Cooperation between Top - Down and Bottom

Top-down and bottom-up theorem proving approaches have each speciic advantages and disadvantages. Bottom-up provers proot from strong redundancy control and suuer from the lack of goal-orientation, whereas top-down provers are goal-oriented but have weak calculi when their proof lengths are considered. In order to integrate both approaches our method is to achieve cooperation between a top-down and a bottom-up prover: The top-down prover generates subgoal clauses, then they are processed by a bottom-up prover. We discuss theoretic aspects of this methodology and we introduce techniques for a relevancy-based ltering of generated subgoal clauses. Experiments with a model elimination and a superposition-based prover reveal the high potential of our cooperation approach.