%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM581+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 : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:15:50 PM UTC 2026
% Result : Theorem 9.30s 2.18s
% Output : Refutation 9.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 42
% Syntax : Number of formulae : 268 ( 47 unt; 22 def)
% Number of atoms : 1070 ( 156 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 1325 ( 523 ~; 554 |; 184 &)
% ( 46 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 16 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 12 con; 0-3 aty)
% Number of variables : 302 ( 0 sgn 283 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f5,axiom,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ~ ? [X1] : aElementOf0(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(f9,axiom,
! [X0] :
( ( aSet0(X0)
& isCountable0(X0) )
=> X0 != slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin_01) ).
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(f14,axiom,
! [X0,X1,X2] :
( ( aSet0(X0)
& aSet0(X1)
& aSet0(X2) )
=> ( ( aSubsetOf0(X0,X1)
& aSubsetOf0(X1,X2) )
=> aSubsetOf0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubTrans) ).
fof(f15,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElement0(X1) )
=> ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& ( aElementOf0(X3,X0)
| X3 = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefCons) ).
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(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
fof(f30,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(sz00,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroLess) ).
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(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(f75,axiom,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
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(f83,axiom,
! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(X1,X0)
=> aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3754) ).
fof(f85,axiom,
aElementOf0(xi,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3989) ).
fof(f86,axiom,
aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3989_02) ).
fof(f88,conjecture,
aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f89,negated_conjecture,
~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f97,plain,
~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(flattening,[],[f89]) ).
fof(f98,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f99,plain,
! [X0] :
( X0 = slcrc0
<=> ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f102,plain,
! [X0] :
( X0 != slcrc0
| ~ aSet0(X0)
| ~ isCountable0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f103,plain,
! [X0] :
( X0 != slcrc0
| ~ aSet0(X0)
| ~ isCountable0(X0) ),
inference(flattening,[],[f102]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f110,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X0)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f111,plain,
! [X0,X1,X2] :
( aSubsetOf0(X0,X2)
| ~ aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X0)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(flattening,[],[f110]) ).
fof(f112,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& ( aElementOf0(X3,X0)
| X3 = X1 ) ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f113,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& ( aElementOf0(X3,X0)
| X3 = X1 ) ) ) ) )
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f112]) ).
fof(f114,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(f115,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,[],[f114]) ).
fof(f133,plain,
! [X0] :
( sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f157,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(f158,plain,
! [X0] :
( ! [X1] :
( X1 = szmzizndt0(X0)
<=> ( aElementOf0(X1,X0)
& ! [X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0) ) ) )
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(flattening,[],[f157]) ).
fof(f172,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(f173,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,[],[f172]) ).
fof(f199,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(f200,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,[],[f199]) ).
fof(f201,plain,
! [X0] :
( ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f202,plain,
! [X0,X1] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f203,plain,
! [X0,X1] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f202]) ).
fof(f206,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(f207,definition,
! [X1,X0] :
( ! [X2] :
( X2 = sdtpldt0(X0,X1)
<=> sP0(X2,X0,X1) )
| ~ sP1(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f208,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(definition_folding,[],[f113,f207,f206]) ).
fof(f209,definition,
! [X2,X0,X1] :
( sP2(X2,X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElement0(X3)
& aElementOf0(X3,X0)
& X3 != X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f210,definition,
! [X1,X0] :
( ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> sP2(X2,X0,X1) )
| ~ sP3(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f211,plain,
! [X0,X1] :
( sP3(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(definition_folding,[],[f115,f210,f209]) ).
fof(f212,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f99]) ).
fof(f213,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X1] : ~ aElementOf0(X1,X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f212]) ).
fof(f214,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| ? [X1] : aElementOf0(X1,X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f213]) ).
fof(f215,plain,
! [X0] :
( ( X0 = slcrc0
| ~ aSet0(X0)
| aElementOf0(sK4(X0),X0) )
& ( ( aSet0(X0)
& ! [X2] : ~ aElementOf0(X2,X0) )
| slcrc0 != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f214]) ).
fof(f216,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,[],[f104]) ).
fof(f217,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,[],[f216]) ).
fof(f218,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,[],[f217]) ).
fof(f219,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK5(X0,X1),X0)
& aElementOf0(sK5(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f218]) ).
fof(f220,plain,
! [X1,X0] :
( ! [X2] :
( ( X2 = sdtpldt0(X0,X1)
| ~ sP0(X2,X0,X1) )
& ( sP0(X2,X0,X1)
| sdtpldt0(X0,X1) != X2 ) )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f207]) ).
fof(f221,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt0(X1,X0) = X2
| ~ sP0(X2,X1,X0) )
& ( sP0(X2,X1,X0)
| sdtpldt0(X1,X0) != X2 ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f220]) ).
fof(f222,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,[],[f206]) ).
fof(f223,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,[],[f222]) ).
fof(f224,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,[],[f223]) ).
fof(f225,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ~ aSet0(X0)
| ( ( ~ aElement0(sK6(X0,X1,X2))
| ( ~ aElementOf0(sK6(X0,X1,X2),X1)
& sK6(X0,X1,X2) != X2 )
| ~ aElementOf0(sK6(X0,X1,X2),X0) )
& ( ( aElement0(sK6(X0,X1,X2))
& ( aElementOf0(sK6(X0,X1,X2),X1)
| sK6(X0,X1,X2) = X2 ) )
| aElementOf0(sK6(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,[sK6]),skolemize(X3,sK6(X0,X1,X2))],[f224]) ).
fof(f226,plain,
! [X1,X0] :
( ! [X2] :
( ( X2 = sdtmndt0(X0,X1)
| ~ sP2(X2,X0,X1) )
& ( sP2(X2,X0,X1)
| sdtmndt0(X0,X1) != X2 ) )
| ~ sP3(X1,X0) ),
inference(nnf_transformation,[],[f210]) ).
fof(f227,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| ~ sP2(X2,X1,X0) )
& ( sP2(X2,X1,X0)
| sdtmndt0(X1,X0) != X2 ) )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f226]) ).
fof(f228,plain,
! [X2,X0,X1] :
( ( sP2(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) ) ) )
| ~ sP2(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f209]) ).
