Consider the following premises. For all x_7, x_7 will play a game or x_7 will not drink water. For all x_7, if x_7 plays a game, then x_7 is working. There is at least one x_7 for which if x_7 works, then x_7 is reading a book. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which if x_7 drinks water, then x_7 is reading a book.
 From the fact that for all x_7, x_7 will play a game or x_7 will not drink water we can infer that for all x_7, if x_7 drinks water, then x_7 is playing a game via universal rewriting. From the fact that for all x_7, if x_7 plays a game, then x_7 is working, and that there is at least one x_7 for which if x_7 works, then x_7 is reading a book we can infer that there is at least one x_7 for which if x_7 plays a game, then x_7 is reading a book via existential transitivity. Finally, from the fact that for all x_7, if x_7 drinks water, then x_7 is playing a game, and that there is at least one x_7 for which if x_7 plays a game, then x_7 is reading a book we can infer that there is at least one x_7 for which if x_7 drinks water, then x_7 is reading a book via existential transitivity. Therefore, the answer is yes.