%------------------------------------------------------------------------------
% File     : SET611^3 : TPTP v9.0.0. Released v3.6.0.
% Domain   : Set Theory
% Problem  : X ^ Y = the empty set iff X \ Y = X
% Version  : [BS+08] axioms.
% English  : The intersection of X and Y is the empty set iff the difference
%            of X and Y is X.

% Refs     : [BS+05] Benzmueller et al. (2005), Can a Higher-Order and a Fi
%          : [BS+08] Benzmueller et al. (2008), Combined Reasoning by Autom
%          : [Ben08] Benzmueller (2008), Email to Geoff Sutcliffe
% Source   : [Ben08]
% Names    :

% Status   : Theorem
% Rating   : 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v3.7.0
% Syntax   : Number of formulae    :   29 (  14 unt;  14 typ;  14 def)
%            Number of atoms       :   40 (  20 equ;   0 cnn)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :   41 (   5   ~;   3   |;   6   &;  25   @)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   72 (  72   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  17 usr;   4 con; 0-3 aty)
%            Number of variables   :   37 (  32   ^;   3   !;   2   ?;  37   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : 
%------------------------------------------------------------------------------
%----Basic set theory definitions
include('Axioms/SET008^0.ax').
%------------------------------------------------------------------------------
thf(thm,conjecture,
    ! [A: $i > $o,B: $i > $o] :
      ( ( ( intersection @ A @ B )
        = emptyset )
    <=> ( ( setminus @ A @ B )
        = A ) ) ).

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