Consider the following premises. forall y_2: T_4(y_2) -> Q(y_2). T_4(a_7) <-> q. forall y_2: Q(y_2) -> T_4(y_2). ~Q(a_7). Can we infer ~q from them?
 From forall y_2: T_4(y_2) -> Q(y_2), forall y_2: Q(y_2) -> T_4(y_2) we can infer forall y_2: T_4(y_2) <-> Q(y_2). From forall y_2: T_4(y_2) <-> Q(y_2) we can infer T_4(a_7) <-> Q(a_7). From T_4(a_7) <-> Q(a_7), ~Q(a_7) we can infer ~T_4(a_7). Finally, from T_4(a_7) <-> q, ~T_4(a_7) we can infer ~q. Therefore, the answer is yes.