In the Big Data era, RDF data, just like other kinds of data, is produced in high volumes. While there exist proposals for reasoning over large RDF graphs using big data platforms, there is a dearth of solutions that do so in environments where RDF data is dynamic, and where new instance and schema triples can arrive at any time. With this in mind, we present in this work the first solution for reasoning over large streams of RDF data using big data platforms. In doing so, we focus on the saturation operation. Unlike existing solutions which saturate RDF data in bulk, our solution carefully identifies the subset of the existing (and already saturated) RDF dataset that needs to be considered given the RDF statements that have recently delivered by the stream. Thereby, it performs the saturation in an incremental manner. The experimental analysis that we performed shows that our solution outperforms existing bulk-based saturation solutions, which we use as a baseline.