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