How do you single-handedly prove wrong a statement like "it helps a lot to have a cofounder"?

I'm not trying to prove that it doesn't help to have a cofounder. In fact, I'd agree that in most cases having a cofounder helps.

It's more that I'd like to demonstrate that there are exceptions -- and so far I can't think of a single instance where having a cofounder would have helped me.

One of the most valuable things a cofounder does is shine light on your blind spots. By definition you can't see these problems, but someone else who's intimately involved can.

A common argument is that it's valuable to have a partner as a sounding board and as a source of moral support. These roles are vital, but they don't necessarily have to be filled by founders. Einstein needed the help of his friend Michele Besso to develop special relativity, but Besso wasn't a coauthor on Zur Elektrodynamik bewegter Körper.

I don't see two as a natural lower bound on the number of founders. As the productivity of individual programmers continues to rise, I expect to see an increasing number of single-founder startups succeed.

I have also come to the same conclusion independently.

You need a sounding board and a source of moral support absolutely. This is best done by a co-founder. However, it CAN also be done by someone who is not a co-founder and more of an advisor.

Also, you do NOT absolutely need co-founders with complimentary skills. That is a myth. Larry and Segie did not have complimentary skills. Bill Gates and Paul Allen did NOT have ALL the skills required to build their business. They had or developed (read learned) a lot of skills on the way, for which they could not hire immidiately - which is the only thing that is required of a founding team.

My co-founder is very useful to me, and our business. He has a completely different but complementary skill set and viewpoint. Furthermore, we push each other when things don't look so hot, business-wise. I wouldn't know what to do _without_ a co-founder.

like showing a case where having a cofounder gives zero or even negative progress?

there should be plenty