Consider the following premises. For all x_5, x_5 is a doctor. For all x_5, if x_5 goes running, then x_5 is excited. For all x_5, x_5 will play a game. For all x_5, if x_5 were a doctor, then x_5 is excited. Can we infer the following from them? For all x_5, x_5 is excited and x_5 will play a game.
 From the fact that for all x_5, x_5 is a doctor we can infer that for all x_5, x_5 is a doctor or x_5 will go running. From the fact that for all x_5, if x_5 were a doctor, then x_5 is excited, that for all x_5, if x_5 goes running, then x_5 is excited, and that for all x_5, x_5 is a doctor or x_5 will go running we can infer that for all x_5, x_5 is excited. Finally, from the fact that for all x_5, x_5 is excited, and that for all x_5, x_5 will play a game we can infer that for all x_5, x_5 is excited and x_5 will play a game. Therefore, the answer is yes.