fof(f229,plain,
! [X2,X0,X1] :
( ( sP2(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) ) ) )
| ~ sP2(X2,X0,X1) ) ),
inference(flattening,[],[f228]) ).
fof(f230,plain,
! [X0,X1,X2] :
( ( sP2(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) ) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f229]) ).
fof(f231,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ~ aSet0(X0)
| ( ( ~ aElement0(sK7(X0,X1,X2))
| ~ aElementOf0(sK7(X0,X1,X2),X1)
| sK7(X0,X1,X2) = X2
| ~ aElementOf0(sK7(X0,X1,X2),X0) )
& ( ( aElement0(sK7(X0,X1,X2))
& aElementOf0(sK7(X0,X1,X2),X1)
& sK7(X0,X1,X2) != X2 )
| aElementOf0(sK7(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) ) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f230]) ).
fof(f237,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,[],[f158]) ).
fof(f238,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,[],[f237]) ).
fof(f239,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,[],[f238]) ).
fof(f240,plain,
! [X0] :
( ! [X1] :
( ( X1 = szmzizndt0(X0)
| ~ aElementOf0(X1,X0)
| ( ~ sdtlseqdt0(X1,sK10(X0,X1))
& aElementOf0(sK10(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,[sK10]),skolemize(X2,sK10(X0,X1))],[f239]) ).
fof(f253,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,[],[f173]) ).
fof(f254,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,[],[f253]) ).
fof(f255,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,[],[f254]) ).
fof(f256,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ( ( ~ aSubsetOf0(sK14(X0,X1,X2),X0)
| sbrdtbr0(sK14(X0,X1,X2)) != X1
| ~ aElementOf0(sK14(X0,X1,X2),X2) )
& ( ( aSubsetOf0(sK14(X0,X1,X2),X0)
& sbrdtbr0(sK14(X0,X1,X2)) = X1 )
| aElementOf0(sK14(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,[sK14]),skolemize(X3,sK14(X0,X1,X2))],[f255]) ).
fof(f272,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f274,plain,
! [X0] :
( aSet0(X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f215]) ).
fof(f278,plain,
! [X0] :
( slcrc0 != X0
| ~ aSet0(X0)
| ~ isCountable0(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f279,plain,
! [X3,X0,X1] :
( ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f219]) ).
fof(f280,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f219]) ).
fof(f281,plain,
! [X0,X1] :
( aElementOf0(sK5(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f219]) ).
fof(f282,plain,
! [X0,X1] :
( ~ aElementOf0(sK5(X0,X1),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f219]) ).
fof(f286,plain,
! [X2,X0,X1] :
( ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X0,X1)
| aSubsetOf0(X0,X2)
| ~ aSet0(X0)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(cnf_transformation,[],[f111]) ).
fof(f287,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| sdtpldt0(X1,X0) != X2
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f221]) ).
fof(f289,plain,
! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| X2 = X4
| ~ aElementOf0(X4,X0)
| aElementOf0(X4,X1) ),
inference(cnf_transformation,[],[f225]) ).
fof(f293,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| aSet0(X0) ),
inference(cnf_transformation,[],[f225]) ).
fof(f298,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f208]) ).
fof(f299,plain,
! [X2,X0,X1] :
( sP2(X2,X1,X0)
| sdtmndt0(X1,X0) != X2
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f227]) ).
fof(f302,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ aElementOf0(X4,X0)
| aElementOf0(X4,X1) ),
inference(cnf_transformation,[],[f231]) ).
fof(f305,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| aSet0(X0) ),
inference(cnf_transformation,[],[f231]) ).
fof(f310,plain,
! [X0,X1] :
( sP3(X1,X0)
| ~ aSet0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f211]) ).
fof(f318,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f319,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f24]) ).
fof(f326,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(sz00,X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f347,plain,
! [X0,X1] :
( aElementOf0(X1,X0)
| szmzizndt0(X0) != X1
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(cnf_transformation,[],[f240]) ).
fof(f373,plain,
! [X2,X0,X1,X4] :
( aSubsetOf0(X4,X0)
| ~ aElementOf0(X4,X2)
| slbdtsldtrb0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f256]) ).
fof(f419,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f75]) ).
fof(f430,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f80]) ).
fof(f433,plain,
xS = sdtlpdtrp0(xN,sz00),
inference(cnf_transformation,[],[f200]) ).
fof(f436,plain,
! [X0] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f201]) ).
fof(f437,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f201]) ).
fof(f438,plain,
! [X0,X1] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(X1,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f203]) ).
fof(f440,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f85]) ).
fof(f441,plain,
aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)),
inference(cnf_transformation,[],[f86]) ).
fof(f443,plain,
~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS),
inference(cnf_transformation,[],[f97]) ).
fof(f444,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f274]) ).
fof(f446,plain,
( ~ aSet0(slcrc0)
| ~ isCountable0(slcrc0) ),
inference(equality_resolution,[],[f278]) ).
fof(f447,plain,
! [X0,X1] :
( sP0(sdtpldt0(X1,X0),X1,X0)
| ~ sP1(X0,X1) ),
inference(equality_resolution,[],[f287]) ).
fof(f449,plain,
! [X0,X1] :
( sP2(sdtmndt0(X1,X0),X1,X0)
| ~ sP3(X0,X1) ),
inference(equality_resolution,[],[f299]) ).
fof(f452,plain,
! [X0] :
( aElementOf0(szmzizndt0(X0),X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| slcrc0 = X0 ),
inference(equality_resolution,[],[f347]) ).
fof(f464,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| aSubsetOf0(X4,X0)
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(equality_resolution,[],[f373]) ).
fof(f481,definition,
sF25 = sdtlpdtrp0(xN,xi),
introduced(definition,[new_symbols(definition,[sF25])],[function_definition]) ).
fof(f482,plain,
sdtlpdtrp0(xN,xi) = sF25,
inference(reorient_equations,[],[f481]) ).
fof(f483,definition,
sF26 = szmzizndt0(sF25),
introduced(definition,[new_symbols(definition,[sF26])],[function_definition]) ).
fof(f484,plain,
szmzizndt0(sF25) = sF26,
inference(reorient_equations,[],[f483]) ).
fof(f485,definition,
sF27 = sdtpldt0(xQ,sF26),
introduced(definition,[new_symbols(definition,[sF27])],[function_definition]) ).
