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 poet, then z is working. For all z, if z works, then z is a poet. There is at least one z for which z is not a poet. For all z, if z climbs a mountain, then z is working.
There is at least one z for which z will not work can be inferred via the existential modus tollens rule. For all z, if z climbs a mountain, then z is a poet can be inferred via the universal transitivity rule. For all z, z is a poet if and only if z will work can be inferred via the universal biconditional introduction rule. For all z, z will work if and only if z is a poet can be inferred via the universal biconditional introduction rule.