Consider the following premises. forall x_11: P_11(x_11) or Q_11(x_11). forall x_11: P_3(x_11) or R_4(x_11). forall x_11: ~P_3(x_11). forall x_11: ~P_11(x_11) or R_11(x_11). forall x_11: Q_11(x_11) -> W(x_11). forall x_11: R_11(x_11) -> W(x_11). Can we infer forall x_11: R_4(x_11) from them?
 From forall x_11: P_11(x_11) or Q_11(x_11), forall x_11: ~P_11(x_11) or R_11(x_11) we can infer forall x_11: Q_11(x_11) or R_11(x_11). From forall x_11: Q_11(x_11) -> W(x_11), forall x_11: R_11(x_11) -> W(x_11), forall x_11: Q_11(x_11) or R_11(x_11) we can infer forall x_11: W(x_11). Finally, from forall x_11: P_3(x_11) or R_4(x_11), forall x_11: ~P_3(x_11) we can infer forall x_11: R_4(x_11). Therefore, the answer is yes.