Consider the following premises. For all x_10, x_10 is a janitor if and only if x_10 is a doctor. For all x_10, if x_10 goes running, then x_10 is a doctor. There is at least one x_10 for which x_10 is not a janitor. For all x_10, if x_10 were a taxi driver, then x_10 is running. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 is not a taxi driver.
 From the fact that for all x_10, x_10 is a janitor if and only if x_10 is a doctor, and that there is at least one x_10 for which x_10 is not a janitor we can infer that there is at least one x_10 for which x_10 is not a doctor via existential biconditional elimination. From the fact that for all x_10, if x_10 were a taxi driver, then x_10 is running, and that for all x_10, if x_10 goes running, then x_10 is a doctor we can infer that for all x_10, if x_10 were a taxi driver, then x_10 is a doctor via universal transitivity. Finally, from the fact that for all x_10, if x_10 were a taxi driver, then x_10 is a doctor, and that there is at least one x_10 for which x_10 is not a doctor we can infer that there is at least one x_10 for which x_10 is not a taxi driver via existential modus tollens. Therefore, the answer is yes.