Consider the following premises. There is at least one x_4 for which if x_4 sleeps, then x_4 is cooking. For all x_4, if x_4 works, then x_4 is sleeping. For all x_4, if x_4 were an astronaut, then x_4 is sleeping. For all x_4, x_4 will work or x_4 is an astronaut. Can we infer the following from them? For all x_4, x_4 will work or x_4 is an astronaut.
That is one of the premises. Therefore, the answer is yes.