%------------------------------------------------------------------------------
% File     : LCL004-0 : TPTP v9.0.0. 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 (   6 unt;   0 nHn;   2 RR)
%            Number of literals    :   11 (   1 equ;   3 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   0 prp; 1-2 aty)
%            Number of functors    :    3 (   3 usr;   0 con; 1-2 aty)
%            Number of variables   :   16 (   1 sgn)
% 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))]).
%------------------------------------------------------------------------------