Consider the following premises. For all x_9, x_9 will work. There is at least one x_9 for which if x_9 works, then x_9 is a writer. For all x_9, x_9 is not a writer. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 is not an astronaut.
The premises are contradictory and we can infer anything from them. Therefore, the answer is yes.