Consider the following premises. forall y_2: P(y_2) <-> U_3(y_2). forall y_2: T(y_2) -> P(y_2). exists y_2: U_3(y_2) -> T(y_2). Can we infer forall y_2: ~(U_3(y_2) <-> P(y_2)) from them?
That contradicts the premises. Therefore the answer is no.