%--------------------------------------------------------------------------
% File     : BOO002-0 : TPTP v9.0.0. Released v1.0.0.
% Domain   : Boolean Algebra
% Axioms   : Boolean algebra axioms
% Version  : [MOW76] axioms.
% English  :

% Refs     : [Whi61] Whitesitt (1961), Boolean Algebra and Its Applications
%          : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% Source   : [MOW76]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses     :   22 (  10 unt;   0 nHn;  12 RR)
%            Number of literals    :   60 (   2 equ;  38 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   0 prp; 2-3 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   82 (   0 sgn)
% SPC      : 

% Comments :
%--------------------------------------------------------------------------
cnf(closure_of_addition,axiom,
    sum(X,Y,add(X,Y)) ).

cnf(closure_of_multiplication,axiom,
    product(X,Y,multiply(X,Y)) ).

cnf(commutativity_of_addition,axiom,
    ( ~ sum(X,Y,Z)
    | sum(Y,X,Z) ) ).

cnf(commutativity_of_multiplication,axiom,
    ( ~ product(X,Y,Z)
    | product(Y,X,Z) ) ).

cnf(additive_identity1,axiom,
    sum(additive_identity,X,X) ).

cnf(additive_identity2,axiom,
    sum(X,additive_identity,X) ).

cnf(multiplicative_identity1,axiom,
    product(multiplicative_identity,X,X) ).

cnf(multiplicative_identity2,axiom,
    product(X,multiplicative_identity,X) ).

cnf(distributivity1,axiom,
    ( ~ product(X,Y,V1)
    | ~ product(X,Z,V2)
    | ~ sum(Y,Z,V3)
    | ~ product(X,V3,V4)
    | sum(V1,V2,V4) ) ).

cnf(distributivity2,axiom,
    ( ~ product(X,Y,V1)
    | ~ product(X,Z,V2)
    | ~ sum(Y,Z,V3)
    | ~ sum(V1,V2,V4)
    | product(X,V3,V4) ) ).

cnf(distributivity3,axiom,
    ( ~ product(Y,X,V1)
    | ~ product(Z,X,V2)
    | ~ sum(Y,Z,V3)
    | ~ product(V3,X,V4)
    | sum(V1,V2,V4) ) ).

cnf(distributivity4,axiom,
    ( ~ product(Y,X,V1)
    | ~ product(Z,X,V2)
    | ~ sum(Y,Z,V3)
    | ~ sum(V1,V2,V4)
    | product(V3,X,V4) ) ).

cnf(distributivity5,axiom,
    ( ~ sum(X,Y,V1)
    | ~ sum(X,Z,V2)
    | ~ product(Y,Z,V3)
    | ~ sum(X,V3,V4)
    | product(V1,V2,V4) ) ).

cnf(distributivity6,axiom,
    ( ~ sum(X,Y,V1)
    | ~ sum(X,Z,V2)
    | ~ product(Y,Z,V3)
    | ~ product(V1,V2,V4)
    | sum(X,V3,V4) ) ).

cnf(distributivity7,axiom,
    ( ~ sum(Y,X,V1)
    | ~ sum(Z,X,V2)
    | ~ product(Y,Z,V3)
    | ~ sum(V3,X,V4)
    | product(V1,V2,V4) ) ).

cnf(distributivity8,axiom,
    ( ~ sum(Y,X,V1)
    | ~ sum(Z,X,V2)
    | ~ product(Y,Z,V3)
    | ~ product(V1,V2,V4)
    | sum(V3,X,V4) ) ).

cnf(additive_inverse1,axiom,
    sum(inverse(X),X,multiplicative_identity) ).

cnf(additive_inverse2,axiom,
    sum(X,inverse(X),multiplicative_identity) ).

cnf(multiplicative_inverse1,axiom,
    product(inverse(X),X,additive_identity) ).

cnf(multiplicative_inverse2,axiom,
    product(X,inverse(X),additive_identity) ).

%-----Well definedness of the operations
cnf(addition_is_well_defined,axiom,
    ( ~ sum(X,Y,U)
    | ~ sum(X,Y,V)
    | U = V ) ).

cnf(multiplication_is_well_defined,axiom,
    ( ~ product(X,Y,U)
    | ~ product(X,Y,V)
    | U = V ) ).

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