Consider the following premises. For all z, if z sleeps, then z is writing a letter. For all z, z is a writer. There is at least one z for which z will sleep or z is an electrician. For all z, if z were an electrician, then z is playing tennis. For all z, if z plays tennis, then z is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: For all z, either z will write a letter or z is a writer are not true.
 From the fact that for all z, if z were an electrician, then z is playing tennis, and that for all z, if z plays tennis, then z is writing a letter we can infer that for all z, if z were an electrician, then z is writing a letter via universal transitivity. From the fact that for all z, if z sleeps, then z is writing a letter, that for all z, if z were an electrician, then z is writing a letter, and that there is at least one z for which z will sleep or z is an electrician we can infer that there is at least one z for which z will write a letter via existential disjunction elimination. Finally, from the fact that there is at least one z for which z will write a letter, and that for all z, z is a writer we can infer that there is at least one z for which z will write a letter and z is a writer via existential conjunction, which contradicts that For all z, either z will write a letter or z is a writer are not true. Therefore, the answer is no.