Consider the following premises. forall x_17: S_2(x_17) <-> S_17(x_17). p. S_17(g_3) or ~p. Can we infer ~S_2(g_3) from them?
 From forall x_17: S_2(x_17) <-> S_17(x_17) we can infer S_2(g_3) <-> S_17(g_3). From S_17(g_3) or ~p we can infer p -> S_17(g_3). From S_2(g_3) <-> S_17(g_3) we can infer S_17(g_3) -> S_2(g_3). From p -> S_17(g_3), S_17(g_3) -> S_2(g_3) we can infer p -> S_2(g_3). Finally, from p -> S_2(g_3), p we can infer S_2(g_3), which contradicts ~S_2(g_3). Therefore, the answer is no.