%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM543+2 : 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 : 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 12:15:40 PM UTC 2026
% Result : Theorem 6.70s 2.03s
% Output : Refutation 8.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 94 ( 13 unt; 5 def)
% Number of atoms : 368 ( 43 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 447 ( 173 ~; 165 |; 80 &)
% ( 18 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 112 ( 0 sgn 97 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ~ ? [X1] : aElementOf0(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
fof(f32,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(X0,X1)
<=> sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccLess) ).
fof(f48,axiom,
! [X0] :
( ( aSubsetOf0(X0,szNzAzT0)
& isFinite0(X0)
& X0 != slcrc0 )
=> ! [X1] :
( X1 = szmzazxdt0(X0)
<=> ( aElementOf0(X1,X0)
& ! [X2] :
( aElementOf0(X2,X0)
=> sdtlseqdt0(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMax) ).
fof(f55,axiom,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isFinite0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1986) ).
fof(f56,conjecture,
? [X0] :
( aElementOf0(X0,szNzAzT0)
& ( ( aSet0(slbdtrb0(X0))
& ! [X1] :
( aElementOf0(X1,slbdtrb0(X0))
<=> ( aElementOf0(X1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X1),X0) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,slbdtrb0(X0)) )
| aSubsetOf0(xS,slbdtrb0(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f57,negated_conjecture,
~ ? [X0] :
( aElementOf0(X0,szNzAzT0)
& ( ( aSet0(slbdtrb0(X0))
& ! [X1] :
( aElementOf0(X1,slbdtrb0(X0))
<=> ( aElementOf0(X1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X1),X0) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,xS)
=> aElementOf0(X1,slbdtrb0(X0)) )
| aSubsetOf0(xS,slbdtrb0(X0)) ) ) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f64,plain,
~ ? [X0] :
( aElementOf0(X0,szNzAzT0)
& ( ( aSet0(slbdtrb0(X0))
& ! [X1] :
( aElementOf0(X1,slbdtrb0(X0))
<=> ( aElementOf0(X1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X1),X0) ) ) )
=> ( ! [X2] :
( aElementOf0(X2,xS)
=> aElementOf0(X2,slbdtrb0(X0)) )
| aSubsetOf0(xS,slbdtrb0(X0)) ) ) ),
inference(rectify,[],[f57]) ).
fof(f66,plain,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f94,plain,
! [X0] :
( ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f102,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) )
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f103,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) )
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f102]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( X1 = szmzazxdt0(X0)
<=> ( aElementOf0(X1,X0)
& ! [X2] :
( sdtlseqdt0(X2,X1)
| ~ aElementOf0(X2,X0) ) ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ isFinite0(X0)
| slcrc0 = X0 ),
inference(ennf_transformation,[],[f48]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( X1 = szmzazxdt0(X0)
<=> ( aElementOf0(X1,X0)
& ! [X2] :
( sdtlseqdt0(X2,X1)
| ~ aElementOf0(X2,X0) ) ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ isFinite0(X0)
| slcrc0 = X0 ),
inference(flattening,[],[f126]) ).
fof(f136,plain,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) )
& aSubsetOf0(xS,szNzAzT0)
& isFinite0(xS) ),
inference(ennf_transformation,[],[f55]) ).
fof(f137,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( ? [X2] :
( ~ aElementOf0(X2,slbdtrb0(X0))
& aElementOf0(X2,xS) )
& ~ aSubsetOf0(xS,slbdtrb0(X0))
& aSet0(slbdtrb0(X0))
& ! [X1] :
( aElementOf0(X1,slbdtrb0(X0))
<=> ( aElementOf0(X1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X1),X0) ) ) ) ),
inference(ennf_transformation,[],[f64]) ).
fof(f138,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( ? [X2] :
( ~ aElementOf0(X2,slbdtrb0(X0))
& aElementOf0(X2,xS) )
& ~ aSubsetOf0(xS,slbdtrb0(X0))
& aSet0(slbdtrb0(X0))
& ! [X1] :
( aElementOf0(X1,slbdtrb0(X0))
<=> ( aElementOf0(X1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X1),X0) ) ) ) ),
inference(flattening,[],[f137]) ).
