## TPTP Problem File: SEV136^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV136^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem THM203
% Version  : Especial.
% English  : B&B-P's defn of TRCL is the minimal transitive reflexive
%            relation containing r.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0426 [Bro09]
%          : THM203 [TPS]

% Status   : Theorem
% Rating   : 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   38 (   0 equality;  38 variable)
%            Maximal formula depth :   15 (   8 average)
%            Number of connectives :   37 (   0   ~;   0   |;   4   &;  26   @)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :   13 (   0 sgn;  13   !;   0   ?;   0   ^)
%                                         (  13   :;   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
%          : Polymorphic definitions expanded.
%------------------------------------------------------------------------------
thf(a_type,type,(
a: \$tType )).

thf(cTHM203_pme,conjecture,(
! [Xr: a > a > \$o,T: ( a > a > \$o ) > a > a > \$o] :
( ( ! [Xx: a] :
( T @ Xr @ Xx @ Xx )
& ! [Xx: a,Xy: a,Xz: a] :
( ( ( T @ Xr @ Xx @ Xy )
& ( T @ Xr @ Xy @ Xz ) )
=> ( T @ Xr @ Xx @ Xz ) )
& ! [Xx: a,Xy: a] :
( ( Xr @ Xx @ Xy )
=> ( T @ Xr @ Xx @ Xy ) ) )
=> ! [Xx: a,Xy: a] :
( ! [Xx0: a > \$o] :
( ! [Xy0: a,Xz: a] :
( ( ( Xr @ Xy0 @ Xz )
& ( Xx0 @ Xy0 ) )
=> ( Xx0 @ Xz ) )
=> ( ( Xx0 @ Xx )
=> ( Xx0 @ Xy ) ) )
=> ( T @ Xr @ Xx @ Xy ) ) ) )).

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