Consider the following premises. For all x_5, x_5 is an astronaut if and only if x_5 will work. For all x_5, if x_5 drives a car, then x_5 is cooking. For all x_5, x_5 is an astronaut if and only if x_5 will drive a car. For all x_5, x_5 will not cook. Can we infer the following from them? For all x_5, x_5 will not work.
 From the fact that for all x_5, if x_5 drives a car, then x_5 is cooking, and that for all x_5, x_5 will not cook we can infer that for all x_5, x_5 will not drive a car. From the fact that for all x_5, x_5 is an astronaut if and only if x_5 will drive a car, and that for all x_5, x_5 will not drive a car we can infer that for all x_5, x_5 is not an astronaut. Finally, from the fact that for all x_5, x_5 is an astronaut if and only if x_5 will work, and that for all x_5, x_5 is not an astronaut we can infer that for all x_5, x_5 will not work. Therefore, the answer is yes.