TPTP Problem File: NUM595+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : NUM595+1 : TPTP v8.2.0. Released v4.0.0.
% Domain : Number Theory
% Problem : Ramsey's Infinite Theorem 15_02_14_04, 00 expansion
% Version : Especial.
% English :
% Refs : [VLP07] Verchinine et al. (2007), System for Automated Deduction
% : [Pas08] Paskevich (2008), Email to G. Sutcliffe
% Source : [Pas08]
% Names : ramsey_15_02_14_04.00 [Pas08]
% Status : Theorem
% Rating : 0.72 v8.2.0, 0.69 v8.1.0, 0.72 v7.5.0, 0.78 v7.4.0, 0.73 v7.3.0, 0.76 v7.1.0, 0.74 v7.0.0, 0.73 v6.3.0, 0.71 v6.2.0, 0.80 v6.1.0, 0.83 v5.5.0, 0.85 v5.4.0, 0.86 v5.3.0, 0.89 v5.2.0, 0.80 v5.1.0, 0.81 v5.0.0, 0.83 v4.1.0, 0.87 v4.0.0
% Syntax : Number of formulae : 97 ( 9 unt; 11 def)
% Number of atoms : 381 ( 69 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 309 ( 25 ~; 4 |; 124 &)
% ( 22 <=>; 134 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 15 con; 0-2 aty)
% Number of variables : 169 ( 158 !; 11 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Problem generated by the SAD system [VLP07]
%------------------------------------------------------------------------------
fof(mSetSort,axiom,
! [W0] :
( aSet0(W0)
=> $true ) ).
fof(mElmSort,axiom,
! [W0] :
( aElement0(W0)
=> $true ) ).
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ) ).
fof(mFinRel,axiom,
! [W0] :
( aSet0(W0)
=> ( isFinite0(W0)
=> $true ) ) ).
fof(mDefEmp,definition,
! [W0] :
( W0 = slcrc0
<=> ( aSet0(W0)
& ~ ? [W1] : aElementOf0(W1,W0) ) ) ).
fof(mEmpFin,axiom,
isFinite0(slcrc0) ).
fof(mCntRel,axiom,
! [W0] :
( aSet0(W0)
=> ( isCountable0(W0)
=> $true ) ) ).
fof(mCountNFin,axiom,
! [W0] :
( ( aSet0(W0)
& isCountable0(W0) )
=> ~ isFinite0(W0) ) ).
fof(mCountNFin_01,axiom,
! [W0] :
( ( aSet0(W0)
& isCountable0(W0) )
=> W0 != slcrc0 ) ).
fof(mDefSub,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ) ).
fof(mSubFSet,axiom,
! [W0] :
( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) ) ).
fof(mSubRefl,axiom,
! [W0] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) ) ).
fof(mSubASymm,axiom,
! [W0,W1] :
( ( aSet0(W0)
& aSet0(W1) )
=> ( ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W0) )
=> W0 = W1 ) ) ).
fof(mSubTrans,axiom,
! [W0,W1,W2] :
( ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) )
=> ( ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
=> aSubsetOf0(W0,W2) ) ) ).
fof(mDefCons,definition,
! [W0,W1] :
( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2] :
( W2 = sdtpldt0(W0,W1)
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& ( aElementOf0(W3,W0)
| W3 = W1 ) ) ) ) ) ) ).
fof(mDefDiff,definition,
! [W0,W1] :
( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2] :
( W2 = sdtmndt0(W0,W1)
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& W3 != W1 ) ) ) ) ) ).
fof(mConsDiff,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ).
fof(mDiffCons,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aSet0(W1) )
=> ( ~ aElementOf0(W0,W1)
=> sdtmndt0(sdtpldt0(W1,W0),W0) = W1 ) ) ).
fof(mCConsSet,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( aSet0(W1)
& isCountable0(W1) )
=> isCountable0(sdtpldt0(W1,W0)) ) ) ).
fof(mCDiffSet,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( aSet0(W1)
& isCountable0(W1) )
=> isCountable0(sdtmndt0(W1,W0)) ) ) ).
fof(mFConsSet,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( aSet0(W1)
& isFinite0(W1) )
=> isFinite0(sdtpldt0(W1,W0)) ) ) ).
fof(mFDiffSet,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( aSet0(W1)
& isFinite0(W1) )
=> isFinite0(sdtmndt0(W1,W0)) ) ) ).
fof(mNATSet,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ) ).
fof(mZeroNum,axiom,
aElementOf0(sz00,szNzAzT0) ).
