Consider the following premises. exists y: ~W(y). forall y: P_4(y) <-> W(y). forall y: P_4(y). Can we infer exists y: T(y) from them?
 From forall y: P_4(y) we can infer forall y: P_4(y) or T(y). From forall y: P_4(y) <-> W(y), exists y: ~W(y) we can infer exists y: ~P_4(y). Finally, from forall y: P_4(y) or T(y), exists y: ~P_4(y) we can infer exists y: T(y). Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.