Consider the following premises. forall x_16: R_4(x_16) <-> Q_16(x_16). forall x_16: P_8(x_16) <-> Q_8(x_16). forall x_16: Q_16(x_16) -> R_10(x_16). exists x_16: R_10(x_16) -> P_8(x_16). Can we infer exists x_16: R_4(x_16) -> Q_8(x_16) from them? If possible, name the inference rules being used at each step.
 From forall x_16: R_4(x_16) <-> Q_16(x_16) we can infer forall x_16: R_4(x_16) -> Q_16(x_16) via universal biconditional elimination. From forall x_16: R_4(x_16) -> Q_16(x_16), forall x_16: Q_16(x_16) -> R_10(x_16) we can infer forall x_16: R_4(x_16) -> R_10(x_16) via universal transitivity. From forall x_16: P_8(x_16) <-> Q_8(x_16) we can infer forall x_16: P_8(x_16) -> Q_8(x_16) via universal biconditional elimination. From exists x_16: R_10(x_16) -> P_8(x_16), forall x_16: P_8(x_16) -> Q_8(x_16) we can infer exists x_16: R_10(x_16) -> Q_8(x_16) via existential transitivity. Finally, from forall x_16: R_4(x_16) -> R_10(x_16), exists x_16: R_10(x_16) -> Q_8(x_16) we can infer exists x_16: R_4(x_16) -> Q_8(x_16) via existential transitivity. Therefore, the answer is yes.