Consider the following premises. For all x_7, x_7 is a doctor if and only if x_7 will sleep. For all x_7, x_7 will not listen to a song. For all x_7, x_7 will listen to a song if and only if x_7 will sleep. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 will not listen to a song.
That is one of the premises. Therefore, the answer is yes.