%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM544+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 4.54s 1.56s
% Output : Refutation 5.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 15
% Syntax : Number of formulae : 117 ( 22 unt; 7 def)
% Number of atoms : 471 ( 54 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 601 ( 247 ~; 263 |; 66 &)
% ( 16 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 5 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn 117 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f23,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefMax) ).
fof(f50,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( X1 = slbdtrb0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSeg) ).
fof(f55,axiom,
( aSubsetOf0(xS,szNzAzT0)
& isFinite0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1986) ).
fof(f56,conjecture,
( xS != slcrc0
=> aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f57,negated_conjecture,
~ ( xS != slcrc0
=> aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
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(f125,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(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(flattening,[],[f125]) ).
fof(f129,plain,
! [X0] :
( ! [X1] :
( X1 = slbdtrb0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) ) ) ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f135,plain,
( ~ aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
& xS != slcrc0 ),
inference(ennf_transformation,[],[f57]) ).
fof(f146,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,[],[f71]) ).
fof(f147,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,[],[f146]) ).
fof(f148,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,[],[f147]) ).
fof(f149,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK5(X0,X1),X0)
& aElementOf0(sK5(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f148]) ).
fof(f163,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(f171,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,[],[f126]) ).
fof(f172,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,[],[f171]) ).
fof(f173,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,[],[f172]) ).
fof(f174,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzazxdt0(X0)
| ~ aElementOf0(X1,X0)
| ( ~ sdtlseqdt0(sK11(X0,X1),X1)
& aElementOf0(sK11(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,[sK11]),skolemize(X2,sK11(X0,X1))],[f173]) ).
fof(f175,plain,
! [X0] :
( ! [X1] :
( ( X1 = slbdtrb0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,X1) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| ~ aElementOf0(X2,X1) ) ) )
| slbdtrb0(X0) != X1 ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(nnf_transformation,[],[f129]) ).
fof(f176,plain,
! [X0] :
( ! [X1] :
( ( X1 = slbdtrb0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,X1) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| ~ aElementOf0(X2,X1) ) ) )
| slbdtrb0(X0) != X1 ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f175]) ).
fof(f177,plain,
! [X0] :
( ! [X1] :
( ( X1 = slbdtrb0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ~ aElementOf0(X2,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,X1) )
& ( ( aElementOf0(X2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X2),X0) )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X3] :
( ( aElementOf0(X3,X1)
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X3),X0) )
& ( ( aElementOf0(X3,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X3),X0) )
| ~ aElementOf0(X3,X1) ) ) )
| slbdtrb0(X0) != X1 ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(rectify,[],[f176]) ).
fof(f178,plain,
! [X0] :
( ! [X1] :
( ( X1 = slbdtrb0(X0)
| ~ aSet0(X1)
| ( ( ~ aElementOf0(sK12(X0,X1),szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(sK12(X0,X1)),X0)
| ~ aElementOf0(sK12(X0,X1),X1) )
& ( ( aElementOf0(sK12(X0,X1),szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(sK12(X0,X1)),X0) )
| aElementOf0(sK12(X0,X1),X1) ) ) )
& ( ( aSet0(X1)
& ! [X3] :
( ( aElementOf0(X3,X1)
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X3),X0) )
& ( ( aElementOf0(X3,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(X3),X0) )
| ~ aElementOf0(X3,X1) ) ) )
| slbdtrb0(X0) != X1 ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X2,sK12(X0,X1))],[f177]) ).
fof(f189,plain,
! [X3,X0,X1] :
( ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f190,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f191,plain,
! [X0,X1] :
( aElementOf0(sK5(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f192,plain,
! [X0,X1] :
( ~ aElementOf0(sK5(X0,X1),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f228,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f231,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f238,plain,
! [X0,X1] :
( sdtlseqdt0(szszuzczcdt0(X0),szszuzczcdt0(X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f163]) ).
fof(f259,plain,
! [X3,X0,X1] :
( sdtlseqdt0(X3,X1)
| ~ aElementOf0(X3,X0)
| szmzazxdt0(X0) != X1
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ isFinite0(X0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f174]) ).
