%--------------------------------------------------------------------------
% File     : SET698+4 : TPTP v9.0.0. Released v2.2.0.
% Domain   : Set Theory (Naive)
% Problem  : Property of union and difference
% Version  : [Pas99] axioms.
% English  : A is a subset of B if and only if the union of A and of the
%            difference of B in E is equal to E.

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

% Status   : Theorem
% Rating   : 0.58 v9.0.0, 0.67 v8.2.0, 0.72 v8.1.0, 0.53 v7.5.0, 0.66 v7.4.0, 0.63 v7.3.0, 0.52 v7.2.0, 0.48 v7.1.0, 0.52 v7.0.0, 0.53 v6.4.0, 0.58 v6.2.0, 0.60 v6.1.0, 0.70 v6.0.0, 0.65 v5.5.0, 0.74 v5.4.0, 0.79 v5.3.0, 0.81 v5.2.0, 0.85 v5.1.0, 0.86 v5.0.0, 0.88 v4.1.0, 0.87 v4.0.1, 0.83 v3.7.0, 0.80 v3.5.0, 0.84 v3.4.0, 0.89 v3.3.0, 0.86 v3.2.0, 0.91 v3.1.0, 0.89 v2.7.0, 0.83 v2.6.0, 0.86 v2.5.0, 0.88 v2.4.0, 0.50 v2.3.0, 0.33 v2.2.1
% Syntax   : Number of formulae    :   12 (   1 unt;   0 def)
%            Number of atoms       :   33 (   3 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   23 (   2   ~;   2   |;   5   &)
%                                         (  11 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   0 prp; 2-2 aty)
%            Number of functors    :    9 (   9 usr;   1 con; 0-2 aty)
%            Number of variables   :   31 (  30   !;   1   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments :
%--------------------------------------------------------------------------
%----Include set theory definitions
include('Axioms/SET006+0.ax').
%--------------------------------------------------------------------------
fof(thI32,conjecture,
    ! [A,B,E] :
      ( ( subset(A,E)
        & subset(B,E) )
     => ( subset(A,B)
      <=> equal_set(union(difference(E,A),B),E) ) ) ).

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