Consider the following premises. exists x_12: P_12(x_12). forall x_12: T(x_12). forall x_12: P_12(x_12) <-> U(x_12). Can we infer exists x_12: U(x_12) and T(x_12) from them? If possible, name the inference rules being used at each step.
 From forall x_12: P_12(x_12) <-> U(x_12) we can infer forall x_12: P_12(x_12) -> U(x_12) via universal biconditional elimination. From forall x_12: P_12(x_12) -> U(x_12), exists x_12: P_12(x_12) we can infer exists x_12: U(x_12) via existential modus ponens. Finally, from exists x_12: U(x_12), forall x_12: T(x_12) we can infer exists x_12: U(x_12) and T(x_12) via existential conjunction. Therefore, the answer is yes.