## TPTP Axioms File: LCL003-0.ax

```%--------------------------------------------------------------------------
% File     : LCL003-0 : TPTP v7.5.0. 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 (   0 non-Horn;   5 unit;   3 RR)
%            Number of atoms      :   13 (   0 equality)
%            Maximal clause size  :    3 (   2 average)
%            Number of predicates :    2 (   0 propositional; 1-1 arity)
%            Number of functors   :    2 (   0 constant; 1-2 arity)
%            Number of variables  :   17 (   1 singleton)
%            Maximal term depth   :    5 (   3 average)
% 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)) )).

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