%------------------------------------------------------------------------------
% File     : LCL535+1 : TPTP v9.0.0. Released v3.3.0.
% Domain   : Logic Calculi (Propositional modal)
% Problem  : Prove axiom m9 from KM5 axiomatization of S5
% Version  : [HC96] axioms.
% English  :

% Refs     : [HC96]  Hughes & Cresswell (1996), A New Introduction to Modal
%          : [Hal]   Halleck (URL), John Halleck's Logic Systems
% Source   : [TPTP]
% Names    :

% Status   : Theorem
% Rating   : 0.52 v9.0.0, 0.53 v8.1.0, 0.56 v7.4.0, 0.57 v7.3.0, 0.66 v7.2.0, 0.69 v7.1.0, 0.70 v7.0.0, 0.67 v6.4.0, 0.69 v6.3.0, 0.67 v6.2.0, 0.64 v6.1.0, 0.70 v6.0.0, 0.65 v5.5.0, 0.74 v5.4.0, 0.75 v5.3.0, 0.78 v5.2.0, 0.65 v5.1.0, 0.71 v4.1.0, 0.74 v4.0.0, 0.71 v3.7.0, 0.75 v3.5.0, 0.68 v3.4.0, 0.79 v3.3.0
% Syntax   : Number of formulae    :   88 (  30 unt;   0 def)
%            Number of atoms       :  155 (  11 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   67 (   0   ~;   0   |;   3   &)
%                                         (  49 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   61 (  60 usr;  59 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   0 con; 1-2 aty)
%            Number of variables   :  110 ( 110   !;   0   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments :
%------------------------------------------------------------------------------
%----Include Hilbert's axiomatization of propositional logic
include('Axioms/LCL006+0.ax').
include('Axioms/LCL006+1.ax').
include('Axioms/LCL006+2.ax').
%----Include axioms of modal logic
include('Axioms/LCL007+0.ax').
include('Axioms/LCL007+1.ax').
%----Include axioms for KM5
include('Axioms/LCL007+2.ax').
%------------------------------------------------------------------------------
%----Modal definitions
fof(s1_0_op_possibly,axiom,
    op_possibly ).

fof(s1_0_op_or,axiom,
    op_or ).

fof(s1_0_op_implies,axiom,
    op_implies ).

fof(s1_0_op_strict_implies,axiom,
    op_strict_implies ).

fof(s1_0_op_equiv,axiom,
    op_equiv ).

fof(s1_0_op_strict_equiv,axiom,
    op_strict_equiv ).

%----Conjecture
fof(s1_0_m6s3m9b_axiom_m9,conjecture,
    axiom_m9 ).

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