Consider the following premises. forall x_8: T(x_8) <-> S_1(x_8). exists x_8: Q_2(x_8) -> T(x_8). forall x_8: S_1(x_8) -> Q_2(x_8). Can we infer exists x_8: T(x_8) <-> S_1(x_8) from them?
 From forall x_8: T(x_8) <-> S_1(x_8) we can infer forall x_8: T(x_8) -> S_1(x_8). From forall x_8: S_1(x_8) -> Q_2(x_8), exists x_8: Q_2(x_8) -> T(x_8) we can infer exists x_8: S_1(x_8) -> T(x_8). Finally, from forall x_8: T(x_8) -> S_1(x_8), exists x_8: S_1(x_8) -> T(x_8) we can infer exists x_8: T(x_8) <-> S_1(x_8). Therefore, the answer is yes.