Consider the following premises. For all x_13, x_13 will not play a game or x_13 will cook. For all x_13, x_13 will sleep. There is at least one x_13 for which x_13 will not read a book. For all x_13, x_13 will play a game or x_13 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_13 for which x_13 will sleep.
 From the fact that for all x_13, x_13 will play a game or x_13 will read a book, and that for all x_13, x_13 will not play a game or x_13 will cook we can infer that for all x_13, x_13 will read a book or x_13 will cook via universal resolution. From the fact that for all x_13, x_13 will read a book or x_13 will cook, and that there is at least one x_13 for which x_13 will not read a book we can infer that there is at least one x_13 for which x_13 will cook via existential disjunctive syllogism. From the fact that for all x_13, x_13 will sleep, and that there is at least one x_13 for which x_13 will cook we can infer that there is at least one x_13 for which x_13 will sleep and x_13 will cook via existential conjunction. Finally, from the fact that there is at least one x_13 for which x_13 will sleep and x_13 will cook we can infer that there is at least one x_13 for which x_13 will sleep via existential simplification. Therefore, the answer is yes.