%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM619+3 : 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 : n016.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 12:16:01 PM UTC 2026
% Result : Theorem 8.64s 2.07s
% Output : Refutation 9.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 22
% Syntax : Number of formulae : 121 ( 33 unt; 8 def)
% Number of atoms : 338 ( 42 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 354 ( 137 ~; 127 |; 66 &)
% ( 9 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 7 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 14 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 69 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
fof(f35,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessASymm) ).
fof(f37,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessTotal) ).
fof(f82,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(f83,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X0))
=> aElementOf0(X2,sdtlpdtrp0(xN,X1)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3754) ).
fof(f91,axiom,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> sdtlseqdt0(sdtlpdtrp0(xe,X0),X1) )
& sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4660) ).
fof(f103,axiom,
( aElementOf0(xp,xQ)
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(xp,X0) )
& xp = szmzizndt0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
fof(f104,axiom,
( aSet0(xP)
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X0) )
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( aElement0(X0)
& aElementOf0(X0,xQ)
& X0 != szmzizndt0(xQ) ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
fof(f111,axiom,
( aElementOf0(xn,szDzozmdt0(xd))
& sdtlpdtrp0(xd,xn) = szDzizrdt0(xd)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0)
& sdtlpdtrp0(xe,xn) = xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5309) ).
fof(f113,axiom,
( aElement0(xx)
& aElementOf0(xx,xQ)
& xx != szmzizndt0(xQ)
& aElementOf0(xx,xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5348) ).
fof(f114,axiom,
( aElementOf0(xx,szNzAzT0)
& ? [X0] :
( aElementOf0(X0,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& sdtlpdtrp0(xe,X0) = xx ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5365) ).
fof(f115,axiom,
( aElementOf0(xm,szNzAzT0)
& xx = sdtlpdtrp0(xe,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5389) ).
fof(f116,axiom,
! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xm))
=> sdtlseqdt0(xx,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5401) ).
fof(f117,conjecture,
aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f118,negated_conjecture,
~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(negated_conjecture,[status(cth)],[f117]) ).
fof(f140,plain,
( aSet0(xP)
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X0) )
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( aElement0(X1)
& aElementOf0(X1,xQ)
& szmzizndt0(xQ) != X1 ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(rectify,[],[f104]) ).
fof(f141,plain,
~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(flattening,[],[f118]) ).
fof(f171,plain,
! [X0] :
( ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f183,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f184,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f183]) ).
fof(f187,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f188,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f187]) ).
fof(f248,plain,
! [X0] :
( ( aSet0(sdtlpdtrp0(xN,X0))
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f249,plain,
! [X0,X1] :
( ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) )
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f250,plain,
! [X0,X1] :
( ( ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X0)) )
& aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) )
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f249]) ).
fof(f264,plain,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X0] :
( ( aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0))
& ! [X1] :
( sdtlseqdt0(sdtlpdtrp0(xe,X0),X1)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
& sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f91]) ).
fof(f275,plain,
( aElementOf0(xp,xQ)
& ! [X0] :
( sdtlseqdt0(xp,X0)
| ~ aElementOf0(X0,xQ) )
& xp = szmzizndt0(xQ) ),
inference(ennf_transformation,[],[f103]) ).
fof(f276,plain,
( aSet0(xP)
& ! [X0] :
( sdtlseqdt0(szmzizndt0(xQ),X0)
| ~ aElementOf0(X0,xQ) )
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( aElement0(X1)
& aElementOf0(X1,xQ)
& szmzizndt0(xQ) != X1 ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(ennf_transformation,[],[f140]) ).
fof(f279,plain,
! [X0] :
( sdtlseqdt0(xx,X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xm)) ),
inference(ennf_transformation,[],[f116]) ).
