Consider the following premises. w_3 <-> R_17(a_17). forall x_17: R_17(x_17) or S_17(x_17). S_17(a_17) -> w_3. Can we infer ~w_3 from them?
 From forall x_17: R_17(x_17) or S_17(x_17) we can infer R_17(a_17) or S_17(a_17). From w_3 <-> R_17(a_17) we can infer R_17(a_17) -> w_3. Finally, from R_17(a_17) -> w_3, S_17(a_17) -> w_3, R_17(a_17) or S_17(a_17) we can infer w_3, which contradicts ~w_3. Therefore, the answer is no.