%------------------------------------------------------------------------------
% File     : LCL006+2 : TPTP v9.0.0. Released v3.3.0.
% Domain   : Logic Calculi (Propositional)
% Axioms   : Hilbert's axiomatization of propositional logic
% Version  : [HB34] axioms.
% English  :

% Refs     : [HB34]  Hilbert & Bernays (1934), Grundlagen der Mathematick
%          : [Hac66] Hackstaff (1966), Systems of Formal Logic
%          : [Hal]   Halleck (URL), John Halleck's Logic Systems
%          : [She06] Shen (2006), Automated Proofs of Equivalence of Modal
% Source   : [Hal]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of formulae    :   18 (  18 unt;   0 def)
%            Number of atoms       :   18 (   0 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    0 (   0   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    1 (   1 avg)
%            Maximal term depth    :    0 (   0 avg)
%            Number of predicates  :   18 (  18 usr;  18 prp; 0-0 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    0 (   0   !;   0   ?)
% SPC      : 

% Comments : Requires LCL006+0, LCL006+1
%------------------------------------------------------------------------------
%----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 ).

%----The one explicit rule
fof(hilbert_modus_ponens,axiom,
    modus_ponens ).

%----The axioms
fof(hilbert_modus_tollens,axiom,
    modus_tollens ).

fof(hilbert_implies_1,axiom,
    implies_1 ).

fof(hilbert_implies_2,axiom,
    implies_2 ).

fof(hilbert_implies_3,axiom,
    implies_3 ).

fof(hilbert_and_1,axiom,
    and_1 ).

fof(hilbert_and_2,axiom,
    and_2 ).

fof(hilbert_and_3,axiom,
    and_3 ).

fof(hilbert_or_1,axiom,
    or_1 ).

fof(hilbert_or_2,axiom,
    or_2 ).

fof(hilbert_or_3,axiom,
    or_3 ).

fof(hilbert_equivalence_1,axiom,
    equivalence_1 ).

fof(hilbert_equivalence_2,axiom,
    equivalence_2 ).

fof(hilbert_equivalence_3,axiom,
    equivalence_3 ).

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

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