Consider the following premises. forall y_3: W_1(y_3). forall y_3: P(y_3) -> R_2(y_3). forall y_3: R_2(y_3) -> ~W_1(y_3). forall y_3: R_2(y_3) -> P(y_3). Can we infer exists y_3: P(y_3) from them?
 From forall y_3: R_2(y_3) -> ~W_1(y_3), forall y_3: W_1(y_3) we can infer forall y_3: ~R_2(y_3). From forall y_3: P(y_3) -> R_2(y_3), forall y_3: R_2(y_3) -> P(y_3) we can infer forall y_3: P(y_3) <-> R_2(y_3). Finally, from forall y_3: P(y_3) <-> R_2(y_3), forall y_3: ~R_2(y_3) we can infer forall y_3: ~P(y_3), which contradicts exists y_3: P(y_3). Therefore, the answer is no.