## TPTP Problem File: SEV076^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV076^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem THM401B
% Version  : Especial.
% English  : In a complete lattice, every set has an upper bound.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0556 [Bro09]
%          : tps_0557 [Bro09]
%          : THM401A [TPS]
%          : THM401B [TPS]
%          : THM401 [TPS]
%          : THM401Z [TPS]

% Status   : Theorem
% Rating   : 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   29 (   0 equality;  29 variable)
%            Maximal formula depth :   13 (   8 average)
%            Number of connectives :   28 (   0   ~;   0   |;   3   &;  19   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   12 (   0 sgn;  11   !;   1   ?;   0   ^)
%                                         (  12   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_NEQ_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(cTHM401B_pme,conjecture,(
! [RRR: a > a > \$o,U: ( a > \$o ) > a] :
( ( ! [Xx: a,Xy: a,Xz: a] :
( ( ( RRR @ Xx @ Xy )
& ( RRR @ Xy @ Xz ) )
=> ( RRR @ Xx @ Xz ) )
& ! [Xs: a > \$o] :
( ! [Xz: a] :
( ( Xs @ Xz )
=> ( RRR @ Xz @ ( U @ Xs ) ) )
& ! [Xj: a] :
( ! [Xk: a] :
( ( Xs @ Xk )
=> ( RRR @ Xk @ Xj ) )
=> ( RRR @ ( U @ Xs ) @ Xj ) ) ) )
=> ! [Xs: a > \$o] :
? [Xb: a] :
! [Xz: a] :
( ( Xs @ Xz )
=> ( RRR @ Xz @ Xb ) ) ) )).

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