%------------------------------------------------------------------------------
% File     : SET600^5 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem BOOL-PROP-59
% Version  : Especial.
% English  : Trybulec's 59th Boolean property of sets

% Refs     : [TS89]  Trybulec & Swieczkowska (1989), Boolean Properties of
%          : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0475 [Bro09]
%          : BOOL-PROP-59 [TPS]

% Status   : Theorem
% Rating   : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unt;   1 typ;   0 def)
%            Number of atoms       :    6 (   3 equ;   0 cnn)
%            Maximal formula atoms :    3 (   6 avg)
%            Number of connectives :    5 (   0   ~;   1   |;   1   &;   2   @)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   0 usr;   1 con; 0-2 aty)
%            Number of variables   :    6 (   4   ^;   2   !;   0   ?;   6   :)
% 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_59_pme,conjecture,
    ! [X: a > $o,Y: a > $o] :
      ( ( ( ^ [Xz: a] :
              ( ( X @ Xz )
              | ( Y @ Xz ) ) )
        = ( ^ [Xx: a] : $false ) )
    <=> ( ( X
          = ( ^ [Xx: a] : $false ) )
        & ( Y
          = ( ^ [Xx: a] : $false ) ) ) ) ).

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