Consider the following premises. For all z, z will not listen to a song or z is rich. There is at least one z for which z will not drink water or z will read a book. For all z, z will drink water or z will listen to a song. For all z, z will not read a book. Can we infer the following from them? If we can, name the inference rule being used: For all z, z is not rich.
 From the fact that for all z, z will drink water or z will listen to a song, and that there is at least one z for which z will not drink water or z will read a book we can infer that there is at least one z for which z will listen to a song or z will read a book via existential resolution. From the fact that there is at least one z for which z will listen to a song or z will read a book, and that for all z, z will not listen to a song or z is rich we can infer that there is at least one z for which z will read a book or z is rich via existential resolution. Finally, from the fact that there is at least one z for which z will read a book or z is rich, and that for all z, z will not read a book we can infer that there is at least one z for which z is rich via existential disjunctive syllogism, which contradicts that For all z, z is not rich. Therefore, the answer is no.