fof(f486,plain,
sdtpldt0(xQ,sF26) = sF27,
inference(reorient_equations,[],[f485]) ).
fof(f487,plain,
~ aSubsetOf0(sF27,xS),
inference(definition_folding,[],[f443,f486,f484,f482]) ).
fof(f492,definition,
( spl28_1
<=> aSet0(slcrc0) ),
introduced(definition,[new_symbols(definition,[spl28_1])],[avatar_definition]) ).
fof(f501,definition,
( spl28_3
<=> isCountable0(slcrc0) ),
introduced(definition,[new_symbols(definition,[spl28_3])],[avatar_definition]) ).
fof(f503,plain,
( ~ isCountable0(slcrc0)
| spl28_3 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f504,plain,
( ~ spl28_3
| ~ spl28_1 ),
inference(avatar_split_clause,[],[f446,f492,f501]) ).
fof(f505,plain,
spl28_1,
inference(avatar_split_clause,[],[f444,f492]) ).
fof(f511,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),xS)
| ~ sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(superposition,[],[f438,f433]) ).
fof(f512,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),xS)
| ~ sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f511,f319]) ).
fof(f516,plain,
! [X0] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),xS)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f512,f326]) ).
fof(f517,plain,
( aSubsetOf0(sF25,xS)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(superposition,[],[f516,f482]) ).
fof(f520,plain,
aSubsetOf0(sF25,xS),
inference(forward_subsumption_resolution,[],[f517,f440]) ).
fof(f523,plain,
( aSubsetOf0(sF25,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(superposition,[],[f437,f482]) ).
fof(f525,plain,
aSubsetOf0(sF25,szNzAzT0),
inference(forward_subsumption_resolution,[],[f523,f440]) ).
fof(f526,plain,
( aElementOf0(sF26,sF25)
| ~ aSubsetOf0(sF25,szNzAzT0)
| slcrc0 = sF25 ),
inference(superposition,[],[f452,f484]) ).
fof(f527,plain,
( aElementOf0(sF26,sF25)
| slcrc0 = sF25 ),
inference(forward_subsumption_resolution,[],[f526,f525]) ).
fof(f529,definition,
( spl28_4
<=> slcrc0 = sF25 ),
introduced(definition,[new_symbols(definition,[spl28_4])],[avatar_definition]) ).
fof(f531,plain,
( slcrc0 = sF25
| ~ spl28_4 ),
inference(avatar_component_clause,[],[f529]) ).
fof(f533,definition,
( spl28_5
<=> aElementOf0(sF26,sF25) ),
introduced(definition,[new_symbols(definition,[spl28_5])],[avatar_definition]) ).
fof(f535,plain,
( aElementOf0(sF26,sF25)
| ~ spl28_5 ),
inference(avatar_component_clause,[],[f533]) ).
fof(f536,plain,
( spl28_4
| spl28_5 ),
inference(avatar_split_clause,[],[f527,f533,f529]) ).
fof(f538,plain,
( aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(xk,szNzAzT0) ),
inference(resolution,[],[f464,f441]) ).
fof(f539,plain,
( aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(forward_subsumption_resolution,[],[f538,f430]) ).
fof(f540,plain,
( aSubsetOf0(xQ,sdtmndt0(sF25,szmzizndt0(sF25)))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(forward_demodulation,[],[f539,f482]) ).
fof(f541,plain,
( aSubsetOf0(xQ,sdtmndt0(sF25,sF26))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(forward_demodulation,[],[f540,f484]) ).
fof(f542,plain,
( ~ aSet0(sdtmndt0(sF25,szmzizndt0(sF25)))
| aSubsetOf0(xQ,sdtmndt0(sF25,sF26)) ),
inference(forward_demodulation,[],[f541,f482]) ).
fof(f543,plain,
( ~ aSet0(sdtmndt0(sF25,sF26))
| aSubsetOf0(xQ,sdtmndt0(sF25,sF26)) ),
inference(forward_demodulation,[],[f542,f484]) ).
fof(f545,definition,
( spl28_6
<=> aSubsetOf0(xQ,sdtmndt0(sF25,sF26)) ),
introduced(definition,[new_symbols(definition,[spl28_6])],[avatar_definition]) ).
fof(f547,plain,
( aSubsetOf0(xQ,sdtmndt0(sF25,sF26))
| ~ spl28_6 ),
inference(avatar_component_clause,[],[f545]) ).
fof(f549,definition,
( spl28_7
<=> aSet0(sdtmndt0(sF25,sF26)) ),
introduced(definition,[new_symbols(definition,[spl28_7])],[avatar_definition]) ).
fof(f550,plain,
( aSet0(sdtmndt0(sF25,sF26))
| ~ spl28_7 ),
inference(avatar_component_clause,[],[f549]) ).
fof(f551,plain,
( ~ aSet0(sdtmndt0(sF25,sF26))
| spl28_7 ),
inference(avatar_component_clause,[],[f549]) ).
fof(f552,plain,
( spl28_6
| ~ spl28_7 ),
inference(avatar_split_clause,[],[f543,f549,f545]) ).
fof(f557,definition,
( spl28_8
<=> sP1(sF26,xQ) ),
introduced(definition,[new_symbols(definition,[spl28_8])],[avatar_definition]) ).
fof(f558,plain,
( sP1(sF26,xQ)
| ~ spl28_8 ),
inference(avatar_component_clause,[],[f557]) ).
fof(f559,plain,
( ~ sP1(sF26,xQ)
| spl28_8 ),
inference(avatar_component_clause,[],[f557]) ).
fof(f568,plain,
( isCountable0(sF25)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(superposition,[],[f436,f482]) ).
fof(f570,plain,
isCountable0(sF25),
inference(forward_subsumption_resolution,[],[f568,f440]) ).
fof(f576,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f280,f419]) ).
fof(f578,plain,
( aSet0(sF25)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f280,f525]) ).
fof(f579,plain,
aSet0(sF25),
inference(forward_subsumption_resolution,[],[f578,f318]) ).
fof(f581,definition,
( spl28_10
<=> aSet0(xS) ),
introduced(definition,[new_symbols(definition,[spl28_10])],[avatar_definition]) ).
fof(f582,plain,
( aSet0(xS)
| ~ spl28_10 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f585,definition,
( spl28_11
<=> aSet0(sF25) ),
introduced(definition,[new_symbols(definition,[spl28_11])],[avatar_definition]) ).
