Consider the following premises. forall x_8: S(x_8) -> Q_1(x_8). forall x_8: ~Q_1(x_8). exists x_8: T_2(x_8) <-> S(x_8). Can we infer exists x_8: ~T_2(x_8) from them?
 From exists x_8: T_2(x_8) <-> S(x_8) we can infer exists x_8: T_2(x_8) -> S(x_8). From forall x_8: S(x_8) -> Q_1(x_8), forall x_8: ~Q_1(x_8) we can infer forall x_8: ~S(x_8). Finally, from exists x_8: T_2(x_8) -> S(x_8), forall x_8: ~S(x_8) we can infer exists x_8: ~T_2(x_8). Therefore, the answer is yes.