Consider the following premises. For all x_3, if x_3 plays a game, then x_3 is reading a book. For all x_3, x_3 will drink water if and only if x_3 will read a book. For all x_3, x_3 is a carpenter or x_3 will drink water. For all x_3, if x_3 were a carpenter, then x_3 is playing a game. Can we infer the following from them? If we can, name the inference rule being used: For all x_3, x_3 will read a book.
 From the fact that for all x_3, if x_3 were a carpenter, then x_3 is playing a game, and that for all x_3, if x_3 plays a game, then x_3 is reading a book we can infer that for all x_3, if x_3 were a carpenter, then x_3 is reading a book via universal transitivity. From the fact that for all x_3, x_3 will drink water if and only if x_3 will read a book we can infer that for all x_3, if x_3 drinks water, then x_3 is reading a book via universal biconditional elimination. Finally, from the fact that for all x_3, if x_3 were a carpenter, then x_3 is reading a book, that for all x_3, if x_3 drinks water, then x_3 is reading a book, and that for all x_3, x_3 is a carpenter or x_3 will drink water we can infer that for all x_3, x_3 will read a book via universal disjunction elimination. Therefore, the answer is yes.