Consider the following premises. exists y: ~W(y). forall y: P_3(y) <-> R_3(y). forall y: P_3(y) -> W(y). forall y: W(y) -> P_3(y). Can we infer forall y: R_3(y) from them?
 From forall y: W(y) -> P_3(y), forall y: P_3(y) -> W(y) we can infer forall y: W(y) <-> P_3(y). From forall y: W(y) <-> P_3(y), exists y: ~W(y) we can infer exists y: ~P_3(y). Finally, from forall y: P_3(y) <-> R_3(y), exists y: ~P_3(y) we can infer exists y: ~R_3(y), which contradicts forall y: R_3(y). Therefore, the answer is no.