fof(f260,plain,
! [X0,X1] :
( aElementOf0(X1,X0)
| szmzazxdt0(X0) != X1
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ isFinite0(X0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f174]) ).
fof(f266,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,szNzAzT0)
| ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| slbdtrb0(X0) != X1
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f178]) ).
fof(f267,plain,
! [X0,X1] :
( aSet0(X1)
| slbdtrb0(X0) != X1
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f178]) ).
fof(f278,plain,
isFinite0(xS),
inference(cnf_transformation,[],[f55]) ).
fof(f279,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f55]) ).
fof(f280,plain,
slcrc0 != xS,
inference(cnf_transformation,[],[f135]) ).
fof(f281,plain,
~ aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))),
inference(cnf_transformation,[],[f135]) ).
fof(f292,plain,
! [X0] :
( aElementOf0(szmzazxdt0(X0),X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ isFinite0(X0)
| slcrc0 = X0 ),
inference(equality_resolution,[],[f260]) ).
fof(f293,plain,
! [X3,X0] :
( sdtlseqdt0(X3,szmzazxdt0(X0))
| ~ aElementOf0(X3,X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ isFinite0(X0)
| slcrc0 = X0 ),
inference(equality_resolution,[],[f259]) ).
fof(f294,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aSet0(slbdtrb0(X0)) ),
inference(equality_resolution,[],[f267]) ).
fof(f295,plain,
! [X3,X0] :
( ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X3,szNzAzT0)
| aElementOf0(X3,slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(equality_resolution,[],[f266]) ).
fof(f299,definition,
sF13 = szmzazxdt0(xS),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f300,plain,
szmzazxdt0(xS) = sF13,
inference(reorient_equations,[],[f299]) ).
fof(f301,definition,
sF14 = szszuzczcdt0(sF13),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f302,plain,
szszuzczcdt0(sF13) = sF14,
inference(reorient_equations,[],[f301]) ).
fof(f303,definition,
sF15 = slbdtrb0(sF14),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f304,plain,
slbdtrb0(sF14) = sF15,
inference(reorient_equations,[],[f303]) ).
fof(f305,plain,
~ aSubsetOf0(xS,sF15),
inference(definition_folding,[],[f281,f304,f302,f300]) ).
fof(f322,plain,
! [X0] :
( sdtlseqdt0(X0,sF13)
| ~ aElementOf0(X0,xS)
| ~ aSubsetOf0(xS,szNzAzT0)
| ~ isFinite0(xS)
| slcrc0 = xS ),
inference(superposition,[],[f293,f300]) ).
fof(f323,plain,
! [X0] :
( sdtlseqdt0(X0,sF13)
| ~ aElementOf0(X0,xS)
| ~ isFinite0(xS)
| slcrc0 = xS ),
inference(forward_subsumption_resolution,[],[f322,f279]) ).
fof(f324,plain,
! [X0] :
( sdtlseqdt0(X0,sF13)
| ~ aElementOf0(X0,xS)
| slcrc0 = xS ),
inference(forward_subsumption_resolution,[],[f323,f278]) ).
fof(f325,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| sdtlseqdt0(X0,sF13) ),
inference(forward_subsumption_resolution,[],[f324,f280]) ).
fof(f326,plain,
! [X0] :
( ~ aSet0(xS)
| aSubsetOf0(xS,X0)
| ~ aSet0(X0)
| sdtlseqdt0(sK5(X0,xS),sF13) ),
inference(resolution,[],[f191,f325]) ).
fof(f328,definition,
( spl16_4
<=> ! [X0] :
( aSubsetOf0(xS,X0)
| sdtlseqdt0(sK5(X0,xS),sF13)
| ~ aSet0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl16_4])],[avatar_definition]) ).
fof(f329,plain,
( ! [X0] :
( sdtlseqdt0(sK5(X0,xS),sF13)
| aSubsetOf0(xS,X0)
| ~ aSet0(X0) )
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f331,definition,
( spl16_5
<=> aSet0(xS) ),
introduced(definition,[new_symbols(definition,[spl16_5])],[avatar_definition]) ).
