Consider the following premises. forall x_3: U(x_3). exists x_3: W(x_3) -> ~U(x_3). forall x_3: S(x_3) <-> W(x_3). Can we infer forall x_3: S(x_3) from them? If possible, name the inference rules being used at each step.
 From exists x_3: W(x_3) -> ~U(x_3), forall x_3: U(x_3) we can infer exists x_3: ~W(x_3) via existential modus tollens. Finally, from forall x_3: S(x_3) <-> W(x_3), exists x_3: ~W(x_3) we can infer exists x_3: ~S(x_3) via existential biconditional elimination, which contradicts forall x_3: S(x_3). Therefore, the answer is no.