Consider the following premises. exists x_11: P_11(x_11) -> Q_11(x_11). forall x_11: P(x_11) or P_11(x_11). forall x_11: R_6(x_11) -> P(x_11). forall x_11: Q_11(x_11) -> R_11(x_11). forall x_11: R_11(x_11) -> R_6(x_11). forall x_11: P(x_11) -> R_6(x_11). Can we infer exists x_11: R_6(x_11) from them?
 From exists x_11: P_11(x_11) -> Q_11(x_11), forall x_11: Q_11(x_11) -> R_11(x_11) we can infer exists x_11: P_11(x_11) -> R_11(x_11). From exists x_11: P_11(x_11) -> R_11(x_11), forall x_11: R_11(x_11) -> R_6(x_11) we can infer exists x_11: P_11(x_11) -> R_6(x_11). From forall x_11: P(x_11) -> R_6(x_11), forall x_11: R_6(x_11) -> P(x_11) we can infer forall x_11: P(x_11) <-> R_6(x_11). From forall x_11: P(x_11) <-> R_6(x_11) we can infer forall x_11: P(x_11) -> R_6(x_11). Finally, from forall x_11: P(x_11) -> R_6(x_11), exists x_11: P_11(x_11) -> R_6(x_11), forall x_11: P(x_11) or P_11(x_11) we can infer exists x_11: R_6(x_11). Therefore, the answer is yes.