Consider the following premises. For all x_8, if x_8 makes tea, then x_8 is reading a book. For all x_8, x_8 will make tea or x_8 will climb a mountain. For all x_8, if x_8 climbs a mountain, then x_8 is reading a book. There is at least one x_8 for which x_8 will work or x_8 is a scientist. For all x_8, if x_8 works, then x_8 is not reading a book. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 is a scientist.
 From the fact that for all x_8, if x_8 makes tea, then x_8 is reading a book, that for all x_8, if x_8 climbs a mountain, then x_8 is reading a book, and that for all x_8, x_8 will make tea or x_8 will climb a mountain we can infer that for all x_8, x_8 will read a book via universal disjunction elimination. From the fact that for all x_8, if x_8 works, then x_8 is not reading a book, and that for all x_8, x_8 will read a book we can infer that for all x_8, x_8 will not work via universal modus tollens. Finally, from the fact that there is at least one x_8 for which x_8 will work or x_8 is a scientist, and that for all x_8, x_8 will not work we can infer that there is at least one x_8 for which x_8 is a scientist via existential disjunctive syllogism. Therefore, the answer is yes.