fof(f332,plain,
( aSet0(xS)
| ~ spl16_5 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f333,plain,
( ~ aSet0(xS)
| spl16_5 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f334,plain,
( spl16_4
| ~ spl16_5 ),
inference(avatar_split_clause,[],[f326,f331,f328]) ).
fof(f348,definition,
( spl16_6
<=> aElementOf0(sF14,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl16_6])],[avatar_definition]) ).
fof(f349,plain,
( aElementOf0(sF14,szNzAzT0)
| ~ spl16_6 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f350,plain,
( ~ aElementOf0(sF14,szNzAzT0)
| spl16_6 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f364,definition,
( spl16_9
<=> aElementOf0(sF13,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl16_9])],[avatar_definition]) ).
fof(f365,plain,
( aElementOf0(sF13,szNzAzT0)
| ~ spl16_9 ),
inference(avatar_component_clause,[],[f364]) ).
fof(f366,plain,
( ~ aElementOf0(sF13,szNzAzT0)
| spl16_9 ),
inference(avatar_component_clause,[],[f364]) ).
fof(f385,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f190,f279]) ).
fof(f389,plain,
( ~ aSet0(szNzAzT0)
| spl16_5 ),
inference(forward_subsumption_resolution,[],[f385,f333]) ).
fof(f390,plain,
( $false
| spl16_5 ),
inference(forward_subsumption_resolution,[],[f389,f228]) ).
fof(f391,plain,
spl16_5,
inference(avatar_contradiction_clause,[],[f390]) ).
fof(f435,plain,
( aElementOf0(sF14,szNzAzT0)
| ~ aElementOf0(sF13,szNzAzT0) ),
inference(superposition,[],[f231,f302]) ).
fof(f441,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szNzAzT0)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f189,f279]) ).
fof(f444,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f441,f228]) ).
fof(f497,plain,
( aElementOf0(szmzazxdt0(xS),szNzAzT0)
| ~ aSubsetOf0(xS,szNzAzT0)
| ~ isFinite0(xS)
| slcrc0 = xS ),
inference(resolution,[],[f444,f292]) ).
fof(f499,plain,
! [X0] :
( aElementOf0(sK5(X0,xS),szNzAzT0)
| ~ aSet0(xS)
| aSubsetOf0(xS,X0)
| ~ aSet0(X0) ),
inference(resolution,[],[f444,f191]) ).
fof(f503,plain,
( ! [X0] :
( aElementOf0(sK5(X0,xS),szNzAzT0)
| aSubsetOf0(xS,X0)
| ~ aSet0(X0) )
| ~ spl16_5 ),
inference(forward_subsumption_resolution,[],[f499,f332]) ).
fof(f505,plain,
( aElementOf0(szmzazxdt0(xS),szNzAzT0)
| ~ isFinite0(xS)
| slcrc0 = xS ),
inference(forward_subsumption_resolution,[],[f497,f279]) ).
fof(f507,plain,
( aElementOf0(szmzazxdt0(xS),szNzAzT0)
| slcrc0 = xS ),
inference(forward_subsumption_resolution,[],[f505,f278]) ).
fof(f508,plain,
aElementOf0(szmzazxdt0(xS),szNzAzT0),
inference(forward_subsumption_resolution,[],[f507,f280]) ).
fof(f509,plain,
aElementOf0(sF13,szNzAzT0),
inference(forward_demodulation,[],[f508,f300]) ).
fof(f510,plain,
( $false
| spl16_9 ),
inference(forward_subsumption_resolution,[],[f509,f366]) ).
fof(f511,plain,
spl16_9,
inference(avatar_contradiction_clause,[],[f510]) ).
fof(f518,plain,
( ~ aElementOf0(sF13,szNzAzT0)
| spl16_6 ),
inference(forward_subsumption_resolution,[],[f435,f350]) ).
fof(f523,plain,
( $false
| spl16_6
| ~ spl16_9 ),
inference(forward_subsumption_resolution,[],[f518,f365]) ).
