Consider the following premises. exists y_1: P(y_1) <-> P_1(y_1). forall y_1: ~P_1(y_1). forall y_1: P(y_1) or U_4(y_1). forall y_1: T(y_1). Can we infer exists y_1: T(y_1) from them?
 From exists y_1: P(y_1) <-> P_1(y_1), forall y_1: ~P_1(y_1) we can infer exists y_1: ~P(y_1). From forall y_1: P(y_1) or U_4(y_1), exists y_1: ~P(y_1) we can infer exists y_1: U_4(y_1). From forall y_1: T(y_1), exists y_1: U_4(y_1) we can infer exists y_1: T(y_1) and U_4(y_1). Finally, from exists y_1: T(y_1) and U_4(y_1) we can infer exists y_1: T(y_1). Therefore, the answer is yes.