%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM621+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 : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:16:01 PM UTC 2026
% Result : Theorem 4.10s 1.18s
% Output : Refutation 4.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 42
% Syntax : Number of formulae : 236 ( 55 unt; 17 def)
% Number of atoms : 734 ( 91 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 844 ( 346 ~; 357 |; 96 &)
% ( 29 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 16 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 12 con; 0-3 aty)
% Number of variables : 170 ( 0 sgn 161 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f6,axiom,
isFinite0(slcrc0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEmpFin) ).
fof(f8,axiom,
! [X0] :
( ( aSet0(X0)
& isCountable0(X0) )
=> ~ isFinite0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin) ).
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(f11,axiom,
! [X0] :
( ( aSet0(X0)
& isFinite0(X0) )
=> ! [X1] :
( aSubsetOf0(X1,X0)
=> isFinite0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubFSet) ).
fof(f16,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElement0(X1) )
=> ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(f23,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
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(f47,axiom,
! [X0] :
( ( aSubsetOf0(X0,szNzAzT0)
& X0 != slcrc0 )
=> ! [X1] :
( X1 = szmzizndt0(X0)
<=> ( aElementOf0(X1,X0)
& ! [X2] :
( aElementOf0(X2,X0)
=> sdtlseqdt0(X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMin) ).
fof(f82,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).
fof(f91,axiom,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4660) ).
fof(f96,axiom,
( aSet0(xO)
& isCountable0(xO) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4908) ).
fof(f100,axiom,
( aSubsetOf0(xQ,xO)
& xQ != slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5093) ).
fof(f101,axiom,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5106) ).
fof(f103,axiom,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
fof(f104,axiom,
( aSet0(xP)
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
fof(f105,axiom,
aElementOf0(xp,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5173) ).
fof(f106,axiom,
aElementOf0(xp,xO),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5182) ).
fof(f107,axiom,
aSubsetOf0(xP,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5195) ).
fof(f111,axiom,
( 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,
aElementOf0(xx,xP),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5348) ).
fof(f114,axiom,
( aElementOf0(xx,szNzAzT0)
& aElementOf0(xx,xO) ),
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,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5401) ).
fof(f118,conjecture,
( aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f119,negated_conjecture,
~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
=> aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(negated_conjecture,[status(cth)],[f118]) ).
fof(f131,plain,
! [X0] :
( ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f147,plain,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X0] :
( sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f91]) ).
fof(f151,plain,
( ~ aElementOf0(xx,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
& aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) ),
inference(ennf_transformation,[],[f119]) ).
fof(f163,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f164,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f163]) ).
fof(f170,plain,
! [X0] :
( ! [X1] :
( isFinite0(X1)
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f171,plain,
! [X0] :
( ! [X1] :
( isFinite0(X1)
| ~ aSubsetOf0(X1,X0) )
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(flattening,[],[f170]) ).
fof(f172,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f173,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ aSet0(X0)
| ~ isCountable0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f174,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ aSet0(X0)
| ~ isCountable0(X0) ),
inference(flattening,[],[f173]) ).
fof(f175,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f201,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f202,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f201]) ).
fof(f220,plain,
! [X0] :
( ! [X1] :
( X1 = szmzizndt0(X0)
<=> ( aElementOf0(X1,X0)
& ! [X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0) ) ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(ennf_transformation,[],[f47]) ).
fof(f221,plain,
! [X0] :
( ! [X1] :
( X1 = szmzizndt0(X0)
<=> ( aElementOf0(X1,X0)
& ! [X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0) ) ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(flattening,[],[f220]) ).
fof(f248,definition,
! [X2,X0,X1] :
( sP0(X2,X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f249,definition,
! [X1,X0] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> sP0(X2,X0,X1) )
| ~ sP1(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f250,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(definition_folding,[],[f164,f249,f248]) ).
fof(f259,plain,
! [X1,X0] :
( ! [X2] :
( ( X2 = sdtmndt0(X0,X1)
| ~ sP0(X2,X0,X1) )
& ( sP0(X2,X0,X1)
| sdtmndt0(X0,X1) != X2 ) )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f249]) ).
fof(f260,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| ~ sP0(X2,X1,X0) )
& ( sP0(X2,X1,X0)
| sdtmndt0(X1,X0) != X2 ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f259]) ).
fof(f261,plain,
! [X2,X0,X1] :
( ( sP0(X2,X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3
| ~ aElementOf0(X3,X2) )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3 )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| ~ aElementOf0(X3,X2) ) ) )
| ~ sP0(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f248]) ).
fof(f262,plain,
! [X2,X0,X1] :
( ( sP0(X2,X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3
| ~ aElementOf0(X3,X2) )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X0)
| X1 = X3 )
& ( ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 )
| ~ aElementOf0(X3,X2) ) ) )
| ~ sP0(X2,X0,X1) ) ),
inference(flattening,[],[f261]) ).
fof(f263,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ~ aSet0(X0)
| ? [X3] :
( ( ~ aElement0(X3)
| ~ aElementOf0(X3,X1)
| X2 = X3
| ~ aElementOf0(X3,X0) )
& ( ( aElement0(X3)
& aElementOf0(X3,X1)
& X2 != X3 )
| aElementOf0(X3,X0) ) ) )
& ( ( aSet0(X0)
& ! [X4] :
( ( aElementOf0(X4,X0)
| ~ aElement0(X4)
| ~ aElementOf0(X4,X1)
| X2 = X4 )
& ( ( aElement0(X4)
& aElementOf0(X4,X1)
& X2 != X4 )
| ~ aElementOf0(X4,X0) ) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f262]) ).