fof(f139,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f140,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f139]) ).
fof(f141,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f140]) ).
fof(f142,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| aElementOf0(sK0(X0),X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f141]) ).
fof(f156,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1)) )
& ( sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1))
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(nnf_transformation,[],[f103]) ).
fof(f164,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzazxdt0(X0)
| ~ aElementOf0(X1,X0)
| ? [X2] :
( ~ sdtlseqdt0(X2,X1)
& aElementOf0(X2,X0) ) )
& ( ( aElementOf0(X1,X0)
& ! [X2] :
( sdtlseqdt0(X2,X1)
| ~ aElementOf0(X2,X0) ) )
| szmzazxdt0(X0) != X1 ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ isFinite0(X0)
| slcrc0 = X0 ),
inference(nnf_transformation,[],[f127]) ).
fof(f165,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzazxdt0(X0)
| ~ aElementOf0(X1,X0)
| ? [X2] :
( ~ sdtlseqdt0(X2,X1)
& aElementOf0(X2,X0) ) )
& ( ( aElementOf0(X1,X0)
& ! [X2] :
( sdtlseqdt0(X2,X1)
| ~ aElementOf0(X2,X0) ) )
| szmzazxdt0(X0) != X1 ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ isFinite0(X0)
| slcrc0 = X0 ),
inference(flattening,[],[f164]) ).
fof(f166,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzazxdt0(X0)
| ~ aElementOf0(X1,X0)
| ? [X2] :
( ~ sdtlseqdt0(X2,X1)
& aElementOf0(X2,X0) ) )
& ( ( aElementOf0(X1,X0)
& ! [X3] :
( sdtlseqdt0(X3,X1)
| ~ aElementOf0(X3,X0) ) )
| szmzazxdt0(X0) != X1 ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ isFinite0(X0)
| slcrc0 = X0 ),
inference(rectify,[],[f165]) ).
fof(f167,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzazxdt0(X0)
| ~ aElementOf0(X1,X0)
| ( ~ sdtlseqdt0(sK7(X0,X1),X1)
& aElementOf0(sK7(X0,X1),X0) ) )
& ( ( aElementOf0(X1,X0)
& ! [X3] :
( sdtlseqdt0(X3,X1)
| ~ aElementOf0(X3,X0) ) )
| szmzazxdt0(X0) != X1 ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ isFinite0(X0)
| slcrc0 = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X2,sK7(X0,X1))],[f166]) ).
fof(f175,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( ? [X2] :
( ~ aElementOf0(X2,slbdtrb0(X0))
& aElementOf0(X2,xS) )
& ~ aSubsetOf0(xS,slbdtrb0(X0))
& aSet0(slbdtrb0(X0))
& ! [X1] :
( ( aElementOf0(X1,slbdtrb0(X0))
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X1),X0) )
& ( ( aElementOf0(X1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X1),X0) )
| ~ aElementOf0(X1,slbdtrb0(X0)) ) ) ) ),
inference(nnf_transformation,[],[f138]) ).
fof(f176,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( ? [X2] :
( ~ aElementOf0(X2,slbdtrb0(X0))
& aElementOf0(X2,xS) )
& ~ aSubsetOf0(xS,slbdtrb0(X0))
& aSet0(slbdtrb0(X0))
& ! [X1] :
( ( aElementOf0(X1,slbdtrb0(X0))
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X1),X0) )
& ( ( aElementOf0(X1,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X1),X0) )
| ~ aElementOf0(X1,slbdtrb0(X0)) ) ) ) ),
inference(flattening,[],[f175]) ).
fof(f177,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( ? [X1] :
( ~ aElementOf0(X1,slbdtrb0(X0))
& aElementOf0(X1,xS) )
& ~ aSubsetOf0(xS,slbdtrb0(X0))
& aSet0(slbdtrb0(X0))
& ! [X2] :
( ( aElementOf0(X2,slbdtrb0(X0))
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| ~ aElementOf0(X2,slbdtrb0(X0)) ) ) ) ),
inference(rectify,[],[f176]) ).
