Consider the following premises. For all x_9, x_9 will play a game or x_9 is sad. For all x_9, x_9 will read a book and x_9 will sleep. There is at least one x_9 for which x_9 will not play a game. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which x_9 is sad and x_9 will read a book.
 From the fact that for all x_9, x_9 will play a game or x_9 is sad, and that there is at least one x_9 for which x_9 will not play a game we can infer that there is at least one x_9 for which x_9 is sad via existential disjunctive syllogism. From the fact that for all x_9, x_9 will read a book and x_9 will sleep we can infer that for all x_9, x_9 will read a book via universal simplification. Finally, from the fact that there is at least one x_9 for which x_9 is sad, and that for all x_9, x_9 will read a book we can infer that there is at least one x_9 for which x_9 is sad and x_9 will read a book via existential conjunction. Therefore, the answer is yes.