fof(mSuccNum,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& szszuzczcdt0(W0) != sz00 ) ) ).
fof(mSuccEquSucc,axiom,
! [W0,W1] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( szszuzczcdt0(W0) = szszuzczcdt0(W1)
=> W0 = W1 ) ) ).
fof(mNatExtra,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( W0 = sz00
| ? [W1] :
( aElementOf0(W1,szNzAzT0)
& W0 = szszuzczcdt0(W1) ) ) ) ).
fof(mNatNSucc,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> W0 != szszuzczcdt0(W0) ) ).
fof(mLessRel,axiom,
! [W0,W1] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W0,W1)
=> $true ) ) ).
fof(mZeroLess,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) ) ).
fof(mNoScLessZr,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ~ sdtlseqdt0(szszuzczcdt0(W0),sz00) ) ).
fof(mSuccLess,axiom,
! [W0,W1] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W0,W1)
<=> sdtlseqdt0(szszuzczcdt0(W0),szszuzczcdt0(W1)) ) ) ).
fof(mLessSucc,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(W0,szszuzczcdt0(W0)) ) ).
fof(mLessRefl,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(W0,W0) ) ).
fof(mLessASymm,axiom,
! [W0,W1] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> W0 = W1 ) ) ).
fof(mLessTrans,axiom,
! [W0,W1,W2] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& aElementOf0(W2,szNzAzT0) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
=> sdtlseqdt0(W0,W2) ) ) ).
fof(mLessTotal,axiom,
! [W0,W1] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0) ) ) ).
fof(mIHSort,axiom,
! [W0,W1] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( iLess0(W0,W1)
=> $true ) ) ).
fof(mIH,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> iLess0(W0,szszuzczcdt0(W0)) ) ).
fof(mCardS,axiom,
! [W0] :
( aSet0(W0)
=> aElement0(sbrdtbr0(W0)) ) ).
fof(mCardNum,axiom,
! [W0] :
( aSet0(W0)
=> ( aElementOf0(sbrdtbr0(W0),szNzAzT0)
<=> isFinite0(W0) ) ) ).
fof(mCardEmpty,axiom,
! [W0] :
( aSet0(W0)
=> ( sbrdtbr0(W0) = sz00
<=> W0 = slcrc0 ) ) ).
fof(mCardCons,axiom,
! [W0] :
( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1] :
( aElement0(W1)
=> ( ~ aElementOf0(W1,W0)
=> sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) ).
fof(mCardDiff,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( ( isFinite0(W0)
& aElementOf0(W1,W0) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ).
fof(mCardSub,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( ( isFinite0(W0)
& aSubsetOf0(W1,W0) )
=> sdtlseqdt0(sbrdtbr0(W1),sbrdtbr0(W0)) ) ) ).
fof(mCardSubEx,axiom,
! [W0,W1] :
( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( isFinite0(W0)
& sdtlseqdt0(W1,sbrdtbr0(W0)) )
=> ? [W2] :
( aSubsetOf0(W2,W0)
& sbrdtbr0(W2) = W1 ) ) ) ).
fof(mDefMin,definition,
! [W0] :
( ( aSubsetOf0(W0,szNzAzT0)
& W0 != slcrc0 )
=> ! [W1] :
( W1 = szmzizndt0(W0)
<=> ( aElementOf0(W1,W0)
& ! [W2] :
( aElementOf0(W2,W0)
=> sdtlseqdt0(W1,W2) ) ) ) ) ).
fof(mDefMax,definition,
! [W0] :
( ( aSubsetOf0(W0,szNzAzT0)
& isFinite0(W0)
& W0 != slcrc0 )
=> ! [W1] :
( W1 = szmzazxdt0(W0)
<=> ( aElementOf0(W1,W0)
& ! [W2] :
( aElementOf0(W2,W0)
=> sdtlseqdt0(W2,W1) ) ) ) ) ).
fof(mMinMin,axiom,
! [W0,W1] :
( ( aSubsetOf0(W0,szNzAzT0)
& aSubsetOf0(W1,szNzAzT0)
& W0 != slcrc0
& W1 != slcrc0 )
=> ( ( aElementOf0(szmzizndt0(W0),W1)
& aElementOf0(szmzizndt0(W1),W0) )
=> szmzizndt0(W0) = szmzizndt0(W1) ) ) ).
fof(mDefSeg,definition,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( W1 = slbdtrb0(W0)
<=> ( aSet0(W1)
& ! [W2] :
( aElementOf0(W2,W1)
<=> ( aElementOf0(W2,szNzAzT0)
& sdtlseqdt0(szszuzczcdt0(W2),W0) ) ) ) ) ) ).
