Third party backup software, how is the log sequence working?

Question

Me and a colleague had a discussion about how third party software and full backups locally on the SQL works together.
If we use TSM that do full backups and then logbackups every hour in between for example.
If I between the two full backups from TSM accidently do a "non copy-only" full backup do I then also break the whole log sequence backup from then and untill the next TSM backup is?
Or can I use the full backup from my mistake and then take the log backups from TSM that occured after that fail and restore the database?
I guess this depends on the third party backup software, but in my mind it should work but according to him it doesn't.
Try to "paint" how I mean:
I = full TSM backup
- = log TSM
F = my fail backup full but not copy only.
I---F-------I
          ^ is where I would want to restore with both my full one and the logs from TSM. Hope you understand what I mean.

Answer 1

yes, you should be able to use the full backup taken in middle and use the rest of the log backups taken afterwards to restore the database.while I do not use TSM, we use QUEST(DELL) LITESPEED, that takes full backup once a day and log backups
every 15mins.
if someone accidentally takes full backup in the middle of day with out 'copy only',
log sequence will break and successive log backups depend on this full back up.
while this should be prevented from happening in first place, you can still restore from native full backup and then apply log backups taken from third party taken after the  native Full backup.
if this happens, I would restore the FULLBACKP with NORECOVERY using NATIVE SQL and then use  lite speed syntax to restore the log backups.Remember, native sql cannot read third party formatted backups(atleast litespeed), thats why I restore the full backup
using native sql, since it was taken with native sql backup and log backups using litespeed syntax.
Hope it Helps!!
Thanks, well it was just a theory discussion we had about the issue. But none of us could find info on the internet easy to prove our point :) Thanks.