%--------------------------------------------------------------------------
% File     : LCL003-0 : TPTP v9.0.0. Released v1.0.0.
% Domain   : Logic Calculi (Propositional)
% Axioms   : Propositional logic deduction
% Version  : [WR27] axioms : Reduced & Augmented.
% English  :

% Refs     : [WR27]  Whitehead & Russell (1927), Principia Mathematica
%          : [ORo89] O'Rourke (1989), LT Revisited: Explanation-Based Learn
%          : [SE94]  Segre & Elkan (1994), A High-Performance Explanation-B
% Source   : [SE94]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses     :    8 (   5 unt;   0 nHn;   3 RR)
%            Number of literals    :   13 (   0 equ;   5 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   2 usr;   0 prp; 1-1 aty)
%            Number of functors    :    2 (   2 usr;   0 con; 1-2 aty)
%            Number of variables   :   17 (   1 sgn)
% SPC      : 

% Comments : Reduced to use only or and not, and includes a redundant rule
%            of transitivity of implication, and a reduced rule of
%            detachment.
%--------------------------------------------------------------------------
cnf(axiom_1_2,axiom,
    axiom(or(not(or(A,A)),A)) ).

cnf(axiom_1_3,axiom,
    axiom(or(not(A),or(B,A))) ).

cnf(axiom_1_4,axiom,
    axiom(or(not(or(A,B)),or(B,A))) ).

cnf(axiom_1_5,axiom,
    axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) ).

cnf(axiom_1_6,axiom,
    axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) ).

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

cnf(rule_2,axiom,
    ( theorem(X)
    | ~ axiom(or(not(Y),X))
    | ~ theorem(Y) ) ).

cnf(rule_3,axiom,
    ( theorem(or(not(X),Z))
    | ~ axiom(or(not(X),Y))
    | ~ theorem(or(not(Y),Z)) ) ).

%--------------------------------------------------------------------------