A single pipe is a bitwise-or, it doesn't do what you are trying to do here (and even if it did, you want and, not or). And your ' +\t +' construct will only match whitespace, followed by a tab, followed by whitespace. I would do it something like this instead:

while(<PERMSFILE>) {
    next if /Everyone\s+R X/;
    next if /Webmins\s+all/;
    next if /Domain Admins\s+all/;
    next if /\s+o\s+/;
    print SHORTPERMS;
}
[download]

The correct way to write the code you have though would be something like:

while(<PERMSFILE>) {
    if( $_ !~ /Everyone\s+R X/ &&
        $_ !~ /Webmins\s+all/ &&
        $_ !~ /Domain Admins\s+all/ &&
        $_ !~ / o /) {
            print SHORTPERMS $_;
    }
}
[download]

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We're not surrounded, we're in a target-rich environment!