Consider the following premises. For all z, z will go running. There is at least one z for which if z were a politician, then z is not running. For all z, if z were a musician, then z is a politician. For all z, if z listens to a song, then z is a musician. Can we infer the following from them? If we can, name the inference rule being used: For all z, z will listen to a song.
 From the fact that for all z, if z listens to a song, then z is a musician, and that for all z, if z were a musician, then z is a politician we can infer that for all z, if z listens to a song, then z is a politician via universal transitivity. From the fact that there is at least one z for which if z were a politician, then z is not running, and that for all z, z will go running we can infer that there is at least one z for which z is not a politician via existential modus tollens. Finally, from the fact that for all z, if z listens to a song, then z is a politician, and that there is at least one z for which z is not a politician we can infer that there is at least one z for which z will not listen to a song via existential modus tollens, which contradicts that For all z, z will listen to a song. Therefore, the answer is no.