## TPTP Problem File: SEV268^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV268^5 : 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_1111 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   50 (   4 equality;  44 variable)
%            Maximal formula depth :   16 (   9 average)
%            Number of connectives :   42 (   1   ~;   0   |;  11   &;  20   @)
%                                         (   1 <=>;   9  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   1   :;   0   =)
%            Number of variables   :   20 (   2 sgn;  13   !;   3   ?;   4   ^)
%                                         (  20   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_UNK_EQU_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%            Mellon University. Distributed under the Creative Commons copyleft
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(cNBHD_THM_pme,conjecture,(
! [T: ( a > \$o ) > \$o] :
( ( ! [R: a > \$o] :
( ( R
= ( ^ [Xx: a] : \$false ) )
=> ( T @ R ) )
& ! [R: a > \$o] :
( ( R
= ( ^ [Xx: a] : ~ ( \$false ) ) )
=> ( T @ R ) )
& ! [K: ( a > \$o ) > \$o,R: a > \$o] :
( ( ! [Xx: a > \$o] :
( ( K @ Xx )
=> ( T @ Xx ) )
& ( R
= ( ^ [Xx: a] :
? [S: a > \$o] :
( ( K @ S )
& ( S @ Xx ) ) ) ) )
=> ( T @ R ) )
& ! [Y: a > \$o,Z: a > \$o,S: a > \$o] :
( ( ( T @ Y )
& ( T @ Z )
& ( S
= ( ^ [Xx: a] :
( ( Y @ Xx )
& ( Z @ Xx ) ) ) ) )
=> ( T @ S ) ) )
=> ! [S: a > \$o] :
( ( T @ S )
<=> ! [Xx: a] :
( ( S @ Xx )
=> ? [R: a > \$o] :
( ? [N: a > \$o] :
( ( T @ N )
& ! [Xx0: a] :
( ( N @ Xx0 )
=> ( R @ Xx0 ) )
& ( N @ Xx ) )
& ! [Xx0: a] :
( ( R @ Xx0 )
=> ( S @ Xx0 ) ) ) ) ) ) )).

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