Consider the following premises. For all x_2, if x_2 were a scientist, then x_2 is listening to a song. There is at least one x_2 for which if x_2 were a scientist, then x_2 is listening to a song. For all x_2, if x_2 listens to a song, then x_2 is a scientist. For all x_2, x_2 is not a scientist. Can we infer the following from them? For all x_2, x_2 will listen to a song.
 From the fact that for all x_2, if x_2 listens to a song, then x_2 is a scientist, and that for all x_2, if x_2 were a scientist, then x_2 is listening to a song we can infer that for all x_2, x_2 will listen to a song if and only if x_2 is a scientist. From the fact that for all x_2, x_2 will listen to a song if and only if x_2 is a scientist we can infer that for all x_2, if x_2 listens to a song, then x_2 is a scientist. From the fact that there is at least one x_2 for which if x_2 were a scientist, then x_2 is listening to a song, and that for all x_2, if x_2 listens to a song, then x_2 is a scientist we can infer that there is at least one x_2 for which x_2 is a scientist if and only if x_2 will listen to a song. Finally, from the fact that there is at least one x_2 for which x_2 is a scientist if and only if x_2 will listen to a song, and that for all x_2, x_2 is not a scientist we can infer that there is at least one x_2 for which x_2 will not listen to a song, which contradicts that For all x_2, x_2 will listen to a song. Therefore, the answer is no.