%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM631+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 : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:16:04 PM UTC 2026
% Result : Theorem 5.25s 6.68s
% Output : Refutation 6.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 43
% Syntax : Number of formulae : 248 ( 72 unt; 11 def)
% Number of atoms : 882 ( 158 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 1050 ( 416 ~; 419 |; 163 &)
% ( 32 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 10 prp; 0-3 aty)
% Number of functors : 33 ( 33 usr; 18 con; 0-3 aty)
% Number of variables : 227 ( 0 sgn 215 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
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(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(f17,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mConsDiff) ).
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(f57,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElementOf0(X1,szNzAzT0) )
=> ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSel) ).
fof(f66,axiom,
! [X0,X1] :
( ( aFunction0(X0)
& aElement0(X1) )
=> ! [X2] :
( X2 = sdtlbdtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,szDzozmdt0(X0))
& sdtlpdtrp0(X0,X3) = X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPtt) ).
fof(f69,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( aElementOf0(X1,szDzozmdt0(X0))
=> aElementOf0(sdtlpdtrp0(X0,X1),sdtlcdtrc0(X0,szDzozmdt0(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mImgRng) ).
fof(f73,axiom,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3291) ).
fof(f76,axiom,
( aFunction0(xc)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3453) ).
fof(f80,axiom,
( aElementOf0(xk,szNzAzT0)
& szszuzczcdt0(xk) = xK ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3533) ).
fof(f81,axiom,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) )
=> ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).
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(f85,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aSet0(X1)
& aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) )
=> aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),slbdtsldtrb0(xS,xK)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3965) ).
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(f92,axiom,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( ( aSet0(X1)
& aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) )
=> sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4730) ).
fof(f94,axiom,
( aElementOf0(szDzizrdt0(xd),xT)
& isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4854) ).
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(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(f109,axiom,
sbrdtbr0(xP) = xk,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5217) ).
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(f112,axiom,
sdtlpdtrp0(xd,xn) = szDzizrdt0(xd),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5321) ).
fof(f113,axiom,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5334) ).
fof(f114,axiom,
xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5585) ).
fof(f115,axiom,
aElementOf0(xP,slbdtsldtrb0(xD,xk)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5599) ).
fof(f116,axiom,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5632) ).
fof(f117,conjecture,
sdtlpdtrp0(xc,xQ) = sdtlpdtrp0(xd,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f118,negated_conjecture,
sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
inference(negated_conjecture,[status(cth)],[f117]) ).
fof(f119,plain,
sdtlpdtrp0(xd,xn) != sdtlpdtrp0(xc,xQ),
inference(flattening,[],[f118]) ).
fof(f129,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f130,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f129]) ).
fof(f131,plain,
! [X0] :
( ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),slbdtsldtrb0(xS,xK))
| ~ aSet0(X1)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f137,plain,
! [X0] :
( ! [X1] :
( aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),slbdtsldtrb0(xS,xK))
| ~ aSet0(X1)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f136]) ).
fof(f147,plain,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X0] :
( sdtlpdtrp0(xe,X0) = szmzizndt0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f91]) ).
fof(f148,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( ! [X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aSet0(X1)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f92]) ).
fof(f149,plain,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X0] :
( ! [X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aSet0(X1)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk)) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f148]) ).
fof(f162,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(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(flattening,[],[f162]) ).
fof(f171,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f174,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f215,plain,
! [X0,X1] :
( ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f216,plain,
! [X0,X1] :
( ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f215]) ).
fof(f221,plain,
! [X0] :
( ! [X1] :
( aElementOf0(sdtlpdtrp0(X0,X1),sdtlcdtrc0(X0,szDzozmdt0(X0)))
| ~ aElementOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f224,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtlbdtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,szDzozmdt0(X0))
& sdtlpdtrp0(X0,X3) = X1 ) ) ) )
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f66]) ).
fof(f225,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtlbdtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,szDzozmdt0(X0))
& sdtlpdtrp0(X0,X3) = X1 ) ) ) )
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f224]) ).
fof(f233,plain,
! [X0] :
( ( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
& szszuzczcdt0(X0) != sz00 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f239,plain,
! [X0] :
( ! [X1] :
( sdtpldt0(sdtmndt0(X0,X1),X1) = X0
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f247,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(f248,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(f249,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(definition_folding,[],[f163,f248,f247]) ).
fof(f258,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,[],[f248]) ).
fof(f259,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,[],[f258]) ).
fof(f260,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,[],[f247]) ).
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(flattening,[],[f260]) ).
fof(f262,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,[],[f261]) ).
fof(f263,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))],[f262]) ).
fof(f264,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,[],[f171]) ).
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(flattening,[],[f264]) ).
fof(f266,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,[],[f265]) ).
fof(f267,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))],[f266]) ).
fof(f277,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1 )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(nnf_transformation,[],[f216]) ).
fof(f278,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1 )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f277]) ).
fof(f279,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1 )
& ( ( aSubsetOf0(X4,X0)
& sbrdtbr0(X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(rectify,[],[f278]) ).
fof(f280,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ( ( ~ aSubsetOf0(sK20(X0,X1,X2),X0)
| sbrdtbr0(sK20(X0,X1,X2)) != X1
| ~ aElementOf0(sK20(X0,X1,X2),X2) )
& ( ( aSubsetOf0(sK20(X0,X1,X2),X0)
& sbrdtbr0(sK20(X0,X1,X2)) = X1 )
| aElementOf0(sK20(X0,X1,X2),X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1 )
& ( ( aSubsetOf0(X4,X0)
& sbrdtbr0(X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X3,sK20(X0,X1,X2))],[f279]) ).