fof(mSegFin,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> isFinite0(slbdtrb0(W0)) ) ).
fof(mSegZero,axiom,
slbdtrb0(sz00) = slcrc0 ).
fof(mSegSucc,axiom,
! [W0,W1] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( aElementOf0(W0,slbdtrb0(szszuzczcdt0(W1)))
<=> ( aElementOf0(W0,slbdtrb0(W1))
| W0 = W1 ) ) ) ).
fof(mSegLess,axiom,
! [W0,W1] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W0,W1)
<=> aSubsetOf0(slbdtrb0(W0),slbdtrb0(W1)) ) ) ).
fof(mFinSubSeg,axiom,
! [W0] :
( ( aSubsetOf0(W0,szNzAzT0)
& isFinite0(W0) )
=> ? [W1] :
( aElementOf0(W1,szNzAzT0)
& aSubsetOf0(W0,slbdtrb0(W1)) ) ) ).
fof(mCardSeg,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sbrdtbr0(slbdtrb0(W0)) = W0 ) ).
fof(mDefSel,definition,
! [W0,W1] :
( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
=> ! [W2] :
( W2 = slbdtsldtrb0(W0,W1)
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> ( aSubsetOf0(W3,W0)
& sbrdtbr0(W3) = W1 ) ) ) ) ) ).
fof(mSelFSet,axiom,
! [W0] :
( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1] :
( aElementOf0(W1,szNzAzT0)
=> isFinite0(slbdtsldtrb0(W0,W1)) ) ) ).
fof(mSelNSet,axiom,
! [W0] :
( ( aSet0(W0)
& ~ isFinite0(W0) )
=> ! [W1] :
( aElementOf0(W1,szNzAzT0)
=> slbdtsldtrb0(W0,W1) != slcrc0 ) ) ).
fof(mSelCSet,axiom,
! [W0] :
( ( aSet0(W0)
& isCountable0(W0) )
=> ! [W1] :
( ( aElementOf0(W1,szNzAzT0)
& W1 != sz00 )
=> isCountable0(slbdtsldtrb0(W0,W1)) ) ) ).
fof(mSelSub,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1,W2] :
( ( aSet0(W1)
& aSet0(W2)
& W0 != sz00 )
=> ( ( aSubsetOf0(slbdtsldtrb0(W1,W0),slbdtsldtrb0(W2,W0))
& slbdtsldtrb0(W1,W0) != slcrc0 )
=> aSubsetOf0(W1,W2) ) ) ) ).
fof(mSelExtra,axiom,
! [W0,W1] :
( ( aSet0(W0)
& aElementOf0(W1,szNzAzT0) )
=> ! [W2] :
( ( aSubsetOf0(W2,slbdtsldtrb0(W0,W1))
& isFinite0(W2) )
=> ? [W3] :
( aSubsetOf0(W3,W0)
& isFinite0(W3)
& aSubsetOf0(W2,slbdtsldtrb0(W3,W1)) ) ) ) ).
fof(mFunSort,axiom,
! [W0] :
( aFunction0(W0)
=> $true ) ).
fof(mDomSet,axiom,
! [W0] :
( aFunction0(W0)
=> aSet0(szDzozmdt0(W0)) ) ).
fof(mImgElm,axiom,
! [W0] :
( aFunction0(W0)
=> ! [W1] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElement0(sdtlpdtrp0(W0,W1)) ) ) ).
fof(mDefPtt,definition,
! [W0,W1] :
( ( aFunction0(W0)
& aElement0(W1) )
=> ! [W2] :
( W2 = sdtlbdtrb0(W0,W1)
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> ( aElementOf0(W3,szDzozmdt0(W0))
& sdtlpdtrp0(W0,W3) = W1 ) ) ) ) ) ).
fof(mPttSet,axiom,
! [W0,W1] :
( ( aFunction0(W0)
& aElement0(W1) )
=> aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ) ).
fof(mDefSImg,definition,
! [W0] :
( aFunction0(W0)
=> ! [W1] :
( aSubsetOf0(W1,szDzozmdt0(W0))
=> ! [W2] :
( W2 = sdtlcdtrc0(W0,W1)
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4] :
( aElementOf0(W4,W1)
& sdtlpdtrp0(W0,W4) = W3 ) ) ) ) ) ) ).
fof(mImgRng,axiom,
! [W0] :
( aFunction0(W0)
=> ! [W1] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ).
