An error occurred during the log file integration, it is recommended to restore the last backup of this database in order to attempt the integrations of this log file.

This message tells us there may be more than one log file on your system and wires are getting crossed.
Please do a search on your computer as well as any connected external drives. Search for: SuccessWare.journal

If you find any of these files move them to the Trash. Do not Empty the Trash until you are back up and running.

Once you move all SuccessWare.journal files to the Trash, launch SuccessWare.
You should now get a message that: The correct log file can not be found.
Click Create.
A Save window will open, leave the name as it is and change the location to wherever you are saving your backups.

SuccessWare should then launch like normal.