fof(f587,plain,
( aSet0(sF25)
| ~ spl28_11 ),
inference(avatar_component_clause,[],[f585]) ).
fof(f589,plain,
aSet0(xS),
inference(forward_subsumption_resolution,[],[f576,f318]) ).
fof(f595,plain,
spl28_11,
inference(avatar_split_clause,[],[f579,f585]) ).
fof(f596,plain,
spl28_10,
inference(avatar_split_clause,[],[f589,f581]) ).
fof(f700,definition,
( spl28_17
<=> aElement0(sF26) ),
introduced(definition,[new_symbols(definition,[spl28_17])],[avatar_definition]) ).
fof(f701,plain,
( aElement0(sF26)
| ~ spl28_17 ),
inference(avatar_component_clause,[],[f700]) ).
fof(f702,plain,
( ~ aElement0(sF26)
| spl28_17 ),
inference(avatar_component_clause,[],[f700]) ).
fof(f708,definition,
( spl28_19
<=> aSet0(xQ) ),
introduced(definition,[new_symbols(definition,[spl28_19])],[avatar_definition]) ).
fof(f709,plain,
( aSet0(xQ)
| ~ spl28_19 ),
inference(avatar_component_clause,[],[f708]) ).
fof(f710,plain,
( ~ aSet0(xQ)
| spl28_19 ),
inference(avatar_component_clause,[],[f708]) ).
fof(f727,plain,
! [X0,X1] :
( aSet0(sdtmndt0(X0,X1))
| ~ sP3(X1,X0) ),
inference(resolution,[],[f305,f449]) ).
fof(f728,plain,
( ~ sP3(sF26,sF25)
| spl28_7 ),
inference(resolution,[],[f727,f551]) ).
fof(f735,plain,
! [X0] :
( ~ aSubsetOf0(X0,sF25)
| aSubsetOf0(X0,xS)
| ~ aSet0(X0)
| ~ aSet0(sF25)
| ~ aSet0(xS) ),
inference(resolution,[],[f286,f520]) ).
fof(f740,plain,
! [X0] :
( ~ aSubsetOf0(X0,sF25)
| aSubsetOf0(X0,xS)
| ~ aSet0(sF25)
| ~ aSet0(xS) ),
inference(forward_subsumption_resolution,[],[f735,f280]) ).
fof(f746,plain,
( ! [X0] :
( ~ aSubsetOf0(X0,sF25)
| aSubsetOf0(X0,xS)
| ~ aSet0(xS) )
| ~ spl28_11 ),
inference(forward_subsumption_resolution,[],[f740,f587]) ).
fof(f752,plain,
( ! [X0] :
( ~ aSubsetOf0(X0,sF25)
| aSubsetOf0(X0,xS) )
| ~ spl28_10
| ~ spl28_11 ),
inference(forward_subsumption_resolution,[],[f746,f582]) ).
fof(f984,plain,
( ~ aSet0(sF25)
| ~ aElement0(sF26)
| spl28_7 ),
inference(resolution,[],[f310,f728]) ).
fof(f1004,plain,
! [X0,X1] :
( aSet0(sdtpldt0(X0,X1))
| ~ sP1(X1,X0) ),
inference(resolution,[],[f293,f447]) ).
fof(f1005,plain,
( aSet0(sF27)
| ~ sP1(sF26,xQ) ),
inference(superposition,[],[f1004,f486]) ).
fof(f1036,plain,
( isCountable0(slcrc0)
| ~ spl28_4 ),
inference(superposition,[],[f570,f531]) ).
fof(f1044,plain,
( $false
| spl28_3
| ~ spl28_4 ),
inference(forward_subsumption_resolution,[],[f1036,f503]) ).
fof(f1045,plain,
( spl28_3
| ~ spl28_4 ),
inference(avatar_contradiction_clause,[],[f1044]) ).
fof(f1102,plain,
( ~ aSet0(xQ)
| ~ aElement0(sF26)
| spl28_8 ),
inference(resolution,[],[f298,f559]) ).
fof(f1245,plain,
( aElement0(sF26)
| ~ aSet0(sF25)
| ~ spl28_5 ),
inference(resolution,[],[f272,f535]) ).
fof(f1251,plain,
( ~ aSet0(sF25)
| ~ spl28_5
| spl28_17 ),
inference(forward_subsumption_resolution,[],[f1245,f702]) ).
fof(f1266,plain,
( $false
| ~ spl28_5
| ~ spl28_11
| spl28_17 ),
inference(forward_subsumption_resolution,[],[f1251,f587]) ).
fof(f1267,plain,
( ~ spl28_5
| ~ spl28_11
| spl28_17 ),
inference(avatar_contradiction_clause,[],[f1266]) ).
fof(f1291,plain,
( ~ aElement0(sF26)
| spl28_7
| ~ spl28_11 ),
inference(forward_subsumption_resolution,[],[f984,f587]) ).
fof(f1309,plain,
( $false
| spl28_7
| ~ spl28_11
| ~ spl28_17 ),
inference(forward_subsumption_resolution,[],[f1291,f701]) ).
fof(f1310,plain,
( spl28_7
| ~ spl28_11
| ~ spl28_17 ),
inference(avatar_contradiction_clause,[],[f1309]) ).
fof(f1364,plain,
( ! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,sdtmndt0(sF25,sF26))
| ~ aSet0(sdtmndt0(sF25,sF26)) )
| ~ spl28_6 ),
inference(resolution,[],[f547,f279]) ).
fof(f1365,plain,
( aSet0(xQ)
| ~ aSet0(sdtmndt0(sF25,sF26))
| ~ spl28_6 ),
inference(resolution,[],[f547,f280]) ).
fof(f1366,plain,
( ~ aSet0(sdtmndt0(sF25,sF26))
| ~ spl28_6
| spl28_19 ),
inference(forward_subsumption_resolution,[],[f1365,f710]) ).
fof(f1367,plain,
( ! [X0] :
( aElementOf0(X0,sdtmndt0(sF25,sF26))
| ~ aElementOf0(X0,xQ) )
| ~ spl28_6
| ~ spl28_7 ),
inference(forward_subsumption_resolution,[],[f1364,f550]) ).
