Consider the following premises. forall x_10: U_3(x_10) <-> S(x_10). forall x_10: U_3(x_10) or ~P(x_10). forall x_10: P(x_10) or S(x_10). Can we infer forall x_10: U_3(x_10) or W_1(x_10) from them? If possible, name the inference rules being used at each step.
 From forall x_10: U_3(x_10) or ~P(x_10) we can infer forall x_10: P(x_10) -> U_3(x_10) via universal rewriting. From forall x_10: U_3(x_10) <-> S(x_10) we can infer forall x_10: S(x_10) -> U_3(x_10) via universal biconditional elimination. From forall x_10: P(x_10) -> U_3(x_10), forall x_10: S(x_10) -> U_3(x_10), forall x_10: P(x_10) or S(x_10) we can infer forall x_10: U_3(x_10) via universal disjunction elimination. Finally, from forall x_10: U_3(x_10) we can infer forall x_10: U_3(x_10) or W_1(x_10) via universal addition. Therefore, the answer is yes.