fof(f264,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ~ aSet0(X0)
| ( ( ~ aElement0(sK11(X0,X1,X2))
| ~ aElementOf0(sK11(X0,X1,X2),X1)
| sK11(X0,X1,X2) = X2
| ~ aElementOf0(sK11(X0,X1,X2),X0) )
& ( ( aElement0(sK11(X0,X1,X2))
& aElementOf0(sK11(X0,X1,X2),X1)
& sK11(X0,X1,X2) != X2 )
| aElementOf0(sK11(X0,X1,X2),X0) ) ) )
& ( ( aSet0(X0)
& ! [X4] :
( ( aElementOf0(X4,X0)
| ~ aElement0(X4)
| ~ aElementOf0(X4,X1)
| X2 = X4 )
& ( ( aElement0(X4)
& aElementOf0(X4,X1)
& X2 != X4 )
| ~ aElementOf0(X4,X0) ) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X3,sK11(X0,X1,X2))],[f263]) ).
fof(f265,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,[],[f172]) ).
fof(f266,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,[],[f265]) ).
fof(f267,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,[],[f266]) ).
fof(f268,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK12(X0,X1),X0)
& aElementOf0(sK12(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X2,sK12(X0,X1))],[f267]) ).
fof(f282,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzizndt0(X0)
| ~ aElementOf0(X1,X0)
| ? [X2] :
( ~ sdtlseqdt0(X1,X2)
& aElementOf0(X2,X0) ) )
& ( ( aElementOf0(X1,X0)
& ! [X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0) ) )
| szmzizndt0(X0) != X1 ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(nnf_transformation,[],[f221]) ).
fof(f283,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzizndt0(X0)
| ~ aElementOf0(X1,X0)
| ? [X2] :
( ~ sdtlseqdt0(X1,X2)
& aElementOf0(X2,X0) ) )
& ( ( aElementOf0(X1,X0)
& ! [X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0) ) )
| szmzizndt0(X0) != X1 ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(flattening,[],[f282]) ).
fof(f284,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzizndt0(X0)
| ~ aElementOf0(X1,X0)
| ? [X2] :
( ~ sdtlseqdt0(X1,X2)
& aElementOf0(X2,X0) ) )
& ( ( aElementOf0(X1,X0)
& ! [X3] :
( sdtlseqdt0(X1,X3)
| ~ aElementOf0(X3,X0) ) )
| szmzizndt0(X0) != X1 ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(rectify,[],[f283]) ).
fof(f285,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzizndt0(X0)
| ~ aElementOf0(X1,X0)
| ( ~ sdtlseqdt0(X1,sK21(X0,X1))
& aElementOf0(sK21(X0,X1),X0) ) )
& ( ( aElementOf0(X1,X0)
& ! [X3] :
( sdtlseqdt0(X1,X3)
| ~ aElementOf0(X3,X0) ) )
| szmzizndt0(X0) != X1 ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(X2,sK21(X0,X1))],[f284]) ).
fof(f330,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f331,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f348,plain,
! [X0] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) = sdtlpdtrp0(xe,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f360,plain,
aSet0(xO),
inference(cnf_transformation,[],[f96]) ).
fof(f366,plain,
slcrc0 != xQ,
inference(cnf_transformation,[],[f100]) ).
fof(f367,plain,
aSubsetOf0(xQ,xO),
inference(cnf_transformation,[],[f100]) ).
fof(f368,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[],[f101]) ).
fof(f370,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[],[f103]) ).
fof(f371,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(cnf_transformation,[],[f104]) ).
fof(f373,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[],[f105]) ).
fof(f374,plain,
aElementOf0(xp,xO),
inference(cnf_transformation,[],[f106]) ).
fof(f375,plain,
aSubsetOf0(xP,xQ),
inference(cnf_transformation,[],[f107]) ).
fof(f379,plain,
xp = sdtlpdtrp0(xe,xn),
inference(cnf_transformation,[],[f111]) ).
fof(f380,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f111]) ).
fof(f383,plain,
aElementOf0(xx,xP),
inference(cnf_transformation,[],[f113]) ).
fof(f385,plain,
aElementOf0(xx,szNzAzT0),
inference(cnf_transformation,[],[f114]) ).
fof(f387,plain,
aElementOf0(xm,szNzAzT0),
inference(cnf_transformation,[],[f115]) ).
fof(f388,plain,
xx = szmzizndt0(sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[],[f116]) ).
fof(f390,plain,
aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)),
inference(cnf_transformation,[],[f151]) ).
fof(f399,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f402,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| sdtmndt0(X1,X0) != X2
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f260]) ).
fof(f403,plain,
! [X2,X0,X1] :
( sdtmndt0(X1,X0) = X2
| ~ sP0(X2,X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f260]) ).
fof(f404,plain,
! [X2,X0,X1,X4] :
( X2 != X4
| ~ aElementOf0(X4,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f264]) ).
fof(f413,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f250]) ).
fof(f417,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| isFinite0(X1)
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(cnf_transformation,[],[f171]) ).
fof(f418,plain,
! [X3,X0,X1] :
( ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f268]) ).
fof(f419,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f268]) ).
fof(f422,plain,
! [X0] :
( ~ isCountable0(X0)
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(cnf_transformation,[],[f174]) ).
fof(f423,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f438,plain,
isFinite0(slcrc0),
inference(cnf_transformation,[],[f6]) ).
fof(f443,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f202]) ).
fof(f470,plain,
! [X3,X0,X1] :
( sdtlseqdt0(X1,X3)
| ~ aElementOf0(X3,X0)
| szmzizndt0(X0) != X1
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f285]) ).
fof(f471,plain,
! [X0,X1] :
( aElementOf0(X1,X0)
| szmzizndt0(X0) != X1
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f285]) ).
fof(f526,plain,
! [X0,X1] :
( sP0(sdtmndt0(X1,X0),X1,X0)
| ~ sP1(X0,X1) ),
inference(equality_resolution,[],[f402]) ).