fof(f1368,plain,
( $false
| ~ spl28_6
| ~ spl28_7
| spl28_19 ),
inference(forward_subsumption_resolution,[],[f1366,f550]) ).
fof(f1369,plain,
( ~ spl28_6
| ~ spl28_7
| spl28_19 ),
inference(avatar_contradiction_clause,[],[f1368]) ).
fof(f1370,plain,
( ~ aElement0(sF26)
| spl28_8
| ~ spl28_19 ),
inference(forward_subsumption_resolution,[],[f1102,f709]) ).
fof(f1373,plain,
( $false
| spl28_8
| ~ spl28_17
| ~ spl28_19 ),
inference(forward_subsumption_resolution,[],[f1370,f701]) ).
fof(f1374,plain,
( spl28_8
| ~ spl28_17
| ~ spl28_19 ),
inference(avatar_contradiction_clause,[],[f1373]) ).
fof(f1379,plain,
( aSet0(sF27)
| ~ spl28_8 ),
inference(forward_subsumption_resolution,[],[f1005,f558]) ).
fof(f1402,definition,
( spl28_55
<=> sP3(sF26,sF25) ),
introduced(definition,[new_symbols(definition,[spl28_55])],[avatar_definition]) ).
fof(f1404,plain,
( ~ sP3(sF26,sF25)
| spl28_55 ),
inference(avatar_component_clause,[],[f1402]) ).
fof(f2124,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X0,sdtmndt0(X1,X2))
| aElementOf0(X0,X1)
| ~ sP3(X2,X1) ),
inference(resolution,[],[f302,f449]) ).
fof(f2125,plain,
( ! [X0] :
( aElementOf0(X0,sF25)
| ~ sP3(sF26,sF25)
| ~ aElementOf0(X0,xQ) )
| ~ spl28_6
| ~ spl28_7 ),
inference(resolution,[],[f2124,f1367]) ).
fof(f2131,definition,
( spl28_104
<=> ! [X0] :
( aElementOf0(X0,sF25)
| ~ aElementOf0(X0,xQ) ) ),
introduced(definition,[new_symbols(definition,[spl28_104])],[avatar_definition]) ).
fof(f2132,plain,
( ! [X0] :
( ~ aElementOf0(X0,xQ)
| aElementOf0(X0,sF25) )
| ~ spl28_104 ),
inference(avatar_component_clause,[],[f2131]) ).
fof(f2307,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X1,sdtpldt0(X2,X0))
| X0 = X1
| aElementOf0(X1,X2)
| ~ sP1(X0,X2) ),
inference(resolution,[],[f289,f447]) ).
fof(f2312,plain,
! [X2,X0,X1] :
( sK5(X1,sdtpldt0(X2,X0)) = X0
| aElementOf0(sK5(X1,sdtpldt0(X2,X0)),X2)
| ~ sP1(X0,X2)
| ~ aSet0(sdtpldt0(X2,X0))
| aSubsetOf0(sdtpldt0(X2,X0),X1)
| ~ aSet0(X1) ),
inference(resolution,[],[f2307,f281]) ).
fof(f2324,plain,
! [X2,X0,X1] :
( aElementOf0(sK5(X1,sdtpldt0(X2,X0)),X2)
| sK5(X1,sdtpldt0(X2,X0)) = X0
| ~ sP1(X0,X2)
| aSubsetOf0(sdtpldt0(X2,X0),X1)
| ~ aSet0(X1) ),
inference(forward_subsumption_resolution,[],[f2312,f1004]) ).
fof(f2352,plain,
! [X0] :
( aElementOf0(sK5(X0,sF27),xQ)
| sF26 = sK5(X0,sF27)
| ~ sP1(sF26,xQ)
| aSubsetOf0(sF27,X0)
| ~ aSet0(X0) ),
inference(superposition,[],[f2324,f486]) ).
fof(f2363,plain,
( ! [X0] :
( aElementOf0(sK5(X0,sF27),xQ)
| sF26 = sK5(X0,sF27)
| aSubsetOf0(sF27,X0)
| ~ aSet0(X0) )
| ~ spl28_8 ),
inference(forward_subsumption_resolution,[],[f2352,f558]) ).
fof(f2463,plain,
( ~ spl28_55
| spl28_104
| ~ spl28_6
| ~ spl28_7 ),
inference(avatar_split_clause,[],[f2125,f549,f545,f2131,f1402]) ).
fof(f2650,plain,
( ~ aSet0(sF25)
| ~ aElement0(sF26)
| spl28_55 ),
inference(resolution,[],[f1404,f310]) ).
fof(f2652,plain,
( ~ aElement0(sF26)
| ~ spl28_11
| spl28_55 ),
inference(forward_subsumption_resolution,[],[f2650,f587]) ).
fof(f2653,plain,
( $false
| ~ spl28_11
| ~ spl28_17
| spl28_55 ),
inference(forward_subsumption_resolution,[],[f2652,f701]) ).
fof(f2654,plain,
( ~ spl28_11
| ~ spl28_17
| spl28_55 ),
inference(avatar_contradiction_clause,[],[f2653]) ).
fof(f2660,plain,
( ! [X0] :
( aElementOf0(sK5(X0,sF27),sF25)
| sF26 = sK5(X0,sF27)
| aSubsetOf0(sF27,X0)
| ~ aSet0(X0) )
| ~ spl28_8
| ~ spl28_104 ),
inference(resolution,[],[f2132,f2363]) ).
fof(f2874,definition,
( spl28_151
<=> aSubsetOf0(sF27,sF25) ),
introduced(definition,[new_symbols(definition,[spl28_151])],[avatar_definition]) ).
fof(f2875,plain,
( ~ aSubsetOf0(sF27,sF25)
| spl28_151 ),
inference(avatar_component_clause,[],[f2874]) ).
fof(f2876,plain,
( aSubsetOf0(sF27,sF25)
| ~ spl28_151 ),
inference(avatar_component_clause,[],[f2874]) ).
fof(f2947,plain,
( sF26 = sK5(sF25,sF27)
| aSubsetOf0(sF27,sF25)
| ~ aSet0(sF25)
| ~ aSet0(sF27)
| aSubsetOf0(sF27,sF25)
| ~ aSet0(sF25)
| ~ spl28_8
| ~ spl28_104 ),
inference(resolution,[],[f2660,f282]) ).
