Extended Resolution Simulates DRAT

Benjamin Kiesl, Adrián Rebola-Pardo, Marijn J. H. Heule

Abstract: We prove that extended resolution—a well-known proof system introduced by Tseitin—polynomially simulates \({\mathsf {DRAT}}\), the standard proof system in modern SAT solving. Our simulation procedure takes as input a \({\mathsf {DRAT}}\) proof and transforms it into an extended-resolution proof whose size is only polynomial with respect to the original proof. Based on our simulation, we implemented a tool that transforms \({\mathsf {DRAT}}\) proofs into extended-resolution proofs. We ran our tool on several benchmark formulas to estimate the increase in size caused by our simulation in practice. Finally, as a side note, we show how blocked-clause addition—a generalization of the extension rule from extended resolution—can be used to replace the addition of resolution asymmetric tautologies in \({\mathsf {DRAT}}\) without introducing new variables.