Consider the following premises. There is at least one x_6 for which x_6 will sleep if and only if x_6 is fast. For all x_6, if x_6 works, then x_6 is fast. For all x_6, if x_6 sleeps, then x_6 is working. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 will sleep if and only if x_6 is fast.
That is one of the premises. Therefore, the answer is yes.