Consider the following premises. forall y_4: U_2(y_4) -> T_1(y_4). exists y_4: T_1(y_4) -> P(y_4). forall y_4: U_2(y_4) <-> T_4(y_4). forall y_4: P(y_4) -> T_4(y_4). Can we infer forall y_4: ~(P(y_4) -> U_2(y_4)) from them?
That contradicts the premises. Therefore the answer is no.