TPTP Axioms File: BOO003-0.ax


%--------------------------------------------------------------------------
% File     : BOO003-0 : TPTP v7.5.0. 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 (   0 non-Horn;  14 unit;   0 RR)
%            Number of atoms      :   14 (  14 equality)
%            Maximal clause size  :    1 (   1 average)
%            Number of predicates :    1 (   0 propositional; 2-2 arity)
%            Number of functors   :    5 (   2 constant; 0-2 arity)
%            Number of variables  :   24 (   0 singleton)
%            Maximal term depth   :    3 (   2 average)
% 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 )).

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