Consider the following premises. Barbara is a server. Michael is not reading a book. Michael is reading a book or Mary is sleeping. If Barbara were a server, then Mary is not sleeping. Can we infer the following from them? Richard is cooking.
 From the fact that Michael is reading a book or Mary is sleeping, and that Michael is not reading a book we can infer that Mary is sleeping. From the fact that Barbara is a server we can infer that Barbara is a server or Richard is cooking. From the fact that if Barbara were a server, then Mary is not sleeping, and that Mary is sleeping we can infer that Barbara is not a server. Finally, from the fact that Barbara is a server or Richard is cooking, and that Barbara is not a server we can infer that Richard is cooking. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.