fof(f527,plain,
! [X0,X1,X4] :
( ~ sP0(X0,X1,X4)
| ~ aElementOf0(X4,X0) ),
inference(equality_resolution,[],[f404]) ).
fof(f539,plain,
! [X0] :
( aElementOf0(szmzizndt0(X0),X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(equality_resolution,[],[f471]) ).
fof(f540,plain,
! [X3,X0] :
( sdtlseqdt0(szmzizndt0(X0),X3)
| ~ aElementOf0(X3,X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(equality_resolution,[],[f470]) ).
fof(f557,plain,
aElementOf0(sdtlpdtrp0(xe,xn),xO),
inference(forward_demodulation,[],[f374,f379]) ).
fof(f558,plain,
aElementOf0(sdtlpdtrp0(xe,xn),xQ),
inference(forward_demodulation,[],[f373,f379]) ).
fof(f575,plain,
! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xn))
| aElementOf0(X0,sdtlpdtrp0(xN,xm))
| ~ aSet0(sdtlpdtrp0(xN,xm)) ),
inference(resolution,[],[f390,f418]) ).
fof(f576,plain,
( aSet0(sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtlpdtrp0(xN,xm)) ),
inference(resolution,[],[f390,f419]) ).
fof(f577,plain,
( isFinite0(sdtlpdtrp0(xN,xn))
| ~ aSet0(sdtlpdtrp0(xN,xm))
| ~ isFinite0(sdtlpdtrp0(xN,xm)) ),
inference(resolution,[],[f390,f417]) ).
fof(f581,definition,
( spl27_1
<=> isFinite0(sdtlpdtrp0(xN,xm)) ),
introduced(definition,[new_symbols(definition,[spl27_1])],[avatar_definition]) ).
fof(f583,plain,
( ~ isFinite0(sdtlpdtrp0(xN,xm))
| spl27_1 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f585,definition,
( spl27_2
<=> aSet0(sdtlpdtrp0(xN,xm)) ),
introduced(definition,[new_symbols(definition,[spl27_2])],[avatar_definition]) ).
fof(f587,plain,
( ~ aSet0(sdtlpdtrp0(xN,xm))
| spl27_2 ),
inference(avatar_component_clause,[],[f585]) ).
fof(f589,definition,
( spl27_3
<=> isFinite0(sdtlpdtrp0(xN,xn)) ),
introduced(definition,[new_symbols(definition,[spl27_3])],[avatar_definition]) ).
fof(f590,plain,
( ~ isFinite0(sdtlpdtrp0(xN,xn))
| spl27_3 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f591,plain,
( isFinite0(sdtlpdtrp0(xN,xn))
| ~ spl27_3 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f592,plain,
( ~ spl27_1
| ~ spl27_2
| spl27_3 ),
inference(avatar_split_clause,[],[f577,f589,f585,f581]) ).
fof(f594,definition,
( spl27_4
<=> aSet0(sdtlpdtrp0(xN,xn)) ),
introduced(definition,[new_symbols(definition,[spl27_4])],[avatar_definition]) ).
fof(f596,plain,
( aSet0(sdtlpdtrp0(xN,xn))
| ~ spl27_4 ),
inference(avatar_component_clause,[],[f594]) ).
fof(f597,plain,
( ~ spl27_2
| spl27_4 ),
inference(avatar_split_clause,[],[f576,f594,f585]) ).
fof(f599,definition,
( spl27_5
<=> ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xn))
| aElementOf0(X0,sdtlpdtrp0(xN,xm)) ) ),
introduced(definition,[new_symbols(definition,[spl27_5])],[avatar_definition]) ).
fof(f600,plain,
( ! [X0] :
( aElementOf0(X0,sdtlpdtrp0(xN,xm))
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xn)) )
| ~ spl27_5 ),
inference(avatar_component_clause,[],[f599]) ).
fof(f601,plain,
( ~ spl27_2
| spl27_5 ),
inference(avatar_split_clause,[],[f575,f599,f585]) ).
fof(f653,plain,
( aSet0(xQ)
| ~ aSet0(xO) ),
inference(resolution,[],[f367,f419]) ).
fof(f657,plain,
aSet0(xQ),
inference(forward_subsumption_resolution,[],[f653,f360]) ).
fof(f660,definition,
( spl27_13
<=> aSet0(xQ) ),
introduced(definition,[new_symbols(definition,[spl27_13])],[avatar_definition]) ).
fof(f661,plain,
( aSet0(xQ)
| ~ spl27_13 ),
inference(avatar_component_clause,[],[f660]) ).
fof(f672,plain,
spl27_13,
inference(avatar_split_clause,[],[f657,f660]) ).
fof(f673,plain,
! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,szNzAzT0)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f368,f418]) ).
fof(f679,plain,
! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xQ) ),
inference(forward_subsumption_resolution,[],[f673,f399]) ).
fof(f699,plain,
! [X0] :
( ~ aElementOf0(X0,xP)
| aElementOf0(X0,xQ)
| ~ aSet0(xQ) ),
inference(resolution,[],[f375,f418]) ).
fof(f705,plain,
( ! [X0] :
( ~ aElementOf0(X0,xP)
| aElementOf0(X0,xQ) )
| ~ spl27_13 ),
inference(forward_subsumption_resolution,[],[f699,f661]) ).
fof(f708,plain,
( ! [X0] :
( ~ aElementOf0(X0,sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(X0,xQ) )
| ~ spl27_13 ),
inference(forward_demodulation,[],[f705,f371]) ).
fof(f1015,plain,
szmzizndt0(xQ) = sdtlpdtrp0(xe,xn),
inference(superposition,[],[f370,f379]) ).
