Consider the following premises. If David listens to a song, then Barbara is a scientist. If Barbara were a scientist, then John is an artist. For all x_3, if x_3 were an artist, then x_3 is playing a game. Can we infer the following from them? If we can, name the inference rule being used: The fact that David listens to a song does not imply that John is playing a game.
That contradicts the premises. Therefore the answer is no.