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: forall z: P_1(z) -> S(z). forall z: P(z) <-> P_1(z). forall z: ~S(z). forall z: P(z) -> P_1(z).
forall z: ~P_1(z) can be inferred via the universal modus tollens rule. forall z: P(z) -> S(z) can be inferred via the universal transitivity rule. forall z: P(z) -> P_1(z) can be inferred via the universal biconditional elimination rule. forall z: P_1(z) -> P(z) can be inferred via the universal biconditional elimination rule.