Consider the following premises. For all x_6, x_6 is curious or x_6 is a cashier. For all x_6, if x_6 reads a book, then x_6 is not a cashier. For all x_6, x_6 is not curious. There is at least one x_6 for which x_6 will read a book or x_6 will play tennis. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 will play tennis.
 From the fact that for all x_6, x_6 is curious or x_6 is a cashier, and that for all x_6, x_6 is not curious we can infer that for all x_6, x_6 is a cashier via universal disjunctive syllogism. From the fact that for all x_6, if x_6 reads a book, then x_6 is not a cashier, and that for all x_6, x_6 is a cashier we can infer that for all x_6, x_6 will not read a book via universal modus tollens. Finally, from the fact that there is at least one x_6 for which x_6 will read a book or x_6 will play tennis, and that for all x_6, x_6 will not read a book we can infer that there is at least one x_6 for which x_6 will play tennis via existential disjunctive syllogism. Therefore, the answer is yes.