Consider the following premises. For all x_8, if x_8 plays tennis, then x_8 is a nurse. For all x_8, if x_8 were a nurse, then x_8 is a musician. For all x_8, x_8 is a musician. There is at least one x_8 for which if x_8 were a musician, then x_8 is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 will not play tennis.
 From the fact that for all x_8, if x_8 plays tennis, then x_8 is a nurse, and that for all x_8, if x_8 were a nurse, then x_8 is a musician we can infer that for all x_8, if x_8 plays tennis, then x_8 is a musician via universal transitivity. From the fact that for all x_8, if x_8 plays tennis, then x_8 is a musician, and that there is at least one x_8 for which if x_8 were a musician, then x_8 is playing tennis we can infer that there is at least one x_8 for which x_8 will play tennis if and only if x_8 is a musician via existential biconditional introduction. From the fact that there is at least one x_8 for which x_8 will play tennis if and only if x_8 is a musician we can infer that there is at least one x_8 for which if x_8 were a musician, then x_8 is playing tennis via existential biconditional elimination. Finally, from the fact that there is at least one x_8 for which if x_8 were a musician, then x_8 is playing tennis, and that for all x_8, x_8 is a musician we can infer that there is at least one x_8 for which x_8 will play tennis via existential modus ponens, which contradicts that For all x_8, x_8 will not play tennis. Therefore, the answer is no.