fof(f461,plain,
( aSet0(xP)
& ! [X0] :
( sdtlseqdt0(szmzizndt0(xQ),X0)
| ~ aElementOf0(X0,xQ) )
& ! [X1] :
( ( aElementOf0(X1,xP)
| ~ aElement0(X1)
| ~ aElementOf0(X1,xQ)
| szmzizndt0(xQ) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,xQ)
& szmzizndt0(xQ) != X1 )
| ~ aElementOf0(X1,xP) ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(nnf_transformation,[],[f276]) ).
fof(f462,plain,
( aSet0(xP)
& ! [X0] :
( sdtlseqdt0(szmzizndt0(xQ),X0)
| ~ aElementOf0(X0,xQ) )
& ! [X1] :
( ( aElementOf0(X1,xP)
| ~ aElement0(X1)
| ~ aElementOf0(X1,xQ)
| szmzizndt0(xQ) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,xQ)
& szmzizndt0(xQ) != X1 )
| ~ aElementOf0(X1,xP) ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(flattening,[],[f461]) ).
fof(f464,plain,
( aElementOf0(xx,szNzAzT0)
& aElementOf0(sK73,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& xx = sdtlpdtrp0(xe,sK73) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(X0,sK73)],[f114]) ).
fof(f514,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f171]) ).
fof(f525,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f184]) ).
fof(f527,plain,
! [X0,X1] :
( sdtlseqdt0(szszuzczcdt0(X1),X0)
| sdtlseqdt0(X0,X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f188]) ).
fof(f685,plain,
! [X0,X1] :
( ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f688,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f250]) ).
fof(f816,plain,
! [X0] :
( aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f264]) ).
fof(f872,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[],[f275]) ).
fof(f873,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| sdtlseqdt0(xp,X0) ),
inference(cnf_transformation,[],[f275]) ).
fof(f876,plain,
! [X1] :
( szmzizndt0(xQ) != X1
| ~ aElementOf0(X1,xP) ),
inference(cnf_transformation,[],[f462]) ).
fof(f891,plain,
xp = sdtlpdtrp0(xe,xn),
inference(cnf_transformation,[],[f111]) ).
fof(f892,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f111]) ).
fof(f897,plain,
aElementOf0(xx,xP),
inference(cnf_transformation,[],[f113]) ).
fof(f899,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f113]) ).
fof(f903,plain,
aElementOf0(xx,szNzAzT0),
inference(cnf_transformation,[],[f464]) ).
fof(f904,plain,
xx = sdtlpdtrp0(xe,xm),
inference(cnf_transformation,[],[f115]) ).
fof(f905,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[],[f115]) ).
fof(f906,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,X0) ),
inference(cnf_transformation,[],[f279]) ).
fof(f907,plain,
~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f141]) ).
fof(f966,plain,
~ aElementOf0(szmzizndt0(xQ),xP),
inference(equality_resolution,[],[f876]) ).
fof(f967,definition,
sF74 = szszuzczcdt0(xn),
introduced(definition,[new_symbols(definition,[sF74])],[function_definition]) ).
fof(f968,plain,
szszuzczcdt0(xn) = sF74,
inference(reorient_equations,[],[f967]) ).
fof(f969,definition,
sF75 = sdtlpdtrp0(xN,sF74),
introduced(definition,[new_symbols(definition,[sF75])],[function_definition]) ).
fof(f970,plain,
sdtlpdtrp0(xN,sF74) = sF75,
inference(reorient_equations,[],[f969]) ).
fof(f971,plain,
~ aElementOf0(xx,sF75),
inference(definition_folding,[],[f907,f970,f968]) ).
fof(f1009,definition,
( spl76_7
<=> aElementOf0(sF74,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl76_7])],[avatar_definition]) ).
fof(f1010,plain,
( aElementOf0(sF74,szNzAzT0)
| ~ spl76_7 ),
inference(avatar_component_clause,[],[f1009]) ).
fof(f1011,plain,
( ~ aElementOf0(sF74,szNzAzT0)
| spl76_7 ),
inference(avatar_component_clause,[],[f1009]) ).
fof(f1017,plain,
( aElementOf0(xx,sdtlpdtrp0(xN,xm))
| ~ aElementOf0(xm,szNzAzT0) ),
inference(superposition,[],[f816,f904]) ).
