## TPTP Problem File: SET598^5.p

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```%------------------------------------------------------------------------------
% File     : SET598^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem BOOL-PROP-57
% Version  : Especial.
% English  : Trybulec's 57th Boolean property of sets

% Refs     : [TS89]  Trybulec & Swieczkowska (1989), Boolean Properties of
%          : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0566 [Bro09]
%          : BOOL-PROP-57 [TPS]

% Status   : Theorem
% Rating   : 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, 0.50 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.60 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   26 (   1 equality;  25 variable)
%            Maximal formula depth :   13 (   8 average)
%            Number of connectives :   23 (   0   ~;   0   |;   4   &;  12   @)
%                                         (   1 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   10 (   0 sgn;   9   !;   0   ?;   1   ^)
%                                         (  10   :;   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
%          : Polymorphic definitions expanded.
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(cBOOL_PROP_57_pme,conjecture,(
! [X: a > \$o,Y: a > \$o,Z: a > \$o] :
( ( X
= ( ^ [Xx: a] :
( ( Y @ Xx )
& ( Z @ Xx ) ) ) )
<=> ( ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) )
& ! [Xx: a] :
( ( X @ Xx )
=> ( Z @ Xx ) )
& ! [V: a > \$o] :
( ( ! [Xx: a] :
( ( V @ Xx )
=> ( Y @ Xx ) )
& ! [Xx: a] :
( ( V @ Xx )
=> ( Z @ Xx ) ) )
=> ! [Xx: a] :
( ( V @ Xx )
=> ( X @ Xx ) ) ) ) ) )).

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