Consider the following premises. For all z, z is not a cashier. There is at least one z for which if z listens to a song, then z is a cashier. For all z, if z listens to a song, then z is a cashier. For all z, if z were a cashier, then z is listening to a song. Can we infer the following from them? There is at least one z for which z will not listen to a song.
 From the fact that there is at least one z for which if z listens to a song, then z is a cashier, and that for all z, if z were a cashier, then z is listening to a song we can infer that there is at least one z for which z will listen to a song if and only if z is a cashier. From the fact that there is at least one z for which z will listen to a song if and only if z is a cashier we can infer that there is at least one z for which if z were a cashier, then z is listening to a song. From the fact that there is at least one z for which if z were a cashier, then z is listening to a song, and that for all z, if z listens to a song, then z is a cashier we can infer that there is at least one z for which z is a cashier if and only if z will listen to a song. Finally, from the fact that there is at least one z for which z is a cashier if and only if z will listen to a song, and that for all z, z is not a cashier we can infer that there is at least one z for which z will not listen to a song. Therefore, the answer is yes.