## TPTP Axioms File: LCL007+1.ax

```%------------------------------------------------------------------------------
% File     : LCL007+1 : TPTP v7.5.0. Released v3.3.0.
% Domain   : Logic Calculi (Propositional modal)
% Axioms   : Propositional modal logic definitions
% Version  : [She06] axioms.
% English  :

% Refs     : [Hal]   Halleck (URL), John Halleck's Logic Systems
%          : [She06] Shen (2006), Automated Proofs of Equivalence of Modal
% Source   : [She06]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of formulae    :    4 (   0 unit)
%            Number of atoms       :    8 (   4 equality)
%            Maximal formula depth :    4 (   4 average)
%            Number of connectives :    4 (   0 ~  ;   0  |;   0  &)
%                                         (   0 <=>;   4 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    5 (   4 propositional; 0-2 arity)
%            Number of functors    :    7 (   0 constant; 1-2 arity)
%            Number of variables   :    6 (   0 singleton;   6 !;   0 ?)
%            Maximal term depth    :    4 (   3 average)
% SPC      :

%------------------------------------------------------------------------------
%----Definitions
fof(op_possibly,axiom,
( op_possibly
=> ! [X] : possibly(X) = not(necessarily(not(X))) )).

fof(op_necessarily,axiom,
( op_necessarily
=> ! [X] : necessarily(X) = not(possibly(not(X))) )).

fof(op_strict_implies,axiom,
( op_strict_implies
=> ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) )).

fof(op_strict_equiv,axiom,
( op_strict_equiv
=> ! [X,Y] : strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) )).

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