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 fast, then z is a poet. For all z, z is not sad. For all z, if z were a poet, then z is sad. There is at least one z for which if z were a poet, then z is fast.
For all z, z is not a poet can be inferred via the universal modus tollens rule. For all z, if z were fast, then z is sad can be inferred via the universal transitivity rule. There is at least one z for which z is a poet if and only if z is fast can be inferred via the existential biconditional introduction rule. There is at least one z for which z is fast if and only if z is a poet can be inferred via the existential biconditional introduction rule.