Consider the following premises. For all x, x will sleep if and only if x will listen to a song. For all x, if x listens to a song, then x is a doctor. There is at least one x for which if x were a doctor, then x is sleeping. Can we infer the following from them? If we can, name the inference rule being used: For all x, if is not true that x will listen to a song if and only if x is a doctor.
That contradicts the premises. Therefore the answer is no.