## TPTP Problem File: SEV258^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV258^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem DISCRETE-TOPOLOGY
% Version  : Especial.
% English  : The discrete topology really is a topology.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0335 [Bro09]
%          : DISCRETE-TOPOLOGY [TPS]

% Status   : Theorem
% Rating   : 0.00 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   27 (   4 equality;  14 variable)
%            Maximal formula depth :   14 (   8 average)
%            Number of connectives :   19 (   1   ~;   0   |;   8   &;   5   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   1   :;   0   =)
%            Number of variables   :   13 (   2 sgn;   8   !;   1   ?;   4   ^)
%                                         (  13   :;   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(cDISCRETE_TOPOLOGY_pme,conjecture,
( ! [R: a > \$o] :
( ( R
= ( ^ [Xx: a] : \$false ) )
=> \$true )
& ! [R: a > \$o] :
( ( R
= ( ^ [Xx: a] : ~ ( \$false ) ) )
=> \$true )
& ! [K: ( a > \$o ) > \$o,R: a > \$o] :
( ( ! [Xx: a > \$o] :
( ( K @ Xx )
=> \$true )
& ( R
= ( ^ [Xx: a] :
? [S: a > \$o] :
( ( K @ S )
& ( S @ Xx ) ) ) ) )
=> \$true )
& ! [Y: a > \$o,Z: a > \$o,S: a > \$o] :
( ( \$true
& \$true
& ( S
= ( ^ [Xx: a] :
( ( Y @ Xx )
& ( Z @ Xx ) ) ) ) )
=> \$true ) )).

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