fof(f285,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtlbdtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElementOf0(X3,szDzozmdt0(X0))
| sdtlpdtrp0(X0,X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,szDzozmdt0(X0))
& sdtlpdtrp0(X0,X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElementOf0(X3,szDzozmdt0(X0))
| sdtlpdtrp0(X0,X3) != X1 )
& ( ( aElementOf0(X3,szDzozmdt0(X0))
& sdtlpdtrp0(X0,X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| sdtlbdtrb0(X0,X1) != X2 ) )
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(nnf_transformation,[],[f225]) ).
fof(f286,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtlbdtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElementOf0(X3,szDzozmdt0(X0))
| sdtlpdtrp0(X0,X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,szDzozmdt0(X0))
& sdtlpdtrp0(X0,X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElementOf0(X3,szDzozmdt0(X0))
| sdtlpdtrp0(X0,X3) != X1 )
& ( ( aElementOf0(X3,szDzozmdt0(X0))
& sdtlpdtrp0(X0,X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| sdtlbdtrb0(X0,X1) != X2 ) )
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f285]) ).
fof(f287,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtlbdtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aElementOf0(X3,szDzozmdt0(X0))
| sdtlpdtrp0(X0,X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,szDzozmdt0(X0))
& sdtlpdtrp0(X0,X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aElementOf0(X4,szDzozmdt0(X0))
| sdtlpdtrp0(X0,X4) != X1 )
& ( ( aElementOf0(X4,szDzozmdt0(X0))
& sdtlpdtrp0(X0,X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| sdtlbdtrb0(X0,X1) != X2 ) )
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(rectify,[],[f286]) ).
fof(f288,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtlbdtrb0(X0,X1)
| ~ aSet0(X2)
| ( ( ~ aElementOf0(sK22(X0,X1,X2),szDzozmdt0(X0))
| sdtlpdtrp0(X0,sK22(X0,X1,X2)) != X1
| ~ aElementOf0(sK22(X0,X1,X2),X2) )
& ( ( aElementOf0(sK22(X0,X1,X2),szDzozmdt0(X0))
& sdtlpdtrp0(X0,sK22(X0,X1,X2)) = X1 )
| aElementOf0(sK22(X0,X1,X2),X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aElementOf0(X4,szDzozmdt0(X0))
| sdtlpdtrp0(X0,X4) != X1 )
& ( ( aElementOf0(X4,szDzozmdt0(X0))
& sdtlpdtrp0(X0,X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| sdtlbdtrb0(X0,X1) != X2 ) )
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(X3,sK22(X0,X1,X2))],[f287]) ).
fof(f309,plain,
aSet0(xT),
inference(cnf_transformation,[],[f73]) ).
fof(f313,plain,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(cnf_transformation,[],[f76]) ).
fof(f314,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(cnf_transformation,[],[f76]) ).
fof(f315,plain,
aFunction0(xc),
inference(cnf_transformation,[],[f76]) ).
fof(f322,plain,
xK = szszuzczcdt0(xk),
inference(cnf_transformation,[],[f80]) ).
fof(f323,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f80]) ).
fof(f326,plain,
xS = sdtlpdtrp0(xN,sz00),
inference(cnf_transformation,[],[f130]) ).
fof(f330,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f333,plain,
! [X0,X1] :
( ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| ~ aSet0(X1)
| aElementOf0(sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))),slbdtsldtrb0(xS,xK))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f347,plain,
! [X0] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) = sdtlpdtrp0(xe,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f350,plain,
! [X0,X1] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xd,X0)
| ~ aSet0(X1)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f355,plain,
aElementOf0(szDzizrdt0(xd),xT),
inference(cnf_transformation,[],[f94]) ).
fof(f359,plain,
aSet0(xO),
inference(cnf_transformation,[],[f96]) ).
fof(f366,plain,
aSubsetOf0(xQ,xO),
inference(cnf_transformation,[],[f100]) ).
fof(f369,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[],[f103]) ).
fof(f370,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(cnf_transformation,[],[f104]) ).
fof(f371,plain,
aSet0(xP),
inference(cnf_transformation,[],[f104]) ).
fof(f372,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[],[f105]) ).
fof(f373,plain,
aElementOf0(xp,xO),
inference(cnf_transformation,[],[f106]) ).
fof(f376,plain,
xk = sbrdtbr0(xP),
inference(cnf_transformation,[],[f109]) ).
fof(f378,plain,
xp = sdtlpdtrp0(xe,xn),
inference(cnf_transformation,[],[f111]) ).
fof(f379,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f111]) ).
fof(f381,plain,
szDzizrdt0(xd) = sdtlpdtrp0(xd,xn),
inference(cnf_transformation,[],[f112]) ).
fof(f382,plain,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(cnf_transformation,[],[f113]) ).
fof(f383,plain,
xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),
inference(cnf_transformation,[],[f114]) ).
fof(f384,plain,
aElementOf0(xP,slbdtsldtrb0(xD,xk)),
inference(cnf_transformation,[],[f115]) ).
fof(f385,plain,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(cnf_transformation,[],[f116]) ).
fof(f386,plain,
sdtlpdtrp0(xd,xn) != sdtlpdtrp0(xc,xQ),
inference(cnf_transformation,[],[f119]) ).
fof(f394,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f397,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| sdtmndt0(X1,X0) != X2
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f259]) ).
