Consider the following premises. forall x_7: R_7(x_7) <-> S_7(x_7). S_7(a_7) <-> w_1. ~w_1. Can we infer R_7(a_7) from them?
 From forall x_7: R_7(x_7) <-> S_7(x_7) we can infer R_7(a_7) <-> S_7(a_7). From S_7(a_7) <-> w_1, ~w_1 we can infer ~S_7(a_7). Finally, from R_7(a_7) <-> S_7(a_7), ~S_7(a_7) we can infer ~R_7(a_7), which contradicts R_7(a_7). Therefore, the answer is no.