Unsatisfiability Proofs for Parallel SAT Solver Portfolios with Clause Sharing and Inprocessing

Abstract

State-of-the-art SAT solvers are highly tuned systematic-search procedures augmented with formula simplification techniques. They emit unsatisfiability proofs in the DRAT format to guarantee correctness of their answers. However, the DRAT format is inadequate to model some parallel SAT solvers such as the award-winning system Plingeling. In Plingeling, each solver in the portfolio applies clause addition and elimination techniques. Clause sharing is restricted to clauses that do not contain melted literals. In this paper, we develop a transition system that models the computation of such parallel portfolio solvers. The transition system allows us to formally reason about portfolio solvers, and we show that the formalism is sound and complete. Based on the formalism, we derive a new proof format, called parallel DRAT, which can be used to certify UNSAT answers.