fof(f398,plain,
! [X2,X0,X1] :
( sdtmndt0(X1,X0) = X2
| ~ sP0(X2,X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f259]) ).
fof(f403,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| aSet0(X0) ),
inference(cnf_transformation,[],[f263]) ).
fof(f408,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f249]) ).
fof(f414,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f267]) ).
fof(f418,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f174]) ).
fof(f459,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1
| slbdtsldtrb0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f280]) ).
fof(f469,plain,
! [X0,X1] :
( aElementOf0(sdtlpdtrp0(X0,X1),sdtlcdtrc0(X0,szDzozmdt0(X0)))
| ~ aElementOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f221]) ).
fof(f471,plain,
! [X2,X0,X1,X4] :
( sdtlpdtrp0(X0,X4) = X1
| ~ aElementOf0(X4,X2)
| sdtlbdtrb0(X0,X1) != X2
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f288]) ).
fof(f473,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X2)
| ~ aElementOf0(X4,szDzozmdt0(X0))
| sdtlpdtrp0(X0,X4) != X1
| sdtlbdtrb0(X0,X1) != X2
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f288]) ).
fof(f488,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f233]) ).
fof(f501,plain,
! [X0,X1] :
( sdtpldt0(sdtmndt0(X0,X1),X1) = X0
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f239]) ).
fof(f521,plain,
! [X0,X1] :
( sP0(sdtmndt0(X1,X0),X1,X0)
| ~ sP1(X0,X1) ),
inference(equality_resolution,[],[f397]) ).
fof(f530,plain,
! [X2,X0,X4] :
( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| slbdtsldtrb0(X0,sbrdtbr0(X4)) != X2
| ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X4),szNzAzT0) ),
inference(equality_resolution,[],[f459]) ).
fof(f531,plain,
! [X0,X4] :
( aElementOf0(X4,slbdtsldtrb0(X0,sbrdtbr0(X4)))
| ~ aSubsetOf0(X4,X0)
| ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X4),szNzAzT0) ),
inference(equality_resolution,[],[f530]) ).
fof(f537,plain,
! [X2,X0,X4] :
( aElementOf0(X4,X2)
| ~ aElementOf0(X4,szDzozmdt0(X0))
| sdtlbdtrb0(X0,sdtlpdtrp0(X0,X4)) != X2
| ~ aFunction0(X0)
| ~ aElement0(sdtlpdtrp0(X0,X4)) ),
inference(equality_resolution,[],[f473]) ).
fof(f538,plain,
! [X0,X4] :
( aElementOf0(X4,sdtlbdtrb0(X0,sdtlpdtrp0(X0,X4)))
| ~ aElementOf0(X4,szDzozmdt0(X0))
| ~ aFunction0(X0)
| ~ aElement0(sdtlpdtrp0(X0,X4)) ),
inference(equality_resolution,[],[f537]) ).
fof(f540,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X4,sdtlbdtrb0(X0,X1))
| sdtlpdtrp0(X0,X4) = X1
| ~ aFunction0(X0)
| ~ aElement0(X1) ),
inference(equality_resolution,[],[f471]) ).
fof(f553,plain,
aElementOf0(sdtlpdtrp0(xe,xn),xO),
inference(forward_demodulation,[],[f373,f378]) ).
fof(f554,plain,
aElementOf0(sdtlpdtrp0(xe,xn),xQ),
inference(forward_demodulation,[],[f372,f378]) ).
fof(f555,plain,
aSet0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(forward_demodulation,[],[f371,f370]) ).
fof(f559,plain,
aElementOf0(sdtlpdtrp0(xd,xn),xT),
inference(forward_demodulation,[],[f355,f381]) ).
fof(f568,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,szszuzczcdt0(xk)),
inference(forward_demodulation,[],[f314,f322]) ).
fof(f574,plain,
szDzozmdt0(xc) = slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)),
inference(forward_demodulation,[],[f568,f326]) ).
fof(f616,plain,
( aSet0(xQ)
| ~ aSet0(xO) ),
inference(resolution,[],[f366,f414]) ).
fof(f620,plain,
aSet0(xQ),
inference(forward_subsumption_resolution,[],[f616,f359]) ).
fof(f623,definition,
( spl27_6
<=> aSet0(xQ) ),
introduced(definition,[new_symbols(definition,[spl27_6])],[avatar_definition]) ).
fof(f624,plain,
( aSet0(xQ)
| ~ spl27_6 ),
inference(avatar_component_clause,[],[f623]) ).
fof(f635,plain,
spl27_6,
inference(avatar_split_clause,[],[f620,f623]) ).
fof(f870,definition,
( spl27_36
<=> aElement0(sdtlpdtrp0(xd,xn)) ),
introduced(definition,[new_symbols(definition,[spl27_36])],[avatar_definition]) ).
fof(f871,plain,
( ~ aElement0(sdtlpdtrp0(xd,xn))
| spl27_36 ),
inference(avatar_component_clause,[],[f870]) ).
fof(f872,plain,
( aElement0(sdtlpdtrp0(xd,xn))
| ~ spl27_36 ),
inference(avatar_component_clause,[],[f870]) ).
fof(f897,plain,
! [X0] :
( aElementOf0(xP,slbdtsldtrb0(X0,xk))
| ~ aSubsetOf0(xP,X0)
| ~ aSet0(X0)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(superposition,[],[f531,f376]) ).
fof(f898,plain,
! [X0] :
( aElementOf0(xP,slbdtsldtrb0(X0,xk))
| ~ aSubsetOf0(xP,X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[],[f897,f323]) ).
