It looks the drive is full. But I don't think it's possible to make a 13GB partiton full during installation, I think.
Open a terminal and run 'df' command. Please post the result. It'll show free and used space for all your partitions. Then please run
Only the last line of the result is important. It'll look like this:
And it this case means that my /tmp dir uses 6.9MB. One of the possibilities is that you have full /tmp (but I don't know how it could happen...).