## TPTP Axioms File: LCL006+3.ax

```%------------------------------------------------------------------------------
% File     : LCL006+3 : TPTP v7.5.0. Released v3.3.0.
% Domain   : Logic Calculi (Propositional)
% Axioms   : Lukasiewicz's axiomatization of propositional logic
% Version  : [Zem73] axioms.
% English  :

% Refs     : [Zem73] Zeman (1973), Modal Logic, the Lewis-Modal systems
%          : [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    :    8 (   8 unit)
%            Number of atoms       :    8 (   0 equality)
%            Maximal formula depth :    1 (   1 average)
%            Number of connectives :    0 (   0 ~  ;   0  |;   0  &)
%                                         (   0 <=>;   0 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    8 (   8 propositional; 0-0 arity)
%            Number of functors    :    0 (   0 constant; --- arity)
%            Number of variables   :    0 (   0 singleton;   0 !;   0 ?)
%            Maximal term depth    :    0 (   0 average)
% SPC      :

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

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

%----The axioms
fof(luka_cn1,axiom,cn1).

fof(luka_cn2,axiom,cn2).

fof(luka_cn3,axiom,cn3 ).

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

%------------------------------------------------------------------------------
```