%--------------------------------------------------------------------------
% File     : BOO003-0 : TPTP v8.2.0. Released v1.0.0.
% Domain   : Boolean Algebra
% Axioms   : Boolean algebra (equality) axioms
% Version  : [ANL] (equality) axioms.
% English  :

% Refs     :
% Source   : [ANL]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses     :   14 (  14 unt;   0 nHn;   0 RR)
%            Number of literals    :   14 (  14 equ;   0 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   24 (   0 sgn)
% SPC      : 

% Comments :
%--------------------------------------------------------------------------
cnf(commutativity_of_add,axiom,
    add(X,Y) = add(Y,X) ).

cnf(commutativity_of_multiply,axiom,
    multiply(X,Y) = multiply(Y,X) ).

cnf(distributivity1,axiom,
    add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ).

cnf(distributivity2,axiom,
    add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ).

cnf(distributivity3,axiom,
    multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ).

cnf(distributivity4,axiom,
    multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ).

cnf(additive_inverse1,axiom,
    add(X,inverse(X)) = multiplicative_identity ).

cnf(additive_inverse2,axiom,
    add(inverse(X),X) = multiplicative_identity ).

cnf(multiplicative_inverse1,axiom,
    multiply(X,inverse(X)) = additive_identity ).

cnf(multiplicative_inverse2,axiom,
    multiply(inverse(X),X) = additive_identity ).

cnf(multiplicative_id1,axiom,
    multiply(X,multiplicative_identity) = X ).

cnf(multiplicative_id2,axiom,
    multiply(multiplicative_identity,X) = X ).

cnf(additive_id1,axiom,
    add(X,additive_identity) = X ).

cnf(additive_id2,axiom,
    add(additive_identity,X) = X ).

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