Cooperation between Top-Down and Bottom-Up Theorem Provers by Subgoal Clause Transfer

• Top-down and bottom-up theorem proving approaches have each specific ad-vantages and disadvantages. Bottom-up provers profit from strong redundancycontrol and suffer from the lack of goal-orientation, whereas top-down provers aregoal-oriented but have weak calculi when their proof lengths are considered. Inorder to integrate both approaches our method is to achieve cooperation betweena top-down and a bottom-up prover: The top-down prover generates subgoalclauses, then they are processed by a bottom-up prover. We discuss theoreticaspects of this methodology and we introduce techniques for a relevancy-basedfiltering of generated subgoal clauses. Experiments with a model eliminationand a superposition-based prover reveal the high potential of our cooperation approach.The author was supported by the Deutsche Forschungsgemeinschaft (DFG).

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