SAT solving for variants of first-order subsumption

• Published in: Formal methods in system design Vol. 67; no. 1; pp. 27 - 70
• Main Authors: Coutelier, Robin, Rath, Jakob, Rawson, Michael, Biere, Armin, Kovács, Laura
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2025; Springer Nature B.V
• Subjects: Automation; CAE) and Design; Circuits and Systems; Computer-Aided Engineering (CAD; Cybersecurity; Electrical Engineering; Engineering; Polynomials; Searching; Software Engineering/Programming and Operating Systems; Solvers; Systems engineering; Theorem proving; Subsumption; First-order theorem proving; Saturation; SAT solving
• ISSN: 0925-9856; 1572-8102; 1572-8102
• DOI: 10.1007/s10703-024-00454-1

Automated reasoners, such as SAT/SMT solvers and first-order provers, are becoming the backbones of rigorous systems engineering, being used for example in applications of system verification, program synthesis, and cybersecurity. Automation in these domains crucially depends on the efficiency of the underlying reasoners towards finding proofs and/or counterexamples of the task to be enforced. In order to gain efficiency, automated reasoners use dedicated proof rules to keep proof search tractable. To this end, (variants of) subsumption is one of the most important proof rules used by automated reasoners, ranging from SAT solvers to first-order theorem provers and beyond. It is common that millions of subsumption checks are performed during proof search, necessitating efficient implementations. However, in contrast to propositional subsumption as used by SAT solvers and implemented using sophisticated polynomial algorithms, first-order subsumption in first-order theorem provers involves NP-complete search queries, turning the efficient use of first-order subsumption into a huge practical burden. In this paper we argue that the integration of a dedicated SAT solver opens up new venues for efficient implementations of first-order subsumption and related rules. We show that, by using a flexible learning approach to choose between various SAT encodings of subsumption variants, we greatly improve the scalability of first-order theorem proving. Our experimental results demonstrate that, by using a tailored SAT solver within first-order reasoning, we gain a large speedup in solving state-of-the-art benchmarks.