fof(f524,plain,
( spl16_6
| ~ spl16_9 ),
inference(avatar_contradiction_clause,[],[f523]) ).
fof(f623,plain,
( aSet0(slbdtrb0(sF14))
| ~ spl16_6 ),
inference(resolution,[],[f349,f294]) ).
fof(f624,plain,
( aSet0(sF15)
| ~ spl16_6 ),
inference(forward_demodulation,[],[f623,f304]) ).
fof(f966,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X0,slbdtrb0(szszuzczcdt0(X1)))
| ~ aElementOf0(szszuzczcdt0(X1),szNzAzT0) ),
inference(resolution,[],[f238,f295]) ).
fof(f970,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,[],[f966]) ).
fof(f976,plain,
! [X0,X1] :
( aElementOf0(X0,slbdtrb0(szszuzczcdt0(X1)))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ sdtlseqdt0(X0,X1) ),
inference(forward_subsumption_resolution,[],[f970,f231]) ).
fof(f1209,plain,
! [X0] :
( aElementOf0(X0,slbdtrb0(sF14))
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sF13,szNzAzT0)
| ~ sdtlseqdt0(X0,sF13) ),
inference(superposition,[],[f976,f302]) ).
fof(f1211,plain,
( ! [X0] :
( aElementOf0(X0,slbdtrb0(sF14))
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X0,sF13) )
| ~ spl16_9 ),
inference(forward_subsumption_resolution,[],[f1209,f365]) ).
fof(f1214,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,sF13)
| ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(X0,sF15) )
| ~ spl16_9 ),
inference(forward_demodulation,[],[f1211,f304]) ).
fof(f1220,plain,
( ! [X0] :
( ~ aElementOf0(sK5(X0,xS),szNzAzT0)
| aElementOf0(sK5(X0,xS),sF15)
| aSubsetOf0(xS,X0)
| ~ aSet0(X0) )
| ~ spl16_4
| ~ spl16_9 ),
inference(resolution,[],[f1214,f329]) ).
fof(f1223,plain,
( ! [X0] :
( aElementOf0(sK5(X0,xS),sF15)
| aSubsetOf0(xS,X0)
| ~ aSet0(X0) )
| ~ spl16_4
| ~ spl16_5
| ~ spl16_9 ),
inference(forward_subsumption_resolution,[],[f1220,f503]) ).
fof(f1238,plain,
( aSubsetOf0(xS,sF15)
| ~ aSet0(sF15)
| ~ aSet0(xS)
| aSubsetOf0(xS,sF15)
| ~ aSet0(sF15)
| ~ spl16_4
| ~ spl16_5
| ~ spl16_9 ),
inference(resolution,[],[f1223,f192]) ).
fof(f1241,plain,
( aSubsetOf0(xS,sF15)
| ~ aSet0(sF15)
| ~ aSet0(xS)
| ~ spl16_4
| ~ spl16_5
| ~ spl16_9 ),
inference(duplicate_literal_removal,[],[f1238]) ).
fof(f1242,plain,
( ~ aSet0(sF15)
| ~ aSet0(xS)
| ~ spl16_4
| ~ spl16_5
| ~ spl16_9 ),
inference(forward_subsumption_resolution,[],[f1241,f305]) ).
fof(f1243,plain,
( ~ aSet0(xS)
| ~ spl16_4
| ~ spl16_5
| ~ spl16_6
| ~ spl16_9 ),
inference(forward_subsumption_resolution,[],[f1242,f624]) ).
fof(f1244,plain,
( $false
| ~ spl16_4
| ~ spl16_5
| ~ spl16_6
| ~ spl16_9 ),
inference(forward_subsumption_resolution,[],[f1243,f332]) ).
fof(f1245,plain,
( ~ spl16_4
| ~ spl16_5
| ~ spl16_6
| ~ spl16_9 ),
inference(avatar_contradiction_clause,[],[f1244]) ).
cnf(s4,plain,
( spl16_4
| ~ spl16_5 ),
inference(sat_conversion,[],[f334]) ).
