Consider the following premises. exists y_4: Q_1(y_4) <-> U_1(y_4). forall y_4: S_3(y_4) <-> Q_1(y_4). forall y_4: ~S_3(y_4). Can we infer exists y_4: ~U_1(y_4) from them? If possible, name the inference rules being used at each step.
 From forall y_4: S_3(y_4) <-> Q_1(y_4), forall y_4: ~S_3(y_4) we can infer forall y_4: ~Q_1(y_4) via universal biconditional elimination. Finally, from exists y_4: Q_1(y_4) <-> U_1(y_4), forall y_4: ~Q_1(y_4) we can infer exists y_4: ~U_1(y_4) via existential biconditional elimination. Therefore, the answer is yes.