Near-Horn Prolog is an extension of Prolog designed to handle disjunction and classical negation. The emphasis here is on minimal change from standard Prolog in regard to notation, derivation form, and speed of inner-loop computation. The procedure is optimized for the input program that is near-Horn; i.e., a program where almost all clauses are definite clauses. This paper goes beyond the near-Horn focus to report on the completeness of one version of nH-Prolog, along with soundness of the procedure. Completeness is important here not only for the usual reasons of guaranteed success on small problems and insight into the behavior of the procedure but also because we anticipate the introduction of negation-as-failure which requires conviction that a proof will be found if a proof exists.