Hi zuki
I'm a 10 day Korg owner, but I'm hoping that if you save the Songbook to a pen drive that you can reload it in the event you need to do a total resptore. Have you tried that yet. In fact it's probably critical to do a backup!
When I opened up my saved file using the Songbook editor on my PC all the initial songs were there in addition to my created songs.
Graham
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Graham, Korg Pa1000, Korg G1 Air, Countryman E6, Roland BA330, 2 x Roland CM-30, , Mackie SRM150