## TPTP Problem File: SEV087^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV087^5 : TPTP v7.5.0. 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_0940 [Bro09]

% Status   : Theorem
% Rating   : 0.64 v7.5.0, 0.29 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.71 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.71 v6.0.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.60 v5.2.0, 0.80 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unit;   0 type;   0 defn)
%            Number of atoms       :   24 (   1 equality;  21 variable)
%            Maximal formula depth :   12 (  12 average)
%            Number of connectives :   22 (   1   ~;   0   |;   5   &;  14   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   0   :;   0   =)
%            Number of variables   :    9 (   2 sgn;   6   !;   1   ?;   2   ^)
%                                         (   9   :;   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
%            Mellon University. Distributed under the Creative Commons copyleft
%            license: http://creativecommons.org/licenses/by-sa/3.0/
%------------------------------------------------------------------------------
thf(cTHM120H_pme,conjecture,(
? [R: ( \$i > \$o ) > ( \$i > \$o ) > \$o] :
( ~ ( R
@ ^ [Xx: \$i] : \$true
@ ^ [Xx: \$i] : \$false )
& ! [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 ) )
=> ( X = Y ) ) ) )).

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