Consider the following premises. forall x_7: R_3(x_7) -> Q_7(x_7). forall x_7: Q_7(x_7) -> U(x_7). forall x_7: U(x_7) -> R_3(x_7). forall x_7: U(x_7) -> R_3(x_7). Can we infer forall x_7: R_3(x_7) -> U(x_7) from them? If possible, name the inference rules being used at each step.
We can infer forall x_7: R_3(x_7) -> U(x_7) via the universal transitivity rule. Therefore, the answer is yes.