%------------------------------------------------------------------------------
% File     : NUM531+2 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Number Theory
% Problem  : Ramsey's Infinite Theorem 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_01.01 [Pas08]

% Status   : Theorem
% Rating   : 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.04 v6.3.0, 0.00 v6.2.0, 0.04 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.04 v5.4.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.05 v5.1.0, 0.10 v5.0.0, 0.17 v4.1.0, 0.22 v4.0.1, 0.61 v4.0.0
% Syntax   : Number of formulae    :    9 (   1 unt;   1 def)
%            Number of atoms       :   24 (   2 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   19 (   4   ~;   0   |;   4   &)
%                                         (   1 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   11 (   9   !;   2   ?)
% 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(m__,conjecture,
    ! [W0] :
      ( ( aSet0(W0)
        & isCountable0(W0) )
     => ~ ( ~ ? [W1] : aElementOf0(W1,W0)
          & W0 = slcrc0 ) ) ).

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