TPTP Problem File: SEV179^5.p

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```%------------------------------------------------------------------------------
% File     : SEV179^5 : TPTP v7.5.0. Bugfixed v5.2.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from CANTOR-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0598 [Bro09]

% Status   : Theorem
% Rating   : 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.2.0
% Syntax   : Number of formulae    :    3 (   0 unit;   1 type;   1 defn)
%            Number of atoms       :   14 (   2 equality;   9 variable)
%            Maximal formula depth :    9 (   6 average)
%            Number of connectives :    9 (   1   ~;   0   |;   1   &;   7   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :    4 (   0 sgn;   1   !;   1   ?;   2   ^)
%                                         (   4   :;   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
% Bugfixes : v5.2.0 - Added missing type declarations.
%------------------------------------------------------------------------------
thf(cD_FOR_X5309_type,type,(
cD_FOR_X5309: ( ( \$i > \$o ) > \$i ) > \$i > \$o )).

thf(cD_FOR_X5309_def,definition,
( cD_FOR_X5309
= ( ^ [Xh: ( \$i > \$o ) > \$i,Xz: \$i] :
? [Xt: \$i > \$o] :
( ~ ( Xt @ ( Xh @ Xt ) )
& ( Xz
= ( Xh @ Xt ) ) ) ) )).

thf(cTHM144C_pme,conjecture,(
! [Xh: ( \$i > \$o ) > \$i] :
( cD_FOR_X5309 @ Xh @ ( Xh @ ( cD_FOR_X5309 @ Xh ) ) ) )).

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