fof(mDefRst,definition,
! [W0] :
( aFunction0(W0)
=> ! [W1] :
( aSubsetOf0(W1,szDzozmdt0(W0))
=> ! [W2] :
( W2 = sdtexdt0(W0,W1)
<=> ( aFunction0(W2)
& szDzozmdt0(W2) = W1
& ! [W3] :
( aElementOf0(W3,W1)
=> sdtlpdtrp0(W2,W3) = sdtlpdtrp0(W0,W3) ) ) ) ) ) ).
fof(mImgCount,axiom,
! [W0] :
( aFunction0(W0)
=> ! [W1] :
( ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
=> ( ! [W2,W3] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& W2 != W3 )
=> sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
=> isCountable0(sdtlcdtrc0(W0,W1)) ) ) ) ).
fof(mDirichlet,axiom,
! [W0] :
( aFunction0(W0)
=> ( ( isCountable0(szDzozmdt0(W0))
& isFinite0(sdtlcdtrc0(W0,szDzozmdt0(W0))) )
=> ( aElement0(szDzizrdt0(W0))
& isCountable0(sdtlbdtrb0(W0,szDzizrdt0(W0))) ) ) ) ).
fof(m__3291,hypothesis,
( aSet0(xT)
& isFinite0(xT) ) ).
fof(m__3418,hypothesis,
aElementOf0(xK,szNzAzT0) ).
fof(m__3435,hypothesis,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ) ).
fof(m__3453,hypothesis,
( aFunction0(xc)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ) ).
fof(m__3398,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( aSubsetOf0(W1,szNzAzT0)
& isCountable0(W1) )
=> ! [W2] :
( ( aFunction0(W2)
& szDzozmdt0(W2) = slbdtsldtrb0(W1,W0)
& aSubsetOf0(sdtlcdtrc0(W2,szDzozmdt0(W2)),xT) )
=> ( iLess0(W0,xK)
=> ? [W3] :
( aElementOf0(W3,xT)
& ? [W4] :
( aSubsetOf0(W4,W1)
& isCountable0(W4)
& ! [W5] :
( aElementOf0(W5,slbdtsldtrb0(W4,W0))
=> sdtlpdtrp0(W2,W5) = W3 ) ) ) ) ) ) ) ).
fof(m__3462,hypothesis,
xK != sz00 ).
fof(m__3520,hypothesis,
xK != sz00 ).
fof(m__3533,hypothesis,
( aElementOf0(xk,szNzAzT0)
& szszuzczcdt0(xk) = xK ) ).
fof(m__3623,hypothesis,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) )
=> ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ).
fof(m__3671,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,W0)) ) ) ).
fof(m__3754,hypothesis,
! [W0,W1] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) ).
fof(m__3821,hypothesis,
! [W0,W1] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& W0 != W1 )
=> szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) ) ).
fof(m__3965,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
=> aElementOf0(sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))),slbdtsldtrb0(xS,xK)) ) ) ).
fof(m__4151,hypothesis,
( aFunction0(xC)
& szDzozmdt0(xC) = szNzAzT0
& ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( aFunction0(sdtlpdtrp0(xC,W0))
& szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)
& ! [W1] :
( ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ).
fof(m__4182,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC,W0),szDzozmdt0(sdtlpdtrp0(xC,W0))),xT) ) ).
fof(m__4331,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(W1) )
=> ! [W2] :
( ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
=> aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ).
fof(m__4411,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ? [W1] :
( aElementOf0(W1,xT)
& ? [W2] :
( aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(W2)
& ! [W3] :
( ( aSet0(W3)
& aElementOf0(W3,slbdtsldtrb0(W2,xk)) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,W0),W3) = W1 ) ) ) ) ).
fof(m__4618,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ? [W1] :
( aElementOf0(W1,xT)
& ! [W2] :
( ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,W0),W2) = W1 ) ) ) ).
fof(m__4660,hypothesis,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ).
fof(m__4730,hypothesis,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) )
=> sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) ).
fof(m__4769,hypothesis,
aSet0(sdtlcdtrc0(xd,szDzozmdt0(xd))) ).
fof(m__4781,hypothesis,
aElementOf0(xx,sdtlcdtrc0(xd,szDzozmdt0(xd))) ).
fof(m__4806,hypothesis,
( aElementOf0(xi,szNzAzT0)
& sdtlpdtrp0(xd,xi) = xx ) ).
fof(m__4826,hypothesis,
( xX = slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xi)),xk)
& xX != slcrc0 ) ).
fof(m__,conjecture,
aElementOf0(xx,xT) ).
%------------------------------------------------------------------------------