Some Experiments with Twee-Style Goal-Directedness

2026-07-29

AI Summary

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.

Abstract

In saturation-based theorem proving, selecting the next clause for processing is a major concern. Twee has successfully applied the idea of preferring clauses that share terms with the conjecture by adding equational definitions to transform the problem. In this paper, we apply the idea to the full first-order case, and offer an alternative implementation based on shared terms that shows very promising results.

Problem

• saturation-based theorem proving
• clause selection
• goal-directedness
• first-order logic
• shared terms

Innovation

• goal-directedness
• saturation-based theorem proving
• first-order logic
• shared terms
• clause selection