  In a supersymmetry model with an axino as the lightest supersymmetric
particle (LSP) and a Bino as the next LSP (NLSP), supersymmetry particles
produced in pair at a high energy collider end up with including two Binos,
followed by each Bino's decay into a photon and an axino. Final states are
diphoton with large missing energy. We have comprehensively studied the
implication of $\gamma\gamma+$MET data from the ALEPH, CDF II, and recent ATLAS
and CMS experiments. No excess over the standard model backgrounds can be
explained in this model if the NLSP Bino decays outside the detector, which
happens when the axino decay constant $f_a$ is large enough. The ALEPH and CDF
II data put a very strong bound on $f_a$ for light Bino case with
$m_{\tilde{B}} < 150$ GeV: the narrow hadronic axion window around $f_a \sim
10^6$ GeV is completely closed. In the case where the gluino mass is smaller
than about 776 GeV, the recent ATLAS data limit $f_a > 10^5$ GeV for the Bino
mass below 700 GeV. This is already stronger than the previous laboratory
bounds.