fof(f2952,plain,
( sF26 = sK5(sF25,sF27)
| aSubsetOf0(sF27,sF25)
| ~ aSet0(sF25)
| ~ aSet0(sF27)
| ~ spl28_8
| ~ spl28_104 ),
inference(duplicate_literal_removal,[],[f2947]) ).
fof(f2954,plain,
( sF26 = sK5(sF25,sF27)
| aSubsetOf0(sF27,sF25)
| ~ aSet0(sF27)
| ~ spl28_8
| ~ spl28_11
| ~ spl28_104 ),
inference(forward_subsumption_resolution,[],[f2952,f587]) ).
fof(f2955,plain,
( sF26 = sK5(sF25,sF27)
| aSubsetOf0(sF27,sF25)
| ~ spl28_8
| ~ spl28_11
| ~ spl28_104 ),
inference(forward_subsumption_resolution,[],[f2954,f1379]) ).
fof(f2957,definition,
( spl28_163
<=> sF26 = sK5(sF25,sF27) ),
introduced(definition,[new_symbols(definition,[spl28_163])],[avatar_definition]) ).
fof(f2959,plain,
( sF26 = sK5(sF25,sF27)
| ~ spl28_163 ),
inference(avatar_component_clause,[],[f2957]) ).
fof(f2960,plain,
( spl28_151
| spl28_163
| ~ spl28_8
| ~ spl28_11
| ~ spl28_104 ),
inference(avatar_split_clause,[],[f2955,f2131,f585,f557,f2957,f2874]) ).
fof(f2961,plain,
( aSubsetOf0(sF27,xS)
| ~ spl28_10
| ~ spl28_11
| ~ spl28_151 ),
inference(resolution,[],[f2876,f752]) ).
fof(f2970,plain,
( $false
| ~ spl28_10
| ~ spl28_11
| ~ spl28_151 ),
inference(forward_subsumption_resolution,[],[f2961,f487]) ).
fof(f2971,plain,
( ~ spl28_10
| ~ spl28_11
| ~ spl28_151 ),
inference(avatar_contradiction_clause,[],[f2970]) ).
fof(f2976,plain,
( ~ aElementOf0(sF26,sF25)
| ~ aSet0(sF27)
| aSubsetOf0(sF27,sF25)
| ~ aSet0(sF25)
| ~ spl28_163 ),
inference(superposition,[],[f282,f2959]) ).
fof(f2978,plain,
( ~ aSet0(sF27)
| aSubsetOf0(sF27,sF25)
| ~ aSet0(sF25)
| ~ spl28_5
| ~ spl28_163 ),
inference(forward_subsumption_resolution,[],[f2976,f535]) ).
fof(f2979,plain,
( aSubsetOf0(sF27,sF25)
| ~ aSet0(sF25)
| ~ spl28_5
| ~ spl28_8
| ~ spl28_163 ),
inference(forward_subsumption_resolution,[],[f2978,f1379]) ).
fof(f2980,plain,
( ~ aSet0(sF25)
| ~ spl28_5
| ~ spl28_8
| spl28_151
| ~ spl28_163 ),
inference(forward_subsumption_resolution,[],[f2979,f2875]) ).
fof(f2981,plain,
( $false
| ~ spl28_5
| ~ spl28_8
| ~ spl28_11
| spl28_151
| ~ spl28_163 ),
inference(forward_subsumption_resolution,[],[f2980,f587]) ).
fof(f2982,plain,
( ~ spl28_5
| ~ spl28_8
| ~ spl28_11
| spl28_151
| ~ spl28_163 ),
inference(avatar_contradiction_clause,[],[f2981]) ).
cnf(s2,plain,
( ~ spl28_1
| ~ spl28_3 ),
inference(sat_conversion,[],[f504]) ).
cnf(s3,plain,
spl28_1,
inference(sat_conversion,[],[f505]) ).
cnf(s4,plain,
( spl28_4
| spl28_5 ),
inference(sat_conversion,[],[f536]) ).
cnf(s5,plain,
( spl28_6
| ~ spl28_7 ),
inference(sat_conversion,[],[f552]) ).
cnf(s9,plain,
spl28_11,
inference(sat_conversion,[],[f595]) ).
cnf(s10,plain,
spl28_10,
inference(sat_conversion,[],[f596]) ).
cnf(s27,plain,
( spl28_3
| ~ spl28_4 ),
inference(sat_conversion,[],[f1045]) ).
cnf(s39,plain,
( ~ spl28_5
| ~ spl28_11
| spl28_17 ),
inference(sat_conversion,[],[f1267]) ).
cnf(s48,plain,
( spl28_7
| ~ spl28_11
| ~ spl28_17 ),
inference(sat_conversion,[],[f1310]) ).
cnf(s50,plain,
( ~ spl28_6
| ~ spl28_7
| spl28_19 ),
inference(sat_conversion,[],[f1369]) ).
cnf(s51,plain,
( spl28_8
| ~ spl28_17
| ~ spl28_19 ),
inference(sat_conversion,[],[f1374]) ).
cnf(s105,plain,
( ~ spl28_6
| ~ spl28_7
| ~ spl28_55
| spl28_104 ),
inference(sat_conversion,[],[f2463]) ).
cnf(s123,plain,
( ~ spl28_11
| ~ spl28_17
| spl28_55 ),
inference(sat_conversion,[],[f2654]) ).
cnf(s152,plain,
( ~ spl28_8
| ~ spl28_11
| ~ spl28_104
| spl28_151
| spl28_163 ),
inference(sat_conversion,[],[f2960]) ).
cnf(s153,plain,
( ~ spl28_10
| ~ spl28_11
| ~ spl28_151 ),
inference(sat_conversion,[],[f2971]) ).
cnf(s155,plain,
( ~ spl28_5
| ~ spl28_8
| ~ spl28_11
| spl28_151
| ~ spl28_163 ),
inference(sat_conversion,[],[f2982]) ).
cnf(s160,plain,
~ spl28_151,
inference(rat,[],[s153,s10,s9]) ).
cnf(s161,plain,
~ spl28_3,
inference(rat,[],[s2,s3]) ).
cnf(s163,plain,
~ spl28_4,
inference(rat,[],[s27,s161]) ).
