Consider the following premises. forall x_10: Q_10(x_10) -> P_10(x_10). forall x_10: ~Q_10(x_10). P_10(a_5) <-> t_4. forall x_10: P_10(x_10) -> Q_10(x_10). Can we infer t_4 from them? If possible, name the inference rules being used at each step.
 From forall x_10: P_10(x_10) -> Q_10(x_10), forall x_10: Q_10(x_10) -> P_10(x_10) we can infer forall x_10: P_10(x_10) <-> Q_10(x_10) via universal biconditional introduction. From forall x_10: P_10(x_10) <-> Q_10(x_10), forall x_10: ~Q_10(x_10) we can infer forall x_10: ~P_10(x_10) via universal biconditional elimination. From forall x_10: ~P_10(x_10) we can infer ~P_10(a_5) via universal instantiation. Finally, from P_10(a_5) <-> t_4, ~P_10(a_5) we can infer ~t_4 via biconditional elimination, which contradicts t_4. Therefore, the answer is no.