%--------------------------------------------------------------------------
% File     : SET766+4 : TPTP v8.2.0. Released v2.2.0.
% Domain   : Set Theory (Equivalence relations)
% Problem  : A member belongs to its equivalence class
% Version  : [Pas99] axioms.
% English  :

% Refs     : [Pas99] Pastre (1999), Email to G. Sutcliffe
% Source   : [Pas99]
% Names    :

% Status   : Theorem
% Rating   : 0.08 v8.1.0, 0.06 v7.4.0, 0.10 v7.3.0, 0.07 v7.1.0, 0.13 v7.0.0, 0.10 v6.4.0, 0.15 v6.3.0, 0.17 v6.2.0, 0.12 v6.1.0, 0.10 v6.0.0, 0.13 v5.5.0, 0.07 v5.3.0, 0.15 v5.2.0, 0.10 v5.0.0, 0.12 v4.1.0, 0.13 v4.0.0, 0.17 v3.7.0, 0.20 v3.5.0, 0.16 v3.4.0, 0.11 v3.3.0, 0.00 v2.2.1
% Syntax   : Number of formulae    :   17 (   1 unt;   0 def)
%            Number of atoms       :   71 (   4 equ)
%            Maximal formula atoms :   13 (   4 avg)
%            Number of connectives :   57 (   3   ~;   2   |;  22   &)
%                                         (  15 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   0 prp; 2-3 aty)
%            Number of functors    :   10 (  10 usr;   1 con; 0-3 aty)
%            Number of variables   :   60 (  56   !;   4   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments :
%--------------------------------------------------------------------------
%----Include set theory definitions
include('Axioms/SET006+0.ax').
%----Include equivalence relation axioms
include('Axioms/SET006+2.ax').
%--------------------------------------------------------------------------
fof(thIII02,conjecture,
    ! [E,R,A] :
      ( ( equivalence(R,E)
        & member(A,E) )
     => member(A,equivalence_class(A,E,R)) ) ).

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