%------------------------------------------------------------------------------
% File     : LCL595^1 : TPTP v9.0.0. Released v3.6.0.
% Domain   : Logical Calculi
% Problem  : Is axiom T equivalent to reflexivity of R in K
% Version  : [BP09] axioms.
% English  :

% Refs     : [BP09]  Benzmueller & Paulson (2009), Exploring Properties of
% Source   : [BP09]
% Names    : K-T-c [BP09]

% Status   : Theorem
% Rating   : 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.33 v3.7.0
% Syntax   : Number of formulae    :   79 (  36 unt;  42 typ;  36 def)
%            Number of atoms       :   94 (  40 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  130 (   6   ~;   3   |;  14   &;  96   @)
%                                         (   2 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   1 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :  224 ( 224   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   48 (  45 usr;   7 con; 0-4 aty)
%            Number of variables   :  109 (  76   ^;  23   !;  10   ?; 109   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : 
%------------------------------------------------------------------------------
%----Include simple maths definitions and axioms
include('Axioms/LCL008^0.ax').
include('Axioms/SET008^2.ax').
%------------------------------------------------------------------------------
%----Signature
thf(r,type,
    r: $i > $i > $o ).

%----Conjecture
thf(thm,conjecture,
    ( ! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ A ) @ A ) )
  <=> ( reflexive @ r ) ) ).

%------------------------------------------------------------------------------