Consider the following premises. For all x_8, x_8 will not read a book or x_8 is sad. For all x_8, if x_8 were sad, then x_8 is a politician. For all x_8, x_8 will read a book or x_8 is a nurse. There is at least one x_8 for which if x_8 were a politician, then x_8 is playing tennis. For all x_8, x_8 is a nurse if and only if x_8 will play 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 were sad, then x_8 is a politician, and that there is at least one x_8 for which if x_8 were a politician, then x_8 is playing tennis we can infer that there is at least one x_8 for which if x_8 were sad, then x_8 is playing tennis via existential transitivity. From the fact that for all x_8, x_8 will read a book or x_8 is a nurse, and that for all x_8, x_8 will not read a book or x_8 is sad we can infer that for all x_8, x_8 is a nurse or x_8 is sad via universal resolution. From the fact that for all x_8, x_8 is a nurse if and only if x_8 will play tennis we can infer that for all x_8, if x_8 were a nurse, then x_8 is playing tennis via universal biconditional elimination. Finally, from the fact that for all x_8, if x_8 were a nurse, then x_8 is playing tennis, that there is at least one x_8 for which if x_8 were sad, then x_8 is playing tennis, and that for all x_8, x_8 is a nurse or x_8 is sad we can infer that there is at least one x_8 for which x_8 will play tennis via existential disjunction elimination, which contradicts that For all x_8, x_8 will not play tennis. Therefore, the answer is no.