fof(f1018,plain,
aElementOf0(xx,sdtlpdtrp0(xN,xm)),
inference(forward_subsumption_resolution,[],[f1017,f905]) ).
fof(f1033,plain,
! [X0] :
( sdtlseqdt0(sF74,X0)
| sdtlseqdt0(X0,xn)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(superposition,[],[f527,f968]) ).
fof(f1034,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(X0,xn)
| sdtlseqdt0(sF74,X0) ),
inference(forward_subsumption_resolution,[],[f1033,f892]) ).
fof(f1035,plain,
! [X0,X1] :
( aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[],[f688,f816]) ).
fof(f1036,plain,
! [X0] :
( aElementOf0(xx,sdtlpdtrp0(xN,X0))
| ~ sdtlseqdt0(X0,xm)
| ~ aElementOf0(xm,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[],[f688,f1018]) ).
fof(f1038,plain,
! [X0,X1] :
( aElementOf0(sdtlpdtrp0(xe,X0),sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(duplicate_literal_removal,[],[f1035]) ).
fof(f1039,plain,
! [X0] :
( aElementOf0(xx,sdtlpdtrp0(xN,X0))
| ~ sdtlseqdt0(X0,xm)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1036,f905]) ).
fof(f1042,plain,
( aElementOf0(xx,sF75)
| ~ sdtlseqdt0(sF74,xm)
| ~ aElementOf0(sF74,szNzAzT0) ),
inference(superposition,[],[f1039,f970]) ).
fof(f1066,plain,
( sdtlseqdt0(xm,xn)
| sdtlseqdt0(sF74,xm) ),
inference(resolution,[],[f905,f1034]) ).
fof(f1068,definition,
( spl76_15
<=> sdtlseqdt0(sF74,xm) ),
introduced(definition,[new_symbols(definition,[spl76_15])],[avatar_definition]) ).
fof(f1070,plain,
( sdtlseqdt0(sF74,xm)
| ~ spl76_15 ),
inference(avatar_component_clause,[],[f1068]) ).
fof(f1072,definition,
( spl76_16
<=> sdtlseqdt0(xm,xn) ),
introduced(definition,[new_symbols(definition,[spl76_16])],[avatar_definition]) ).
fof(f1074,plain,
( sdtlseqdt0(xm,xn)
| ~ spl76_16 ),
inference(avatar_component_clause,[],[f1072]) ).
fof(f1075,plain,
( spl76_15
| spl76_16 ),
inference(avatar_split_clause,[],[f1066,f1072,f1068]) ).
fof(f1099,plain,
( aElementOf0(sF74,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(superposition,[],[f514,f968]) ).
fof(f1100,plain,
( ~ aElementOf0(xn,szNzAzT0)
| spl76_7 ),
inference(forward_subsumption_resolution,[],[f1099,f1011]) ).
fof(f1101,plain,
( $false
| spl76_7 ),
inference(forward_subsumption_resolution,[],[f1100,f892]) ).
fof(f1102,plain,
spl76_7,
inference(avatar_contradiction_clause,[],[f1101]) ).
fof(f1104,plain,
( ~ sdtlseqdt0(sF74,xm)
| ~ aElementOf0(sF74,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1042,f971]) ).
fof(f1109,plain,
( ~ aElementOf0(sF74,szNzAzT0)
| ~ spl76_15 ),
inference(forward_subsumption_resolution,[],[f1104,f1070]) ).
fof(f1113,plain,
( $false
| ~ spl76_7
| ~ spl76_15 ),
inference(forward_subsumption_resolution,[],[f1109,f1010]) ).
fof(f1114,plain,
( ~ spl76_7
| ~ spl76_15 ),
inference(avatar_contradiction_clause,[],[f1113]) ).
fof(f1168,plain,
sdtlseqdt0(xp,xx),
inference(resolution,[],[f873,f899]) ).
