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 will not play tennis. For all z, z will play tennis or z is not a writer. For all z, if z plays tennis, then z is a writer. There is at least one z for which if z were a writer, then z is playing tennis.
There is at least one z for which z is not a writer can be inferred via the existential modus tollens rule. For all z, if z were a writer, then z is playing tennis can be inferred via the universal rewriting rule. There is at least one z for which z is a writer if and only if z will play tennis can be inferred via the existential biconditional introduction rule. There is at least one z for which z will play tennis if and only if z is a writer can be inferred via the existential biconditional introduction rule.