Consider the following premises. For all x_12, if x_12 sleeps, then x_12 is not listening to a song. If William plays a game, then Jessica is sleeping. For all x_12, x_12 will listen to a song and x_12 will cook. Can we infer the following from them? If we can, name the inference rule being used: William is playing a game.
 From the fact that for all x_12, x_12 will listen to a song and x_12 will cook we can infer that for all x_12, x_12 will listen to a song via universal simplification. From the fact that for all x_12, if x_12 sleeps, then x_12 is not listening to a song, and that for all x_12, x_12 will listen to a song we can infer that for all x_12, x_12 will not sleep via universal modus tollens. From the fact that for all x_12, x_12 will not sleep we can infer that Jessica is not sleeping via universal instantiation. Finally, from the fact that if William plays a game, then Jessica is sleeping, and that Jessica is not sleeping we can infer that William is not playing a game via modus tollens, which contradicts that William is playing a game. Therefore, the answer is no.