fof(f1031,plain,
( aElement0(sdtlpdtrp0(xe,xn))
| ~ aSet0(xO) ),
inference(resolution,[],[f557,f423]) ).
fof(f1032,plain,
aElement0(sdtlpdtrp0(xe,xn)),
inference(forward_subsumption_resolution,[],[f1031,f360]) ).
fof(f1033,plain,
aElement0(szmzizndt0(xQ)),
inference(forward_demodulation,[],[f1032,f1015]) ).
fof(f1129,plain,
aElementOf0(xx,sdtmndt0(xQ,szmzizndt0(xQ))),
inference(superposition,[],[f383,f371]) ).
fof(f1149,plain,
! [X0] :
( sdtlseqdt0(xx,X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xm))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| slcrc0 = sdtlpdtrp0(xN,xm) ),
inference(superposition,[],[f540,f388]) ).
fof(f1154,definition,
( spl27_58
<=> slcrc0 = sdtlpdtrp0(xN,xm) ),
introduced(definition,[new_symbols(definition,[spl27_58])],[avatar_definition]) ).
fof(f1156,plain,
( slcrc0 = sdtlpdtrp0(xN,xm)
| ~ spl27_58 ),
inference(avatar_component_clause,[],[f1154]) ).
fof(f1158,definition,
( spl27_59
<=> aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl27_59])],[avatar_definition]) ).
fof(f1159,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| ~ spl27_59 ),
inference(avatar_component_clause,[],[f1158]) ).
fof(f1160,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),szNzAzT0)
| spl27_59 ),
inference(avatar_component_clause,[],[f1158]) ).
fof(f1172,definition,
( spl27_62
<=> ! [X0] :
( sdtlseqdt0(xx,X0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,xm)) ) ),
introduced(definition,[new_symbols(definition,[spl27_62])],[avatar_definition]) ).
fof(f1173,plain,
( ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xm))
| sdtlseqdt0(xx,X0) )
| ~ spl27_62 ),
inference(avatar_component_clause,[],[f1172]) ).
fof(f1174,plain,
( spl27_58
| ~ spl27_59
| spl27_62 ),
inference(avatar_split_clause,[],[f1149,f1172,f1158,f1154]) ).
fof(f1179,plain,
! [X0] :
( ~ isFinite0(sdtlpdtrp0(xN,X0))
| ~ aSet0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[],[f330,f422]) ).
fof(f1268,definition,
( spl27_65
<=> sP1(szmzizndt0(xQ),xQ) ),
introduced(definition,[new_symbols(definition,[spl27_65])],[avatar_definition]) ).
fof(f1269,plain,
( sP1(szmzizndt0(xQ),xQ)
| ~ spl27_65 ),
inference(avatar_component_clause,[],[f1268]) ).
fof(f1270,plain,
( ~ sP1(szmzizndt0(xQ),xQ)
| spl27_65 ),
inference(avatar_component_clause,[],[f1268]) ).
fof(f1371,plain,
( ~ aSet0(xQ)
| ~ aElement0(szmzizndt0(xQ))
| spl27_65 ),
inference(resolution,[],[f1270,f413]) ).
fof(f1376,plain,
( ~ aElement0(szmzizndt0(xQ))
| ~ spl27_13
| spl27_65 ),
inference(forward_subsumption_resolution,[],[f1371,f661]) ).
fof(f1379,plain,
( $false
| ~ spl27_13
| spl27_65 ),
inference(forward_subsumption_resolution,[],[f1376,f1033]) ).
fof(f1380,plain,
( ~ spl27_13
| spl27_65 ),
inference(avatar_contradiction_clause,[],[f1379]) ).
fof(f2252,plain,
( ~ aElementOf0(xm,szNzAzT0)
| spl27_59 ),
inference(resolution,[],[f1160,f331]) ).
fof(f2254,plain,
( $false
| spl27_59 ),
inference(forward_subsumption_resolution,[],[f2252,f387]) ).
fof(f2255,plain,
spl27_59,
inference(avatar_contradiction_clause,[],[f2254]) ).
fof(f2327,plain,
( ~ isFinite0(slcrc0)
| spl27_1
| ~ spl27_58 ),
inference(superposition,[],[f583,f1156]) ).
fof(f2364,plain,
( $false
| spl27_1
| ~ spl27_58 ),
inference(forward_subsumption_resolution,[],[f2327,f438]) ).
fof(f2365,plain,
( spl27_1
| ~ spl27_58 ),
inference(avatar_contradiction_clause,[],[f2364]) ).
fof(f2486,plain,
( aSet0(sdtlpdtrp0(xN,xm))
| ~ aSet0(szNzAzT0)
| ~ spl27_59 ),
inference(resolution,[],[f1159,f419]) ).
fof(f2489,plain,
( ~ aSet0(szNzAzT0)
| spl27_2
| ~ spl27_59 ),
inference(forward_subsumption_resolution,[],[f2486,f587]) ).
fof(f2491,plain,
( $false
| spl27_2
| ~ spl27_59 ),
inference(forward_subsumption_resolution,[],[f2489,f399]) ).
fof(f2492,plain,
( spl27_2
| ~ spl27_59 ),
inference(avatar_contradiction_clause,[],[f2491]) ).
fof(f2767,plain,
aElementOf0(szmzizndt0(xQ),xQ),
inference(superposition,[],[f558,f1015]) ).
fof(f3140,definition,
( spl27_127
<=> slcrc0 = sdtlpdtrp0(xN,xn) ),
introduced(definition,[new_symbols(definition,[spl27_127])],[avatar_definition]) ).
fof(f3141,plain,
( slcrc0 != sdtlpdtrp0(xN,xn)
| spl27_127 ),
inference(avatar_component_clause,[],[f3140]) ).
