Consider the following premises. If Charles listens to a song, then Michael is playing a game. Charles is listening to a song or Michael is not playing a game. Charles is not listening to a song. Can we infer the following from them? If we can, name the inference rule being used: Michael is playing a game.
 From the fact that Charles is listening to a song or Michael is not playing a game we can infer that if Michael plays a game, then Charles is listening to a song via rewriting. From the fact that if Michael plays a game, then Charles is listening to a song, and that if Charles listens to a song, then Michael is playing a game we can infer that Michael is playing a game if and only if Charles is listening to a song via biconditional introduction. Finally, from the fact that Michael is playing a game if and only if Charles is listening to a song, and that Charles is not listening to a song we can infer that Michael is not playing a game via biconditional elimination, which contradicts that Michael is playing a game. Therefore, the answer is no.