Consider the following premises. For all x_14, if x_14 drinks water, then x_14 is a doctor. For all x_14, x_14 will drink water. For all x_14, if x_14 were poor, then x_14 is a politician. For all x_14, x_14 will sleep or x_14 is poor. For all x_14, x_14 is a politician or x_14 will not play a game. For all x_14, x_14 will not sleep or x_14 will play a game. Can we infer the following from them? If we can, name the inference rule being used: For all x_14, x_14 is a doctor and x_14 is a politician.
 From the fact that for all x_14, x_14 will sleep or x_14 is poor, and that for all x_14, x_14 will not sleep or x_14 will play a game we can infer that for all x_14, x_14 is poor or x_14 will play a game via universal resolution. From the fact that for all x_14, x_14 is a politician or x_14 will not play a game we can infer that for all x_14, if x_14 plays a game, then x_14 is a politician via universal rewriting. From the fact that for all x_14, if x_14 were poor, then x_14 is a politician, that for all x_14, if x_14 plays a game, then x_14 is a politician, and that for all x_14, x_14 is poor or x_14 will play a game we can infer that for all x_14, x_14 is a politician via universal disjunction elimination. From the fact that for all x_14, if x_14 drinks water, then x_14 is a doctor, and that for all x_14, x_14 will drink water we can infer that for all x_14, x_14 is a doctor via universal modus ponens. Finally, from the fact that for all x_14, x_14 is a doctor, and that for all x_14, x_14 is a politician we can infer that for all x_14, x_14 is a doctor and x_14 is a politician via universal conjunction. Therefore, the answer is yes.