Consider the following premises. exists x_10: P_10(x_10) -> P(x_10). forall x_10: P_10(x_10) or Q_10(x_10). forall x_10: P(x_10) -> R(x_10). forall x_10: W_4(x_10) -> R(x_10). forall x_10: Q_10(x_10) -> P(x_10). Can we infer exists x_10: R(x_10) from them?
 From exists x_10: P_10(x_10) -> P(x_10), forall x_10: Q_10(x_10) -> P(x_10), forall x_10: P_10(x_10) or Q_10(x_10) we can infer exists x_10: P(x_10). From exists x_10: P(x_10) we can infer exists x_10: P(x_10) or W_4(x_10). Finally, from forall x_10: P(x_10) -> R(x_10), forall x_10: W_4(x_10) -> R(x_10), exists x_10: P(x_10) or W_4(x_10) we can infer exists x_10: R(x_10). Therefore, the answer is yes.