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% File     : ROB001-0 : TPTP v7.2.0. Released v1.0.0.
% Domain   : Robbins algebra
% Axioms   : Robbins algebra axioms
% Version  : [Win90] (equality) axioms.
% English  :

% Refs     : [HMT71] Henkin et al. (1971), Cylindrical Algebras
%          : [Win90] Winker (1990), Robbins Algebra: Conditions that make a
% Source   : [OTTER]
% Names    : Lemma 2.2 [Win90]

% Status   : Satisfiable
% Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR)
%            Number of atoms      :    3 (   3 equality)
%            Maximal clause size  :    1 (   1 average)
%            Number of predicates :    1 (   0 propositional; 2-2 arity)
%            Number of functors   :    2 (   0 constant; 1-2 arity)
%            Number of variables  :    7 (   0 singleton)
%            Maximal term depth   :    6 (   3 average)
% SPC      : 

% Comments :
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cnf(commutativity_of_add,axiom,
    ( add(X,Y) = add(Y,X) )).

cnf(associativity_of_add,axiom,
    ( add(add(X,Y),Z) = add(X,add(Y,Z)) )).

cnf(robbins_axiom,axiom,
    ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X )).

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