Consider the following premises. S_2(i) <-> w. q_6 -> p. p -> w. u_1 -> q_6. forall y: ~S_2(y). Can we infer ~u_1 from them?
 From forall y: ~S_2(y) we can infer ~S_2(i). From S_2(i) <-> w, ~S_2(i) we can infer ~w. From u_1 -> q_6, q_6 -> p we can infer u_1 -> p. From p -> w, ~w we can infer ~p. Finally, from u_1 -> p, ~p we can infer ~u_1. Therefore, the answer is yes.