fof(f903,plain,
! [X0] :
( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(X0,xk))
| ~ aSubsetOf0(xP,X0)
| ~ aSet0(X0) ),
inference(forward_demodulation,[],[f898,f370]) ).
fof(f907,plain,
! [X0] :
( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(X0,xk))
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),X0)
| ~ aSet0(X0) ),
inference(forward_demodulation,[],[f903,f370]) ).
fof(f956,plain,
szmzizndt0(xQ) = sdtlpdtrp0(xe,xn),
inference(superposition,[],[f369,f378]) ).
fof(f978,plain,
( aElement0(sdtlpdtrp0(xe,xn))
| ~ aSet0(xO) ),
inference(resolution,[],[f553,f418]) ).
fof(f979,plain,
aElement0(sdtlpdtrp0(xe,xn)),
inference(forward_subsumption_resolution,[],[f978,f359]) ).
fof(f980,plain,
aElement0(szmzizndt0(xQ)),
inference(forward_demodulation,[],[f979,f956]) ).
fof(f997,plain,
( aElement0(sdtlpdtrp0(xd,xn))
| ~ aSet0(xT) ),
inference(resolution,[],[f559,f418]) ).
fof(f998,plain,
( ~ aSet0(xT)
| spl27_36 ),
inference(forward_subsumption_resolution,[],[f997,f871]) ).
fof(f999,plain,
( $false
| spl27_36 ),
inference(forward_subsumption_resolution,[],[f998,f309]) ).
fof(f1000,plain,
spl27_36,
inference(avatar_contradiction_clause,[],[f999]) ).
fof(f1025,plain,
( aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ aSet0(xT) ),
inference(resolution,[],[f313,f414]) ).
fof(f1030,plain,
aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(forward_subsumption_resolution,[],[f1025,f309]) ).
fof(f1034,plain,
aSet0(sdtlcdtrc0(xc,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))),
inference(forward_demodulation,[],[f1030,f574]) ).
fof(f1078,plain,
aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(xD,xk)),
inference(superposition,[],[f384,f370]) ).
fof(f1083,plain,
aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)),
inference(forward_demodulation,[],[f1078,f383]) ).
fof(f1089,plain,
aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(superposition,[],[f382,f370]) ).
fof(f1096,definition,
( spl27_51
<=> aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
introduced(definition,[new_symbols(definition,[spl27_51])],[avatar_definition]) ).
fof(f1097,plain,
( aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ spl27_51 ),
inference(avatar_component_clause,[],[f1096]) ).
fof(f1098,plain,
( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| spl27_51 ),
inference(avatar_component_clause,[],[f1096]) ).
fof(f1164,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aSet0(sdtlpdtrp0(xN,X0))
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f330,f414]) ).
fof(f1175,plain,
! [X0] :
( aSet0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f1164,f394]) ).
fof(f1219,definition,
( spl27_59
<=> sP1(szmzizndt0(xQ),xQ) ),
introduced(definition,[new_symbols(definition,[spl27_59])],[avatar_definition]) ).
fof(f1220,plain,
( sP1(szmzizndt0(xQ),xQ)
| ~ spl27_59 ),
inference(avatar_component_clause,[],[f1219]) ).
fof(f1221,plain,
( ~ sP1(szmzizndt0(xQ),xQ)
| spl27_59 ),
inference(avatar_component_clause,[],[f1219]) ).
fof(f1318,plain,
( ~ aSet0(xQ)
| ~ aElement0(szmzizndt0(xQ))
| spl27_59 ),
inference(resolution,[],[f1221,f408]) ).
fof(f1323,plain,
( ~ aElement0(szmzizndt0(xQ))
| ~ spl27_6
| spl27_59 ),
inference(forward_subsumption_resolution,[],[f1318,f624]) ).
fof(f1326,plain,
( $false
| ~ spl27_6
| spl27_59 ),
inference(forward_subsumption_resolution,[],[f1323,f980]) ).
fof(f1327,plain,
( ~ spl27_6
| spl27_59 ),
inference(avatar_contradiction_clause,[],[f1326]) ).
fof(f1394,plain,
( aElementOf0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))),sdtlbdtrb0(xc,sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)))
| ~ aElementOf0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))),szDzozmdt0(xc))
| ~ aFunction0(xc)
| ~ aElement0(sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)) ),
inference(superposition,[],[f538,f385]) ).
fof(f1395,plain,
( aElementOf0(sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ aElementOf0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))),szDzozmdt0(xc))
| ~ aFunction0(xc) ),
inference(superposition,[],[f469,f385]) ).
fof(f1398,plain,
( aElementOf0(sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ aElementOf0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))),szDzozmdt0(xc)) ),
inference(forward_subsumption_resolution,[],[f1395,f315]) ).
fof(f1399,plain,
( aElementOf0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))),sdtlbdtrb0(xc,sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)))
| ~ aElementOf0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))),szDzozmdt0(xc))
| ~ aElement0(sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)) ),
inference(forward_subsumption_resolution,[],[f1394,f315]) ).
fof(f1404,plain,
( aElementOf0(sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),sdtlcdtrc0(xc,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk))))
| ~ aElementOf0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))),szDzozmdt0(xc)) ),
inference(forward_demodulation,[],[f1398,f574]) ).
fof(f1405,plain,
( aElementOf0(sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))),sdtlbdtrb0(xc,sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElementOf0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))),szDzozmdt0(xc))
| ~ aElement0(sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)) ),
inference(forward_demodulation,[],[f1399,f370]) ).
