Consider the following premises. For all x_5, if x_5 cooks, then x_5 is a carpenter. For all x_5, x_5 will cook if and only if x_5 will go running. For all x_5, x_5 will not play a game. For all x_5, if x_5 were a carpenter, then x_5 is playing a game. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 will not play a game.
That is one of the premises. Therefore, the answer is yes.