Consider the following premises. For all x_10, if x_10 cooks, then x_10 is playing tennis. There is at least one x_10 for which x_10 will cook or x_10 will take a plane. For all x_10, if x_10 takes a plane, then x_10 is working. For all x_10, if x_10 works, then x_10 is playing tennis. For all x_10, x_10 will read a book. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 will play tennis and x_10 will read a book.
 From the fact that for all x_10, if x_10 takes a plane, then x_10 is working, and that for all x_10, if x_10 works, then x_10 is playing tennis we can infer that for all x_10, if x_10 takes a plane, then x_10 is playing tennis via universal transitivity. From the fact that for all x_10, if x_10 cooks, then x_10 is playing tennis, that for all x_10, if x_10 takes a plane, then x_10 is playing tennis, and that there is at least one x_10 for which x_10 will cook or x_10 will take a plane we can infer that there is at least one x_10 for which x_10 will play tennis via existential disjunction elimination. Finally, from the fact that there is at least one x_10 for which x_10 will play tennis, and that for all x_10, x_10 will read a book we can infer that there is at least one x_10 for which x_10 will play tennis and x_10 will read a book via existential conjunction. Therefore, the answer is yes.