cnf(s8,plain,
spl16_5,
inference(sat_conversion,[],[f391]) ).
cnf(s12,plain,
spl16_9,
inference(sat_conversion,[],[f511]) ).
cnf(s13,plain,
( spl16_6
| ~ spl16_9 ),
inference(sat_conversion,[],[f524]) ).
cnf(s46,plain,
( ~ spl16_4
| ~ spl16_5
| ~ spl16_6
| ~ spl16_9 ),
inference(sat_conversion,[],[f1245]) ).
cnf(s51,plain,
spl16_6,
inference(rat,[],[s13,s12]) ).
cnf(s59,plain,
~ spl16_4,
inference(rat,[],[s46,s12,s51,s8]) ).
cnf(s65,plain,
$false,
inference(rat,[],[s4,s8,s59]) ).
fof(f1246,plain,
$false,
inference(avatar_sat_refutation,[],[s65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM544+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n020.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 20:26:20 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.54/1.56 % (3721581)Detected formulas, will run a generic FOF schedule.
% 4.54/1.56 % (3721586)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=2251597245:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.54/1.56 % (3721587)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=2298335865:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.54/1.56 % (3721590)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2186940580:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.54/1.56 % (3721589)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3301866753:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.54/1.56 % (3721592)dis-21_1_sil=8000:lcm=predicate:random_seed=402470489: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)
% 4.54/1.56 % (3721588)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=1501409052:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.54/1.56 % (3721591)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4053047768:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.54/1.56 % (3721589)Refutation not found, incomplete strategy
% 4.54/1.56 % (3721589)------------------------------
% 4.54/1.56 % (3721589)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.54/1.56 % (3721589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.54/1.56 % (3721589)CaDiCaL version: 2.1.3
% 4.54/1.56 % (3721589)Termination reason: Refutation not found, incomplete strategy
% 4.54/1.56 % (3721589)Time elapsed: 0.003 s
% 4.54/1.56 % (3721589)Peak memory usage: 88 MB
% 4.54/1.56 % (3721589)Instructions burned: 3 (million)
% 4.54/1.56 % (3721592)Instruction limit reached!
% 4.54/1.56 % (3721592)------------------------------
% 4.54/1.56 % (3721592)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.54/1.56 % (3721592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.54/1.56 % (3721592)CaDiCaL version: 2.1.3
% 4.54/1.56 % (3721592)Termination reason: Instruction limit
% 4.54/1.56 % (3721592)Termination phase: Saturation
% 4.54/1.56 % (3721592)Time elapsed: 0.057 s
% 4.54/1.56 % (3721592)Peak memory usage: 88 MB
% 4.54/1.56 % (3721592)Instructions burned: 132 (million)
% 4.54/1.56 % (3721590)Instruction limit reached!
% 4.54/1.56 % (3721590)------------------------------
% 4.54/1.56 % (3721590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.54/1.56 % (3721590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.54/1.56 % (3721590)CaDiCaL version: 2.1.3
% 4.54/1.56 % (3721590)Termination reason: Instruction limit
% 4.54/1.56 % (3721590)Termination phase: Saturation
% 4.54/1.56 % (3721590)Time elapsed: 0.075 s
% 4.54/1.56 % (3721590)Peak memory usage: 88 MB
% 4.54/1.56 % (3721590)Instructions burned: 120 (million)
% 4.54/1.56 % (3721591)Instruction limit reached!
