Consider the following premises. forall x_11: P_11(x_11) -> R_11(x_11). forall x_11: Q_11(x_11) -> R_11(x_11). forall x_11: P_11(x_11) or Q_11(x_11). forall x_11: P_4(x_11) -> Q_4(x_11). forall x_11: P_4(x_11). Can we infer Q_4(a) from them?
 From forall x_11: P_11(x_11) -> R_11(x_11), forall x_11: Q_11(x_11) -> R_11(x_11), forall x_11: P_11(x_11) or Q_11(x_11) we can infer forall x_11: R_11(x_11). From forall x_11: P_4(x_11) -> Q_4(x_11), forall x_11: P_4(x_11) we can infer forall x_11: Q_4(x_11). From forall x_11: Q_4(x_11), forall x_11: R_11(x_11) we can infer forall x_11: Q_4(x_11) and R_11(x_11). From forall x_11: Q_4(x_11) and R_11(x_11) we can infer Q_4(a) and R_11(a). Finally, from Q_4(a) and R_11(a) we can infer Q_4(a). Therefore, the answer is yes.