%------------------------------------------------------------------------------
% File     : NUM534+2 : TPTP v9.0.0. Released v4.0.0.
% Domain   : Number Theory
% Problem  : Ramsey's Infinite Theorem 04, 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_04.01 [Pas08]

% Status   : Theorem
% Rating   : 0.36 v9.0.0, 0.33 v8.2.0, 0.36 v7.5.0, 0.44 v7.4.0, 0.30 v7.3.0, 0.31 v7.2.0, 0.28 v7.1.0, 0.35 v7.0.0, 0.37 v6.4.0, 0.42 v6.3.0, 0.33 v6.2.0, 0.40 v6.1.0, 0.50 v6.0.0, 0.39 v5.5.0, 0.52 v5.4.0, 0.57 v5.3.0, 0.63 v5.2.0, 0.50 v5.1.0, 0.62 v5.0.0, 0.71 v4.1.0, 0.74 v4.0.1, 0.87 v4.0.0
% Syntax   : Number of formulae    :   19 (   3 unt;   4 def)
%            Number of atoms       :   74 (  10 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :   60 (   5   ~;   2   |;  22   &)
%                                         (   8 <=>;  23  =>;   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   :   31 (  30   !;   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(m__617,hypothesis,
    aSet0(xS) ).

fof(m__617_02,hypothesis,
    aElementOf0(xx,xS) ).

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

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