fof(f178,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( ~ aElementOf0(sK9(X0),slbdtrb0(X0))
& aElementOf0(sK9(X0),xS)
& ~ aSubsetOf0(xS,slbdtrb0(X0))
& aSet0(slbdtrb0(X0))
& ! [X2] :
( ( aElementOf0(X2,slbdtrb0(X0))
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| ~ aElementOf0(X2,slbdtrb0(X0)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X1,sK9(X0))],[f177]) ).
fof(f180,plain,
! [X2,X0] :
( ~ aElementOf0(X2,X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f142]) ).
fof(f220,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f24]) ).
fof(f222,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f229,plain,
! [X0,X1] :
( sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f156]) ).
fof(f251,plain,
! [X3,X0,X1] :
( sdtlseqdt0(X3,X1)
| ~ aElementOf0(X3,X0)
| szmzazxdt0(X0) != X1
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ isFinite0(X0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f167]) ).
fof(f252,plain,
! [X0,X1] :
( aElementOf0(X1,X0)
| szmzazxdt0(X0) != X1
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ isFinite0(X0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f167]) ).
fof(f270,plain,
isFinite0(xS),
inference(cnf_transformation,[],[f136]) ).
fof(f271,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f136]) ).
fof(f272,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f276,plain,
! [X2,X0] :
( ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| aElementOf0(X2,slbdtrb0(X0))
| ~ aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f178]) ).
fof(f279,plain,
! [X0] :
( aElementOf0(sK9(X0),xS)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f178]) ).
fof(f280,plain,
! [X0] :
( ~ aElementOf0(sK9(X0),slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f178]) ).
fof(f282,plain,
! [X2] : ~ aElementOf0(X2,slcrc0),
inference(equality_resolution,[],[f180]) ).
fof(f299,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| aElementOf0(szmzazxdt0(X0),X0)
| slcrc0 = X0 ),
inference(equality_resolution,[],[f252]) ).
fof(f300,plain,
! [X3,X0] :
( ~ isFinite0(X0)
| ~ aElementOf0(X3,X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| sdtlseqdt0(X3,szmzazxdt0(X0))
| slcrc0 = X0 ),
inference(equality_resolution,[],[f251]) ).
fof(f322,plain,
! [X0] :
( aElementOf0(sK9(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[],[f272,f279]) ).
fof(f330,definition,
( spl10_4
<=> slcrc0 = xS ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
fof(f331,plain,
( slcrc0 = xS
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f347,plain,
( ! [X0] :
( aElementOf0(sK9(X0),slcrc0)
| ~ aElementOf0(X0,szNzAzT0) )
| ~ spl10_4 ),
inference(superposition,[],[f279,f331]) ).
fof(f352,plain,
( ! [X0] : ~ aElementOf0(X0,szNzAzT0)
| ~ spl10_4 ),
inference(forward_subsumption_resolution,[],[f347,f282]) ).
fof(f392,plain,
( $false
| ~ spl10_4 ),
inference(unit_resulting_resolution,[],[f322,f352,f220]) ).
fof(f398,plain,
~ spl10_4,
inference(avatar_contradiction_clause,[],[f392]) ).
fof(f553,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(X0,slbdtrb0(szszuzczcdt0(X1)))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(szszuzczcdt0(X1),szNzAzT0) ),
inference(resolution,[],[f229,f276]) ).
fof(f555,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| aElementOf0(X0,slbdtrb0(szszuzczcdt0(X1)))
| ~ aElementOf0(szszuzczcdt0(X1),szNzAzT0) ),
inference(duplicate_literal_removal,[],[f553]) ).
fof(f557,plain,
! [X0,X1] :
( aElementOf0(X0,slbdtrb0(szszuzczcdt0(X1)))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X0,X1) ),
inference(forward_subsumption_resolution,[],[f555,f222]) ).
fof(f562,plain,
! [X0] :
( ~ aElementOf0(sK9(szszuzczcdt0(X0)),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(sK9(szszuzczcdt0(X0)),X0)
| ~ aElementOf0(szszuzczcdt0(X0),szNzAzT0) ),
inference(resolution,[],[f557,f280]) ).