fof(f1421,plain,
( aElementOf0(sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))),sdtlcdtrc0(xc,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk))))
| ~ aElementOf0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))),szDzozmdt0(xc)) ),
inference(forward_demodulation,[],[f1404,f370]) ).
fof(f1422,plain,
( ~ aElementOf0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| aElementOf0(sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))),sdtlbdtrb0(xc,sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElement0(sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)) ),
inference(forward_demodulation,[],[f1405,f574]) ).
fof(f1425,plain,
( ~ aElementOf0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| aElementOf0(sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))),sdtlcdtrc0(xc,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))) ),
inference(forward_demodulation,[],[f1421,f574]) ).
fof(f1426,plain,
( ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| aElementOf0(sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))),sdtlbdtrb0(xc,sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ aElement0(sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)) ),
inference(forward_demodulation,[],[f1422,f370]) ).
fof(f1435,plain,
( ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| aElementOf0(sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))),sdtlcdtrc0(xc,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))) ),
inference(forward_demodulation,[],[f1425,f370]) ).
fof(f1436,plain,
( ~ aElement0(sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))))
| ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| aElementOf0(sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))),sdtlbdtrb0(xc,sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))))) ),
inference(forward_demodulation,[],[f1426,f370]) ).
fof(f1438,definition,
( spl27_71
<=> aElementOf0(sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))),sdtlcdtrc0(xc,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))) ),
introduced(definition,[new_symbols(definition,[spl27_71])],[avatar_definition]) ).
fof(f1440,plain,
( aElementOf0(sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))),sdtlcdtrc0(xc,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk))))
| ~ spl27_71 ),
inference(avatar_component_clause,[],[f1438]) ).
fof(f1442,definition,
( spl27_72
<=> aElementOf0(sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk))) ),
introduced(definition,[new_symbols(definition,[spl27_72])],[avatar_definition]) ).
fof(f1444,plain,
( ~ aElementOf0(sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk)))
| spl27_72 ),
inference(avatar_component_clause,[],[f1442]) ).
fof(f1445,plain,
( spl27_71
| ~ spl27_72 ),
inference(avatar_split_clause,[],[f1435,f1442,f1438]) ).
fof(f1447,definition,
( spl27_73
<=> aElementOf0(sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))),sdtlbdtrb0(xc,sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))))) ),
introduced(definition,[new_symbols(definition,[spl27_73])],[avatar_definition]) ).
fof(f1449,plain,
( aElementOf0(sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))),sdtlbdtrb0(xc,sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ spl27_73 ),
inference(avatar_component_clause,[],[f1447]) ).
fof(f1451,definition,
( spl27_74
<=> aElement0(sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ)))) ),
introduced(definition,[new_symbols(definition,[spl27_74])],[avatar_definition]) ).
fof(f1453,plain,
( ~ aElement0(sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))))
| spl27_74 ),
inference(avatar_component_clause,[],[f1451]) ).
fof(f1454,plain,
( spl27_73
| ~ spl27_72
| ~ spl27_74 ),
inference(avatar_split_clause,[],[f1436,f1451,f1442,f1447]) ).
fof(f2119,plain,
aElementOf0(szmzizndt0(xQ),xQ),
inference(superposition,[],[f554,f956]) ).
fof(f2121,plain,
( szmzizndt0(xQ) = szmzizndt0(sdtlpdtrp0(xN,xn))
| ~ aElementOf0(xn,szNzAzT0) ),
inference(superposition,[],[f347,f956]) ).
fof(f2128,plain,
szmzizndt0(xQ) = szmzizndt0(sdtlpdtrp0(xN,xn)),
inference(forward_subsumption_resolution,[],[f2121,f379]) ).
fof(f2615,plain,
( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
| spl27_51 ),
inference(resolution,[],[f1175,f1098]) ).
fof(f2635,plain,
( ~ aElementOf0(xn,szNzAzT0)
| spl27_51 ),
inference(resolution,[],[f2615,f488]) ).
fof(f2637,plain,
( $false
| spl27_51 ),
inference(forward_subsumption_resolution,[],[f2635,f379]) ).
fof(f2638,plain,
spl27_51,
inference(avatar_contradiction_clause,[],[f2637]) ).
fof(f4073,plain,
( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| aElementOf0(sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))),slbdtsldtrb0(xS,xK))
| ~ aElementOf0(xn,szNzAzT0) ),
inference(resolution,[],[f1083,f333]) ).
fof(f4091,plain,
( aElementOf0(sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))),slbdtsldtrb0(xS,xK))
| ~ aElementOf0(xn,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f4073,f555]) ).
fof(f4098,plain,
aElementOf0(sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))),slbdtsldtrb0(xS,xK)),
inference(forward_subsumption_resolution,[],[f4091,f379]) ).
fof(f4103,plain,
aElementOf0(sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))),slbdtsldtrb0(xS,szszuzczcdt0(xk))),
inference(forward_demodulation,[],[f4098,f322]) ).
fof(f4104,plain,
aElementOf0(sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))),slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk))),
inference(forward_demodulation,[],[f4103,f326]) ).
fof(f4105,plain,
( $false
| spl27_72 ),
inference(forward_subsumption_resolution,[],[f4104,f1444]) ).
fof(f4106,plain,
spl27_72,
inference(avatar_contradiction_clause,[],[f4105]) ).
fof(f4532,plain,
( aElement0(sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))))
| ~ aSet0(sdtlcdtrc0(xc,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk))))
| ~ spl27_71 ),
inference(resolution,[],[f1440,f418]) ).
