The Search Eeciency of Theorem Proving Strategies: an Analytical Comparison K I N F O R M a T I K Im Stadtwald D 66123 Saarbr Ucken Germany Authors' Addresses Publication Notes

We analyze the search e ciency of a number of common refutational theorem proving strategies for rst-order logic. Search e ciency is concerned with the total number of proofs and partial proofs generated, rather than with the sizes of the proofs. We show that most common strategies produce search spaces of exponential size even on simple sets of clauses, or else are not sensitive to the goal. However, clause linking, which uses a reduction to propositional calculus, has behavior that is more favorable in some respects, a property that it shares with methods that cache subgoals. A strategy which is of interest for term-rewriting based theorem proving is the A-ordering strategy, and we discuss it in some detail. We show some advantages of A-ordering over other strategies, which may help to explain its e ciency in practice. We also point out some of its combinatorial ine ciencies, especially in relation to goal-sensitivity and irrelevant clauses. In addition, SLD-resolution, which is of importance for Prolog implementation, has combinatorial ine ciencies; this may suggest basing Prolog implementations on a di erent theorem proving strategy.