Consider the following premises. exists y_1: T(y_1) -> ~W_2(y_1). forall y_1: T(y_1) <-> P(y_1). forall y_1: W_2(y_1). Can we infer exists y_1: ~P(y_1) from them?
 From forall y_1: T(y_1) <-> P(y_1) we can infer forall y_1: P(y_1) -> T(y_1). From exists y_1: T(y_1) -> ~W_2(y_1), forall y_1: W_2(y_1) we can infer exists y_1: ~T(y_1). Finally, from forall y_1: P(y_1) -> T(y_1), exists y_1: ~T(y_1) we can infer exists y_1: ~P(y_1). Therefore, the answer is yes.