Consider the following premises. For all x_2, if x_2 were a scientist, then x_2 is listening to a song. For all x_2, x_2 is not a poet. For all x_2, if x_2 were a poet, then x_2 is a scientist. For all x_2, if x_2 listens to a song, then x_2 is a poet. Can we infer the following from them? For all x_2, x_2 is not a scientist.
 From the fact that for all x_2, 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 poet we can infer that for all x_2, if x_2 were a scientist, then x_2 is a poet. From the fact that for all x_2, if x_2 were a poet, then x_2 is a scientist, and that for all x_2, if x_2 were a scientist, then x_2 is a poet we can infer that for all x_2, x_2 is a poet if and only if x_2 is a scientist. Finally, from the fact that for all x_2, x_2 is a poet if and only if x_2 is a scientist, and that for all x_2, x_2 is not a poet we can infer that for all x_2, x_2 is not a scientist. Therefore, the answer is yes.