Consider the following premises. For all x, if x plays a game, then x is a scientist. For all x, if x were a scientist, then x is reading a book. For all x, x is not a soldier. For all x, if x reads a book, then x is a soldier. For all x, if x reads a book, then x is playing a game. Can we infer the following from them? If we can, name the inference rule being used: For all x, x will not play a game.
 From the fact that for all x, if x plays a game, then x is a scientist, and that for all x, if x were a scientist, then x is reading a book we can infer that for all x, if x plays a game, then x is reading a book via universal transitivity. From the fact that for all x, if x reads a book, then x is a soldier, and that for all x, x is not a soldier we can infer that for all x, x will not read a book via universal modus tollens. From the fact that for all x, if x plays a game, then x is reading a book, and that for all x, if x reads a book, then x is playing a game we can infer that for all x, x will play a game if and only if x will read a book via universal biconditional introduction. Finally, from the fact that for all x, x will play a game if and only if x will read a book, and that for all x, x will not read a book we can infer that for all x, x will not play a game via universal biconditional elimination. Therefore, the answer is yes.