%------------------------------------------------------------------------------
% File     : SET597^5 : TPTP v9.0.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem BOOL-PROP-56
% Version  : Especial.
% English  : Trybulec's 56th Boolean property of sets

% Refs     : [TS89]  Trybulec & Swieczkowska (1989), Boolean Properties of
%          : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0564 [Bro09]
%          : BOOL-PROP-56 [TPS]

% Status   : Theorem
% Rating   : 0.25 v9.0.0, 0.20 v8.2.0, 0.46 v8.1.0, 0.45 v7.5.0, 0.43 v7.4.0, 0.56 v7.2.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.67 v5.4.0, 0.60 v5.3.0, 0.80 v5.2.0, 0.60 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    2 (   1 unt;   1 typ;   0 def)
%            Number of atoms       :    1 (   1 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   23 (   0   ~;   1   |;   3   &;  12   @)
%                                         (   1 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (  13 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    1 (   0 usr;   0 con; 2-2 aty)
%            Number of variables   :   10 (   1   ^;   9   !;   0   ?;  10   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%            Mellon University. Distributed under the Creative Commons copyleft
%            license: http://creativecommons.org/licenses/by-sa/3.0/
%          : Polymorphic definitions expanded.
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

thf(cBOOL_PROP_56_pme,conjecture,
    ! [X: a > $o,Y: a > $o,Z: a > $o] :
      ( ( X
        = ( ^ [Xz: a] :
              ( ( Y @ Xz )
              | ( Z @ Xz ) ) ) )
    <=> ( ! [Xx: a] :
            ( ( Y @ Xx )
           => ( X @ Xx ) )
        & ! [Xx: a] :
            ( ( Z @ Xx )
           => ( X @ Xx ) )
        & ! [V: a > $o] :
            ( ( ! [Xx: a] :
                  ( ( Y @ Xx )
                 => ( V @ Xx ) )
              & ! [Xx: a] :
                  ( ( Z @ Xx )
                 => ( V @ Xx ) ) )
           => ! [Xx: a] :
                ( ( X @ Xx )
               => ( V @ Xx ) ) ) ) ) ).

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