Some Experiments with Twee-Style Goal-Directedness
This work addresses the inefficiency of clause selection in saturation-based automated theorem proving by introducing a novel goal-directed clause selection strategy. The approach extends, for the first time, the idea of prioritizing clauses that share terms with the conjecture—originally employed in the Twee system—to full first-order logic. To achieve this generalization, the authors devise a term-sharing analysis mechanism that does not rely on equality-specific definitions. Experimental results demonstrate that the proposed strategy significantly enhances both the solving efficiency and success rate of the prover, thereby confirming its effectiveness and potential in general first-order logical reasoning scenarios.