%------------------------------------------------------------------------------
% File     : LCL473+1 : TPTP v9.0.0. Released v3.3.0.
% Domain   : Logic Calculi (Propositional)
% Problem  : Prove Hilbert's equivalence_2 axiom from Lukasiewicz's system
% Version  : [Zen73] axioms.
% English  :

% Refs     : [Zem73] Zeman (1973), Modal Logic, the Lewis-Modal systems
%          : [Hal]   Halleck (URL), John Halleck's Logic Systems
% Source   : [TPTP]
% Names    :

% Status   : Theorem
% Rating   : 0.85 v9.0.0, 0.86 v8.1.0, 0.81 v7.5.0, 0.78 v7.4.0, 0.77 v7.3.0, 0.79 v7.2.0, 0.83 v6.4.0, 0.85 v6.3.0, 0.83 v6.2.0, 0.88 v6.1.0, 0.90 v6.0.0, 0.91 v5.5.0, 0.96 v5.4.0, 1.00 v5.2.0, 0.95 v5.1.0, 0.86 v5.0.0, 0.79 v4.1.0, 0.78 v4.0.0, 0.79 v3.7.0, 0.80 v3.5.0, 0.79 v3.4.0, 0.84 v3.3.0
% Syntax   : Number of formulae    :   43 (  12 unt;   0 def)
%            Number of atoms       :   77 (   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 Lukasiewicz's axiomatization of propositional logic
include('Axioms/LCL006+3.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 ).

fof(hilbert_equivalence_2,conjecture,
    equivalence_2 ).

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