Consider the following premises. forall x_12: P_2(x_12) -> R_2(x_12). exists x_12: R_2(x_12) -> P_2(x_12). forall x_12: R_2(x_12) -> Q_12(x_12). forall x_12: Q_12(x_12) -> R_2(x_12). Can we infer exists x_12: R_2(x_12) -> P_2(x_12) from them? If possible, name the inference rules being used at each step.
That is one of the premises. Therefore, the answer is yes.