We first refute Scheepers' conjecture. More precisely, we prove the following.

Assuming CH, there is a subset of reals $X$ such that $C_p(X)$ has property ($\alpha_2$) and $X$ does not satisfy $S_1(\Gamma, \Gamma)$.

It is known that by Dow and Hales' results, Scheepers' conjecture is consistent. So some additional assumption is needed. We will reveal the idea and some details.

All but two implications are known in Scheepers Diagram. We then complete Scheepers Diagram by proving the following.

$U_{fin}(\Gamma, \Gamma)$ implies $S_{fin}(\Gamma, \Omega)$.

$U_{fin}(\Gamma, \Omega)$ does not imply $S_{fin}(\Gamma, \Omega)$. More precisely, assuming CH, there is a subset of reals $X$ satisfying $U_{fin}(\Gamma, \Omega)$ such that $X$ does not satisfy $S_{fin}(\Gamma, \Omega)$.