% 4.54/1.56 % (3721591)------------------------------
% 4.54/1.56 % (3721591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.54/1.56 % (3721591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.54/1.56 % (3721591)CaDiCaL version: 2.1.3
% 4.54/1.56 % (3721591)Termination reason: Instruction limit
% 4.54/1.56 % (3721591)Termination phase: Saturation
% 4.54/1.56 % (3721591)Time elapsed: 0.095 s
% 4.54/1.56 % (3721591)Peak memory usage: 90 MB
% 4.54/1.56 % (3721591)Instructions burned: 140 (million)
% 4.54/1.56 % (3721600)lrs+10_1_sil=8000:sp=occurrence:random_seed=24233271:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.54/1.56 % (3721601)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2079092829:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.54/1.56 % (3721601)Refutation not found, incomplete strategy
% 4.54/1.56 % (3721601)------------------------------
% 4.54/1.56 % (3721601)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.54/1.56 % (3721601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.54/1.56 % (3721601)CaDiCaL version: 2.1.3
% 4.54/1.56 % (3721601)Termination reason: Refutation not found, incomplete strategy
% 4.54/1.56 % (3721601)Time elapsed: 0.005 s
% 4.54/1.56 % (3721601)Peak memory usage: 89 MB
% 4.54/1.56 % (3721601)Instructions burned: 5 (million)
% 4.54/1.56 % (3721602)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2616869414:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.54/1.56 % (3721589)------------------------------
% 4.54/1.56 % (3721589)------------------------------
% 4.54/1.56 % (3721600)Instruction limit reached!
% 4.54/1.56 % (3721600)------------------------------
% 4.54/1.56 % (3721600)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.54/1.56 % (3721600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.54/1.56 % (3721600)CaDiCaL version: 2.1.3
% 4.54/1.56 % (3721600)Termination reason: Instruction limit
% 4.54/1.56 % (3721600)Termination phase: Saturation
% 4.54/1.56 % (3721600)Time elapsed: 0.181 s
% 4.54/1.56 % (3721600)Peak memory usage: 91 MB
% 4.54/1.56 % (3721600)Instructions burned: 286 (million)
% 4.54/1.56 % (3721606)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=2329239932:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.54/1.56 % (3721586)First to succeed.
% 4.54/1.56 % (3721586)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3721581"
% 4.54/1.56 % (3721602)Instruction limit reached!
% 4.54/1.56 % (3721602)------------------------------
% 4.54/1.56 % (3721602)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.54/1.56 % (3721602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.54/1.56 % (3721602)CaDiCaL version: 2.1.3
% 4.54/1.56 % (3721602)Termination reason: Instruction limit
% 4.54/1.56 % (3721602)Termination phase: Saturation
% 4.54/1.56 % (3721602)Time elapsed: 0.209 s
% 4.54/1.56 % (3721602)Peak memory usage: 91 MB
% 4.54/1.56 % (3721602)Instructions burned: 325 (million)
% 4.54/1.56 % (3721601)------------------------------
% 4.54/1.56 % (3721601)------------------------------
% 4.54/1.56 % (3721608)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2123913301:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 4.54/1.56 % (3721606)Instruction limit reached!
% 4.54/1.56 % (3721606)------------------------------
% 4.54/1.56 % (3721606)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.54/1.56 % (3721606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.54/1.56 % (3721606)CaDiCaL version: 2.1.3
% 4.54/1.56 % (3721606)Termination reason: Instruction limit
% 4.54/1.56 % (3721606)Termination phase: Saturation
% 4.54/1.56 % (3721606)Time elapsed: 0.156 s
% 4.54/1.56 % (3721606)Peak memory usage: 92 MB
% 4.54/1.56 % (3721606)Instructions burned: 248 (million)
% 4.54/1.56 % (3721586)Refutation found. Thanks to Tanya!
% 4.54/1.56 % SZS status Theorem for theBenchmark
% 4.54/1.56 % SZS output start Proof for theBenchmark
% See solution above
% 5.49/1.76 % (3721586)------------------------------
% 5.49/1.76 % (3721586)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.49/1.76 % (3721586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.49/1.76 % (3721586)CaDiCaL version: 2.1.3
% 5.49/1.76 % (3721586)Termination reason: Refutation
% 5.49/1.76 % (3721586)Time elapsed: 0.413 s
% 5.49/1.76 % (3721586)Peak memory usage: 131 MB
% 5.49/1.76 % (3721586)Instructions burned: 1075 (million)
% 5.49/1.76 % (3721586)------------------------------
% 5.49/1.76 % (3721586)------------------------------
% 5.49/1.76 % (3721581)Success in time 0.695 s
% 5.49/1.76 % Vampire exiting
%------------------------------------------------------------------------------