fof(f563,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(sK9(szszuzczcdt0(X0)),X0)
| ~ aElementOf0(szszuzczcdt0(X0),szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f562,f322]) ).
fof(f564,plain,
! [X0] :
( ~ sdtlseqdt0(sK9(szszuzczcdt0(X0)),X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f563,f222]) ).
fof(f622,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| ~ aSubsetOf0(xS,szNzAzT0)
| sdtlseqdt0(X0,szmzazxdt0(xS))
| slcrc0 = xS ),
inference(resolution,[],[f270,f300]) ).
fof(f623,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| sdtlseqdt0(X0,szmzazxdt0(xS))
| slcrc0 = xS ),
inference(forward_subsumption_resolution,[],[f622,f271]) ).
fof(f625,definition,
( spl10_20
<=> ! [X0] :
( ~ aElementOf0(X0,xS)
| sdtlseqdt0(X0,szmzazxdt0(xS)) ) ),
introduced(definition,[new_symbols(definition,[spl10_20])],[avatar_definition]) ).
fof(f626,plain,
( ! [X0] :
( sdtlseqdt0(X0,szmzazxdt0(xS))
| ~ aElementOf0(X0,xS) )
| ~ spl10_20 ),
inference(avatar_component_clause,[],[f625]) ).
fof(f627,plain,
( spl10_4
| spl10_20 ),
inference(avatar_split_clause,[],[f623,f625,f330]) ).
fof(f630,plain,
( ~ aElementOf0(sK9(szszuzczcdt0(szmzazxdt0(xS))),xS)
| ~ aElementOf0(szmzazxdt0(xS),szNzAzT0)
| ~ spl10_20 ),
inference(resolution,[],[f626,f564]) ).
fof(f634,definition,
( spl10_21
<=> aElementOf0(szmzazxdt0(xS),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl10_21])],[avatar_definition]) ).
fof(f635,plain,
( ~ aElementOf0(szmzazxdt0(xS),szNzAzT0)
| spl10_21 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f637,definition,
( spl10_22
<=> aElementOf0(sK9(szszuzczcdt0(szmzazxdt0(xS))),xS) ),
introduced(definition,[new_symbols(definition,[spl10_22])],[avatar_definition]) ).
fof(f638,plain,
( ~ aElementOf0(sK9(szszuzczcdt0(szmzazxdt0(xS))),xS)
| spl10_22 ),
inference(avatar_component_clause,[],[f637]) ).
fof(f639,plain,
( ~ spl10_21
| ~ spl10_22
| ~ spl10_20 ),
inference(avatar_split_clause,[],[f630,f625,f637,f634]) ).
fof(f698,plain,
( ~ aSubsetOf0(xS,szNzAzT0)
| aElementOf0(szmzazxdt0(xS),xS)
| slcrc0 = xS ),
inference(resolution,[],[f299,f270]) ).
fof(f699,plain,
( aElementOf0(szmzazxdt0(xS),xS)
| slcrc0 = xS ),
inference(forward_subsumption_resolution,[],[f698,f271]) ).
fof(f701,definition,
( spl10_28
<=> aElementOf0(szmzazxdt0(xS),xS) ),
introduced(definition,[new_symbols(definition,[spl10_28])],[avatar_definition]) ).
fof(f702,plain,
( aElementOf0(szmzazxdt0(xS),xS)
| ~ spl10_28 ),
inference(avatar_component_clause,[],[f701]) ).
fof(f703,plain,
( spl10_4
| spl10_28 ),
inference(avatar_split_clause,[],[f699,f701,f330]) ).
fof(f707,plain,
( aElementOf0(szmzazxdt0(xS),szNzAzT0)
| ~ spl10_28 ),
inference(resolution,[],[f702,f272]) ).
fof(f710,plain,
( $false
| spl10_21
| ~ spl10_28 ),
inference(forward_subsumption_resolution,[],[f707,f635]) ).
