Consider the following premises. For all y_4, if y_4 works, then y_4 is an astronaut. For all y_4, if y_4 were an astronaut, then y_4 is listening to a song. For all y_4, if y_4 were an astronaut, then y_4 is working. For all y_4, if y_4 listens to a song, then y_4 is working. Can we infer the following from them? There is at least one y_4 for which the fact that y_4 listens to a song does not imply that y_4 is an astronaut.
 From the fact that for all y_4, if y_4 were an astronaut, then y_4 is working, and that for all y_4, if y_4 works, then y_4 is an astronaut we can infer that for all y_4, y_4 is an astronaut if and only if y_4 will work. From the fact that for all y_4, y_4 is an astronaut if and only if y_4 will work we can infer that for all y_4, if y_4 works, then y_4 is an astronaut. From the fact that for all y_4, if y_4 listens to a song, then y_4 is working, and that for all y_4, if y_4 works, then y_4 is an astronaut we can infer that for all y_4, if y_4 listens to a song, then y_4 is an astronaut. From the fact that for all y_4, if y_4 were an astronaut, then y_4 is listening to a song, and that for all y_4, if y_4 listens to a song, then y_4 is an astronaut we can infer that for all y_4, y_4 is an astronaut if and only if y_4 will listen to a song. Finally, from the fact that for all y_4, y_4 is an astronaut if and only if y_4 will listen to a song we can infer that for all y_4, if y_4 listens to a song, then y_4 is an astronaut, which contradicts that There is at least one y_4 for which the fact that y_4 listens to a song does not imply that y_4 is an astronaut. Therefore, the answer is no.