Consider the following premises. forall x_8: W_2(x_8) -> ~Q_2(x_8). forall x_8: W_2(x_8) <-> U_2(x_8). forall x_8: Q_2(x_8). Can we infer forall x_8: ~U_2(x_8) from them? If possible, name the inference rules being used at each step.
 From forall x_8: W_2(x_8) <-> U_2(x_8) we can infer forall x_8: U_2(x_8) -> W_2(x_8) via universal biconditional elimination. From forall x_8: W_2(x_8) -> ~Q_2(x_8), forall x_8: Q_2(x_8) we can infer forall x_8: ~W_2(x_8) via universal modus tollens. Finally, from forall x_8: U_2(x_8) -> W_2(x_8), forall x_8: ~W_2(x_8) we can infer forall x_8: ~U_2(x_8) via universal modus tollens. Therefore, the answer is yes.