Consider the following premises. There is at least one x_10 for which x_10 is an astronaut. For all x_10, x_10 will cook or x_10 is not a cashier. For all x_10, if x_10 cooks, then x_10 is not an astronaut. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, if x_10 cooks, then x_10 is not an astronaut.
That is one of the premises. Therefore, the answer is yes.