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Distributed clause-sharing SAT solvers can solve challenging problems hundreds of times faster than sequential SAT solvers by sharing derived information among multiple sequential solvers. Unlike sequential solvers, however, distributed solvers have not been able to produce proofs of unsatisfiability in a scalable manner, which limits their use in critical applications. In this work, we present a method to produce unsatisfiability proofs for distributed SAT solvers by combining the partial proofs produced by each sequential solver into a single, linear proof. We first describe a simple sequential algorithm and then present a fully distributed algorithm for proof composition, which is substantially more scalable and general than prior works. Our empirical evaluation with over 1500 solver threads shows that our distributed approach allows proof composition and checking within around 3x its own (highly competitive) solving time. 

Modern SAT solvers produce proofs of unsatisfiability to justify the correctness of their results. These proofs, which are usually represented in the well-known DRAT format, can often become huge, requiring multiple gigabytes of disk storage. We present a technique for semantic proof compression that selects a subset of important clauses from a proof and stores them as a so-called proof skeleton. This proof skeleton can later be used to efficiently reconstruct a full proof by exploiting parallelism. We implemented our approach on top of the award-winning SAT solver CaDiCaL and the proof checker DRAT-trim. In an experimental evaluation, we demonstrate that we can compress proofs into skeletons that are 100 to 5,000 times smaller than the original proofs. For almost all problems, proof reconstruction using a skeleton improves the solving time on a single core, and is around five times faster when using 24 cores.