Consider the following premises. forall y_2: S(y_2) -> R_3(y_2). forall y_2: R_3(y_2) -> W(y_2). forall y_2: W(y_2) or S(y_2). exists y_2: P_4(y_2) -> ~R_3(y_2). forall y_2: W(y_2) -> R_3(y_2). Can we infer forall y_2: P_4(y_2) from them?
 From forall y_2: W(y_2) -> R_3(y_2), forall y_2: R_3(y_2) -> W(y_2) we can infer forall y_2: W(y_2) <-> R_3(y_2). From forall y_2: W(y_2) <-> R_3(y_2) we can infer forall y_2: W(y_2) -> R_3(y_2). From forall y_2: W(y_2) -> R_3(y_2), forall y_2: S(y_2) -> R_3(y_2), forall y_2: W(y_2) or S(y_2) we can infer forall y_2: R_3(y_2). Finally, from exists y_2: P_4(y_2) -> ~R_3(y_2), forall y_2: R_3(y_2) we can infer exists y_2: ~P_4(y_2), which contradicts forall y_2: P_4(y_2). Therefore, the answer is no.