Consider the following premises. ~Q_3(i). forall y_1: Q_3(y_1) -> T_4(y_1). T_4(i) -> Q_3(i). Can we infer T_4(i) from them? If possible, name the inference rules being used at each step.
 From forall y_1: Q_3(y_1) -> T_4(y_1) we can infer Q_3(i) -> T_4(i) via universal instantiation. From T_4(i) -> Q_3(i), Q_3(i) -> T_4(i) we can infer T_4(i) <-> Q_3(i) via biconditional introduction. Finally, from T_4(i) <-> Q_3(i), ~Q_3(i) we can infer ~T_4(i) via biconditional elimination, which contradicts T_4(i). Therefore, the answer is no.