## TPTP Axioms File: LCL006+1.ax

```%------------------------------------------------------------------------------
% File     : LCL006+1 : TPTP v7.5.0. Released v3.3.0.
% Domain   : Logic Calculi (Propositional)
% Axioms   : Propositional 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    :    5 (   0 unit)
%            Number of atoms       :   10 (   5 equality)
%            Maximal formula depth :    4 (   4 average)
%            Number of connectives :    5 (   0 ~  ;   0  |;   0  &)
%                                         (   0 <=>;   5 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    6 (   5 propositional; 0-2 arity)
%            Number of functors    :    5 (   0 constant; 1-2 arity)
%            Number of variables   :   10 (   0 singleton;  10 !;   0 ?)
%            Maximal term depth    :    4 (   3 average)
% SPC      :

%------------------------------------------------------------------------------
%----Definitions
fof(op_or,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) )).

fof(op_and,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) )).

fof(op_implies_and,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) )).

fof(op_implies_or,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) )).

fof(op_equiv,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X))  )).

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