Consider the following premises. For all x_7, x_7 will work. For all x_7, x_7 will work if and only if x_7 will play a game. There is at least one x_7 for which if x_7 plays a game, then x_7 is running. Can we infer the following from them? There is at least one x_7 for which if x_7 plays a game, then x_7 is running.
That is one of the premises. Therefore, the answer is yes.