fof(f3142,plain,
( slcrc0 = sdtlpdtrp0(xN,xn)
| ~ spl27_127 ),
inference(avatar_component_clause,[],[f3140]) ).
fof(f3144,definition,
( spl27_128
<=> aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl27_128])],[avatar_definition]) ).
fof(f3145,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
| ~ spl27_128 ),
inference(avatar_component_clause,[],[f3144]) ).
fof(f3146,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
| spl27_128 ),
inference(avatar_component_clause,[],[f3144]) ).
fof(f3206,plain,
( ~ isFinite0(slcrc0)
| spl27_3
| ~ spl27_127 ),
inference(superposition,[],[f590,f3142]) ).
fof(f3249,plain,
( $false
| spl27_3
| ~ spl27_127 ),
inference(forward_subsumption_resolution,[],[f3206,f438]) ).
fof(f3250,plain,
( spl27_3
| ~ spl27_127 ),
inference(avatar_contradiction_clause,[],[f3249]) ).
fof(f3292,plain,
( ~ aElementOf0(xn,szNzAzT0)
| spl27_128 ),
inference(resolution,[],[f3146,f331]) ).
fof(f3295,plain,
( $false
| spl27_128 ),
inference(forward_subsumption_resolution,[],[f3292,f380]) ).
fof(f3296,plain,
spl27_128,
inference(avatar_contradiction_clause,[],[f3295]) ).
fof(f3524,plain,
( ! [X0] :
( ~ aElementOf0(X0,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(xx,X0) )
| ~ spl27_5
| ~ spl27_62 ),
inference(resolution,[],[f1173,f600]) ).
fof(f3627,plain,
( aElementOf0(xx,xQ)
| ~ spl27_13 ),
inference(resolution,[],[f708,f1129]) ).
fof(f3739,plain,
( sdtlseqdt0(xx,szmzizndt0(sdtlpdtrp0(xN,xn)))
| ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
| slcrc0 = sdtlpdtrp0(xN,xn)
| ~ spl27_5
| ~ spl27_62 ),
inference(resolution,[],[f3524,f539]) ).
fof(f3754,plain,
( sdtlseqdt0(xx,szmzizndt0(sdtlpdtrp0(xN,xn)))
| slcrc0 = sdtlpdtrp0(xN,xn)
| ~ spl27_5
| ~ spl27_62
| ~ spl27_128 ),
inference(forward_subsumption_resolution,[],[f3739,f3145]) ).
fof(f3757,plain,
( sdtlseqdt0(xx,szmzizndt0(sdtlpdtrp0(xN,xn)))
| ~ spl27_5
| ~ spl27_62
| spl27_127
| ~ spl27_128 ),
inference(forward_subsumption_resolution,[],[f3754,f3141]) ).
fof(f3778,plain,
( sdtlseqdt0(xx,sdtlpdtrp0(xe,xn))
| ~ aElementOf0(xn,szNzAzT0)
| ~ spl27_5
| ~ spl27_62
| spl27_127
| ~ spl27_128 ),
inference(superposition,[],[f3757,f348]) ).
fof(f3781,plain,
( sdtlseqdt0(xx,sdtlpdtrp0(xe,xn))
| ~ spl27_5
| ~ spl27_62
| spl27_127
| ~ spl27_128 ),
inference(forward_subsumption_resolution,[],[f3778,f380]) ).
fof(f3783,plain,
( sdtlseqdt0(xx,szmzizndt0(xQ))
| ~ spl27_5
| ~ spl27_62
| spl27_127
| ~ spl27_128 ),
inference(forward_demodulation,[],[f3781,f1015]) ).
fof(f3797,plain,
( ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| szmzizndt0(xQ) = xx
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ aElementOf0(xx,szNzAzT0)
| ~ spl27_5
| ~ spl27_62
| spl27_127
| ~ spl27_128 ),
inference(resolution,[],[f3783,f443]) ).
fof(f3802,plain,
( ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| szmzizndt0(xQ) = xx
| ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| ~ spl27_5
| ~ spl27_62
| spl27_127
| ~ spl27_128 ),
inference(forward_subsumption_resolution,[],[f3797,f385]) ).
fof(f3806,definition,
( spl27_173
<=> aElementOf0(szmzizndt0(xQ),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl27_173])],[avatar_definition]) ).
fof(f3808,plain,
( ~ aElementOf0(szmzizndt0(xQ),szNzAzT0)
| spl27_173 ),
inference(avatar_component_clause,[],[f3806]) ).
fof(f3810,definition,
( spl27_174
<=> szmzizndt0(xQ) = xx ),
introduced(definition,[new_symbols(definition,[spl27_174])],[avatar_definition]) ).
fof(f3812,plain,
( szmzizndt0(xQ) = xx
| ~ spl27_174 ),
inference(avatar_component_clause,[],[f3810]) ).
fof(f3814,definition,
( spl27_175
<=> sdtlseqdt0(szmzizndt0(xQ),xx) ),
introduced(definition,[new_symbols(definition,[spl27_175])],[avatar_definition]) ).
fof(f3816,plain,
( ~ sdtlseqdt0(szmzizndt0(xQ),xx)
| spl27_175 ),
inference(avatar_component_clause,[],[f3814]) ).
fof(f3817,plain,
( ~ spl27_173
| spl27_174
| ~ spl27_175
| ~ spl27_5
| ~ spl27_62
| spl27_127
| ~ spl27_128 ),
inference(avatar_split_clause,[],[f3802,f3144,f3140,f1172,f599,f3814,f3810,f3806]) ).
fof(f3820,plain,
( ~ aElementOf0(szmzizndt0(xQ),xQ)
| spl27_173 ),
inference(resolution,[],[f3808,f679]) ).
