Consider the following premises. forall x_10: ~Q_10(x_10). q -> T(a_5). forall x_10: T(x_10) <-> P_10(x_10). forall x_10: P_10(x_10) -> Q_10(x_10). Can we infer ~q from them? If possible, name the inference rules being used at each step.
 From forall x_10: P_10(x_10) -> Q_10(x_10), forall x_10: ~Q_10(x_10) we can infer forall x_10: ~P_10(x_10) via universal modus tollens. From forall x_10: T(x_10) <-> P_10(x_10), forall x_10: ~P_10(x_10) we can infer forall x_10: ~T(x_10) via universal biconditional elimination. From forall x_10: ~T(x_10) we can infer ~T(a_5) via universal instantiation. Finally, from q -> T(a_5), ~T(a_5) we can infer ~q via modus tollens. Therefore, the answer is yes.