Consider the following premises. forall x_8: R_4(x_8) -> U(x_8). forall x_8: U(x_8) <-> P_1(x_8). forall x_8: R_4(x_8) or P_1(x_8). exists x_8: W(x_8) -> ~U(x_8). Can we infer forall x_8: W(x_8) from them? If possible, name the inference rules being used at each step.
 From forall x_8: U(x_8) <-> P_1(x_8) we can infer forall x_8: P_1(x_8) -> U(x_8) via universal biconditional elimination. From forall x_8: R_4(x_8) -> U(x_8), forall x_8: P_1(x_8) -> U(x_8), forall x_8: R_4(x_8) or P_1(x_8) we can infer forall x_8: U(x_8) via universal disjunction elimination. Finally, from exists x_8: W(x_8) -> ~U(x_8), forall x_8: U(x_8) we can infer exists x_8: ~W(x_8) via existential modus tollens, which contradicts forall x_8: W(x_8). Therefore, the answer is no.