fof(f1169,plain,
( ~ sdtlseqdt0(xx,xp)
| xp = xx
| ~ aElementOf0(xx,szNzAzT0)
| ~ aElementOf0(xp,szNzAzT0) ),
inference(resolution,[],[f1168,f525]) ).
fof(f1170,plain,
( ~ sdtlseqdt0(xx,xp)
| xp = xx
| ~ aElementOf0(xp,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1169,f903]) ).
fof(f1172,definition,
( spl76_24
<=> aElementOf0(xp,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl76_24])],[avatar_definition]) ).
fof(f1174,plain,
( ~ aElementOf0(xp,szNzAzT0)
| spl76_24 ),
inference(avatar_component_clause,[],[f1172]) ).
fof(f1176,definition,
( spl76_25
<=> xp = xx ),
introduced(definition,[new_symbols(definition,[spl76_25])],[avatar_definition]) ).
fof(f1178,plain,
( xp = xx
| ~ spl76_25 ),
inference(avatar_component_clause,[],[f1176]) ).
fof(f1180,definition,
( spl76_26
<=> sdtlseqdt0(xx,xp) ),
introduced(definition,[new_symbols(definition,[spl76_26])],[avatar_definition]) ).
fof(f1182,plain,
( ~ sdtlseqdt0(xx,xp)
| spl76_26 ),
inference(avatar_component_clause,[],[f1180]) ).
fof(f1183,plain,
( ~ spl76_24
| spl76_25
| ~ spl76_26 ),
inference(avatar_split_clause,[],[f1170,f1180,f1176,f1172]) ).
fof(f1237,plain,
! [X0] :
( aElementOf0(xp,sdtlpdtrp0(xN,X0))
| ~ sdtlseqdt0(X0,xn)
| ~ aElementOf0(xn,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[],[f1038,f891]) ).
fof(f1238,plain,
( aElementOf0(xp,sdtlpdtrp0(xN,xn))
| ~ aElementOf0(xn,szNzAzT0) ),
inference(superposition,[],[f816,f891]) ).
fof(f1239,plain,
aElementOf0(xp,sdtlpdtrp0(xN,xn)),
inference(forward_subsumption_resolution,[],[f1238,f892]) ).
fof(f1240,plain,
! [X0] :
( aElementOf0(xp,sdtlpdtrp0(xN,X0))
| ~ sdtlseqdt0(X0,xn)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1237,f892]) ).
fof(f1243,plain,
( aElementOf0(xp,szNzAzT0)
| ~ aElementOf0(xn,szNzAzT0) ),
inference(resolution,[],[f1239,f685]) ).
fof(f1247,plain,
( ~ aElementOf0(xn,szNzAzT0)
| spl76_24 ),
inference(forward_subsumption_resolution,[],[f1243,f1174]) ).
fof(f1249,plain,
( $false
| spl76_24 ),
inference(forward_subsumption_resolution,[],[f1247,f892]) ).
fof(f1250,plain,
spl76_24,
inference(avatar_contradiction_clause,[],[f1249]) ).
fof(f1678,plain,
~ aElementOf0(xp,xP),
inference(superposition,[],[f966,f872]) ).
fof(f1908,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xm,szNzAzT0)
| sdtlseqdt0(xx,xp) ),
inference(resolution,[],[f1240,f906]) ).
fof(f1921,plain,
( ~ aElementOf0(xm,szNzAzT0)
| sdtlseqdt0(xx,xp)
| ~ spl76_16 ),
inference(forward_subsumption_resolution,[],[f1908,f1074]) ).
fof(f1922,plain,
( sdtlseqdt0(xx,xp)
| ~ spl76_16 ),
inference(forward_subsumption_resolution,[],[f1921,f905]) ).
fof(f1923,plain,
( $false
| ~ spl76_16
| spl76_26 ),
inference(forward_subsumption_resolution,[],[f1922,f1182]) ).
fof(f1924,plain,
( ~ spl76_16
| spl76_26 ),
inference(avatar_contradiction_clause,[],[f1923]) ).