fof(f711,plain,
( spl10_21
| ~ spl10_28 ),
inference(avatar_contradiction_clause,[],[f710]) ).
fof(f712,plain,
( ~ aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0)
| spl10_22 ),
inference(resolution,[],[f638,f279]) ).
fof(f814,plain,
( ~ aElementOf0(szmzazxdt0(xS),szNzAzT0)
| spl10_22 ),
inference(resolution,[],[f712,f222]) ).
fof(f816,plain,
( $false
| spl10_22
| ~ spl10_28 ),
inference(forward_subsumption_resolution,[],[f814,f707]) ).
fof(f817,plain,
( spl10_22
| ~ spl10_28 ),
inference(avatar_contradiction_clause,[],[f816]) ).
cnf(s10,plain,
~ spl10_4,
inference(sat_conversion,[],[f398]) ).
cnf(s20,plain,
( spl10_4
| spl10_20 ),
inference(sat_conversion,[],[f627]) ).
cnf(s21,plain,
( ~ spl10_20
| ~ spl10_21
| ~ spl10_22 ),
inference(sat_conversion,[],[f639]) ).
cnf(s27,plain,
( spl10_4
| spl10_28 ),
inference(sat_conversion,[],[f703]) ).
cnf(s30,plain,
( spl10_21
| ~ spl10_28 ),
inference(sat_conversion,[],[f711]) ).
cnf(s46,plain,
( spl10_22
| ~ spl10_28 ),
inference(sat_conversion,[],[f817]) ).
cnf(s50,plain,
spl10_28,
inference(rat,[],[s27,s10]) ).
cnf(s51,plain,
spl10_20,
inference(rat,[],[s20,s10]) ).
cnf(s53,plain,
spl10_22,
inference(rat,[],[s46,s50]) ).
cnf(s54,plain,
spl10_21,
inference(rat,[],[s30,s50]) ).
cnf(s55,plain,
$false,
inference(rat,[],[s21,s53,s54,s51]) ).
fof(f818,plain,
$false,
inference(avatar_sat_refutation,[],[s55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM543+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n017.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 20:20:50 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 6.70/2.03 % (2911927)Detected formulas, will run a generic FOF schedule.
% 6.70/2.03 % (2911935)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1874009402:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.70/2.03 % (2911935)Instruction limit reached!
% 6.70/2.03 % (2911935)------------------------------
% 6.70/2.03 % (2911935)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.03 % (2911935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.03 % (2911935)CaDiCaL version: 2.1.3
% 6.70/2.03 % (2911935)Termination reason: Instruction limit
% 6.70/2.03 % (2911935)Termination phase: Saturation
% 6.70/2.03 % (2911935)Time elapsed: 0.027 s
% 6.70/2.03 % (2911935)Peak memory usage: 90 MB
% 6.70/2.03 % (2911935)Instructions burned: 113 (million)
% 6.70/2.03 % (2911934)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=2394865482:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.70/2.03 % (2911937)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3052884613:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.70/2.03 % (2911936)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3360878432:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.70/2.03 % (2911932)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=3390276492:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.70/2.03 % (2911938)dis-21_1_sil=8000:lcm=predicate:random_seed=798092811: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)
% 6.70/2.03 % (2911933)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=2032621176:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.70/2.03 % (2911938)Instruction limit reached!
% 6.70/2.03 % (2911938)------------------------------
% 6.70/2.03 % (2911938)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.03 % (2911938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.03 % (2911938)CaDiCaL version: 2.1.3
% 6.70/2.03 % (2911938)Termination reason: Instruction limit
% 6.70/2.03 % (2911938)Termination phase: Saturation
% 6.70/2.03 % (2911938)Time elapsed: 0.057 s
% 6.70/2.03 % (2911938)Peak memory usage: 88 MB
% 6.70/2.03 % (2911938)Instructions burned: 131 (million)
% 6.70/2.03 % (2911936)Instruction limit reached!
