Consider the following premises. forall x_3: P(x_3) -> P_3(x_3). forall x_3: P(x_3) or Q_3(x_3). exists x_3: P_3(x_3) or ~Q_3(x_3). Can we infer exists x_3: P_3(x_3) from them?
 From exists x_3: P_3(x_3) or ~Q_3(x_3) we can infer exists x_3: Q_3(x_3) -> P_3(x_3). Finally, from forall x_3: P(x_3) -> P_3(x_3), exists x_3: Q_3(x_3) -> P_3(x_3), forall x_3: P(x_3) or Q_3(x_3) we can infer exists x_3: P_3(x_3). Therefore, the answer is yes.