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 a taxi driver if and only if z will climb a mountain. There is at least one z for which if z were a taxi driver, then z is working. For all z, z is not an astronaut. For all z, if z works, then z is an astronaut.
For all z, z will not work can be inferred via the universal modus tollens rule. There is at least one z for which if z were a taxi driver, then z is an astronaut can be inferred via the existential transitivity rule. For all z, if z were a taxi driver, then z is climbing a mountain can be inferred via the universal biconditional elimination rule. For all z, if z climbs a mountain, then z is a taxi driver can be inferred via the universal biconditional elimination rule.