Consider the following premises. For all z, if z were sad, then z is excited. There is at least one z for which z is not excited. For all z, z is excited or z is not sad. For all z, if z were excited, then z is sad. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z for which z is not excited.
That is one of the premises. Therefore, the answer is yes.