Consider the following premises. forall x_10: Q(x_10) <-> U_3(x_10). forall x_10: ~P(x_10). forall x_10: Q(x_10) -> U_3(x_10). forall x_10: U_3(x_10) -> P(x_10). Can we infer forall x_10: ~Q(x_10) from them? If possible, name the inference rules being used at each step.
 From forall x_10: U_3(x_10) -> P(x_10), forall x_10: ~P(x_10) we can infer forall x_10: ~U_3(x_10) via universal modus tollens. From forall x_10: Q(x_10) <-> U_3(x_10) we can infer forall x_10: U_3(x_10) -> Q(x_10) via universal biconditional elimination. From forall x_10: Q(x_10) -> U_3(x_10), forall x_10: U_3(x_10) -> Q(x_10) we can infer forall x_10: Q(x_10) <-> U_3(x_10) via universal biconditional introduction. From forall x_10: Q(x_10) <-> U_3(x_10) we can infer forall x_10: Q(x_10) -> U_3(x_10) via universal biconditional elimination. Finally, from forall x_10: Q(x_10) -> U_3(x_10), forall x_10: ~U_3(x_10) we can infer forall x_10: ~Q(x_10) via universal modus tollens. Therefore, the answer is yes.