Consider the following premises. forall x_6: U_4(x_6) or W_4(x_6). forall x_6: U_2(x_6) or S_1(x_6). forall x_6: ~U_2(x_6). forall x_6: ~U_4(x_6). Can we infer forall x_6: W_4(x_6) and S_1(x_6) from them? If possible, name the inference rules being used at each step.
 From forall x_6: U_4(x_6) or W_4(x_6), forall x_6: ~U_4(x_6) we can infer forall x_6: W_4(x_6) via universal disjunctive syllogism. From forall x_6: U_2(x_6) or S_1(x_6), forall x_6: ~U_2(x_6) we can infer forall x_6: S_1(x_6) via universal disjunctive syllogism. Finally, from forall x_6: W_4(x_6), forall x_6: S_1(x_6) we can infer forall x_6: W_4(x_6) and S_1(x_6) via universal conjunction. Therefore, the answer is yes.