Consider the following premises. For all x_16, if x_16 drinks water, then x_16 is making tea. For all x_16, x_16 will sleep if and only if x_16 will read a book. For all x_16, x_16 will play a game if and only if x_16 will make tea. For all x_16, if x_16 plays a game, then x_16 is reading a book. For all x_16, x_16 will not sleep. Can we infer the following from them? If we can, name the inference rule being used: For all x_16, x_16 will not drink water.
 From the fact that for all x_16, x_16 will play a game if and only if x_16 will make tea we can infer that for all x_16, if x_16 makes tea, then x_16 is playing a game via universal biconditional elimination. From the fact that for all x_16, if x_16 makes tea, then x_16 is playing a game, and that for all x_16, if x_16 plays a game, then x_16 is reading a book we can infer that for all x_16, if x_16 makes tea, then x_16 is reading a book via universal transitivity. From the fact that for all x_16, x_16 will sleep if and only if x_16 will read a book, and that for all x_16, x_16 will not sleep we can infer that for all x_16, x_16 will not read a book via universal biconditional elimination. From the fact that for all x_16, if x_16 drinks water, then x_16 is making tea, and that for all x_16, if x_16 makes tea, then x_16 is reading a book we can infer that for all x_16, if x_16 drinks water, then x_16 is reading a book via universal transitivity. Finally, from the fact that for all x_16, if x_16 drinks water, then x_16 is reading a book, and that for all x_16, x_16 will not read a book we can infer that for all x_16, x_16 will not drink water via universal modus tollens. Therefore, the answer is yes.