Consider the following premises. forall x_15: Q_15(x_15) <-> P_3(x_15). exists x_15: P_15(x_15) -> P_3(x_15). forall x_15: P_15(x_15) <-> Q_15(x_15). Can we infer exists x_15: P_15(x_15) -> P_3(x_15) from them?
That is one of the premises. Therefore, the answer is yes.