Consider the following premises. For all x_8, x_8 will play a game if and only if x_8 is an astronaut. For all x_8, x_8 will play a game or x_8 will not sleep. For all x_8, x_8 is not an astronaut. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 will play a game if and only if x_8 is an astronaut.
That is one of the premises. Therefore, the answer is yes.