## TPTP Problem File: SEV263^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV263^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from TOPOLOGY-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0971 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   25 (   0 equality;  21 variable)
%            Maximal formula depth :   12 (   8 average)
%            Number of connectives :   24 (   0   ~;   0   |;   4   &;  13   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   10 (   0 sgn;   7   !;   2   ?;   1   ^)
%                                         (  10   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_UNK_NEQ_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%------------------------------------------------------------------------------
thf(cOPEN,type,(
cOPEN: ( \$i > \$o ) > \$o )).

thf(cEXISTS_INTERIOR_EXT_pme,conjecture,
( ! [G: ( \$i > \$o ) > \$o] :
( ! [Xx: \$i > \$o] :
( ( G @ Xx )
=> ( cOPEN @ Xx ) )
=> ( cOPEN
@ ^ [Xx: \$i] :
? [S: \$i > \$o] :
( ( G @ S )
& ( S @ Xx ) ) ) )
=> ! [A: \$i > \$o] :
? [B: \$i > \$o] :
( ( cOPEN @ B )
& ! [Xx: \$i] :
( ( B @ Xx )
=> ( A @ Xx ) )
& ! [C: \$i > \$o] :
( ( ( cOPEN @ C )
& ! [Xx: \$i] :
( ( C @ Xx )
=> ( A @ Xx ) ) )
=> ! [Xx: \$i] :
( ( C @ Xx )
=> ( B @ Xx ) ) ) ) )).

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