Consider the following premises. There is at least one z_3 for which z_3 is bored or z_3 is a soldier. For all z_3, if z_3 were bored, then z_3 is a doctor. For all z_3, z_3 is a doctor or z_3 is not a soldier. Can we infer the following from them? If we can, name the inference rule being used: For all z_3, z_3 is not a doctor.
 From the fact that for all z_3, z_3 is a doctor or z_3 is not a soldier we can infer that for all z_3, if z_3 were a soldier, then z_3 is a doctor via universal rewriting. Finally, from the fact that for all z_3, if z_3 were bored, then z_3 is a doctor, that for all z_3, if z_3 were a soldier, then z_3 is a doctor, and that there is at least one z_3 for which z_3 is bored or z_3 is a soldier we can infer that there is at least one z_3 for which z_3 is a doctor via existential disjunction elimination, which contradicts that For all z_3, z_3 is not a doctor. Therefore, the answer is no.