Consider the following premises. For all x_10, if x_10 drinks water, then x_10 is a doctor. For all x_10, x_10 will drink water. For all x_10, x_10 is a doctor if and only if x_10 is a nurse. For all x_10, x_10 is not a nurse. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 is a taxi driver.
 From the fact that for all x_10, x_10 is a doctor if and only if x_10 is a nurse, and that for all x_10, x_10 is not a nurse we can infer that for all x_10, x_10 is not a doctor via universal biconditional elimination. From the fact that for all x_10, if x_10 drinks water, then x_10 is a doctor, and that for all x_10, x_10 is not a doctor we can infer that for all x_10, x_10 will not drink water via universal modus tollens. From the fact that for all x_10, x_10 will drink water we can infer that for all x_10, x_10 will drink water or x_10 is a taxi driver via universal addition. Finally, from the fact that for all x_10, x_10 will drink water or x_10 is a taxi driver, and that for all x_10, x_10 will not drink water we can infer that for all x_10, x_10 is a taxi driver via universal disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.