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