% 6.70/2.03 % (2911936)------------------------------
% 6.70/2.03 % (2911936)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.03 % (2911936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.03 % (2911936)CaDiCaL version: 2.1.3
% 6.70/2.03 % (2911936)Termination reason: Instruction limit
% 6.70/2.03 % (2911936)Termination phase: Saturation
% 6.70/2.03 % (2911936)Time elapsed: 0.075 s
% 6.70/2.03 % (2911936)Peak memory usage: 88 MB
% 6.70/2.03 % (2911936)Instructions burned: 119 (million)
% 6.70/2.03 % (2911937)Instruction limit reached!
% 6.70/2.03 % (2911937)------------------------------
% 6.70/2.03 % (2911937)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.03 % (2911937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.03 % (2911937)CaDiCaL version: 2.1.3
% 6.70/2.03 % (2911937)Termination reason: Instruction limit
% 6.70/2.03 % (2911937)Termination phase: Saturation
% 6.70/2.03 % (2911937)Time elapsed: 0.098 s
% 6.70/2.03 % (2911937)Peak memory usage: 90 MB
% 6.70/2.03 % (2911937)Instructions burned: 140 (million)
% 6.70/2.03 % (2911940)lrs+10_1_sil=8000:sp=occurrence:random_seed=332978738:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.70/2.03 % (2911940)Instruction limit reached!
% 6.70/2.03 % (2911940)------------------------------
% 6.70/2.03 % (2911940)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.03 % (2911940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.03 % (2911940)CaDiCaL version: 2.1.3
% 6.70/2.03 % (2911940)Termination reason: Instruction limit
% 6.70/2.03 % (2911940)Termination phase: Saturation
% 6.70/2.03 % (2911940)Time elapsed: 0.090 s
% 6.70/2.03 % (2911940)Peak memory usage: 91 MB
% 6.70/2.03 % (2911940)Instructions burned: 288 (million)
% 6.70/2.03 % (2911947)lrs+10_1_sil=32000:urr=on:br=off:random_seed=331795326:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.70/2.03 % (2911947)Refutation not found, incomplete strategy
% 6.70/2.03 % (2911947)------------------------------
% 6.70/2.03 % (2911947)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.03 % (2911947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.03 % (2911947)CaDiCaL version: 2.1.3
% 6.70/2.03 % (2911947)Termination reason: Refutation not found, incomplete strategy
% 6.70/2.03 % (2911947)Time elapsed: 0.004 s
% 6.70/2.03 % (2911947)Peak memory usage: 89 MB
% 6.70/2.03 % (2911947)Instructions burned: 4 (million)
% 6.70/2.03 % (2911948)lrs+1011_1_sil=32000:sp=occurrence:random_seed=781382764:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.70/2.03 % (2911949)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1524775140:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.70/2.03 % (2911951)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3075608832:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 6.70/2.03 % (2911949)Instruction limit reached!
% 6.70/2.03 % (2911949)------------------------------
% 6.70/2.03 % (2911949)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.03 % (2911949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.03 % (2911949)CaDiCaL version: 2.1.3
% 6.70/2.03 % (2911949)Termination reason: Instruction limit
% 6.70/2.03 % (2911949)Termination phase: Saturation
% 6.70/2.03 % (2911949)Time elapsed: 0.151 s
% 6.70/2.03 % (2911949)Peak memory usage: 91 MB
% 6.70/2.03 % (2911949)Instructions burned: 248 (million)
% 6.70/2.03 % (2911951)Instruction limit reached!
% 6.70/2.03 % (2911951)------------------------------
% 6.70/2.03 % (2911951)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.03 % (2911951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.03 % (2911951)CaDiCaL version: 2.1.3
% 6.70/2.03 % (2911951)Termination reason: Instruction limit
% 6.70/2.03 % (2911951)Termination phase: Saturation
% 6.70/2.03 % (2911951)Time elapsed: 0.091 s
% 6.70/2.03 % (2911951)Peak memory usage: 89 MB
% 6.70/2.03 % (2911951)Instructions burned: 294 (million)
% 6.70/2.03 % (2911947)------------------------------
% 6.70/2.03 % (2911947)------------------------------
% 6.70/2.03 % (2911948)Instruction limit reached!
