TPTP Problem File: SEV392^5.p

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```%------------------------------------------------------------------------------
% File     : SEV392^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem THM38
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0284 [Bro09]
%          : THM38 [TPS]

% Status   : Theorem
% Rating   : 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 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, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   13 (   1 equality;   6 variable)
%            Maximal formula depth :    6 (   4 average)
%            Number of connectives :   10 (   0   ~;   1   |;   1   &;   6   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :    3 (   0 sgn;   1   !;   0   ?;   2   ^)
%                                         (   3   :;   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(cS,type,(
cS: \$i > \$o )).

thf(cR,type,(
cR: \$i > \$o )).

thf(cTHM38_pme,conjecture,
( ( ( ^ [Xx: \$i] :
( ( cR @ Xx )
& ( cS @ Xx ) ) )
= ( ^ [Xz: \$i] :
( ( cR @ Xz )
| ( cS @ Xz ) ) ) )
=> ! [Xx: \$i] :
( ( cR @ Xx )
=> ( cS @ Xx ) ) )).

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