fof(f3825,plain,
( $false
| spl27_173 ),
inference(forward_subsumption_resolution,[],[f3820,f2767]) ).
fof(f3826,plain,
spl27_173,
inference(avatar_contradiction_clause,[],[f3825]) ).
fof(f3861,plain,
( ~ aElementOf0(xx,xQ)
| ~ aSubsetOf0(xQ,szNzAzT0)
| slcrc0 = xQ
| spl27_175 ),
inference(resolution,[],[f3816,f540]) ).
fof(f3868,plain,
( ~ aSubsetOf0(xQ,szNzAzT0)
| slcrc0 = xQ
| ~ spl27_13
| spl27_175 ),
inference(forward_subsumption_resolution,[],[f3861,f3627]) ).
fof(f3872,plain,
( slcrc0 = xQ
| ~ spl27_13
| spl27_175 ),
inference(forward_subsumption_resolution,[],[f3868,f368]) ).
fof(f3873,plain,
( $false
| ~ spl27_13
| spl27_175 ),
inference(forward_subsumption_resolution,[],[f3872,f366]) ).
fof(f3874,plain,
( ~ spl27_13
| spl27_175 ),
inference(avatar_contradiction_clause,[],[f3873]) ).
fof(f3900,plain,
( aElementOf0(szmzizndt0(xQ),sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ spl27_174 ),
inference(superposition,[],[f1129,f3812]) ).
fof(f4625,plain,
( ! [X0] :
( aElementOf0(szmzizndt0(xQ),X0)
| ~ sP0(X0,xQ,szmzizndt0(xQ))
| ~ sP1(szmzizndt0(xQ),xQ) )
| ~ spl27_174 ),
inference(superposition,[],[f3900,f403]) ).
fof(f4626,plain,
( ! [X0] :
( ~ sP0(X0,xQ,szmzizndt0(xQ))
| ~ sP1(szmzizndt0(xQ),xQ) )
| ~ spl27_174 ),
inference(forward_subsumption_resolution,[],[f4625,f527]) ).
fof(f4629,plain,
( ! [X0] : ~ sP0(X0,xQ,szmzizndt0(xQ))
| ~ spl27_65
| ~ spl27_174 ),
inference(forward_subsumption_resolution,[],[f4626,f1269]) ).
fof(f4634,plain,
( ~ sP1(szmzizndt0(xQ),xQ)
| ~ spl27_65
| ~ spl27_174 ),
inference(resolution,[],[f4629,f526]) ).
fof(f4639,plain,
( $false
| ~ spl27_65
| ~ spl27_174 ),
inference(forward_subsumption_resolution,[],[f4634,f1269]) ).
fof(f4640,plain,
( ~ spl27_65
| ~ spl27_174 ),
inference(avatar_contradiction_clause,[],[f4639]) ).
fof(f4652,plain,
( ~ aSet0(sdtlpdtrp0(xN,xn))
| ~ aElementOf0(xn,szNzAzT0)
| ~ spl27_3 ),
inference(resolution,[],[f591,f1179]) ).
fof(f4653,plain,
( ~ aElementOf0(xn,szNzAzT0)
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f4652,f596]) ).
fof(f4654,plain,
( $false
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f4653,f380]) ).
fof(f4655,plain,
( ~ spl27_3
| ~ spl27_4 ),
inference(avatar_contradiction_clause,[],[f4654]) ).
cnf(s1,plain,
( ~ spl27_1
| ~ spl27_2
| spl27_3 ),
inference(sat_conversion,[],[f592]) ).
cnf(s2,plain,
( ~ spl27_2
| spl27_4 ),
inference(sat_conversion,[],[f597]) ).
cnf(s3,plain,
( ~ spl27_2
| spl27_5 ),
inference(sat_conversion,[],[f601]) ).
cnf(s9,plain,
spl27_13,
inference(sat_conversion,[],[f672]) ).
cnf(s39,plain,
( spl27_58
| ~ spl27_59
| spl27_62 ),
inference(sat_conversion,[],[f1174]) ).
cnf(s49,plain,
( ~ spl27_13
| spl27_65 ),
inference(sat_conversion,[],[f1380]) ).
cnf(s67,plain,
spl27_59,
inference(sat_conversion,[],[f2255]) ).
cnf(s72,plain,
( spl27_1
| ~ spl27_58 ),
inference(sat_conversion,[],[f2365]) ).
cnf(s76,plain,
( spl27_2
| ~ spl27_59 ),
inference(sat_conversion,[],[f2492]) ).
cnf(s101,plain,
( spl27_3
| ~ spl27_127 ),
inference(sat_conversion,[],[f3250]) ).
cnf(s105,plain,
spl27_128,
inference(sat_conversion,[],[f3296]) ).
cnf(s131,plain,
( ~ spl27_5
| ~ spl27_62
| spl27_127
| ~ spl27_128
| ~ spl27_173
| spl27_174
| ~ spl27_175 ),
inference(sat_conversion,[],[f3817]) ).
cnf(s132,plain,
spl27_173,
inference(sat_conversion,[],[f3826]) ).
cnf(s133,plain,
( ~ spl27_13
| spl27_175 ),
inference(sat_conversion,[],[f3874]) ).
cnf(s152,plain,
( ~ spl27_65
| ~ spl27_174 ),
inference(sat_conversion,[],[f4640]) ).
cnf(s153,plain,
( ~ spl27_3
| ~ spl27_4 ),
inference(sat_conversion,[],[f4655]) ).
cnf(s155,plain,
( ~ spl27_5
| ~ spl27_62
| spl27_127
| ~ spl27_128
| spl27_174
| ~ spl27_175 ),
inference(rat,[],[s131,s132]) ).
