Consider the following premises. For all x_5, x_5 is not a nurse. For all x_5, if x_5 were a taxi driver, then x_5 is working. There is at least one x_5 for which if x_5 were an astronaut, then x_5 is a taxi driver. For all x_5, if x_5 works, then x_5 is a nurse. Can we infer the following from them? There is at least one x_5 for which x_5 is not an astronaut.
 From the fact that for all x_5, if x_5 were a taxi driver, then x_5 is working, and that for all x_5, if x_5 works, then x_5 is a nurse we can infer that for all x_5, if x_5 were a taxi driver, then x_5 is a nurse. From the fact that for all x_5, if x_5 were a taxi driver, then x_5 is a nurse, and that for all x_5, x_5 is not a nurse we can infer that for all x_5, x_5 is not a taxi driver. Finally, from the fact that there is at least one x_5 for which if x_5 were an astronaut, then x_5 is a taxi driver, and that for all x_5, x_5 is not a taxi driver we can infer that there is at least one x_5 for which x_5 is not an astronaut. Therefore, the answer is yes.