%------------------------------------------------------------------------------
% File     : LCL553+1 : TPTP v9.0.0. Released v3.3.0.
% Domain   : Logic Calculi (Propositional modal)
% Problem  : Prove Hilbert's implies_2 axiom from the S1-0 system
% Version  : [Fey50] axioms.
% English  :

% Refs     : [Fey50] Feys (1950), Les systemes formalises de modalites aris
%          : [Hal]   Halleck (URL), John Halleck's Logic Systems
% Source   : [TPTP]
% Names    :

% Status   : Theorem
% Rating   : 0.70 v9.0.0, 0.72 v8.2.0, 0.78 v8.1.0, 0.81 v7.5.0, 0.84 v7.4.0, 0.83 v7.1.0, 0.87 v7.0.0, 0.93 v6.4.0, 0.88 v6.3.0, 0.83 v6.2.0, 0.88 v6.1.0, 0.90 v6.0.0, 0.91 v5.5.0, 0.89 v5.4.0, 0.93 v5.2.0, 0.85 v5.1.0, 0.86 v5.0.0, 0.88 v4.1.0, 0.83 v4.0.1, 0.87 v4.0.0, 0.88 v3.7.0, 0.95 v3.3.0
% Syntax   : Number of formulae    :   77 (  19 unt;   0 def)
%            Number of atoms       :  144 (  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 axioms of propositional logic
include('Axioms/LCL006+0.ax').
include('Axioms/LCL006+1.ax').
%----Include axioms of modal logic
include('Axioms/LCL007+0.ax').
include('Axioms/LCL007+1.ax').
%----Include axioms for S1-0
include('Axioms/LCL007+4.ax').
%------------------------------------------------------------------------------
%----Operator definitions to reduce everything to and & not
fof(hilbert_op_or,axiom,
    op_or ).

fof(hilbert_op_implies_and,axiom,
    op_implies_and ).

fof(hilbert_op_equiv,axiom,
    op_equiv ).

%----Admissible but not required for completeness. With it much more can
%----be done.
fof(substitution_of_equivalents,axiom,
    substitution_of_equivalents ).

%----Conjecture
fof(hilbert_implies_2,conjecture,
    implies_2 ).

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