Consider the following premises. For all x_13, if x_13 makes tea, then x_13 is working. For all x_13, if x_13 works, then x_13 is playing a game. John is playing a game if and only if John is making tea. John is not playing a game. Can we infer the following from them? If we can, name the inference rule being used: John is making tea.
 From the fact that for all x_13, if x_13 makes tea, then x_13 is working, and that for all x_13, if x_13 works, then x_13 is playing a game we can infer that for all x_13, if x_13 makes tea, then x_13 is playing a game via universal transitivity. From the fact that for all x_13, if x_13 makes tea, then x_13 is playing a game we can infer that if John makes tea, then John is playing a game via universal instantiation. From the fact that John is playing a game if and only if John is making tea we can infer that if John plays a game, then John is making tea via biconditional elimination. From the fact that if John makes tea, then John is playing a game, and that if John plays a game, then John is making tea we can infer that John is making tea if and only if John is playing a game via biconditional introduction. Finally, from the fact that John is making tea if and only if John is playing a game, and that John is not playing a game we can infer that John is not making tea via biconditional elimination, which contradicts that John is making tea. Therefore, the answer is no.