Consider the following premises. There is at least one x_11 for which if x_11 cooks, then x_11 is a nurse. For all x_11, x_11 will not listen to a song or x_11 is a doctor. For all x_11, x_11 will listen to a song or x_11 will cook. For all x_11, x_11 is fast or x_11 is not a nurse. For all x_11, if x_11 were a doctor, then x_11 is fast. Can we infer the following from them? For all x_11, x_11 is fast or x_11 is not a nurse.
That is one of the premises. Therefore, the answer is yes.