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In the directory backup/logs you can find the log from the last backup:
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-rw-r--r-- 1 oracle oinstall 222940 Apr 5 20:16 2017-04-05-ARCH-CDRATOR.log...
-rw-r--r-- 1 oracle oinstall 957155 Apr 5 23:53 2017-04-05-FULL-CDRATOR.log
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-rw-r--r-- 1 oracle oinstall 221481 Apr 6 20:16 2017-04-06-ARCH-CDRATOR.log
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-rw-r--r-- 1 oracle oinstall 961216 Apr 6 23:53 2017-04-06-FULL-CDRATOR.log
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-rw-r--r-- 1 oracle oinstall 58713 Apr 7 11:16 2017-04-07-ARCH-CDRATOR.log
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Find DBID of database
From that logfile, you can find the start of the last backup, where you can find the DBID of the database.
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