Declarative process models define the behaviour of business processes as a set of constraints. Declarative process discovery aims at inferring such constraints from event logs. Existing discovery techniques verify the satisfaction of candidate constraints over the log, but completely neglect their interactions. As a result, the inferred constraints can be mutually contradicting and their interplay may lead to an inconsistent process model that does not accept any trace. In such a case, the output turns out to be unusable for enactment, simulation or verification purposes. In addition, the discovered model contains, in general, redundancies that are due to complex interactions of several constraints and that cannot be cured using existing pruning approaches. We address these problems by proposing a technique that automatically resolves conflicts within the discovered models and is more powerful than existing pruning techniques to eliminate redundancies. First, we formally define the problems of constraint redundancy and conflict resolution. Second, we introduce techniques based on the notion of automata-product monoid, which guarantees the consistency of the discovered models and, at * Corresponding author. E-mail address: claudio.di.ciccio@wu.ac.at Postal address: Vienna University of Economics and Business, Institute for Information Business (Building D2, Entrance C) -Welthandelsplatz 1, A-1020 Vienna, Austria Phone number: +43 1 31336 5222Email addresses: claudio.di.ciccio@wu.ac.at (Claudio Di Ciccio), f.m.maggi@ut.ee (Fabrizio Maria Maggi), montali@inf.unibz.it (Marco Montali), jan.mendling@wu.ac.at (Jan Mendling) Preprint submitted to Information Systems 7th October 2016 the same time, keeps the most interesting constraints in the pruned set. The level of interestingness is dictated by user-specified prioritisation criteria. We evaluate the devised techniques on a set of real-world event logs.