Consider the following premises. There is at least one y for which if y listens to a song, then y is taking a plane. For all y, if y were a taxi driver, then y is listening to a song. For all y, y is a janitor. For all y, y is a taxi driver. Can we infer the following from them? If we can, name the inference rule being used: For all y, y will not take a plane.
 From the fact that for all y, if y were a taxi driver, then y is listening to a song, and that for all y, y is a taxi driver we can infer that for all y, y will listen to a song via universal modus ponens. From the fact that there is at least one y for which if y listens to a song, then y is taking a plane, and that for all y, y will listen to a song we can infer that there is at least one y for which y will take a plane via existential modus ponens. From the fact that there is at least one y for which y will take a plane, and that for all y, y is a janitor we can infer that there is at least one y for which y will take a plane and y is a janitor via existential conjunction. Finally, from the fact that there is at least one y for which y will take a plane and y is a janitor we can infer that there is at least one y for which y will take a plane via existential simplification, which contradicts that For all y, y will not take a plane. Therefore, the answer is no.