Consider the following premises. forall x_11: P_11(x_11) or Q_8(x_11). forall x_11: Q_8(x_11) -> T(x_11). forall x_11: U(x_11) and Q_3(x_11). forall x_11: P_11(x_11) <-> T(x_11). Can we infer forall x_11: U(x_11) and T(x_11) from them? If possible, name the inference rules being used at each step.
 From forall x_11: P_11(x_11) <-> T(x_11) we can infer forall x_11: P_11(x_11) -> T(x_11) via universal biconditional elimination. From forall x_11: P_11(x_11) -> T(x_11), forall x_11: Q_8(x_11) -> T(x_11), forall x_11: P_11(x_11) or Q_8(x_11) we can infer forall x_11: T(x_11) via universal disjunction elimination. From forall x_11: U(x_11) and Q_3(x_11) we can infer forall x_11: U(x_11) via universal simplification. Finally, from forall x_11: U(x_11), forall x_11: T(x_11) we can infer forall x_11: U(x_11) and T(x_11) via universal conjunction. Therefore, the answer is yes.