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grep -- displays process ids
-v -- negates the matching, displays all but what is specified in the other options
-u -- specifies the user to display, or in this case negate
The process loops through all PIDs that are found by pgrep, then orders a forced kill to the processes in numerical order, effectively killing the parent processes first including the shells in use which will force the users to logout.
Tested on Slackware Linux 12.2 and Slackware-current