Consider the following premises. forall x_12: U(x_12) -> Q_12(x_12). ~U(a_11). forall x_12: Q_12(x_12) -> U(x_12). p. Can we infer p and ~Q_12(a_11) from them? If possible, name the inference rules being used at each step.
 From forall x_12: U(x_12) -> Q_12(x_12), forall x_12: Q_12(x_12) -> U(x_12) we can infer forall x_12: U(x_12) <-> Q_12(x_12) via universal biconditional introduction. From forall x_12: U(x_12) <-> Q_12(x_12) we can infer U(a_11) <-> Q_12(a_11) via universal instantiation. From U(a_11) <-> Q_12(a_11), ~U(a_11) we can infer ~Q_12(a_11) via biconditional elimination. Finally, from p, ~Q_12(a_11) we can infer p and ~Q_12(a_11) via conjunction. Therefore, the answer is yes.