TPTP Axioms File: BOO004-0.ax


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% File     : BOO004-0 : TPTP v7.5.0. Released v1.0.0.
% Domain   : Boolean Algebra
% Axioms   : Boolean algebra (equality) axioms
% Version  : [Ver94] (equality) axioms.
% English  :

% Refs     : [Ver94] Veroff (1994), Problem Set
% Source   : [Ver94]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses    :    8 (   0 non-Horn;   8 unit;   0 RR)
%            Number of atoms      :    8 (   8 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  :   14 (   0 singleton)
%            Maximal term depth   :    3 (   2 average)
% SPC      : 

% Comments :
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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(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) )).

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

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

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

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

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

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