Consider the following premises. forall y_1: U(y_1) or ~S_2(y_1). forall y_1: S_2(y_1) or ~U(y_1). Can we infer forall y_1: S_2(y_1) <-> U(y_1) from them?
 From forall y_1: U(y_1) or ~S_2(y_1) we can infer forall y_1: S_2(y_1) -> U(y_1). From forall y_1: S_2(y_1) or ~U(y_1) we can infer forall y_1: U(y_1) -> S_2(y_1). Finally, from forall y_1: S_2(y_1) -> U(y_1), forall y_1: U(y_1) -> S_2(y_1) we can infer forall y_1: S_2(y_1) <-> U(y_1). Therefore, the answer is yes.