Consider the following premises. For all y, if y plays tennis, then y is running. For all y, y will play tennis or y is not a nurse. For all y, y is a nurse and y will listen to a song. Can we infer the following from them? If we can, name the inference rule being used: For all y, y will go running.
 From the fact that for all y, y is a nurse and y will listen to a song we can infer that for all y, y is a nurse via universal simplification. From the fact that for all y, y will play tennis or y is not a nurse we can infer that for all y, if y were a nurse, then y is playing tennis via universal rewriting. From the fact that for all y, if y were a nurse, then y is playing tennis, and that for all y, y is a nurse we can infer that for all y, y will play tennis via universal modus ponens. Finally, from the fact that for all y, if y plays tennis, then y is running, and that for all y, y will play tennis we can infer that for all y, y will go running via universal modus ponens. Therefore, the answer is yes.