Consider the following premises. For all y, y is fast or y will not listen to a song. For all y, if y were fast, then y is listening to a song. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y for which if is not true that y will listen to a song if and only if y is fast.
 From the fact that for all y, y is fast or y will not listen to a song we can infer that for all y, if y listens to a song, then y is fast via universal rewriting. Finally, from the fact that for all y, if y listens to a song, then y is fast, and that for all y, if y were fast, then y is listening to a song we can infer that for all y, y will listen to a song if and only if y is fast via universal biconditional introduction, which contradicts that There is at least one y for which if is not true that y will listen to a song if and only if y is fast. Therefore, the answer is no.