Consider the following premises. If John sleeps, then Michael is a poet. Michael is a poet or Richard is not a writer. John is sleeping or Richard is a writer. Can we infer the following from them? Michael is a poet or Robert is playing tennis.
 From the fact that Michael is a poet or Richard is not a writer we can infer that if Richard were a writer, then Michael is a poet. From the fact that if John sleeps, then Michael is a poet, that if Richard were a writer, then Michael is a poet, and that John is sleeping or Richard is a writer we can infer that Michael is a poet. Finally, from the fact that Michael is a poet we can infer that Michael is a poet or Robert is playing tennis. Therefore, the answer is yes.