On the Completeness of FLH-Resolution

First-literal hyper-resolution (FLH) is a reenement of ordinary hyper-resolution in that positive clauses are only resolved upon their rst literals. In this respect, positive literals are ordered in every clause, but negative literals are not. Due to the ordering of literals in this resolution method, standard techniques for demonstrating ground completeness have proven ineeective. In this paper we prove both the ground completeness and the general completeness of rst-literal hyper-resolution for rst-order logic (FOL) using a clause-ordering and modeling procedure. This technique also suggests a new proof procedure, ETOS-FLH-resolution, a reenement of FLH-resolution, which is more restrictive in that clauses are ordered in a tree with the consequent advantage that only one resolvent is generated at each resolution step. This proof also has an important implication in the completeness of a version of the interactive prover IMPLY.