Even shorter proofs without new variables

TL;DR

This paper introduces a novel approach combining subsumption redundancy and overwrite logic to produce shorter proofs in SAT solving, improving efficiency in proof length and unsatisfiable core generation.

Contribution

It combines two existing frameworks to enable more concise proofs and enhances understanding of proof limits in SAT solvers.

Findings

Shorter proofs for the pigeonhole principle.

Smaller unsatisfiable core generation.

Improved proof efficiency in SAT solving.

Abstract

Proof formats for SAT solvers have diversified over the last decade, enabling new features such as extended resolution-like capabilities, very general extension-free rules, inclusion of proof hints, and pseudo-boolean reasoning. Interference-based methods have been proven effective, and some theoretical work has been undertaken to better explain their limits and semantics. In this work, we combine the subsumption redundancy notion from (Buss, Thapen 2019) and the overwrite logic framework from (Rebola-Pardo, Suda 2018). Natural generalizations then become apparent, enabling even shorter proofs of the pigeonhole principle (compared to those from (Heule, Kiesl, Biere 2017)) and smaller unsatisfiable core generation.