fof(f1927,plain,
( aElementOf0(xp,xP)
| ~ spl76_25 ),
inference(superposition,[],[f897,f1178]) ).
fof(f1954,plain,
( $false
| ~ spl76_25 ),
inference(forward_subsumption_resolution,[],[f1927,f1678]) ).
fof(f1955,plain,
~ spl76_25,
inference(avatar_contradiction_clause,[],[f1954]) ).
cnf(s10,plain,
( spl76_15
| spl76_16 ),
inference(sat_conversion,[],[f1075]) ).
cnf(s11,plain,
spl76_7,
inference(sat_conversion,[],[f1102]) ).
cnf(s12,plain,
( ~ spl76_7
| ~ spl76_15 ),
inference(sat_conversion,[],[f1114]) ).
cnf(s17,plain,
( ~ spl76_24
| spl76_25
| ~ spl76_26 ),
inference(sat_conversion,[],[f1183]) ).
cnf(s21,plain,
spl76_24,
inference(sat_conversion,[],[f1250]) ).
cnf(s58,plain,
( ~ spl76_16
| spl76_26 ),
inference(sat_conversion,[],[f1924]) ).
cnf(s60,plain,
~ spl76_25,
inference(sat_conversion,[],[f1955]) ).
cnf(s64,plain,
~ spl76_26,
inference(rat,[],[s17,s60,s21]) ).
cnf(s65,plain,
~ spl76_16,
inference(rat,[],[s58,s64]) ).
cnf(s70,plain,
~ spl76_15,
inference(rat,[],[s12,s11]) ).
cnf(s72,plain,
$false,
inference(rat,[],[s10,s65,s70]) ).
fof(f1956,plain,
$false,
inference(avatar_sat_refutation,[],[s72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM619+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 20:52:32 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 8.64/2.07 % (2977399)Detected formulas, will run a generic FOF schedule.
% 8.64/2.07 % (2977406)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=3285753097:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.64/2.07 % (2977404)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=4014765684:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.64/2.07 % (2977405)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=416977268:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.64/2.07 % (2977408)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1930353419:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.64/2.07 % (2977407)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3984642757:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.64/2.07 % (2977410)dis-21_1_sil=8000:lcm=predicate:random_seed=2557126022: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)
% 8.64/2.07 % (2977409)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=703313835:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.64/2.07 % (2977407)Instruction limit reached!
% 8.64/2.07 % (2977407)------------------------------
% 8.64/2.07 % (2977407)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.64/2.07 % (2977407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.64/2.07 % (2977407)CaDiCaL version: 2.1.3
% 8.64/2.07 % (2977407)Termination reason: Instruction limit
% 8.64/2.07 % (2977407)Termination phase: Saturation
% 8.64/2.07 % (2977407)Time elapsed: 0.069 s
% 8.64/2.07 % (2977407)Peak memory usage: 90 MB
% 8.64/2.07 % (2977407)Instructions burned: 110 (million)
% 8.64/2.07 % (2977410)Instruction limit reached!
% 8.64/2.07 % (2977410)------------------------------
% 8.64/2.07 % (2977410)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.64/2.07 % (2977410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.64/2.07 % (2977410)CaDiCaL version: 2.1.3
% 8.64/2.07 % (2977410)Termination reason: Instruction limit
% 8.64/2.07 % (2977410)Termination phase: Saturation
% 8.64/2.07 % (2977410)Time elapsed: 0.068 s
% 8.64/2.07 % (2977410)Peak memory usage: 90 MB
% 8.64/2.07 % (2977410)Instructions burned: 130 (million)
% 8.64/2.07 % (2977408)Instruction limit reached!
% 8.64/2.07 % (2977408)------------------------------
% 8.64/2.07 % (2977408)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.64/2.07 % (2977408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.64/2.07 % (2977408)CaDiCaL version: 2.1.3
% 8.64/2.07 % (2977408)Termination reason: Instruction limit
% 8.64/2.07 % (2977408)Termination phase: Saturation
% 8.64/2.07 % (2977408)Time elapsed: 0.076 s
% 8.64/2.07 % (2977408)Peak memory usage: 89 MB
% 8.64/2.07 % (2977408)Instructions burned: 120 (million)
% 8.64/2.07 % (2977409)Instruction limit reached!
