Consider the following premises. For all x_17, if x_17 were a police officer, then x_17 is a taxi driver. For all x_17, if x_17 were a janitor, then x_17 is a police officer. There is at least one x_17 for which x_17 is not a taxi driver. For all x_17, if x_17 takes a plane, then x_17 is a janitor. For all x_17, if x_17 were a janitor, then x_17 is taking a plane. Can we infer the following from them? If we can, name the inference rule being used: For all x_17, x_17 will take a plane.
 From the fact that for all x_17, if x_17 were a janitor, then x_17 is taking a plane, and that for all x_17, if x_17 takes a plane, then x_17 is a janitor we can infer that for all x_17, x_17 is a janitor if and only if x_17 will take a plane via universal biconditional introduction. From the fact that for all x_17, if x_17 were a police officer, then x_17 is a taxi driver, and that there is at least one x_17 for which x_17 is not a taxi driver we can infer that there is at least one x_17 for which x_17 is not a police officer via existential modus tollens. From the fact that for all x_17, if x_17 were a janitor, then x_17 is a police officer, and that there is at least one x_17 for which x_17 is not a police officer we can infer that there is at least one x_17 for which x_17 is not a janitor via existential modus tollens. Finally, from the fact that for all x_17, x_17 is a janitor if and only if x_17 will take a plane, and that there is at least one x_17 for which x_17 is not a janitor we can infer that there is at least one x_17 for which x_17 will not take a plane via existential biconditional elimination, which contradicts that For all x_17, x_17 will take a plane. Therefore, the answer is no.