Consider the following premises. forall x_12: P_12(x_12) -> T(x_12). forall x_12: P_12(x_12). exists x_12: P_8(x_12) and Q_8(x_12). Can we infer exists x_12: P_8(x_12) and Q_8(x_12) from them?
That is one of the premises. Therefore, the answer is yes.