Consider the following premises. For all x_7, x_7 will sleep if and only if x_7 will drink water. For all x_7, x_7 will not sleep. For all x_7, x_7 will drink water if and only if x_7 will play tennis. For all x_7, x_7 will cook if and only if x_7 will play tennis. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 will not sleep.
That is one of the premises. Therefore, the answer is yes.