## TPTP Axioms File: LCL007+2.ax

```%------------------------------------------------------------------------------
% File     : LCL007+2 : TPTP v7.5.0. Released v3.3.0.
% Domain   : Logic Calculi (Propositional modal)
% Axioms   : KM5 axiomatization of S5 based on Hilbert's PC
% Version  : [HC96] axioms.
% English  :

% Refs     : [HC96]  Hughes & Cresswell (1996), A New Introduction to Modal
%          : [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    :    5 (   5 unit)
%            Number of atoms       :    5 (   0 equality)
%            Maximal formula depth :    1 (   1 average)
%            Number of connectives :    0 (   0 ~  ;   0  |;   0  &)
%                                         (   0 <=>;   0 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    5 (   5 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, LCL006+2 LCL007+0 LCL007+1
%------------------------------------------------------------------------------
%----Modal definitions
fof(km5_op_possibly,axiom,op_possibly).

%----Modal rules
fof(km5_necessitation,axiom,necessitation).

%----Modal axioms
fof(km5_axiom_K,axiom,axiom_K).

fof(km5_axiom_M,axiom,axiom_M).

fof(km5_axiom_5,axiom,axiom_5).

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