Consider the following premises. forall x_5: R(x_5) -> Q_1(x_5). exists x_5: P_5(x_5) -> Q_5(x_5). forall x_5: Q_1(x_5) -> P_5(x_5). forall x_5: Q_5(x_5) -> R(x_5). Can we infer exists x_5: P_5(x_5) -> Q_5(x_5) from them?
That is one of the premises. Therefore, the answer is yes.