Consider the following premises. For all x_6, x_6 will play a game if and only if x_6 is a scientist. For all x_6, x_6 is a writer or x_6 is a scientist. For all x_6, x_6 is not a writer or x_6 will sleep. For all x_6, if x_6 sleeps, then x_6 is playing a game. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, if x_6 sleeps, then x_6 is playing a game.
That is one of the premises. Therefore, the answer is yes.