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Deductive reasoning lies in the expressive intersection of Datalog and Description Logics. In this paper, we present the D2R2 engine, which implements deductive reasoning capabilities based on the Query-Sub-Query (QSQR) algorithm on top of the disk-oriented RDF- 3X engine. D2R2 aims to bridge the gap between rule-oriented (intensional) reasoning with deduction rules and data-oriented (extensional) processing of large joins, over a set of highly tuned, disk-based index structures for large RDF collections. We present a generalization of QSQR, which allows for dynamic sub-query scheduling and chaining of extensional predicates into atomic join patterns--two key extensions for coupling QSQR with a disk-oriented storage backend. Experiments over a set of recursive queries and a very large knowledge base, consisting of 20 million RDF facts, as well as comparisons to disk-oriented reasoning engines, confirm the practical viability and significant runtime improvements of D2R2 compared to these engines.