## TPTP Problem File: SEU998^5.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : SEU998^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem 3-DIAMOND-THM
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0560 [Bro09]
%          : 3-DIAMOND-THM [TPS]

% Status   : Theorem
% Rating   : 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.57 v6.1.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :  203 (  39 equality; 164 variable)
%            Maximal formula depth :   42 (  22 average)
%            Number of connectives :  135 (  11   ~;   0   |;  36   &;  86   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   1   :;   0   =)
%            Number of variables   :   26 (   0 sgn;  21   !;   5   ?;   0   ^)
%                                         (  26   :;   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(c3_DIAMOND_THM_pme,conjecture,(
! [JOIN: a > a > a,MEET: a > a > a] :
( ( ! [Xx: a] :
( ( JOIN @ Xx @ Xx )
= Xx )
& ! [Xx: a] :
( ( MEET @ Xx @ Xx )
= Xx )
& ! [Xx: a,Xy: a,Xz: a] :
( ( JOIN @ ( JOIN @ Xx @ Xy ) @ Xz )
= ( JOIN @ Xx @ ( JOIN @ Xy @ Xz ) ) )
& ! [Xx: a,Xy: a,Xz: a] :
( ( MEET @ ( MEET @ Xx @ Xy ) @ Xz )
= ( MEET @ Xx @ ( MEET @ Xy @ Xz ) ) )
& ! [Xx: a,Xy: a] :
( ( JOIN @ Xx @ Xy )
= ( JOIN @ Xy @ Xx ) )
& ! [Xx: a,Xy: a] :
( ( MEET @ Xx @ Xy )
= ( MEET @ Xy @ Xx ) )
& ! [Xx: a,Xy: a] :
( ( JOIN @ ( MEET @ Xx @ Xy ) @ Xy )
= Xy )
& ! [Xx: a,Xy: a] :
( ( MEET @ ( JOIN @ Xx @ Xy ) @ Xy )
= Xy ) )
=> ( ? [Xx: a,Xy: a,Xa: a,Xb: a,Xc: a] :
( ( Xa != Xb )
& ( Xa != Xc )
& ( Xa != Xx )
& ( Xa != Xy )
& ( Xb != Xc )
& ( Xb != Xx )
& ( Xb != Xy )
& ( Xc != Xx )
& ( Xc != Xy )
& ( Xx != Xy )
& ( ( MEET @ Xx @ Xy )
= Xy )
& ( ( JOIN @ Xx @ Xy )
= Xx )
& ( ( MEET @ Xx @ Xa )
= Xa )
& ( ( JOIN @ Xx @ Xa )
= Xx )
& ( ( MEET @ Xx @ Xb )
= Xb )
& ( ( JOIN @ Xx @ Xb )
= Xx )
& ( ( MEET @ Xx @ Xc )
= Xc )
& ( ( JOIN @ Xx @ Xc )
= Xx )
& ( ( MEET @ Xa @ Xb )
= Xy )
& ( ( JOIN @ Xa @ Xb )
= Xx )
& ( ( MEET @ Xa @ Xc )
= Xy )
& ( ( JOIN @ Xa @ Xc )
= Xx )
& ( ( MEET @ Xa @ Xy )
= Xy )
& ( ( JOIN @ Xa @ Xy )
= Xa )
& ( ( MEET @ Xb @ Xc )
= Xy )
& ( ( JOIN @ Xb @ Xc )
= Xx )
& ( ( MEET @ Xb @ Xy )
= Xy )
& ( ( JOIN @ Xb @ Xy )
= Xb )
& ( ( MEET @ Xc @ Xy )
= Xy )
& ( ( JOIN @ Xc @ Xy )
= Xc ) )
=> ~ ( ! [Xx: a,Xy: a,Xz: a] :
( ( MEET @ Xx @ ( JOIN @ Xy @ Xz ) )
= ( JOIN @ ( MEET @ Xx @ Xy ) @ ( MEET @ Xx @ Xz ) ) ) ) ) ) )).

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