# On Tackling the Limits of Resolution in SAT Solving

## TL;DR

This paper introduces a new transformation that enables solving hard SAT problems more efficiently using MaxSAT solvers, surpassing traditional CDCL SAT solver limitations.

## Contribution

It proposes a novel problem transformation reducing CNF SAT decision to MaxSAT over Horn formulas, with polynomial bounds and practical efficiency demonstrated.

## Key findings

- Polynomial bounds on MaxSAT resolution steps for pigeonhole formulas.
- Modern MaxSAT solvers efficiently solve CNF formulas hard for CDCL.
- Experimental validation shows improved performance on hard SAT instances.

## Abstract

The practical success of Boolean Satisfiability (SAT) solvers stems from the CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a propositional proof complexity perspective, CDCL is no more powerful than the resolution proof system, for which many hard examples exist. This paper proposes a new problem transformation, which enables reducing the decision problem for formulas in conjunctive normal form (CNF) to the problem of solving maximum satisfiability over Horn formulas. Given the new transformation, the paper proves a polynomial bound on the number of MaxSAT resolution steps for pigeonhole formulas. This result is in clear contrast with earlier results on the length of proofs of MaxSAT resolution for pigeonhole formulas. The paper also establishes the same polynomial bound in the case of modern core-guided MaxSAT solvers. Experimental results, obtained on CNF formulas known to be hard for CDCL SAT solvers, show that these can be efficiently solved with modern MaxSAT solvers.