TPTP Axioms File: CAT002-0.ax


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% File     : CAT002-0 : TPTP v7.4.0. Released v1.0.0.
% Domain   : Category theory
% Axioms   : Category theory (equality) axioms
% Version  : [Qua89] (equality) axioms.
% English  :

% Refs     : [Qua89] Quaife (1989), Email to L. Wos
% Source   : [ANL]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of clauses    :    7 (   0 non-Horn;   4 unit;   3 RR)
%            Number of atoms      :   11 (  11 equality)
%            Maximal clause size  :    3 (   2 average)
%            Number of predicates :    1 (   0 propositional; 2-2 arity)
%            Number of functors   :    3 (   0 constant; 1-2 arity)
%            Number of variables  :   11 (   0 singleton)
%            Maximal term depth   :    3 (   2 average)
% SPC      : 

% Comments :
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%----Composition is read right-to-left: compose(x,y)(G) means -y(x(G)) The
%----axioms themselves
cnf(codomain_of_domain_is_domain,axiom,
    ( codomain(domain(X)) = domain(X) )).

cnf(domain_of_codomain_is_codomain,axiom,
    ( domain(codomain(X)) = codomain(X) )).

cnf(domain_composition,axiom,
    ( compose(domain(X),X) = X )).

cnf(codomain_composition,axiom,
    ( compose(X,codomain(X)) = X )).

cnf(codomain_domain1,axiom,
    ( codomain(X) != domain(Y)
    | domain(compose(X,Y)) = domain(X) )).

cnf(codomain_domain2,axiom,
    ( codomain(X) != domain(Y)
    | codomain(compose(X,Y)) = codomain(Y) )).

cnf(star_property,axiom,
    ( codomain(X) != domain(Y)
    | codomain(Y) != domain(Z)
    | compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )).

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