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% File     : ROB001-0 : TPTP v8.2.0. 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 (   3 unt;   0 nHn;   0 RR)
%            Number of literals    :    3 (   3 equ;   0 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    2 (   2 usr;   0 con; 1-2 aty)
%            Number of variables   :    7 (   0 sgn)
% 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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