Efficiently Checking Propositional Resolution Proofs in Isabelle/HOL

This paper describes the integration of zChaff and MiniSat, currently two leading SAT solvers, with Isabelle/HOL. Both SAT solvers generate resolution-style proofs for (instances of) propositional tautologies. These proofs are verified by the theorem prover. The presented approach significantly improves Isabelle’s performance on propositional problems, and exhibits counterexamples for unprovable conjectures. It is shown that an LCF-style theorem prover can serve as a viable proof checker 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.