% 6.70/2.03 % (2911948)------------------------------
% 6.70/2.03 % (2911948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.03 % (2911948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.03 % (2911948)CaDiCaL version: 2.1.3
% 6.70/2.03 % (2911948)Termination reason: Instruction limit
% 6.70/2.03 % (2911948)Termination phase: Saturation
% 6.70/2.03 % (2911948)Time elapsed: 0.230 s
% 6.70/2.03 % (2911948)Peak memory usage: 92 MB
% 6.70/2.03 % (2911948)Instructions burned: 326 (million)
% 6.70/2.03 % (2911956)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2176003351:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.70/2.03 % (2911957)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=191306117:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.70/2.03 % (2911958)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1898016463:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.70/2.03 % (2911959)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3748182677:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 6.70/2.03 % (2911957)Instruction limit reached!
% 6.70/2.03 % (2911957)------------------------------
% 6.70/2.03 % (2911957)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.03 % (2911957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.03 % (2911957)CaDiCaL version: 2.1.3
% 6.70/2.03 % (2911957)Termination reason: Instruction limit
% 6.70/2.03 % (2911957)Termination phase: Saturation
% 6.70/2.03 % (2911957)Time elapsed: 0.078 s
% 6.70/2.03 % (2911957)Peak memory usage: 90 MB
% 6.70/2.03 % (2911957)Instructions burned: 114 (million)
% 6.70/2.03 % (2911958)Instruction limit reached!
% 6.70/2.03 % (2911958)------------------------------
% 6.70/2.03 % (2911958)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.03 % (2911958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.03 % (2911958)CaDiCaL version: 2.1.3
% 6.70/2.03 % (2911958)Termination reason: Instruction limit
% 6.70/2.03 % (2911958)Termination phase: Saturation
% 6.70/2.03 % (2911958)Time elapsed: 0.071 s
% 6.70/2.03 % (2911958)Peak memory usage: 89 MB
% 6.70/2.03 % (2911958)Instructions burned: 128 (million)
% 6.70/2.03 % (2911933)First to succeed.
% 6.70/2.03 % (2911933)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2911927"
% 6.70/2.03 % (2911959)Instruction limit reached!
% 6.70/2.03 % (2911959)------------------------------
% 6.70/2.03 % (2911959)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.70/2.03 % (2911959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.70/2.03 % (2911959)CaDiCaL version: 2.1.3
% 6.70/2.03 % (2911959)Termination reason: Instruction limit
% 6.70/2.03 % (2911959)Termination phase: Saturation
% 6.70/2.03 % (2911959)Time elapsed: 0.074 s
% 6.70/2.03 % (2911959)Peak memory usage: 89 MB
% 6.70/2.03 % (2911959)Instructions burned: 114 (million)
% 6.70/2.03 % (2911932)Also succeeded, but the first one will report.
% 6.70/2.03 % (2911964)lrs+10_1_sil=8000:sp=occurrence:random_seed=1903084593:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.70/2.03 % (2911965)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1361395128:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.70/2.03 % (2911966)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2672884931:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.70/2.03 % (2911956)Also succeeded, but the first one will report.
% 6.70/2.03 % (2911933)Refutation found. Thanks to Tanya!
% 6.70/2.03 % SZS status Theorem for theBenchmark
% 6.70/2.03 % SZS output start Proof for theBenchmark
% See solution above
% 8.70/2.22 % (2911933)------------------------------
% 8.70/2.22 % (2911933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.70/2.22 % (2911933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.70/2.22 % (2911933)CaDiCaL version: 2.1.3
% 8.70/2.22 % (2911933)Termination reason: Refutation
% 8.70/2.22 % (2911933)Time elapsed: 0.701 s
% 8.70/2.22 % (2911933)Peak memory usage: 128 MB
% 8.70/2.22 % (2911933)Instructions burned: 1024 (million)
% 8.70/2.22 % (2911933)------------------------------
% 8.70/2.22 % (2911933)------------------------------
% 8.70/2.22 % (2911927)Success in time 1.145 s
% 8.70/2.22 % Vampire exiting
%------------------------------------------------------------------------------