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Kim Soo Hyun enlisted for his mandatory military service back on October 23, 2017 at a new recruit training center in Paju in Kyeonggi province. His discharge is set for July 22, 2019. 

It seems the actor was allowed a brief outing in the midst of his soldier duties, and he chose to spend some time at a PC cafe! You can see him immersed in what he's doing, with his military uniform jacket hung on the back of his chair.