2420	 Experiments with an Automatic Theorem-Prover HavingPartial Ordering Inference Rules	 Automatic theorem-provers need to be made much more efficient. With this in mind Slagle has shown how the axioms for partial ordering can be replaced by built-in inference rules when using a particular theorem-proving algorithm based upon hyper-resolution and paramodulation. The new rules embody the transitivity of partial orderings and the close relationship between predicates. A program has been developed using a modified version of these rules. This new theorem-prover has been found to be very powerful for solving problems involving partial orderings. This paper presents a detailed description of the program and a comprehensive account of the experiments that have been performed with it. theorem-proving partial ordering resolution hyper-resolution P -resolution paramodulation inference rules heuristics
