Consider the following premises. exists x_7: R_3(x_7) -> P(x_7). forall x_7: R_7(x_7) -> R_3(x_7). forall x_7: P(x_7) -> Q_7(x_7). forall x_7: Q_7(x_7) -> R_7(x_7). Can we infer exists x_7: R_3(x_7) -> P(x_7) from them?
That is one of the premises. Therefore, the answer is yes.