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, z is rich if and only if z will sleep. For all z, if z were a taxi driver, then z is an astronaut. There is at least one z for which if z were an astronaut, then z is rich. For all z, z will not sleep.
There is at least one z for which if z were a taxi driver, then z is rich can be inferred via the existential transitivity rule. For all z, if z were rich, then z is sleeping can be inferred via the universal biconditional elimination rule. For all z, if z sleeps, then z is rich can be inferred via the universal biconditional elimination rule. For all z, z is not rich can be inferred via the universal biconditional elimination rule.