%------------------------------------------------------------------------------
% File     : NUM532+1 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Number Theory
% Problem  : Ramsey's Infinite Theorem 02, 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_02.00 [Pas08]

% Status   : Theorem
% Rating   : 0.06 v8.2.0, 0.08 v8.1.0, 0.06 v7.5.0, 0.09 v7.4.0, 0.13 v7.3.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.00 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.04 v6.1.0, 0.07 v6.0.0, 0.00 v5.5.0, 0.04 v5.4.0, 0.07 v5.2.0, 0.05 v5.1.0, 0.14 v5.0.0, 0.21 v4.1.0, 0.26 v4.0.1, 0.57 v4.0.0
% Syntax   : Number of formulae    :   13 (   3 unt;   2 def)
%            Number of atoms       :   34 (   2 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   24 (   3   ~;   0   |;   5   &)
%                                         (   2 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   15 (  14   !;   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(m__467,hypothesis,
    aSet0(xA) ).

fof(m__,conjecture,
    aSubsetOf0(xA,xA) ).

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