Consider the following premises. William is sleeping if and only if Robert is listening to a song. Robert is not listening to a song. If William sleeps, then John is fast. If John were fast, then William is sleeping. Can we infer the following from them? If we can, name the inference rule being used: John is not fast.
 From the fact that if William sleeps, then John is fast, and that if John were fast, then William is sleeping we can infer that William is sleeping if and only if John is fast via biconditional introduction. From the fact that William is sleeping if and only if John is fast we can infer that if John were fast, then William is sleeping via biconditional elimination. From the fact that William is sleeping if and only if Robert is listening to a song, and that Robert is not listening to a song we can infer that William is not sleeping via biconditional elimination. Finally, from the fact that if John were fast, then William is sleeping, and that William is not sleeping we can infer that John is not fast via modus tollens. Therefore, the answer is yes.