## TPTP Problem File: SEV267^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV267^5 : 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_1057 [Bro09]

% Status   : Theorem
% Rating   : 0.45 v7.5.0, 0.71 v7.4.0, 0.56 v7.2.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.80 v6.2.0, 0.43 v6.1.0, 0.57 v5.5.0, 0.33 v5.4.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   36 (   1 equality;  35 variable)
%            Maximal formula depth :   15 (   8 average)
%            Number of connectives :   33 (   0   ~;   0   |;   7   &;  17   @)
%                                         (   1 <=>;   8  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   14 (   0 sgn;  10   !;   3   ?;   1   ^)
%                                         (  14   :;   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
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(cNBHD_THM1_pme,conjecture,(
! [T: ( a > \$o ) > \$o] :
( ! [S: a > \$o,R: a > \$o] :
( ( ! [Xx: a > \$o] :
( ( ( T @ Xx )
& ! [Xx0: a] :
( ( Xx @ Xx0 )
=> ( S @ Xx0 ) ) )
=> ( T @ Xx ) )
& ( R
= ( ^ [Xx: a] :
? [S_19: a > \$o] :
( ( T @ S_19 )
& ! [Xx0: a] :
( ( S_19 @ Xx0 )
=> ( S @ Xx0 ) )
& ( S_19 @ Xx ) ) ) ) )
=> ( T @ R ) )
=> ! [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 ) ) ) ) ) ) )).

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