## TPTP Problem File: SEV262^5.p

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```%------------------------------------------------------------------------------
% File     : SEV262^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem NBHD-THM2
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0551 [Bro09]
%          : NBHD-THM2 [TPS]

% Status   : Theorem
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   28 (   1 equality;  27 variable)
%            Maximal formula depth :   15 (   8 average)
%            Number of connectives :   25 (   0   ~;   0   |;   5   &;  13   @)
%                                         (   1 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   12 (   0 sgn;   8   !;   3   ?;   1   ^)
%                                         (  12   :;   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(cNBHD_THM2_pme,conjecture,(
! [T: ( a > \$o ) > \$o] :
( ! [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 ) )
=> ! [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 ) ) ) ) ) ) )).

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