Consider the following premises. exists x_10: ~Q_10(x_10). forall x_10: S(x_10) -> Q_10(x_10). forall x_10: U(x_10) -> S(x_10). forall x_10: R(x_10) <-> U(x_10). Can we infer forall x_10: R(x_10) from them? If possible, name the inference rules being used at each step.
 From forall x_10: S(x_10) -> Q_10(x_10), exists x_10: ~Q_10(x_10) we can infer exists x_10: ~S(x_10) via existential modus tollens. From forall x_10: U(x_10) -> S(x_10), exists x_10: ~S(x_10) we can infer exists x_10: ~U(x_10) via existential modus tollens. Finally, from forall x_10: R(x_10) <-> U(x_10), exists x_10: ~U(x_10) we can infer exists x_10: ~R(x_10) via existential biconditional elimination, which contradicts forall x_10: R(x_10). Therefore, the answer is no.