This paper describes the integration of zChaff and MiniSat, currently two leading SAT solvers, with Higher Order Logic (HOL) theorem provers. Both SAT solvers generate resolution-style proofs for (instances of) propositional tautologies. These proofs are verified by the theorem provers. The presented approach significantly improves the provers' performance on propositional problems, and exhibits counterexamples for unprovable conjectures. It is also shown that LCF-style theorem provers can serve as viable proof checkers even for large SAT problems. An efficient representation of the propositional problem in the theorem prover turns out to be crucial; several possible solutions are discussed.

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We report initial results on shortening propositional resolution refutation proofs. This has an application in speeding up deductive reconstruction (in theorem provers) of large propositional refutations, such as those produced by SAT-solvers.

Abstract. Separation logic allows simple proofs of concurrent algorithms which use blocking mechanisms such as semaphores. It can even deal with non-blocking algorithms. With the addition of mechanisms borrowed from rely-guarantee, we can make reasonably simple proofs of some simple non-blocking algorithms. We show that it extends to proofs of some intricate algorithms, including Simpson's famous asynchronous four-slot buffer and Harris's novel three-slot algorithm, in a manner that is arguably simpler than earlier treatments, though we cannot claim that we have yet found proofs that are as simple as we would wish. Our example proofs show functional correctness but do not deal with questions of liveness.

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