%------------------------------------------------------------------------------
% File     : NUM537+2 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Number Theory
% Problem  : Ramsey's Infinite Theorem 05_01, 01 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_05_01.01 [Pas08]

% Status   : Theorem
% Rating   : 0.31 v8.2.0, 0.28 v8.1.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.17 v7.2.0, 0.14 v7.1.0, 0.17 v7.0.0, 0.13 v6.4.0, 0.19 v6.3.0, 0.12 v6.2.0, 0.16 v6.1.0, 0.23 v6.0.0, 0.17 v5.5.0, 0.30 v5.4.0, 0.36 v5.3.0, 0.41 v5.2.0, 0.30 v5.1.0, 0.43 v5.0.0, 0.50 v4.1.0, 0.61 v4.0.1, 0.78 v4.0.0
% Syntax   : Number of formulae    :   20 (   2 unt;   4 def)
%            Number of atoms       :   93 (  12 equ)
%            Maximal formula atoms :   26 (   4 avg)
%            Number of connectives :   80 (   7   ~;   5   |;  29   &)
%                                         (  10 <=>;  29  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   37 (  36   !;   1   ?)
% 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(m__679,hypothesis,
    ( aElement0(xx)
    & aSet0(xS) ) ).

fof(m__679_02,hypothesis,
    ~ aElementOf0(xx,xS) ).

fof(m__,conjecture,
    ( ( ( aSet0(sdtpldt0(xS,xx))
        & ! [W0] :
            ( aElementOf0(W0,sdtpldt0(xS,xx))
          <=> ( aElement0(W0)
              & ( aElementOf0(W0,xS)
                | W0 = xx ) ) ) )
     => ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
          & ! [W0] :
              ( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
            <=> ( aElement0(W0)
                & aElementOf0(W0,sdtpldt0(xS,xx))
                & W0 != xx ) ) )
       => ( ! [W0] :
              ( aElementOf0(W0,xS)
             => aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx)) )
          | aSubsetOf0(xS,sdtmndt0(sdtpldt0(xS,xx),xx)) ) ) )
    & ( ( aSet0(sdtpldt0(xS,xx))
        & ! [W0] :
            ( aElementOf0(W0,sdtpldt0(xS,xx))
          <=> ( aElement0(W0)
              & ( aElementOf0(W0,xS)
                | W0 = xx ) ) ) )
     => ( ( aSet0(sdtmndt0(sdtpldt0(xS,xx),xx))
          & ! [W0] :
              ( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
            <=> ( aElement0(W0)
                & aElementOf0(W0,sdtpldt0(xS,xx))
                & W0 != xx ) ) )
       => ( ! [W0] :
              ( aElementOf0(W0,sdtmndt0(sdtpldt0(xS,xx),xx))
             => aElementOf0(W0,xS) )
          | aSubsetOf0(sdtmndt0(sdtpldt0(xS,xx),xx),xS) ) ) ) ) ).

%------------------------------------------------------------------------------