Consider the following premises. forall x_1: P_1(x_1) -> R(x_1). forall x_1: R(x_1) <-> W_3(x_1). exists x_1: W_3(x_1) -> P_1(x_1). Can we infer exists x_1: R(x_1) -> W_3(x_1) from them?
 From exists x_1: W_3(x_1) -> P_1(x_1), forall x_1: P_1(x_1) -> R(x_1) we can infer exists x_1: W_3(x_1) -> R(x_1). From forall x_1: R(x_1) <-> W_3(x_1) we can infer forall x_1: R(x_1) -> W_3(x_1). From exists x_1: W_3(x_1) -> R(x_1), forall x_1: R(x_1) -> W_3(x_1) we can infer exists x_1: W_3(x_1) <-> R(x_1). Finally, from exists x_1: W_3(x_1) <-> R(x_1) we can infer exists x_1: R(x_1) -> W_3(x_1). Therefore, the answer is yes.