TPTP Problem File: NUM553+3.p
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%------------------------------------------------------------------------------
% File : NUM553+3 : TPTP v8.2.0. Released v4.0.0.
% Domain : Number Theory
% Problem : Ramsey's Infinite Theorem 12_05, 02 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_12_05.02 [Pas08]
% Status : Theorem
% Rating : 1.00 v4.0.0
% Syntax : Number of formulae : 69 ( 7 unt; 8 def)
% Number of atoms : 289 ( 46 equ)
% Maximal formula atoms : 43 ( 4 avg)
% Number of connectives : 240 ( 20 ~; 8 |; 96 &)
% ( 17 <=>; 99 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 118 ( 113 !; 5 ?)
% 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(m__2202,hypothesis,
aElementOf0(xk,szNzAzT0) ).
fof(m__2202_02,hypothesis,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ) ).
fof(m__2227,hypothesis,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [W0] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& sbrdtbr0(W0) = xk ) )
& ( ( ( ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& sbrdtbr0(W0) = xk )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0] :
( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& sbrdtbr0(W0) = xk ) )
& ( ( ( ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) ) )
| aSubsetOf0(W0,xT) )
& sbrdtbr0(W0) = xk )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
& ! [W0] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ~ ( ! [W0] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& sbrdtbr0(W0) = xk ) )
& ( ( ( ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& sbrdtbr0(W0) = xk )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
=> ( ~ ? [W0] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
| slbdtsldtrb0(xS,xk) = slcrc0 ) ) ) ).
fof(m__2256,hypothesis,
aElementOf0(xx,xS) ).
fof(m__2270,hypothesis,
( aSet0(xQ)
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
& aSubsetOf0(xQ,xS)
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ) ).
fof(m__2291,hypothesis,
( aSet0(xQ)
& isFinite0(xQ)
& sbrdtbr0(xQ) = xk ) ).
fof(m__2304,hypothesis,
( aElement0(xy)
& aElementOf0(xy,xQ) ) ).
fof(m__2323,hypothesis,
~ aElementOf0(xx,xQ) ).
fof(m__,conjecture,
aElementOf0(xx,xT) ).
%------------------------------------------------------------------------------