## TPTP Problem File: SET619^5.p

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```%------------------------------------------------------------------------------
% File     : SET619^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem BOOL-PROP-95
% Version  : Especial.
% English  : Trybulec's 95th Boolean property of sets

% Refs     : [TS89]  Trybulec & Swieczkowska (1989), Boolean Properties of
%          : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0353 [Bro09]
%          : BOOL-PROP-95 [TPS]

% Status   : Theorem
% Rating   : 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.17 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 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   17 (   1 equality;  16 variable)
%            Maximal formula depth :   10 (   6 average)
%            Number of connectives :   16 (   2   ~;   3   |;   3   &;   8   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :    4 (   0 sgn;   2   !;   0   ?;   2   ^)
%                                         (   4   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% 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
%          : Polymorphic definitions expanded.
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(cBOOL_PROP_95_pme,conjecture,(
! [X: a > \$o,Y: a > \$o] :
( ( ^ [Xz: a] :
( ( X @ Xz )
| ( Y @ Xz ) ) )
= ( ^ [Xz: a] :
( ( ( X @ Xz )
& ~ ( Y @ Xz ) )
| ( ( Y @ Xz )
& ~ ( X @ Xz ) )
| ( ( X @ Xz )
& ( Y @ Xz ) ) ) ) ) )).

%------------------------------------------------------------------------------
```