Consider the following premises. forall x: R(x) -> P(x). forall x: ~P(x). R(i) <-> q. forall x: P(x) -> R(x). Can we infer q from them? If possible, name the inference rules being used at each step.
 From forall x: P(x) -> R(x), forall x: R(x) -> P(x) we can infer forall x: P(x) <-> R(x) via universal biconditional introduction. From forall x: P(x) <-> R(x), forall x: ~P(x) we can infer forall x: ~R(x) via universal biconditional elimination. From forall x: ~R(x) we can infer ~R(i) via universal instantiation. Finally, from R(i) <-> q, ~R(i) we can infer ~q via biconditional elimination, which contradicts q. Therefore, the answer is no.