Consider the following premises. ~w. R(a_7) -> w. forall x: Q(x) <-> R(x). Can we infer Q(a_7) from them?
 From forall x: Q(x) <-> R(x) we can infer Q(a_7) <-> R(a_7). From R(a_7) -> w, ~w we can infer ~R(a_7). Finally, from Q(a_7) <-> R(a_7), ~R(a_7) we can infer ~Q(a_7), which contradicts Q(a_7). Therefore, the answer is no.