cnf(s167,plain,
spl28_5,
inference(rat,[],[s4,s163]) ).
cnf(s169,plain,
spl28_17,
inference(rat,[],[s39,s9,s167]) ).
cnf(s170,plain,
spl28_55,
inference(rat,[],[s123,s9,s169]) ).
cnf(s171,plain,
spl28_7,
inference(rat,[],[s48,s9,s169]) ).
cnf(s172,plain,
spl28_6,
inference(rat,[],[s5,s171]) ).
cnf(s173,plain,
spl28_104,
inference(rat,[],[s105,s171,s170,s172]) ).
cnf(s175,plain,
spl28_19,
inference(rat,[],[s50,s171,s172]) ).
cnf(s176,plain,
spl28_8,
inference(rat,[],[s51,s169,s175]) ).
cnf(s177,plain,
~ spl28_163,
inference(rat,[],[s155,s167,s160,s9,s176]) ).
cnf(s178,plain,
$false,
inference(rat,[],[s152,s173,s160,s9,s177,s176]) ).
fof(f2983,plain,
$false,
inference(avatar_sat_refutation,[],[s178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM581+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n002.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 20:38:37 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.30/2.18 % (3857751)Detected formulas, will run a generic FOF schedule.
% 9.30/2.18 % (3857760)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3700949253:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.30/2.18 % (3857758)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=2884193312:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.30/2.18 % (3857757)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=2620612774:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.30/2.18 % (3857756)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=1023856078:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.30/2.18 % (3857759)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3421609231:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.30/2.18 % (3857760)Instruction limit reached!
% 9.30/2.18 % (3857760)------------------------------
% 9.30/2.18 % (3857760)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.30/2.18 % (3857760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.30/2.18 % (3857760)CaDiCaL version: 2.1.3
% 9.30/2.18 % (3857760)Termination reason: Instruction limit
% 9.30/2.18 % (3857760)Termination phase: Saturation
% 9.30/2.18 % (3857760)Time elapsed: 0.031 s
% 9.30/2.18 % (3857760)Peak memory usage: 88 MB
% 9.30/2.18 % (3857760)Instructions burned: 120 (million)
% 9.30/2.18 % (3857762)dis-21_1_sil=8000:lcm=predicate:random_seed=2309540280: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)
% 9.30/2.18 % (3857761)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3869134332:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.30/2.18 % (3857759)Instruction limit reached!
% 9.30/2.18 % (3857759)------------------------------
% 9.30/2.18 % (3857759)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.30/2.18 % (3857759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.30/2.18 % (3857759)CaDiCaL version: 2.1.3
% 9.30/2.18 % (3857759)Termination reason: Instruction limit
% 9.30/2.18 % (3857759)Termination phase: Saturation
% 9.30/2.18 % (3857759)Time elapsed: 0.071 s
% 9.30/2.18 % (3857759)Peak memory usage: 89 MB
% 9.30/2.18 % (3857759)Instructions burned: 109 (million)
% 9.30/2.18 % (3857762)Instruction limit reached!
% 9.30/2.18 % (3857762)------------------------------
% 9.30/2.18 % (3857762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.30/2.18 % (3857762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.30/2.18 % (3857762)CaDiCaL version: 2.1.3
% 9.30/2.18 % (3857762)Termination reason: Instruction limit
% 9.30/2.18 % (3857762)Termination phase: Saturation
% 9.30/2.18 % (3857762)Time elapsed: 0.063 s
% 9.30/2.18 % (3857762)Peak memory usage: 88 MB
% 9.30/2.18 % (3857762)Instructions burned: 131 (million)
% 9.30/2.18 % (3857761)Instruction limit reached!
% 9.30/2.18 % (3857761)------------------------------
% 9.30/2.18 % (3857761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.30/2.18 % (3857761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.30/2.18 % (3857761)CaDiCaL version: 2.1.3
% 9.30/2.18 % (3857761)Termination reason: Instruction limit
% 9.30/2.18 % (3857761)Termination phase: Saturation
% 9.30/2.18 % (3857761)Time elapsed: 0.101 s
% 9.30/2.18 % (3857761)Peak memory usage: 90 MB
% 9.30/2.18 % (3857761)Instructions burned: 139 (million)
% 9.30/2.18 % (3857768)lrs+10_1_sil=8000:sp=occurrence:random_seed=1271192190:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 9.30/2.18 % (3857771)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2132861151:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 9.30/2.18 % (3857772)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3761005157:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 9.30/2.18 % (3857771)Refutation not found, incomplete strategy
% 9.30/2.18 % (3857771)------------------------------
% 9.30/2.18 % (3857771)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.30/2.18 % (3857771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.30/2.18 % (3857771)CaDiCaL version: 2.1.3
% 9.30/2.18 % (3857771)Termination reason: Refutation not found, incomplete strategy
% 9.30/2.18 % (3857771)Time elapsed: 0.005 s
% 9.30/2.18 % (3857771)Peak memory usage: 89 MB
% 9.30/2.18 % (3857771)Instructions burned: 6 (million)
% 9.30/2.18 % (3857768)Instruction limit reached!
% 9.30/2.18 % (3857768)------------------------------
% 9.30/2.18 % (3857768)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.30/2.18 % (3857768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.30/2.18 % (3857768)CaDiCaL version: 2.1.3
% 9.30/2.18 % (3857768)Termination reason: Instruction limit
% 9.30/2.18 % (3857768)Termination phase: Saturation
% 9.30/2.18 % (3857768)Time elapsed: 0.102 s
% 9.30/2.18 % (3857768)Peak memory usage: 92 MB
% 9.30/2.18 % (3857768)Instructions burned: 288 (million)
% 9.30/2.18 % (3857773)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=3814095635:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 9.30/2.18 % (3857777)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1543605444:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 9.30/2.18 % (3857772)Instruction limit reached!
% 9.30/2.18 % (3857772)------------------------------
% 9.30/2.18 % (3857772)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.30/2.18 % (3857772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.30/2.18 % (3857772)CaDiCaL version: 2.1.3
% 9.30/2.18 % (3857772)Termination reason: Instruction limit
% 9.30/2.18 % (3857772)Termination phase: Saturation
% 9.30/2.18 % (3857772)Time elapsed: 0.168 s
% 9.30/2.18 % (3857772)Peak memory usage: 90 MB
% 9.30/2.18 % (3857772)Instructions burned: 326 (million)
% 9.30/2.18 % (3857773)Instruction limit reached!
