## TPTP Problem File: SEV084^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV084^5 : 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_0897 [Bro09]

% Status   : Theorem
% Rating   : 0.50 v7.5.0, 0.42 v7.4.0, 0.44 v7.3.0, 0.50 v7.1.0, 0.57 v7.0.0, 0.50 v6.4.0, 0.57 v6.3.0, 0.50 v6.2.0, 0.67 v6.1.0, 0.50 v6.0.0, 0.33 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 v4.0.1, 1.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   17 (   0 equality;  13 variable)
%            Maximal formula depth :   11 (   6 average)
%            Number of connectives :   19 (   3   ~;   1   |;   4   &;  10   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :    7 (   2 sgn;   4   !;   1   ?;   2   ^)
%                                         (   7   :;   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(cP,type,(
cP: \$o )).

thf(cTHM120J_pme,conjecture,(
? [R: ( \$i > \$o ) > ( \$i > \$o ) > \$o] :
( ~ ( R
@ ^ [Xx: \$i] :
( cP
| ~ ( cP ) )
@ ^ [Xx: \$i] :
( cP
& ~ ( cP ) ) )
& ! [Xx: \$i > \$o] :
( R @ Xx @ Xx )
& ! [Xx: \$i > \$o,Xy: \$i > \$o,Xz: \$i > \$o] :
( ( ( R @ Xx @ Xy )
& ( R @ Xy @ Xz ) )
=> ( R @ Xx @ Xz ) ) ) )).

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