Consider the following premises. For all x_6, x_6 is an astronaut if and only if x_6 will work. There is at least one x_6 for which x_6 will sleep or x_6 is an astronaut. For all x_6, x_6 will work or x_6 will not sleep. Can we infer the following from them? There is at least one x_6 for which x_6 will work.
 From the fact that for all x_6, x_6 will work or x_6 will not sleep we can infer that for all x_6, if x_6 sleeps, then x_6 is working. From the fact that for all x_6, x_6 is an astronaut if and only if x_6 will work we can infer that for all x_6, if x_6 were an astronaut, then x_6 is working. Finally, from the fact that for all x_6, if x_6 sleeps, then x_6 is working, that for all x_6, if x_6 were an astronaut, then x_6 is working, and that there is at least one x_6 for which x_6 will sleep or x_6 is an astronaut we can infer that there is at least one x_6 for which x_6 will work. Therefore, the answer is yes.