cnf(s161,plain,
spl27_2,
inference(rat,[],[s76,s67]) ).
cnf(s170,plain,
( spl27_58
| spl27_62 ),
inference(rat,[],[s39,s67]) ).
cnf(s184,plain,
spl27_175,
inference(rat,[],[s133,s9]) ).
cnf(s186,plain,
spl27_65,
inference(rat,[],[s49,s9]) ).
cnf(s187,plain,
~ spl27_174,
inference(rat,[],[s152,s186]) ).
cnf(s192,plain,
spl27_5,
inference(rat,[],[s3,s161]) ).
cnf(s193,plain,
spl27_4,
inference(rat,[],[s2,s161]) ).
cnf(s194,plain,
~ spl27_3,
inference(rat,[],[s153,s193]) ).
cnf(s195,plain,
~ spl27_127,
inference(rat,[],[s101,s194]) ).
cnf(s198,plain,
~ spl27_62,
inference(rat,[],[s155,s184,s187,s105,s192,s195]) ).
cnf(s200,plain,
spl27_58,
inference(rat,[],[s170,s198]) ).
cnf(s201,plain,
spl27_1,
inference(rat,[],[s72,s200]) ).
cnf(s202,plain,
$false,
inference(rat,[],[s1,s194,s161,s201]) ).
fof(f4656,plain,
$false,
inference(avatar_sat_refutation,[],[s202]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM621+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Sun Sep 27 20:47:04 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 4.10/1.18 % (2721591)Detected formulas, will run a generic FOF schedule.
% 4.10/1.18 % (2721596)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=1404648425:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.10/1.18 % (2721602)dis-21_1_sil=8000:lcm=predicate:random_seed=1759006633: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)
% 4.10/1.18 % (2721601)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2121439524:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.10/1.18 % (2721598)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=1518695269:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.10/1.18 % (2721600)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1226227422:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.10/1.18 % (2721597)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=4091996031:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.10/1.18 % (2721599)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=876778363:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.10/1.18 % (2721599)Instruction limit reached!
% 4.10/1.18 % (2721599)------------------------------
% 4.10/1.18 % (2721599)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.10/1.18 % (2721599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.10/1.18 % (2721599)CaDiCaL version: 2.1.3
% 4.10/1.18 % (2721599)Termination reason: Instruction limit
% 4.10/1.18 % (2721599)Termination phase: Saturation
% 4.10/1.18 % (2721599)Time elapsed: 0.037 s
% 4.10/1.18 % (2721599)Peak memory usage: 89 MB
% 4.10/1.18 % (2721599)Instructions burned: 109 (million)
% 4.10/1.18 % (2721600)Instruction limit reached!
% 4.10/1.18 % (2721600)------------------------------
% 4.10/1.18 % (2721600)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.10/1.18 % (2721600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.10/1.18 % (2721600)CaDiCaL version: 2.1.3
% 4.10/1.18 % (2721600)Termination reason: Instruction limit
% 4.10/1.18 % (2721600)Termination phase: Saturation
% 4.10/1.18 % (2721600)Time elapsed: 0.040 s
% 4.10/1.18 % (2721600)Peak memory usage: 89 MB
% 4.10/1.18 % (2721600)Instructions burned: 122 (million)
% 4.10/1.18 % (2721602)Instruction limit reached!
% 4.10/1.18 % (2721602)------------------------------
% 4.10/1.18 % (2721602)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.10/1.18 % (2721602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.10/1.18 % (2721602)CaDiCaL version: 2.1.3
% 4.10/1.18 % (2721602)Termination reason: Instruction limit
% 4.10/1.18 % (2721602)Termination phase: Saturation
% 4.10/1.18 % (2721602)Time elapsed: 0.040 s
% 4.10/1.18 % (2721602)Peak memory usage: 91 MB
% 4.10/1.18 % (2721602)Instructions burned: 130 (million)
% 4.10/1.18 % (2721601)Instruction limit reached!
% 4.10/1.18 % (2721601)------------------------------
% 4.10/1.18 % (2721601)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.10/1.18 % (2721601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.10/1.18 % (2721601)CaDiCaL version: 2.1.3
% 4.10/1.18 % (2721601)Termination reason: Instruction limit
% 4.10/1.18 % (2721601)Termination phase: Saturation
% 4.10/1.18 % (2721601)Time elapsed: 0.054 s
% 4.10/1.18 % (2721601)Peak memory usage: 90 MB
% 4.10/1.18 % (2721601)Instructions burned: 140 (million)
% 4.10/1.18 % (2721612)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2501554655:i=325:sd=1:ss=axioms:sgt=32_2998 on theBenchmark for (2998ds/325Mi)
% 4.10/1.18 % (2721611)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3254200074:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 4.10/1.18 % (2721610)lrs+10_1_sil=8000:sp=occurrence:random_seed=1585744341:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.10/1.18 % (2721611)Refutation not found, incomplete strategy
% 4.10/1.18 % (2721611)------------------------------
% 4.10/1.18 % (2721611)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.10/1.18 % (2721611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.10/1.18 % (2721611)CaDiCaL version: 2.1.3
% 4.10/1.18 % (2721611)Termination reason: Refutation not found, incomplete strategy
% 4.10/1.18 % (2721611)Time elapsed: 0.002 s
% 4.10/1.18 % (2721611)Peak memory usage: 89 MB
% 4.10/1.18 % (2721611)Instructions burned: 4 (million)
% 4.10/1.18 % (2721613)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=2806665428:s2a=on:i=248:s2at=1.23:gtg=position_2998 on theBenchmark for (2998ds/248Mi)
% 4.10/1.18 % (2721613)Instruction limit reached!
