Consider the following premises. For all x_10, if x_10 listens to a song, then x_10 is playing a game. For all x_10, if x_10 plays a game, then x_10 is listening to a song. If it is cloudy, then Jennifer is playing a game. Jennifer is listening to a song or it is cloudy. Can we infer the following from them? David is writing a letter.
We cannot infer that from the premises. Therefore the answer is no.