TPTP Axioms File: LCL004-0.ax

```%------------------------------------------------------------------------------
% File     : LCL004-0 : TPTP v7.5.0. Released v2.3.0.
% Domain   : Logic Calculi (Propositional)
% Axioms   : Propositional logic deduction
% Version  : [WR27] axioms.
% English  :

% Refs     : [WR27]  Whitehead & Russell (1927), Principia Mathematica
% Source   : [WR27]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses    :    8 (   0 non-Horn;   6 unit;   2 RR)
%            Number of atoms      :   11 (   1 equality)
%            Maximal clause size  :    3 (   1 average)
%            Number of predicates :    3 (   0 propositional; 1-2 arity)
%            Number of functors   :    3 (   0 constant; 1-2 arity)
%            Number of variables  :   16 (   1 singleton)
%            Maximal term depth   :    4 (   2 average)
% SPC      :

% Comments : This axiomatization follows [WR27], allowing full detachment
%            but no chaining (which is a dependant theorem). Compare with
%            LCL003-0.ax.
%------------------------------------------------------------------------------
cnf(axiom_1_2,axiom,
( axiom(implies(or(A,A),A)) )).

cnf(axiom_1_3,axiom,
( axiom(implies(A,or(B,A))) )).

cnf(axiom_1_4,axiom,
( axiom(implies(or(A,B),or(B,A))) )).

cnf(axiom_1_5,axiom,
( axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) )).

cnf(axiom_1_6,axiom,
( axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))) )).

cnf(implies_definition,axiom,
( implies(X,Y) = or(not(X),Y) )).

cnf(rule_1,axiom,
( theorem(X)
| ~ axiom(X) )).

cnf(rule_2,axiom,
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) )).

% input_clause(rule_3,axiom,
%     [++theorem(implies(X,Z)),
%      --theorem(implies(X,Y)),
%      --theorem(implies(Y,Z))]).
%------------------------------------------------------------------------------
```