TPTP Problem File: SEV086^5.p

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```%------------------------------------------------------------------------------
% File     : SEV086^5 : TPTP v8.1.2. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem from RELN-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0918 [Bro09]

% Status   : Theorem
% Rating   : 0.27 v8.1.0, 0.33 v7.5.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.30 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.50 v6.4.0, 0.43 v6.3.0, 0.50 v5.5.0, 0.40 v5.4.0, 0.25 v5.2.0, 0.50 v5.1.0, 0.75 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 typ;   0 def)
%            Number of atoms       :    0 (   0 equ;   0 cnn)
%            Maximal formula atoms :    0 (   0 avg)
%            Number of connectives :   21 (   0   ~;   0   |;   4   &;  14   @)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    8 (   0   ^   7   !;   1   ?;   8   :)
% 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(cTHM120I_pme,conjecture,
? [R: ( \$i > \$o ) > ( \$i > \$o ) > \$o] :
( ! [Xx: \$i > \$o] : ( R @ Xx @ Xx )
& ! [Xx: \$i > \$o,Xy: \$i > \$o,Xz: \$i > \$o] :
( ( ( R @ Xx @ Xy )
& ( R @ Xy @ Xz ) )
=> ( R @ Xx @ Xz ) )
& ! [X: \$i > \$o,Y: \$i > \$o] :
( ( ( R @ X @ Y )
& ( R @ Y @ X ) )
=> ! [Xx: \$i] :
( ( X @ Xx )
<=> ( Y @ Xx ) ) ) ) ).

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