Consider the following premises. forall x_17: U_1(x_17) -> Q_10(x_17). forall x_17: R(x_17) -> S_4(x_17). forall x_17: S_4(x_17) -> U_1(x_17). exists x_17: ~Q_10(x_17). forall x_17: S_4(x_17) -> R(x_17). Can we infer forall x_17: R(x_17) from them? If possible, name the inference rules being used at each step.
 From forall x_17: S_4(x_17) -> R(x_17), forall x_17: R(x_17) -> S_4(x_17) we can infer forall x_17: S_4(x_17) <-> R(x_17) via universal biconditional introduction. From forall x_17: U_1(x_17) -> Q_10(x_17), exists x_17: ~Q_10(x_17) we can infer exists x_17: ~U_1(x_17) via existential modus tollens. From forall x_17: S_4(x_17) -> U_1(x_17), exists x_17: ~U_1(x_17) we can infer exists x_17: ~S_4(x_17) via existential modus tollens. Finally, from forall x_17: S_4(x_17) <-> R(x_17), exists x_17: ~S_4(x_17) we can infer exists x_17: ~R(x_17) via existential biconditional elimination, which contradicts forall x_17: R(x_17). Therefore, the answer is no.