Consider the following premises. For all x_14, x_14 is not a bartender or x_14 will play tennis. For all x_14, if x_14 drives a car, then x_14 is playing a game. For all x_14, x_14 is a bartender or x_14 will make tea. For all x_14, if x_14 makes tea, then x_14 is a nurse. For all x_14, x_14 is a nurse or x_14 will not play tennis. For all x_14, x_14 will drive a car. Can we infer the following from them? If we can, name the inference rule being used: For all x_14, x_14 will play a game and x_14 is a nurse.
 From the fact that for all x_14, x_14 is a bartender or x_14 will make tea, and that for all x_14, x_14 is not a bartender or x_14 will play tennis we can infer that for all x_14, x_14 will make tea or x_14 will play tennis via universal resolution. From the fact that for all x_14, x_14 is a nurse or x_14 will not play tennis we can infer that for all x_14, if x_14 plays tennis, then x_14 is a nurse via universal rewriting. From the fact that for all x_14, if x_14 makes tea, then x_14 is a nurse, that for all x_14, if x_14 plays tennis, then x_14 is a nurse, and that for all x_14, x_14 will make tea or x_14 will play tennis we can infer that for all x_14, x_14 is a nurse via universal disjunction elimination. From the fact that for all x_14, if x_14 drives a car, then x_14 is playing a game, and that for all x_14, x_14 will drive a car we can infer that for all x_14, x_14 will play a game via universal modus ponens. Finally, from the fact that for all x_14, x_14 will play a game, and that for all x_14, x_14 is a nurse we can infer that for all x_14, x_14 will play a game and x_14 is a nurse via universal conjunction. Therefore, the answer is yes.