% 4.10/1.18 % (2721613)------------------------------
% 4.10/1.18 % (2721613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.10/1.18 % (2721613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.10/1.18 % (2721613)CaDiCaL version: 2.1.3
% 4.10/1.18 % (2721613)Termination reason: Instruction limit
% 4.10/1.18 % (2721613)Termination phase: Saturation
% 4.10/1.18 % (2721613)Time elapsed: 0.082 s
% 4.10/1.18 % (2721613)Peak memory usage: 92 MB
% 4.10/1.18 % (2721613)Instructions burned: 249 (million)
% 4.10/1.18 % (2721610)Instruction limit reached!
% 4.10/1.18 % (2721610)------------------------------
% 4.10/1.18 % (2721610)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.10/1.18 % (2721610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.10/1.18 % (2721610)CaDiCaL version: 2.1.3
% 4.10/1.18 % (2721610)Termination reason: Instruction limit
% 4.10/1.18 % (2721610)Termination phase: Saturation
% 4.10/1.18 % (2721610)Time elapsed: 0.102 s
% 4.10/1.18 % (2721610)Peak memory usage: 92 MB
% 4.10/1.18 % (2721610)Instructions burned: 285 (million)
% 4.10/1.18 % (2721612)Instruction limit reached!
% 4.10/1.18 % (2721612)------------------------------
% 4.10/1.18 % (2721612)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.10/1.18 % (2721612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.10/1.18 % (2721612)CaDiCaL version: 2.1.3
% 4.10/1.18 % (2721612)Termination reason: Instruction limit
% 4.10/1.18 % (2721612)Termination phase: Saturation
% 4.10/1.18 % (2721612)Time elapsed: 0.123 s
% 4.10/1.18 % (2721612)Peak memory usage: 92 MB
% 4.10/1.18 % (2721612)Instructions burned: 326 (million)
% 4.10/1.18 % (2721611)------------------------------
% 4.10/1.18 % (2721611)------------------------------
% 4.10/1.18 % (2721618)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2999501911:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 4.10/1.18 % (2721619)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1339337694:i=2350_2996 on theBenchmark for (2996ds/2350Mi)
% 4.10/1.18 % (2721620)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2186230874:cts=off:i=113:fsr=off:ss=included:sgt=4_2996 on theBenchmark for (2996ds/113Mi)
% 4.10/1.18 % (2721618)First to succeed.
% 4.10/1.18 % (2721621)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2810758627:i=127:av=off:fsr=off:sup=off_2996 on theBenchmark for (2996ds/127Mi)
% 4.10/1.18 % (2721618)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2721591"
% 4.10/1.18 % (2721620)Instruction limit reached!
% 4.10/1.18 % (2721620)------------------------------
% 4.10/1.18 % (2721620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.10/1.18 % (2721620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.10/1.18 % (2721620)CaDiCaL version: 2.1.3
% 4.10/1.18 % (2721620)Termination reason: Instruction limit
% 4.10/1.18 % (2721620)Termination phase: Saturation
% 4.10/1.18 % (2721620)Time elapsed: 0.041 s
% 4.10/1.18 % (2721620)Peak memory usage: 91 MB
% 4.10/1.18 % (2721620)Instructions burned: 115 (million)
% 4.10/1.18 % (2721621)Instruction limit reached!
% 4.10/1.18 % (2721621)------------------------------
% 4.10/1.18 % (2721621)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.10/1.18 % (2721621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.10/1.18 % (2721621)CaDiCaL version: 2.1.3
% 4.10/1.18 % (2721621)Termination reason: Instruction limit
% 4.10/1.18 % (2721621)Termination phase: Saturation
% 4.10/1.18 % (2721621)Time elapsed: 0.037 s
% 4.10/1.18 % (2721621)Peak memory usage: 89 MB
% 4.10/1.18 % (2721621)Instructions burned: 130 (million)
% 4.10/1.18 % (2721596)Also succeeded, but the first one will report.
% 4.10/1.18 % (2721626)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=109139928:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2995 on theBenchmark for (2995ds/114Mi)
% 4.10/1.18 % (2721597)Also succeeded, but the first one will report.
% 4.10/1.18 % (2721626)Instruction limit reached!
% 4.10/1.18 % (2721626)------------------------------
% 4.10/1.18 % (2721626)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.10/1.18 % (2721626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.10/1.18 % (2721626)CaDiCaL version: 2.1.3
% 4.10/1.18 % (2721626)Termination reason: Instruction limit
% 4.10/1.18 % (2721626)Termination phase: Saturation
% 4.10/1.18 % (2721626)Time elapsed: 0.038 s
% 4.10/1.18 % (2721626)Peak memory usage: 89 MB
% 4.10/1.18 % (2721626)Instructions burned: 114 (million)
% 4.10/1.18 % (2721627)lrs+10_1_sil=8000:sp=occurrence:random_seed=4019671015:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2994 on theBenchmark for (2994ds/907Mi)
% 4.10/1.18 % (2721618)Refutation found. Thanks to Tanya!
% 4.10/1.18 % SZS status Theorem for theBenchmark
% 4.10/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 4.74/1.28 % (2721618)------------------------------
% 4.74/1.28 % (2721618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.74/1.28 % (2721618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.74/1.28 % (2721618)CaDiCaL version: 2.1.3
% 4.74/1.28 % (2721618)Termination reason: Refutation
% 4.74/1.28 % (2721618)Time elapsed: 0.076 s
% 4.74/1.28 % (2721618)Peak memory usage: 91 MB
% 4.74/1.28 % (2721618)Instructions burned: 209 (million)
% 4.74/1.28 % (2721618)------------------------------
% 4.74/1.28 % (2721618)------------------------------
% 4.74/1.28 % (2721591)Success in time 0.655 s
% 4.74/1.28 % Vampire exiting
%------------------------------------------------------------------------------