Consider the following premises. For all x_6, if x_6 were a bartender, then x_6 is an astronaut. There is at least one x_6 for which if x_6 were a janitor, then x_6 is working. For all x_6, x_6 will not read a book or x_6 is a bartender. For all x_6, x_6 will read a book or x_6 is a janitor. For all x_6, if x_6 were an astronaut, then x_6 is working. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will not work.
 From the fact that for all x_6, x_6 will read a book or x_6 is a janitor, and that for all x_6, x_6 will not read a book or x_6 is a bartender we can infer that for all x_6, x_6 is a janitor or x_6 is a bartender via universal resolution. From the fact that for all x_6, if x_6 were a bartender, then x_6 is an astronaut, and that for all x_6, if x_6 were an astronaut, then x_6 is working we can infer that for all x_6, if x_6 were a bartender, then x_6 is working via universal transitivity. Finally, from the fact that there is at least one x_6 for which if x_6 were a janitor, then x_6 is working, that for all x_6, if x_6 were a bartender, then x_6 is working, and that for all x_6, x_6 is a janitor or x_6 is a bartender we can infer that there is at least one x_6 for which x_6 will work via existential disjunction elimination, which contradicts that For all x_6, x_6 will not work. Therefore, the answer is no.