% 8.64/2.07 % (2977409)------------------------------
% 8.64/2.07 % (2977409)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.64/2.07 % (2977409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.64/2.07 % (2977409)CaDiCaL version: 2.1.3
% 8.64/2.07 % (2977409)Termination reason: Instruction limit
% 8.64/2.07 % (2977409)Termination phase: Saturation
% 8.64/2.07 % (2977409)Time elapsed: 0.096 s
% 8.64/2.07 % (2977409)Peak memory usage: 90 MB
% 8.64/2.07 % (2977409)Instructions burned: 139 (million)
% 8.64/2.07 % (2977420)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2336879326:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 8.64/2.07 % (2977419)lrs+10_1_sil=32000:urr=on:br=off:random_seed=947611334:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.64/2.07 % (2977418)lrs+10_1_sil=8000:sp=occurrence:random_seed=1667874762:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 8.64/2.07 % (2977419)Refutation not found, incomplete strategy
% 8.64/2.07 % (2977419)------------------------------
% 8.64/2.07 % (2977419)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.64/2.07 % (2977419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.64/2.07 % (2977419)CaDiCaL version: 2.1.3
% 8.64/2.07 % (2977419)Termination reason: Refutation not found, incomplete strategy
% 8.64/2.07 % (2977419)Time elapsed: 0.004 s
% 8.64/2.07 % (2977419)Peak memory usage: 88 MB
% 8.64/2.07 % (2977419)Instructions burned: 4 (million)
% 8.64/2.07 % (2977421)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=2942145397:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 8.64/2.07 % (2977418)Instruction limit reached!
% 8.64/2.07 % (2977418)------------------------------
% 8.64/2.07 % (2977418)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.64/2.07 % (2977418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.64/2.07 % (2977418)CaDiCaL version: 2.1.3
% 8.64/2.07 % (2977418)Termination reason: Instruction limit
% 8.64/2.07 % (2977418)Termination phase: Saturation
% 8.64/2.07 % (2977418)Time elapsed: 0.175 s
% 8.64/2.07 % (2977418)Peak memory usage: 92 MB
% 8.64/2.07 % (2977418)Instructions burned: 286 (million)
% 8.64/2.07 % (2977421)Instruction limit reached!
% 8.64/2.07 % (2977421)------------------------------
% 8.64/2.07 % (2977421)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.64/2.07 % (2977421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.64/2.07 % (2977421)CaDiCaL version: 2.1.3
% 8.64/2.07 % (2977421)Termination reason: Instruction limit
% 8.64/2.07 % (2977421)Termination phase: Saturation
% 8.64/2.07 % (2977421)Time elapsed: 0.144 s
% 8.64/2.07 % (2977421)Peak memory usage: 92 MB
% 8.64/2.07 % (2977421)Instructions burned: 248 (million)
% 8.64/2.07 % (2977420)Instruction limit reached!
% 8.64/2.07 % (2977420)------------------------------
% 8.64/2.07 % (2977420)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.64/2.07 % (2977420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.64/2.07 % (2977420)CaDiCaL version: 2.1.3
% 8.64/2.07 % (2977420)Termination reason: Instruction limit
% 8.64/2.07 % (2977420)Termination phase: Saturation
% 8.64/2.07 % (2977420)Time elapsed: 0.229 s
% 8.64/2.07 % (2977420)Peak memory usage: 92 MB
% 8.64/2.07 % (2977420)Instructions burned: 325 (million)
% 8.64/2.07 % (2977419)------------------------------
% 8.64/2.07 % (2977419)------------------------------
% 8.64/2.07 % (2977427)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3253969407:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 8.64/2.07 % (2977426)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3681439030:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 8.64/2.07 % (2977428)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=653792354:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 8.64/2.07 % (2977429)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2287991039:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 8.64/2.07 % (2977428)Instruction limit reached!
