ORA-01180 when restoring the database
Community Wiki answer from a self-answer originally edited into the question (and based on a comment by Balazs Papp).

I forgot an incarnation:



RMAN&gt; list incarnation;

List of Database Incarnations
DB Key  Inc Key DB Name  DB ID            STATUS  Reset SCN  Reset Time
------- ------- -------- ---------------- --- ---------- ----------
1       1       PROD     130474031        PARENT  1          10-MAY-10
2       2       PROD     130474031        PARENT  195833299  21-OCT-10
3       3       PROD     130474031        PARENT  3655020271 06-OCT-12
4       4       PROD     130474031        PARENT  3655121615 08-OCT-12
5       5       PROD     130474031        CURRENT 5588371557 19-OCT-14

RMAN&gt; reset database to incarnation 4;

database reset to incarnation 4

RMAN&gt; restore database;

Starting restore at 22-DEC-15
allocated channel: ORA_DISK_1
channel ORA_DISK_1: sid=10993 devtype=DISK

creating datafile fno=3 name=/opt/oracle/oradata/prod/sysaux01.dbf
creating datafile fno=4 name=/opt/oracle/oradata/prod/users01.dbf


The problem is now solved.