Consider the following premises. forall x: R_1(x) -> R(x). exists x: R_3(x) -> R_1(x). forall x: R_1(x) -> R_3(x). forall x: R(x) -> R_1(x). Can we infer exists x: R(x) -> R_3(x) from them?
 From forall x: R_1(x) -> R(x), forall x: R(x) -> R_1(x) we can infer forall x: R_1(x) <-> R(x). From forall x: R_1(x) -> R_3(x), exists x: R_3(x) -> R_1(x) we can infer exists x: R_1(x) <-> R_3(x). From exists x: R_1(x) <-> R_3(x) we can infer exists x: R_1(x) -> R_3(x). From forall x: R_1(x) <-> R(x) we can infer forall x: R(x) -> R_1(x). Finally, from forall x: R(x) -> R_1(x), exists x: R_1(x) -> R_3(x) we can infer exists x: R(x) -> R_3(x). Therefore, the answer is yes.