Consider the following premises. forall x_9: P_9(x_9) -> Q_9(x_9). forall x_9: ~Q_9(x_9). forall x_9: T_3(x_9) <-> P_7(x_9). exists x_9: P_7(x_9) <-> P_9(x_9). Can we infer exists x_9: P_7(x_9) <-> P_9(x_9) from them?
That is one of the premises. Therefore, the answer is yes.