Consider the following premises. forall x_2: R(x_2) -> U(x_2). exists x_2: U(x_2) -> Q_2(x_2). forall x_2: ~Q_2(x_2). forall x_2: U(x_2) -> R(x_2). Can we infer forall x_2: R(x_2) from them? If possible, name the inference rules being used at each step.
 From exists x_2: U(x_2) -> Q_2(x_2), forall x_2: ~Q_2(x_2) we can infer exists x_2: ~U(x_2) via existential modus tollens. From forall x_2: U(x_2) -> R(x_2), forall x_2: R(x_2) -> U(x_2) we can infer forall x_2: U(x_2) <-> R(x_2) via universal biconditional introduction. Finally, from forall x_2: U(x_2) <-> R(x_2), exists x_2: ~U(x_2) we can infer exists x_2: ~R(x_2) via existential biconditional elimination, which contradicts forall x_2: R(x_2). Therefore, the answer is no.