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%--------------------------------------------------------------------------
% File : BOO003-0 : TPTP v6.4.0. 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 )).
%--------------------------------------------------------------------------
|
