Consider the following premises. exists x_11: W_2(x_11) -> Q_1(x_11). forall x_11: Q_1(x_11) <-> Q_11(x_11). forall x_11: Q_11(x_11) -> R_5(x_11). forall x_11: R_5(x_11) -> R_1(x_11). Can we infer exists x_11: W_2(x_11) -> R_1(x_11) from them? If possible, name the inference rules being used at each step.
 From forall x_11: Q_1(x_11) <-> Q_11(x_11) we can infer forall x_11: Q_1(x_11) -> Q_11(x_11) via universal biconditional elimination. From forall x_11: Q_1(x_11) -> Q_11(x_11), forall x_11: Q_11(x_11) -> R_5(x_11) we can infer forall x_11: Q_1(x_11) -> R_5(x_11) via universal transitivity. From forall x_11: Q_1(x_11) -> R_5(x_11), forall x_11: R_5(x_11) -> R_1(x_11) we can infer forall x_11: Q_1(x_11) -> R_1(x_11) via universal transitivity. Finally, from exists x_11: W_2(x_11) -> Q_1(x_11), forall x_11: Q_1(x_11) -> R_1(x_11) we can infer exists x_11: W_2(x_11) -> R_1(x_11) via existential transitivity. Therefore, the answer is yes.