[raheemm]

Here is one way you could structure this. Create goals for him to reach. If he repeatedly fails to reach them, then you can ask him for compromises such as giving up equity, etc. If you do it in the right way (that is a win-win, helping him to make more contribution), then it can be worked out. If he repeatedly fails, then you can involve your board and work out a solution that is best for the startup.

[RougeFemme]

I agree except that since it's apparently been going on for a while, there's no time now to allow him to "repeatedly" fail. Ideally, this improvement plan would have already been attempted and the results of that (assuming there were repeated failures) could be included in the info provided to the Board.

At this point, he should just go directly to the Board and include his proposed improvement plan in his presentation. The co-founder has already indicated an unwillingness to change or leave; the Board should be able to force it.

[kordless]

"Managing" the cofounder creates more work for everyone involved. As the OP is already trying to figure out a way to maximize work output by kicking the cofounder out, you run the risk of creating double work. In a startup, this is highly risky. And, it's business.