%------------------------------------------------------------------------------
% File     : LCL453+1 : TPTP v8.2.0. Released v3.3.0.
% Domain   : Logic Calculi (Propositional)
% Problem  : Prove Lukasiewicz's cn3 axiom from Hilbert's axiomatization
% Version  : [HB34] axioms.
% English  :

% Refs     : [HB34]  Hilbert & Bernays (1934), Grundlagen der Mathematick
%          : [Hal]   Halleck (URL), John Halleck's Logic Systems
% Source   : [TPTP]
% Names    :

% Status   : Theorem
% Rating   : 0.36 v8.2.0, 0.33 v8.1.0, 0.36 v7.5.0, 0.34 v7.4.0, 0.30 v7.3.0, 0.38 v7.1.0, 0.35 v7.0.0, 0.33 v6.4.0, 0.38 v6.3.0, 0.29 v6.2.0, 0.32 v6.1.0, 0.40 v6.0.0, 0.52 v5.4.0, 0.54 v5.3.0, 0.56 v5.2.0, 0.45 v5.1.0, 0.48 v5.0.0, 0.46 v4.1.0, 0.48 v4.0.0, 0.46 v3.7.0, 0.40 v3.5.0, 0.37 v3.4.0, 0.47 v3.3.0
% Syntax   : Number of formulae    :   53 (  22 unt;   0 def)
%            Number of atoms       :   87 (   6 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   34 (   0   ~;   0   |;   1   &)
%                                         (  26 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   34 (  33 usr;  32 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   0 con; 1-2 aty)
%            Number of variables   :   65 (  65   !;   0   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments :
%------------------------------------------------------------------------------
%----Include axioms of propositional logic
include('Axioms/LCL006+0.ax').
include('Axioms/LCL006+1.ax').
%----Include Hilbert's axiomatization of propositional logic
include('Axioms/LCL006+2.ax').
%------------------------------------------------------------------------------
%----Operator definitions to reduce everything to and & not
fof(luka_op_or,axiom,
    op_or ).

fof(luka_op_implies,axiom,
    op_implies ).

fof(luka_op_equiv,axiom,
    op_equiv ).

fof(luka_cn3,conjecture,
    cn3 ).

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