fof(f4542,plain,
( ~ aSet0(sdtlcdtrc0(xc,slbdtsldtrb0(sdtlpdtrp0(xN,sz00),szszuzczcdt0(xk))))
| ~ spl27_71
| spl27_74 ),
inference(forward_subsumption_resolution,[],[f4532,f1453]) ).
fof(f4545,plain,
( $false
| ~ spl27_71
| spl27_74 ),
inference(forward_subsumption_resolution,[],[f4542,f1034]) ).
fof(f4546,plain,
( ~ spl27_71
| spl27_74 ),
inference(avatar_contradiction_clause,[],[f4545]) ).
fof(f4547,plain,
( aElementOf0(sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)),sdtlbdtrb0(xc,sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ)))))
| ~ spl27_73 ),
inference(forward_demodulation,[],[f1449,f2128]) ).
fof(f5141,definition,
( spl27_172
<=> sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) ),
introduced(definition,[new_symbols(definition,[spl27_172])],[avatar_definition]) ).
fof(f5142,plain,
( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ spl27_172 ),
inference(avatar_component_clause,[],[f5141]) ).
fof(f5143,plain,
( sdtlpdtrp0(xd,xn) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ)))
| spl27_172 ),
inference(avatar_component_clause,[],[f5141]) ).
fof(f5409,plain,
( aElementOf0(sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)),sdtlbdtrb0(xc,sdtlpdtrp0(xd,xn)))
| ~ spl27_73
| ~ spl27_172 ),
inference(superposition,[],[f4547,f5142]) ).
fof(f5508,plain,
( aElementOf0(xQ,sdtlbdtrb0(xc,sdtlpdtrp0(xd,xn)))
| ~ aElementOf0(szmzizndt0(xQ),xQ)
| ~ aSet0(xQ)
| ~ spl27_73
| ~ spl27_172 ),
inference(superposition,[],[f5409,f501]) ).
fof(f5511,plain,
( aElementOf0(xQ,sdtlbdtrb0(xc,sdtlpdtrp0(xd,xn)))
| ~ aSet0(xQ)
| ~ spl27_73
| ~ spl27_172 ),
inference(forward_subsumption_resolution,[],[f5508,f2119]) ).
fof(f5517,plain,
( aElementOf0(xQ,sdtlbdtrb0(xc,sdtlpdtrp0(xd,xn)))
| ~ spl27_6
| ~ spl27_73
| ~ spl27_172 ),
inference(forward_subsumption_resolution,[],[f5511,f624]) ).
fof(f5551,plain,
( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(xc,xQ)
| ~ aFunction0(xc)
| ~ aElement0(sdtlpdtrp0(xd,xn))
| ~ spl27_6
| ~ spl27_73
| ~ spl27_172 ),
inference(resolution,[],[f5517,f540]) ).
fof(f5554,plain,
( ~ aFunction0(xc)
| ~ aElement0(sdtlpdtrp0(xd,xn))
| ~ spl27_6
| ~ spl27_73
| ~ spl27_172 ),
inference(forward_subsumption_resolution,[],[f5551,f386]) ).
fof(f5555,plain,
( ~ aElement0(sdtlpdtrp0(xd,xn))
| ~ spl27_6
| ~ spl27_73
| ~ spl27_172 ),
inference(forward_subsumption_resolution,[],[f5554,f315]) ).
fof(f5556,plain,
( $false
| ~ spl27_6
| ~ spl27_36
| ~ spl27_73
| ~ spl27_172 ),
inference(forward_subsumption_resolution,[],[f5555,f872]) ).
fof(f5557,plain,
( ~ spl27_6
| ~ spl27_36
| ~ spl27_73
| ~ spl27_172 ),
inference(avatar_contradiction_clause,[],[f5556]) ).
fof(f5562,plain,
( ! [X0] :
( sdtlpdtrp0(xd,xn) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),X0)
| ~ sP0(X0,xQ,szmzizndt0(xQ))
| ~ sP1(szmzizndt0(xQ),xQ) )
| spl27_172 ),
inference(superposition,[],[f5143,f398]) ).
fof(f5565,plain,
( ! [X0] :
( sdtlpdtrp0(xd,xn) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),X0)
| ~ sP0(X0,xQ,szmzizndt0(xQ)) )
| ~ spl27_59
| spl27_172 ),
inference(forward_subsumption_resolution,[],[f5562,f1220]) ).
fof(f5572,plain,
( ! [X0] :
( sdtlpdtrp0(xd,xn) != sdtlpdtrp0(xd,xn)
| ~ sP0(X0,xQ,szmzizndt0(xQ))
| ~ aSet0(X0)
| ~ aElementOf0(X0,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ aElementOf0(xn,szNzAzT0) )
| ~ spl27_59
| spl27_172 ),
inference(superposition,[],[f5565,f350]) ).
fof(f5578,plain,
( ! [X0] :
( ~ sP0(X0,xQ,szmzizndt0(xQ))
| ~ aSet0(X0)
| ~ aElementOf0(X0,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ aElementOf0(xn,szNzAzT0) )
| ~ spl27_59
| spl27_172 ),
inference(trivial_inequality_removal,[],[f5572]) ).
fof(f5579,plain,
( ! [X0] :
( ~ sP0(X0,xQ,szmzizndt0(xQ))
| ~ aElementOf0(X0,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ aElementOf0(xn,szNzAzT0) )
| ~ spl27_59
| spl27_172 ),
inference(forward_subsumption_resolution,[],[f5578,f403]) ).
