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 climbs a mountain, then z is a doctor. For all z, if z were a doctor, then z is sleeping. For all z, if z sleeps, then z is climbing a mountain. There is at least one z for which z will not sleep.
There is at least one z for which z is not a doctor can be inferred via the existential modus tollens rule. For all z, if z climbs a mountain, then z is sleeping can be inferred via the universal transitivity rule. For all z, if z were a doctor, then z is climbing a mountain can be inferred via the universal transitivity rule. For all z, if z sleeps, then z is a doctor can be inferred via the universal transitivity rule.