## TPTP Axioms File: RNG004-0.ax

```%--------------------------------------------------------------------------
% File     : RNG004-0 : TPTP v7.5.0. Released v1.0.0.
% Domain   : Ring Theory (Alternative)
% Axioms   : Alternative ring theory (equality) axioms
% Version  : [AH90] (equality) axioms.
% English  :

% Refs     : [AH90]  Anantharaman & Hsiang (1990), Automated Proofs of the
% Source   : [AH90]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses    :   17 (   0 non-Horn;  15 unit;   3 RR)
%            Number of atoms      :   19 (  19 equality)
%            Maximal clause size  :    2 (   1 average)
%            Number of predicates :    1 (   0 propositional; 2-2 arity)
%            Number of functors   :    4 (   1 constant; 0-2 arity)
%            Number of variables  :   32 (   2 singleton)
%            Maximal term depth   :    3 (   2 average)
% SPC      :

%--------------------------------------------------------------------------
%----There exists an additive identity element [1]

%----Multiplicative identity [2] & [3]
cnf(left_multiplicative_zero,axiom,

cnf(right_multiplicative_zero,axiom,

%----Sum of inverses [5]
cnf(sum_of_inverses,axiom,

%----Inverse of additive_inverse of X is X [6]

%----Distribution of multiply over add [7] & [8]

%----Right alternative law [9]
cnf(right_alternative,axiom,
( multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)) )).

%----Left alternative law [10]
cnf(left_alternative,axiom,
( multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)) )).

%----Inverse and product [11] & [12]
cnf(inverse_product1,axiom,

cnf(inverse_product2,axiom,