Consider the following premises. forall x_1: S(x_1) -> ~T_2(x_1). forall x_1: T_2(x_1). forall x_1: Q_1(x_1) <-> S(x_1). Can we infer forall x_1: ~Q_1(x_1) from them?
 From forall x_1: S(x_1) -> ~T_2(x_1), forall x_1: T_2(x_1) we can infer forall x_1: ~S(x_1). Finally, from forall x_1: Q_1(x_1) <-> S(x_1), forall x_1: ~S(x_1) we can infer forall x_1: ~Q_1(x_1). Therefore, the answer is yes.