Consider the following premises. For all x_9, if x_9 cooks, then x_9 is a scientist. For all x_9, x_9 will play a game or x_9 will cook. For all x_9, x_9 is a scientist or x_9 will not play a game. For all x_9, x_9 is a nurse. Can we infer the following from them? If we can, name the inference rule being used: Michael is a scientist.
 From the fact that for all x_9, x_9 is a scientist or x_9 will not play a game we can infer that for all x_9, if x_9 plays a game, then x_9 is a scientist via universal rewriting. From the fact that for all x_9, if x_9 plays a game, then x_9 is a scientist, that for all x_9, if x_9 cooks, then x_9 is a scientist, and that for all x_9, x_9 will play a game or x_9 will cook we can infer that for all x_9, x_9 is a scientist via universal disjunction elimination. From the fact that for all x_9, x_9 is a scientist, and that for all x_9, x_9 is a nurse we can infer that for all x_9, x_9 is a scientist and x_9 is a nurse via universal conjunction. From the fact that for all x_9, x_9 is a scientist and x_9 is a nurse we can infer that Michael is a scientist and Michael is a nurse via universal instantiation. Finally, from the fact that Michael is a scientist and Michael is a nurse we can infer that Michael is a scientist via simplification. Therefore, the answer is yes.