fof(f5580,plain,
( ! [X0] :
( ~ aElementOf0(X0,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
| ~ sP0(X0,xQ,szmzizndt0(xQ)) )
| ~ spl27_59
| spl27_172 ),
inference(forward_subsumption_resolution,[],[f5579,f379]) ).
fof(f5583,plain,
( ~ sP0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ,szmzizndt0(xQ))
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ spl27_59
| spl27_172 ),
inference(resolution,[],[f5580,f907]) ).
fof(f5644,plain,
( ~ sP0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ,szmzizndt0(xQ))
| ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ spl27_59
| spl27_172 ),
inference(forward_subsumption_resolution,[],[f5583,f1089]) ).
fof(f5645,plain,
( ~ sP0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ,szmzizndt0(xQ))
| ~ spl27_51
| ~ spl27_59
| spl27_172 ),
inference(forward_subsumption_resolution,[],[f5644,f1097]) ).
fof(f5733,plain,
( ~ sP1(szmzizndt0(xQ),xQ)
| ~ spl27_51
| ~ spl27_59
| spl27_172 ),
inference(resolution,[],[f5645,f521]) ).
fof(f5741,plain,
( $false
| ~ spl27_51
| ~ spl27_59
| spl27_172 ),
inference(forward_subsumption_resolution,[],[f5733,f1220]) ).
fof(f5742,plain,
( ~ spl27_51
| ~ spl27_59
| spl27_172 ),
inference(avatar_contradiction_clause,[],[f5741]) ).
cnf(s5,plain,
spl27_6,
inference(sat_conversion,[],[f635]) ).
cnf(s26,plain,
spl27_36,
inference(sat_conversion,[],[f1000]) ).
cnf(s42,plain,
( ~ spl27_6
| spl27_59 ),
inference(sat_conversion,[],[f1327]) ).
cnf(s46,plain,
( spl27_71
| ~ spl27_72 ),
inference(sat_conversion,[],[f1445]) ).
cnf(s47,plain,
( ~ spl27_72
| spl27_73
| ~ spl27_74 ),
inference(sat_conversion,[],[f1454]) ).
cnf(s84,plain,
spl27_51,
inference(sat_conversion,[],[f2638]) ).
cnf(s144,plain,
spl27_72,
inference(sat_conversion,[],[f4106]) ).
cnf(s150,plain,
( ~ spl27_71
| spl27_74 ),
inference(sat_conversion,[],[f4546]) ).
cnf(s165,plain,
( ~ spl27_6
| ~ spl27_36
| ~ spl27_73
| ~ spl27_172 ),
inference(sat_conversion,[],[f5557]) ).
cnf(s175,plain,
( ~ spl27_51
| ~ spl27_59
| spl27_172 ),
inference(sat_conversion,[],[f5742]) ).
cnf(s204,plain,
( spl27_73
| ~ spl27_74 ),
inference(rat,[],[s47,s144]) ).
cnf(s205,plain,
spl27_71,
inference(rat,[],[s46,s144]) ).
cnf(s206,plain,
spl27_74,
inference(rat,[],[s150,s205]) ).
cnf(s208,plain,
spl27_73,
inference(rat,[],[s204,s206]) ).
cnf(s230,plain,
~ spl27_172,
inference(rat,[],[s165,s26,s208,s5]) ).
cnf(s232,plain,
spl27_59,
inference(rat,[],[s42,s5]) ).
cnf(s233,plain,
$false,
inference(rat,[],[s175,s84,s230,s232]) ).
fof(f5745,plain,
$false,
inference(avatar_sat_refutation,[],[s233]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM631+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/5.39 % Computer : n017.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Sun Sep 27 20:46:27 UTC 2026
% 0.12/5.40 % CPUTime :
% 0.12/5.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 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
% 5.25/6.68 % (2924587)Detected formulas, will run a generic FOF schedule.
% 5.25/6.68 % (2924596)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=626749865:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.25/6.68 % (2924597)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3843307112:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.25/6.68 % (2924592)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=3266321557:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.25/6.68 % (2924598)dis-21_1_sil=8000:lcm=predicate:random_seed=4062844995: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)
% 5.25/6.68 % (2924595)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3837142924:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.25/6.68 % (2924593)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=3735619393:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.25/6.68 % (2924594)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=3963050333:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.25/6.68 % (2924596)Instruction limit reached!
% 5.25/6.68 % (2924596)------------------------------
% 5.25/6.68 % (2924596)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/6.68 % (2924596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/6.68 % (2924596)CaDiCaL version: 2.1.3
% 5.25/6.68 % (2924596)Termination reason: Instruction limit
% 5.25/6.68 % (2924596)Termination phase: Saturation
% 5.25/6.68 % (2924596)Time elapsed: 0.041 s
% 5.25/6.68 % (2924596)Peak memory usage: 89 MB
% 5.25/6.68 % (2924596)Instructions burned: 119 (million)
% 5.25/6.68 % (2924595)Instruction limit reached!
% 5.25/6.68 % (2924595)------------------------------
% 5.25/6.68 % (2924595)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/6.68 % (2924595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/6.68 % (2924595)CaDiCaL version: 2.1.3
% 5.25/6.68 % (2924595)Termination reason: Instruction limit
% 5.25/6.68 % (2924595)Termination phase: Saturation
% 5.25/6.68 % (2924595)Time elapsed: 0.070 s
% 5.25/6.68 % (2924595)Peak memory usage: 89 MB
% 5.25/6.68 % (2924595)Instructions burned: 110 (million)
% 5.25/6.68 % (2924598)Instruction limit reached!
