Conformance checking strongly relies on the computation of artefacts, which enable reasoning on the relation between observed and modeled behavior. This paper shows how important conformance artefacts like alignments, anti-alignments or even multi-alignments, defined over the edit distance, can be computed by encoding the problem as a SAT instance. From a general perspective, the work advocates for a unified family of techniques that can compute conformance artefacts in the same way. The prototype implementation of the techniques presented in this paper show capabilities for dealing with some of the current benchmarks, and potential for the near future when optimizations similar to the ones in the literature are incorporated.