What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: For all z, if z were a cashier, then z is a server. For all z, z will write a letter if and only if z will take a plane. For all z, if z takes a plane, then z is a cashier. There is at least one z for which z is not a server.
There is at least one z for which z is not a cashier can be inferred via the existential modus tollens rule. For all z, if z takes a plane, then z is a server can be inferred via the universal transitivity rule. For all z, if z writes a letter, then z is taking a plane can be inferred via the universal biconditional elimination rule. For all z, if z takes a plane, then z is writing a letter can be inferred via the universal biconditional elimination rule.