Consider the following premises. For all x_7, x_7 is a musician and x_7 will go running. There is at least one x_7 for which x_7 will sleep or x_7 is not a musician. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 will sleep.
 From the fact that there is at least one x_7 for which x_7 will sleep or x_7 is not a musician we can infer that there is at least one x_7 for which if x_7 were a musician, then x_7 is sleeping via existential rewriting. From the fact that for all x_7, x_7 is a musician and x_7 will go running we can infer that for all x_7, x_7 is a musician via universal simplification. Finally, from the fact that there is at least one x_7 for which if x_7 were a musician, then x_7 is sleeping, and that for all x_7, x_7 is a musician we can infer that there is at least one x_7 for which x_7 will sleep via existential modus ponens. Therefore, the answer is yes.