Consider the following premises. forall x_17: P_17(x_17) <-> Q_17(x_17). forall x_17: U(x_17). forall x_17: P_17(x_17). exists x_17: Q_17(x_17) -> R_11(x_17). Can we infer exists x_17: U(x_17) and R_11(x_17) from them? If possible, name the inference rules being used at each step.
 From forall x_17: P_17(x_17) <-> Q_17(x_17) we can infer forall x_17: P_17(x_17) -> Q_17(x_17) via universal biconditional elimination. From forall x_17: P_17(x_17) -> Q_17(x_17), exists x_17: Q_17(x_17) -> R_11(x_17) we can infer exists x_17: P_17(x_17) -> R_11(x_17) via existential transitivity. From exists x_17: P_17(x_17) -> R_11(x_17), forall x_17: P_17(x_17) we can infer exists x_17: R_11(x_17) via existential modus ponens. Finally, from forall x_17: U(x_17), exists x_17: R_11(x_17) we can infer exists x_17: U(x_17) and R_11(x_17) via existential conjunction. Therefore, the answer is yes.