Consider the following premises. For all x_7, x_7 will listen to a song. For all x_7, x_7 is a scientist or x_7 will not sleep. There is at least one x_7 for which if x_7 were a scientist, then x_7 is not listening to a song. Can we infer the following from them? There is at least one x_7 for which x_7 will not sleep.
 From the fact that there is at least one x_7 for which if x_7 were a scientist, then x_7 is not listening to a song, and that for all x_7, x_7 will listen to a song we can infer that there is at least one x_7 for which x_7 is not a scientist. From the fact that for all x_7, x_7 is a scientist or x_7 will not sleep we can infer that for all x_7, if x_7 sleeps, then x_7 is a scientist. Finally, from the fact that for all x_7, if x_7 sleeps, then x_7 is a scientist, and that there is at least one x_7 for which x_7 is not a scientist we can infer that there is at least one x_7 for which x_7 will not sleep. Therefore, the answer is yes.