% 9.30/2.18 % (3857773)------------------------------
% 9.30/2.18 % (3857773)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.30/2.18 % (3857773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.30/2.18 % (3857773)CaDiCaL version: 2.1.3
% 9.30/2.18 % (3857773)Termination reason: Instruction limit
% 9.30/2.18 % (3857773)Termination phase: Saturation
% 9.30/2.18 % (3857773)Time elapsed: 0.146 s
% 9.30/2.18 % (3857773)Peak memory usage: 92 MB
% 9.30/2.18 % (3857773)Instructions burned: 249 (million)
% 9.30/2.18 % (3857771)------------------------------
% 9.30/2.18 % (3857771)------------------------------
% 9.30/2.18 % (3857777)Instruction limit reached!
% 9.30/2.18 % (3857777)------------------------------
% 9.30/2.18 % (3857777)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.30/2.18 % (3857777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.30/2.18 % (3857777)CaDiCaL version: 2.1.3
% 9.30/2.18 % (3857777)Termination reason: Instruction limit
% 9.30/2.18 % (3857777)Termination phase: Saturation
% 9.30/2.18 % (3857777)Time elapsed: 0.096 s
% 9.30/2.18 % (3857777)Peak memory usage: 90 MB
% 9.30/2.18 % (3857777)Instructions burned: 297 (million)
% 9.30/2.18 % (3857780)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3135410892:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 9.30/2.18 % (3857781)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3727568785:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 9.30/2.18 % (3857782)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=4069848819:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 9.30/2.18 % (3857782)Instruction limit reached!
% 9.30/2.18 % (3857782)------------------------------
% 9.30/2.18 % (3857782)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.30/2.18 % (3857782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.30/2.18 % (3857782)CaDiCaL version: 2.1.3
% 9.30/2.18 % (3857782)Termination reason: Instruction limit
% 9.30/2.18 % (3857782)Termination phase: Saturation
% 9.30/2.18 % (3857782)Time elapsed: 0.035 s
% 9.30/2.18 % (3857782)Peak memory usage: 89 MB
% 9.30/2.18 % (3857782)Instructions burned: 128 (million)
% 9.30/2.18 % (3857783)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2788454525:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 9.30/2.18 % (3857781)Instruction limit reached!
% 9.30/2.18 % (3857781)------------------------------
% 9.30/2.18 % (3857781)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.30/2.18 % (3857781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.30/2.18 % (3857781)CaDiCaL version: 2.1.3
% 9.30/2.18 % (3857781)Termination reason: Instruction limit
% 9.30/2.18 % (3857781)Termination phase: Saturation
% 9.30/2.18 % (3857781)Time elapsed: 0.075 s
% 9.30/2.18 % (3857781)Peak memory usage: 91 MB
% 9.30/2.18 % (3857781)Instructions burned: 113 (million)
% 9.30/2.18 % (3857783)Instruction limit reached!
% 9.30/2.18 % (3857783)------------------------------
% 9.30/2.18 % (3857783)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.30/2.18 % (3857783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.30/2.18 % (3857783)CaDiCaL version: 2.1.3
% 9.30/2.18 % (3857783)Termination reason: Instruction limit
% 9.30/2.18 % (3857783)Termination phase: Saturation
% 9.30/2.18 % (3857783)Time elapsed: 0.067 s
% 9.30/2.18 % (3857783)Peak memory usage: 89 MB
% 9.30/2.18 % (3857783)Instructions burned: 114 (million)
% 9.30/2.18 % (3857787)lrs+10_1_sil=8000:sp=occurrence:random_seed=541056861:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 9.30/2.18 % (3857789)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2294344355:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 9.30/2.18 % (3857790)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=394152265:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 9.30/2.18 % (3857756)First to succeed.
% 9.30/2.18 % (3857756)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3857751"
% 9.30/2.18 % (3857787)Instruction limit reached!
% 9.30/2.18 % (3857787)------------------------------
% 9.30/2.18 % (3857787)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.30/2.18 % (3857787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.30/2.18 % (3857787)CaDiCaL version: 2.1.3
% 9.30/2.18 % (3857787)Termination reason: Instruction limit
% 9.30/2.18 % (3857787)Termination phase: Saturation
% 9.30/2.18 % (3857787)Time elapsed: 0.302 s
% 9.30/2.18 % (3857787)Peak memory usage: 98 MB
% 9.30/2.18 % (3857787)Instructions burned: 907 (million)
% 9.30/2.18 % (3857789)Instruction limit reached!
% 9.30/2.18 % (3857789)------------------------------
% 9.30/2.18 % (3857789)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.30/2.18 % (3857789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.30/2.18 % (3857789)CaDiCaL version: 2.1.3
% 9.30/2.18 % (3857789)Termination reason: Instruction limit
% 9.30/2.18 % (3857789)Termination phase: Saturation
% 9.30/2.18 % (3857789)Time elapsed: 0.277 s
% 9.30/2.18 % (3857789)Peak memory usage: 92 MB
% 9.30/2.18 % (3857789)Instructions burned: 438 (million)
% 9.30/2.18 % (3857756)Refutation found. Thanks to Tanya!
% 9.30/2.18 % SZS status Theorem for theBenchmark
% 9.30/2.18 % SZS output start Proof for theBenchmark
% See solution above
% 9.71/2.28 % (3857756)------------------------------
% 9.71/2.28 % (3857756)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.71/2.28 % (3857756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.71/2.28 % (3857756)CaDiCaL version: 2.1.3
% 9.71/2.28 % (3857756)Termination reason: Refutation
% 9.71/2.28 % (3857756)Time elapsed: 0.880 s
% 9.71/2.28 % (3857756)Peak memory usage: 132 MB
% 9.71/2.28 % (3857756)Instructions burned: 1292 (million)
% 9.71/2.28 % (3857756)------------------------------
% 9.71/2.28 % (3857756)------------------------------
% 9.71/2.28 % (3857751)Success in time 1.311 s
% 9.71/2.28 % Vampire exiting
%------------------------------------------------------------------------------