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 x_12: P(x_12) -> P_12(x_12). forall x_12: P(x_12) -> Q_8(x_12). forall x_12: R_8(x_12) -> P(x_12). exists x_12: Q_8(x_12) -> R_8(x_12). forall x_12: P_12(x_12) -> P(x_12). forall x_12: ~P_12(x_12).
forall x_12: ~P(x_12) can be inferred via the universal modus tollens rule. forall x_12: R_8(x_12) -> P_12(x_12) can be inferred via the universal transitivity rule. forall x_12: R_8(x_12) -> Q_8(x_12) can be inferred via the universal transitivity rule. forall x_12: P_12(x_12) -> Q_8(x_12) can be inferred via the universal transitivity rule. exists x_12: Q_8(x_12) -> P(x_12) can be inferred via the existential transitivity rule. exists x_12: P(x_12) -> R_8(x_12) can be inferred via the existential transitivity rule. forall x_12: P(x_12) <-> P_12(x_12) can be inferred via the universal biconditional introduction rule. forall x_12: P_12(x_12) <-> P(x_12) can be inferred via the universal biconditional introduction rule.