Consider the following premises. forall x_12: P_8(x_12) or Q_12(x_12). exists x_12: S(x_12) or ~Q_12(x_12). forall x_12: P_8(x_12) -> S(x_12). Can we infer exists x_12: S(x_12) or R_4(x_12) from them?
 From exists x_12: S(x_12) or ~Q_12(x_12) we can infer exists x_12: Q_12(x_12) -> S(x_12). From forall x_12: P_8(x_12) -> S(x_12), exists x_12: Q_12(x_12) -> S(x_12), forall x_12: P_8(x_12) or Q_12(x_12) we can infer exists x_12: S(x_12). Finally, from exists x_12: S(x_12) we can infer exists x_12: S(x_12) or R_4(x_12). Therefore, the answer is yes.