Consider the following premises. For all z, z will take a plane if and only if z will write a letter. For all z, z is a bartender or z will drink water. For all z, if z drinks water, then z is writing a letter. For all z, z is not a bartender or z will take a plane. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z for which z will not write a letter.
 From the fact that for all z, z is a bartender or z will drink water, and that for all z, z is not a bartender or z will take a plane we can infer that for all z, z will drink water or z will take a plane via universal resolution. From the fact that for all z, z will take a plane if and only if z will write a letter we can infer that for all z, if z takes a plane, then z is writing a letter via universal biconditional elimination. Finally, from the fact that for all z, if z drinks water, then z is writing a letter, that for all z, if z takes a plane, then z is writing a letter, and that for all z, z will drink water or z will take a plane we can infer that for all z, z will write a letter via universal disjunction elimination, which contradicts that There is at least one z for which z will not write a letter. Therefore, the answer is no.