% 5.25/6.68 % (2924598)------------------------------
% 5.25/6.68 % (2924598)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/6.68 % (2924598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/6.68 % (2924598)CaDiCaL version: 2.1.3
% 5.25/6.68 % (2924598)Termination reason: Instruction limit
% 5.25/6.68 % (2924598)Termination phase: Saturation
% 5.25/6.68 % (2924598)Time elapsed: 0.075 s
% 5.25/6.68 % (2924598)Peak memory usage: 91 MB
% 5.25/6.68 % (2924598)Instructions burned: 131 (million)
% 5.25/6.68 % (2924597)Instruction limit reached!
% 5.25/6.68 % (2924597)------------------------------
% 5.25/6.68 % (2924597)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/6.68 % (2924597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/6.68 % (2924597)CaDiCaL version: 2.1.3
% 5.25/6.68 % (2924597)Termination reason: Instruction limit
% 5.25/6.68 % (2924597)Termination phase: Saturation
% 5.25/6.68 % (2924597)Time elapsed: 0.102 s
% 5.25/6.68 % (2924597)Peak memory usage: 90 MB
% 5.25/6.68 % (2924597)Instructions burned: 139 (million)
% 5.25/6.68 % (2924606)lrs+10_1_sil=8000:sp=occurrence:random_seed=1878546158:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 5.25/6.68 % (2924608)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1619459632:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.25/6.68 % (2924607)lrs+10_1_sil=32000:urr=on:br=off:random_seed=655887708:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.25/6.68 % (2924607)Refutation not found, incomplete strategy
% 5.25/6.68 % (2924607)------------------------------
% 5.25/6.68 % (2924607)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/6.68 % (2924607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/6.68 % (2924607)CaDiCaL version: 2.1.3
% 5.25/6.68 % (2924607)Termination reason: Refutation not found, incomplete strategy
% 5.25/6.68 % (2924607)Time elapsed: 0.003 s
% 5.25/6.68 % (2924607)Peak memory usage: 88 MB
% 5.25/6.68 % (2924607)Instructions burned: 3 (million)
% 5.25/6.68 % (2924606)Instruction limit reached!
% 5.25/6.68 % (2924606)------------------------------
% 5.25/6.68 % (2924606)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/6.68 % (2924606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/6.68 % (2924606)CaDiCaL version: 2.1.3
% 5.25/6.68 % (2924606)Termination reason: Instruction limit
% 5.25/6.68 % (2924606)Termination phase: Saturation
% 5.25/6.68 % (2924606)Time elapsed: 0.099 s
% 5.25/6.68 % (2924606)Peak memory usage: 92 MB
% 5.25/6.68 % (2924606)Instructions burned: 285 (million)
% 5.25/6.68 % (2924609)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=4160601238:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.25/6.68 % (2924613)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1692808805:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.25/6.68 % (2924609)Instruction limit reached!
% 5.25/6.68 % (2924609)------------------------------
% 5.25/6.68 % (2924609)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/6.68 % (2924609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/6.68 % (2924609)CaDiCaL version: 2.1.3
% 5.25/6.68 % (2924609)Termination reason: Instruction limit
% 5.25/6.68 % (2924609)Termination phase: Saturation
% 5.25/6.68 % (2924609)Time elapsed: 0.153 s
% 5.25/6.68 % (2924609)Peak memory usage: 92 MB
% 5.25/6.68 % (2924609)Instructions burned: 248 (million)
% 5.25/6.68 % (2924608)Instruction limit reached!
% 5.25/6.68 % (2924608)------------------------------
% 5.25/6.68 % (2924608)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.25/6.68 % (2924608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.25/6.68 % (2924608)CaDiCaL version: 2.1.3
% 5.25/6.68 % (2924608)Termination reason: Instruction limit
% 5.25/6.68 % (2924608)Termination phase: Saturation
% 5.25/6.68 % (2924608)Time elapsed: 0.232 s
% 5.25/6.68 % (2924608)Peak memory usage: 92 MB
% 5.25/6.68 % (2924608)Instructions burned: 326 (million)
% 5.25/6.68 % (2924607)------------------------------
% 5.25/6.68 % (2924607)------------------------------
% 5.25/6.68 % (2924613)First to succeed.
% 5.25/6.68 % (2924613)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2924587"
% 5.25/6.68 % (2924616)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2117302493:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.25/6.68 % (2924617)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2864277071:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 5.25/6.68 % (2924618)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2263405354:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 5.25/6.68 % (2924613)Refutation found. Thanks to Tanya!
% 5.25/6.68 % SZS status Theorem for theBenchmark
% 5.25/6.68 % SZS output start Proof for theBenchmark
% See solution above
% 6.27/6.88 % (2924613)------------------------------
% 6.27/6.88 % (2924613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.27/6.88 % (2924613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.27/6.88 % (2924613)CaDiCaL version: 2.1.3
% 6.27/6.88 % (2924613)Termination reason: Refutation
% 6.27/6.88 % (2924613)Time elapsed: 0.100 s
% 6.27/6.88 % (2924613)Peak memory usage: 91 MB
% 6.27/6.88 % (2924613)Instructions burned: 287 (million)
% 6.27/6.88 % (2924613)------------------------------
% 6.27/6.88 % (2924613)------------------------------
% 6.27/6.88 % (2924587)Success in time 0.81 s
% 6.27/6.88 % Vampire exiting
%------------------------------------------------------------------------------