Consider the following premises. For all x_8, if x_8 were a server, then x_8 is writing a letter. For all x_8, x_8 will read a book if and only if x_8 is a nurse. There is at least one x_8 for which if x_8 writes a letter, then x_8 is a nurse. For all x_8, x_8 will read a book or x_8 is a server. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 is not a nurse.
 From the fact that for all x_8, x_8 will read a book if and only if x_8 is a nurse we can infer that for all x_8, if x_8 reads a book, then x_8 is a nurse via universal biconditional elimination. From the fact that for all x_8, if x_8 were a server, then x_8 is writing a letter, and that there is at least one x_8 for which if x_8 writes a letter, then x_8 is a nurse we can infer that there is at least one x_8 for which if x_8 were a server, then x_8 is a nurse via existential transitivity. Finally, from the fact that for all x_8, if x_8 reads a book, then x_8 is a nurse, that there is at least one x_8 for which if x_8 were a server, then x_8 is a nurse, and that for all x_8, x_8 will read a book or x_8 is a server we can infer that there is at least one x_8 for which x_8 is a nurse via existential disjunction elimination, which contradicts that For all x_8, x_8 is not a nurse. Therefore, the answer is no.