Consider the following premises. exists y_1: Q_1(y_1) -> Q_3(y_1). forall y_1: Q_1(y_1) or ~Q_3(y_1). Can we infer exists y_1: Q_3(y_1) -> Q_1(y_1) from them?
 From forall y_1: Q_1(y_1) or ~Q_3(y_1) we can infer forall y_1: Q_3(y_1) -> Q_1(y_1). From exists y_1: Q_1(y_1) -> Q_3(y_1), forall y_1: Q_3(y_1) -> Q_1(y_1) we can infer exists y_1: Q_1(y_1) <-> Q_3(y_1). Finally, from exists y_1: Q_1(y_1) <-> Q_3(y_1) we can infer exists y_1: Q_3(y_1) -> Q_1(y_1). Therefore, the answer is yes.