Consider the following premises. forall y_3: S(y_3) or ~Q_3(y_3). exists y_3: Q_3(y_3) or ~S(y_3). Can we infer exists y_3: S(y_3) <-> Q_3(y_3) from them?
 From forall y_3: S(y_3) or ~Q_3(y_3) we can infer forall y_3: Q_3(y_3) -> S(y_3). From exists y_3: Q_3(y_3) or ~S(y_3) we can infer exists y_3: S(y_3) -> Q_3(y_3). Finally, from exists y_3: S(y_3) -> Q_3(y_3), forall y_3: Q_3(y_3) -> S(y_3) we can infer exists y_3: S(y_3) <-> Q_3(y_3). Therefore, the answer is yes.