Expressing Symmetry Breaking in DRAT Proofs

An effective SAT preprocessing technique is using symmetrybreaking predicates, i.e., auxiliary clauses that guide a solver away from needless exploration of isomorphic sub-problems. Although symmetrybreaking predicates have been in use for over a decade, it was not known how to express them in proofs of unsatisfiability. Consequently, results obtained by symmetry breaking cannot be validated by existing proof checkers. We present a method to express symmetry-breaking predicates in DRAT, a proof format that is supported by the top-tier solvers. We applied this method to generate proofs of problems that have not been solved without symmetry-breaking predicates. We validated these proofs with both an ACL2-based, mechanically-verified checker and the proofchecking tool of SAT Competition 2014.