Consider the following premises. forall x_7: T(x_7) or W_4(x_7). forall x_7: W_4(x_7) -> R_2(x_7). forall x_7: T(x_7) <-> R_2(x_7). forall x_7: U(x_7) -> ~R_2(x_7). Can we infer forall x_7: ~U(x_7) from them? If possible, name the inference rules being used at each step.
 From forall x_7: T(x_7) <-> R_2(x_7) we can infer forall x_7: T(x_7) -> R_2(x_7) via universal biconditional elimination. From forall x_7: T(x_7) -> R_2(x_7), forall x_7: W_4(x_7) -> R_2(x_7), forall x_7: T(x_7) or W_4(x_7) we can infer forall x_7: R_2(x_7) via universal disjunction elimination. Finally, from forall x_7: U(x_7) -> ~R_2(x_7), forall x_7: R_2(x_7) we can infer forall x_7: ~U(x_7) via universal modus tollens. Therefore, the answer is yes.