Consider the following premises. For all x_18, x_18 is happy or x_18 will not play a game. For all x_18, if x_18 makes tea, then x_18 is happy. For all x_18, x_18 is not a writer or x_18 will make tea. For all x_18, x_18 will not read a book. There is at least one x_18 for which x_18 is a writer or x_18 will play a game. For all x_18, x_18 will read a book or x_18 will sleep. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_18 for which x_18 will sleep and x_18 is happy.
 From the fact that for all x_18, x_18 is happy or x_18 will not play a game we can infer that for all x_18, if x_18 plays a game, then x_18 is happy via universal rewriting. From the fact that there is at least one x_18 for which x_18 is a writer or x_18 will play a game, and that for all x_18, x_18 is not a writer or x_18 will make tea we can infer that there is at least one x_18 for which x_18 will play a game or x_18 will make tea via existential resolution. From the fact that for all x_18, if x_18 plays a game, then x_18 is happy, that for all x_18, if x_18 makes tea, then x_18 is happy, and that there is at least one x_18 for which x_18 will play a game or x_18 will make tea we can infer that there is at least one x_18 for which x_18 is happy via existential disjunction elimination. From the fact that for all x_18, x_18 will read a book or x_18 will sleep, and that for all x_18, x_18 will not read a book we can infer that for all x_18, x_18 will sleep via universal disjunctive syllogism. Finally, from the fact that for all x_18, x_18 will sleep, and that there is at least one x_18 for which x_18 is happy we can infer that there is at least one x_18 for which x_18 will sleep and x_18 is happy via existential conjunction. Therefore, the answer is yes.