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: exists x_9: P_9(x_9) -> U(x_9). forall x_9: R_3(x_9) -> U(x_9). forall x_9: ~P_9(x_9). forall x_9: U(x_9) -> P_9(x_9).
forall x_9: ~U(x_9) can be inferred via the universal modus tollens rule. forall x_9: R_3(x_9) -> P_9(x_9) can be inferred via the universal transitivity rule. exists x_9: P_9(x_9) <-> U(x_9) can be inferred via the existential biconditional introduction rule. exists x_9: U(x_9) <-> P_9(x_9) can be inferred via the existential biconditional introduction rule.