## TPTP Problem File: SEV240^5.p

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```%------------------------------------------------------------------------------
% File     : SEV240^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from SETS-OF-SETS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0748 [Bro09]

% Status   : Theorem
% Rating   : 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :    8 (   0 equality;   6 variable)
%            Maximal formula depth :    8 (   5 average)
%            Number of connectives :    7 (   0   ~;   0   |;   1   &;   4   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :    3 (   0 sgn;   2   !;   1   ?;   0   ^)
%                                         (   3   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_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(a_type,type,(
a: \$tType )).

thf(cA,type,(
cA: ( a > \$o ) > \$o )).

thf(cDOMTHM1_pme,conjecture,(
! [Xx: a > \$o] :
( ( cA @ Xx )
=> ! [Xx0: a] :
( ( Xx @ Xx0 )
=> ? [S: a > \$o] :
( ( cA @ S )
& ( S @ Xx0 ) ) ) ) )).

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