Consider the following premises. For all y_2, y_2 is happy. For all y_2, if y_2 were an astronaut, then y_2 is drinking water. For all y_2, if y_2 drinks water, then y_2 is not happy. For all y_2, if y_2 drinks water, then y_2 is an astronaut. For all y_2, if y_2 drinks water, then y_2 is an astronaut. Can we infer the following from them? For all y_2, y_2 is not an astronaut.
 From the fact that for all y_2, if y_2 drinks water, then y_2 is not happy, and that for all y_2, y_2 is happy we can infer that for all y_2, y_2 will not drink water. From the fact that for all y_2, if y_2 drinks water, then y_2 is an astronaut, and that for all y_2, if y_2 were an astronaut, then y_2 is drinking water we can infer that for all y_2, y_2 will drink water if and only if y_2 is an astronaut. From the fact that for all y_2, y_2 will drink water if and only if y_2 is an astronaut we can infer that for all y_2, if y_2 were an astronaut, then y_2 is drinking water. From the fact that for all y_2, if y_2 were an astronaut, then y_2 is drinking water, and that for all y_2, if y_2 drinks water, then y_2 is an astronaut we can infer that for all y_2, y_2 is an astronaut if and only if y_2 will drink water. Finally, from the fact that for all y_2, y_2 is an astronaut if and only if y_2 will drink water, and that for all y_2, y_2 will not drink water we can infer that for all y_2, y_2 is not an astronaut. Therefore, the answer is yes.