Consider the following premises. For all z, if z were an artist, then z is a doctor. For all z, z is a doctor or z will not work. For all z, z will not sleep or z is an artist. There is at least one z for which z will sleep or z will work. Can we infer the following from them? If we can, name the inference rule being used: For all z, z is not a doctor.
 From the fact that for all z, z is a doctor or z will not work we can infer that for all z, if z works, then z is a doctor via universal rewriting. From the fact that there is at least one z for which z will sleep or z will work, and that for all z, z will not sleep or z is an artist we can infer that there is at least one z for which z will work or z is an artist via existential resolution. Finally, from the fact that for all z, if z works, then z is a doctor, that for all z, if z were an artist, then z is a doctor, and that there is at least one z for which z will work or z is an artist we can infer that there is at least one z for which z is a doctor via existential disjunction elimination, which contradicts that For all z, z is not a doctor. Therefore, the answer is no.