"Big data can be an adequate solution to that" is too simple a statement for this problem.
Ensuring scalability of OWL ontologies is a very complex issue. The main variables involved are number of axioms and expressivity of the ontology; however, these are not always the most important characteristics. A lot depends also on the api used and, for apis where the reasoning step is separate from parsing, which reasoner is being used.
SWRL rules add another level of complexity, as they are of (almost) arbitrary complexity - so it is not possible to guarantee scalability in general. For specific ontologies and specific sets of rules, it is possible to provide better guesses.
A translation to a MapReduce format /might/ help, but there is no standard transformation as far as I'm aware, and it would be quite complex to guarantee that the transformation preserves the semantics of the ontology and of the rule entailments. So, the task would amount to rewrite the data in a way that allows you to answer the queries you need to run, but this might prove impossible, depending on the specific ontology.
On the other hand, what is the size of this ontology and the amount of memory you allocated to the task?