Consider the following premises. forall x: W_1(x) or U_1(x). exists x: ~W(x). forall x: W(x) <-> W_1(x). Can we infer forall x: ~U_1(x) from them? If possible, name the inference rules being used at each step.
 From forall x: W(x) <-> W_1(x), exists x: ~W(x) we can infer exists x: ~W_1(x) via existential biconditional elimination. Finally, from forall x: W_1(x) or U_1(x), exists x: ~W_1(x) we can infer exists x: U_1(x) via existential disjunctive syllogism, which contradicts forall x: ~U_1(x). Therefore, the answer is no.