## TPTP Problem File: SET623^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SET623^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem BOOL-PROP-99
% Version  : Especial.
% English  : Trybulec's 99th Boolean property of sets

% Refs     : [TS89]  Trybulec & Swieczkowska (1989), Boolean Properties of
%          : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0485 [Bro09]
%          : BOOL-PROP-99 [TPS]

% Status   : Theorem
% Rating   : 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, 0.14 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 v5.1.0, 0.40 v5.0.0, 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       :   41 (   1 equality;  40 variable)
%            Maximal formula depth :   13 (   8 average)
%            Number of connectives :   50 (  12   ~;   6   |;  12   &;  20   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :    5 (   0 sgn;   3   !;   0   ?;   2   ^)
%                                         (   5   :;   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_99_pme,conjecture,(
! [X: a > \$o,Y: a > \$o,Z: a > \$o] :
( ( ^ [Xz: a] :
( ( ( X @ Xz )
& ~ ( ( ( Y @ Xz )
& ~ ( Z @ Xz ) )
| ( ( Z @ Xz )
& ~ ( Y @ Xz ) ) ) )
| ( ( ( ( Y @ Xz )
& ~ ( Z @ Xz ) )
| ( ( Z @ Xz )
& ~ ( Y @ Xz ) ) )
& ~ ( X @ Xz ) ) ) )
= ( ^ [Xz: a] :
( ( ( ( ( X @ Xz )
& ~ ( Y @ Xz ) )
| ( ( Y @ Xz )
& ~ ( X @ Xz ) ) )
& ~ ( Z @ Xz ) )
| ( ( Z @ Xz )
& ~ ( ( ( X @ Xz )
& ~ ( Y @ Xz ) )
| ( ( Y @ Xz )
& ~ ( X @ Xz ) ) ) ) ) ) ) )).

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