inference(trivial_inequality_removal,[],[f715]) ).
fof(f723,plain,
! [X0] :
( slcrc0 = sK2(X0,xS)
| ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(X0,xT) ),
inference(forward_subsumption_resolution,[],[f720,f437]) ).
fof(f746,plain,
! [X0] :
( sdtlpdtrp0(xc,slcrc0) != X0
| ~ aSubsetOf0(xS,xS)
| ~ isCountable0(xS)
| ~ aElementOf0(X0,xT)
| ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(X0,xT) ),
inference(superposition,[],[f187,f723]) ).
fof(f749,plain,
! [X0] :
( sdtlpdtrp0(xc,slcrc0) != X0
| ~ aSubsetOf0(xS,xS)
| ~ isCountable0(xS)
| ~ aElementOf0(X0,xT) ),
inference(duplicate_literal_removal,[],[f746]) ).
fof(f756,plain,
! [X0] :
( sdtlpdtrp0(xc,slcrc0) != X0
| ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(X0,xT) ),
inference(forward_subsumption_resolution,[],[f749,f176]) ).
fof(f773,plain,
( ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),xT)
| ~ aSubsetOf0(xS,xS) ),
inference(equality_resolution,[],[f756]) ).
fof(f774,plain,
! [X0] :
( ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),X0)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[],[f773,f195]) ).
fof(f775,plain,
! [X0] :
( ~ aElementOf0(sdtlpdtrp0(xc,slcrc0),X0)
| ~ aSubsetOf0(xS,xS)
| ~ aSubsetOf0(X0,xT) ),
inference(forward_subsumption_resolution,[],[f774,f174]) ).
fof(f783,plain,
( ~ aSubsetOf0(xS,xS)
| ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aElementOf0(slcrc0,szDzozmdt0(xc))
| ~ aFunction0(xc) ),
inference(resolution,[],[f775,f218]) ).
fof(f786,plain,
( ~ aSubsetOf0(xS,xS)
| ~ aElementOf0(slcrc0,szDzozmdt0(xc))
| ~ aFunction0(xc) ),
inference(forward_subsumption_resolution,[],[f783,f178]) ).
fof(f787,plain,
( ~ aSubsetOf0(xS,xS)
| ~ aFunction0(xc) ),
inference(forward_subsumption_resolution,[],[f786,f584]) ).
fof(f788,plain,
~ aSubsetOf0(xS,xS),
inference(forward_subsumption_resolution,[],[f787,f180]) ).
fof(f793,plain,
~ aSet0(xS),
inference(resolution,[],[f788,f194]) ).
fof(f796,plain,
$false,
inference(forward_subsumption_resolution,[],[f793,f300]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM563+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 20:30:13 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.33 Running first-order theorem proving
% 0.08/0.33 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
% 0.77/0.84 % (2709939)Detected formulas, will run a generic FOF schedule.
% 0.77/0.84 % (2709949)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2143426237:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.77/0.84 % (2709950)dis-21_1_sil=8000:lcm=predicate:random_seed=2592386048: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)
% 0.77/0.84 % (2709946)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=2762160533:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.77/0.84 % (2709948)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3413268799:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.77/0.84 % (2709944)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=3245225700:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.77/0.84 % (2709947)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1481978099:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.77/0.84 % (2709945)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=568916134:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.77/0.84 % (2709948)First to succeed.
% 0.77/0.84 % (2709948)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2709939"
% 0.77/0.84 % (2709950)Instruction limit reached!
% 0.77/0.84 % (2709950)------------------------------
% 0.77/0.84 % (2709950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.77/0.84 % (2709950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.84 % (2709950)CaDiCaL version: 2.1.3
% 0.77/0.84 % (2709950)Termination reason: Instruction limit
% 0.77/0.84 % (2709950)Termination phase: Saturation
% 0.77/0.84 % (2709950)Time elapsed: 0.039 s
% 0.77/0.84 % (2709950)Peak memory usage: 89 MB
% 0.77/0.84 % (2709950)Instructions burned: 134 (million)
% 0.77/0.84 % (2709947)Instruction limit reached!
% 0.77/0.84 % (2709947)------------------------------
% 0.77/0.84 % (2709947)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.77/0.84 % (2709947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.84 % (2709947)CaDiCaL version: 2.1.3
% 0.77/0.84 % (2709947)Termination reason: Instruction limit
% 0.77/0.84 % (2709947)Termination phase: Saturation
% 0.77/0.84 % (2709947)Time elapsed: 0.040 s
% 0.77/0.84 % (2709947)Peak memory usage: 89 MB
% 0.77/0.84 % (2709947)Instructions burned: 112 (million)
% 0.77/0.84 % (2709949)Instruction limit reached!
% 0.77/0.84 % (2709949)------------------------------
% 0.77/0.84 % (2709949)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.77/0.84 % (2709949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.84 % (2709949)CaDiCaL version: 2.1.3
% 0.77/0.84 % (2709949)Termination reason: Instruction limit
% 0.77/0.84 % (2709949)Termination phase: Saturation
% 0.77/0.84 % (2709949)Time elapsed: 0.057 s
% 0.77/0.84 % (2709949)Peak memory usage: 90 MB
% 0.77/0.84 % (2709949)Instructions burned: 141 (million)
% 0.77/0.84 % (2709958)lrs+10_1_sil=8000:sp=occurrence:random_seed=831573236:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.77/0.84 % (2709959)lrs+10_1_sil=32000:urr=on:br=off:random_seed=144990784:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 0.77/0.84 % (2709948)Refutation found. Thanks to Tanya!
% 0.77/0.84 % SZS status Theorem for theBenchmark
% 0.77/0.84 % SZS output start Proof for theBenchmark
% See solution above
% 2.38/0.95 % (2709948)------------------------------
% 2.38/0.95 % (2709948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.38/0.95 % (2709948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.95 % (2709948)CaDiCaL version: 2.1.3
% 2.38/0.95 % (2709948)Termination reason: Refutation
% 2.38/0.95 % (2709948)Time elapsed: 0.010 s
% 2.38/0.95 % (2709948)Peak memory usage: 88 MB
% 2.38/0.95 % (2709948)Instructions burned: 26 (million)
% 2.38/0.95 % (2709948)------------------------------
% 2.38/0.95 % (2709948)------------------------------
% 2.38/0.95 % (2709939)Success in time 0.306 s
% 2.38/0.95 % Vampire exiting
%------------------------------------------------------------------------------