## TPTP Problem File: SEV074^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV074^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem THM523
% Version  : Especial.
% English  : Theorem about reflexive closure of relations.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0522 [Bro09]
%          : THM523 [TPS]

% Status   : Theorem
% Rating   : 0.73 v7.5.0, 0.57 v7.4.0, 0.78 v7.2.0, 0.88 v7.1.0, 0.75 v7.0.0, 0.71 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.71 v5.5.0, 0.83 v5.4.0, 0.80 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   18 (   1 equality;  17 variable)
%            Maximal formula depth :   13 (   8 average)
%            Number of connectives :   15 (   0   ~;   1   |;   1   &;  10   @)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :    7 (   0 sgn;   7   !;   0   ?;   0   ^)
%                                         (   7   :;   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(a_type,type,(
a: \$tType )).

thf(cTHM523_pme,conjecture,(
! [Xr: a > a > \$o,Xx: a,Xy: a] :
( ( ( Xr @ Xx @ Xy )
| ( Xx = Xy ) )
<=> ! [Xp: a > a > \$o] :
( ( ! [Xx0: a,Xy0: a] :
( ( Xr @ Xx0 @ Xy0 )
=> ( Xp @ Xx0 @ Xy0 ) )
& ! [Xx0: a] :
( Xp @ Xx0 @ Xx0 ) )
=> ( Xp @ Xx @ Xy ) ) ) )).

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