% 8.64/2.07 % (2977428)------------------------------
% 8.64/2.07 % (2977428)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.64/2.07 % (2977428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.64/2.07 % (2977428)CaDiCaL version: 2.1.3
% 8.64/2.07 % (2977428)Termination reason: Instruction limit
% 8.64/2.07 % (2977428)Termination phase: Saturation
% 8.64/2.07 % (2977428)Time elapsed: 0.072 s
% 8.64/2.07 % (2977428)Peak memory usage: 91 MB
% 8.64/2.07 % (2977428)Instructions burned: 113 (million)
% 8.64/2.07 % (2977429)Instruction limit reached!
% 8.64/2.07 % (2977429)------------------------------
% 8.64/2.07 % (2977429)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.64/2.07 % (2977429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.64/2.07 % (2977429)CaDiCaL version: 2.1.3
% 8.64/2.07 % (2977429)Termination reason: Instruction limit
% 8.64/2.07 % (2977429)Termination phase: Saturation
% 8.64/2.07 % (2977429)Time elapsed: 0.068 s
% 8.64/2.07 % (2977429)Peak memory usage: 89 MB
% 8.64/2.07 % (2977429)Instructions burned: 129 (million)
% 8.64/2.07 % (2977426)Instruction limit reached!
% 8.64/2.07 % (2977426)------------------------------
% 8.64/2.07 % (2977426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.64/2.07 % (2977426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.64/2.07 % (2977426)CaDiCaL version: 2.1.3
% 8.64/2.07 % (2977426)Termination reason: Instruction limit
% 8.64/2.07 % (2977426)Termination phase: Saturation
% 8.64/2.07 % (2977426)Time elapsed: 0.177 s
% 8.64/2.07 % (2977426)Peak memory usage: 90 MB
% 8.64/2.07 % (2977426)Instructions burned: 295 (million)
% 8.64/2.07 % (2977404)First to succeed.
% 8.64/2.07 % (2977404)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2977399"
% 8.64/2.07 % (2977434)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=836837232:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 8.64/2.07 % (2977435)lrs+10_1_sil=8000:sp=occurrence:random_seed=3929544211:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 8.64/2.07 % (2977436)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3833355669:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 8.64/2.07 % (2977434)Instruction limit reached!
% 8.64/2.07 % (2977434)------------------------------
% 8.64/2.07 % (2977434)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.64/2.07 % (2977434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.64/2.07 % (2977434)CaDiCaL version: 2.1.3
% 8.64/2.07 % (2977434)Termination reason: Instruction limit
% 8.64/2.07 % (2977434)Termination phase: Saturation
% 8.64/2.07 % (2977434)Time elapsed: 0.068 s
% 8.64/2.07 % (2977434)Peak memory usage: 89 MB
% 8.64/2.07 % (2977434)Instructions burned: 114 (million)
% 8.64/2.07 % (2977404)Refutation found. Thanks to Tanya!
% 8.64/2.07 % SZS status Theorem for theBenchmark
% 8.64/2.07 % SZS output start Proof for theBenchmark
% See solution above
% 9.10/2.27 % (2977404)------------------------------
% 9.10/2.27 % (2977404)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.10/2.27 % (2977404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.10/2.27 % (2977404)CaDiCaL version: 2.1.3
% 9.10/2.27 % (2977404)Termination reason: Refutation
% 9.10/2.27 % (2977404)Time elapsed: 0.779 s
% 9.10/2.27 % (2977404)Peak memory usage: 134 MB
% 9.10/2.27 % (2977404)Instructions burned: 1177 (million)
% 9.10/2.27 % (2977404)------------------------------
% 9.10/2.27 % (2977404)------------------------------
% 9.10/2.27 % (2977399)Success in time 1.213 s
% 9.10/2.27 % Vampire exiting
%------------------------------------------------------------------------------