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: There is at least one z_2 for which if z_2 writes a letter, then z_2 is not a janitor. For all z_2, z_2 will write a letter if and only if z_2 is a poet. For all z_2, z_2 is a janitor.
There is at least one z_2 for which z_2 will not write a letter can be inferred via the existential modus tollens rule. For all z_2, if z_2 writes a letter, then z_2 is a poet can be inferred via the universal biconditional elimination rule. For all z_2, if z_2 were a poet, then z_2 is writing a letter can be inferred via the universal biconditional elimination rule.