%------------------------------------------------------------------------------
% File     : LCL580^1 : TPTP v4.0.1. Released v3.6.0.
% Domain   : Logical Calculi
% Problem  : Popkorn problem 1
% Version  : [BP09] axioms.
% English  :

% Refs     : [Pop95] Popkorn (1995), First Steps in Modal Logic
%          : [BP09]  Benzmueller & Paulson (2009), Exploring Properties of
% Source   : [BP09]
% Names    : K-a [BP09]

% Status   : Theorem
% Rating   : 0.00 v4.0.0, 0.33 v3.7.0
% Syntax   : Number of formulae    :   37 (   2 unit;  21 type;  15 defn)
%            Number of atoms       :  219 (  15 equality;  40 variable)
%            Maximal formula depth :    9 (   5 average)
%            Number of connectives :   38 (   3   ~;   1   |;   2   &;  31   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&;   0  !!;   0  ??)
%            Number of type conns  :   81 (  81   >;   0   *;   0   +)
%            Number of symbols     :   22 (  21   :;   0  :=)
%            Number of variables   :   36 (   2 sgn;   4   !;   4   ?;  28   ^)
%                                         (  36   :;   0  :=;   0  !>;   0  ?*)

% Comments : THF0 syntax
%------------------------------------------------------------------------------
%----Include simple maths definitions and axioms
include('Axioms/LCL008^0.ax').
%------------------------------------------------------------------------------
%----Signature
thf(r,type,(
    r: $i > $i > $o )).

%----Conjecture
thf(thm,conjecture,
    ( mvalid @ ( mbox @ r @ mtrue ) )).

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