Consider the following premises. forall x_2: U(x_2) <-> W_2(x_2). exists x_2: ~Q_2(x_2). forall x_2: W_2(x_2) -> Q_2(x_2). Can we infer exists x_2: ~U(x_2) from them?
 From forall x_2: W_2(x_2) -> Q_2(x_2), exists x_2: ~Q_2(x_2) we can infer exists x_2: ~W_2(x_2). Finally, from forall x_2: U(x_2) <-> W_2(x_2), exists x_2: ~W_2(x_2) we can infer exists x_2: ~U(x_2). Therefore, the answer is yes.