Consider the following premises. forall x_11: U(x_11) <-> Q_11(x_11). forall x_11: U(x_11) -> Q_4(x_11). forall x_11: Q_4(x_11) -> Q_11(x_11). Can we infer Q_11(c_2) -> U(c_2) from them? If possible, name the inference rules being used at each step.
 From forall x_11: U(x_11) <-> Q_11(x_11) we can infer forall x_11: Q_11(x_11) -> U(x_11) via universal biconditional elimination. From forall x_11: U(x_11) -> Q_4(x_11), forall x_11: Q_4(x_11) -> Q_11(x_11) we can infer forall x_11: U(x_11) -> Q_11(x_11) via universal transitivity. From forall x_11: U(x_11) -> Q_11(x_11), forall x_11: Q_11(x_11) -> U(x_11) we can infer forall x_11: U(x_11) <-> Q_11(x_11) via universal biconditional introduction. From forall x_11: U(x_11) <-> Q_11(x_11) we can infer U(c_2) <-> Q_11(c_2) via universal instantiation. Finally, from U(c_2) <-> Q_11(c_2) we can infer Q_11(c_2) -> U(c_2) via biconditional elimination. Therefore, the answer is yes.