Consider the following premises. For all z_1, z_1 will not play squash. For all z_1, z_1 will play squash if and only if z_1 will sleep. There is at least one z_1 for which if z_1 listens to a song, then z_1 is sleeping. For all z_1, if z_1 sleeps, then z_1 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 z_1 for which z_1 will not listen to a song.
 From the fact that for all z_1, z_1 will play squash if and only if z_1 will sleep, and that for all z_1, z_1 will not play squash we can infer that for all z_1, z_1 will not sleep via universal biconditional elimination. From the fact that there is at least one z_1 for which if z_1 listens to a song, then z_1 is sleeping, and that for all z_1, if z_1 sleeps, then z_1 is listening to a song we can infer that there is at least one z_1 for which z_1 will listen to a song if and only if z_1 will sleep via existential biconditional introduction. Finally, from the fact that there is at least one z_1 for which z_1 will listen to a song if and only if z_1 will sleep, and that for all z_1, z_1 will not sleep we can infer that there is at least one z_1 for which z_1 will not listen to a song via existential biconditional elimination. Therefore, the answer is yes.