Consider the following premises. For all z_2, z_2 is a scientist if and only if z_2 will listen to a song. There is at least one z_2 for which if z_2 were a scientist, then z_2 is a bartender. For all z_2, z_2 will listen to a song if and only if z_2 is a scientist. Can we infer the following from them? There is at least one z_2 for which if z_2 listens to a song, then z_2 is a bartender.
 From the fact that for all z_2, z_2 will listen to a song if and only if z_2 is a scientist we can infer that for all z_2, if z_2 were a scientist, then z_2 is listening to a song. From the fact that for all z_2, z_2 is a scientist if and only if z_2 will listen to a song we can infer that for all z_2, if z_2 listens to a song, then z_2 is a scientist. From the fact that for all z_2, if z_2 were a scientist, then z_2 is listening to a song, and that for all z_2, if z_2 listens to a song, then z_2 is a scientist we can infer that for all z_2, z_2 is a scientist if and only if z_2 will listen to a song. From the fact that for all z_2, z_2 is a scientist if and only if z_2 will listen to a song we can infer that for all z_2, if z_2 listens to a song, then z_2 is a scientist. Finally, from the fact that for all z_2, if z_2 listens to a song, then z_2 is a scientist, and that there is at least one z_2 for which if z_2 were a scientist, then z_2 is a bartender we can infer that there is at least one z_2 for which if z_2 listens to a song, then z_2 is a bartender. Therefore, the answer is yes.