MUP: a minimal unsatisfiability prover

After establishing the unsatisfiability of a SAT instance encoding a typical design task, there is a practical need to identify its minimal unsatisfiable subsets, which pinpoint the reasons for the infeasibility of the design. Due to the potentially expensive computation, existing tools for the extraction of unsatisfiable subformulas do not guarantee the minimality of the results. This paper describes a practical algorithm that decides the minimal unsatisfiability of any CNF formula through BDD manipulation. This algorithm has a worse-case complexity that is exponential only in the treewidth of the CNF formula. We provide an empirical evaluation of the algorithm, highlighting its efficiency on a set of hard problems as well as its ability to work with existing subformula extraction tools to achieve optimal results.