Consider the following premises. forall x_2: R(x_2) -> ~Q_2(x_2). forall x_2: Q_2(x_2). exists x_2: U(x_2) <-> R(x_2). Can we infer exists x_2: ~U(x_2) from them? If possible, name the inference rules being used at each step.
 From forall x_2: R(x_2) -> ~Q_2(x_2), forall x_2: Q_2(x_2) we can infer forall x_2: ~R(x_2) via universal modus tollens. Finally, from exists x_2: U(x_2) <-> R(x_2), forall x_2: ~R(x_2) we can infer exists x_2: ~U(x_2) via existential biconditional elimination. Therefore, the answer is yes.