No, you can't take the intellectual property, it belongs to the existing company. However, if the two co-founders quit, you should have vesting in place, so that they should forfeit 75% of their stock (1 year out of a standard 4-year vesting). Assuming you initially split equally among the 3 of you, that would put you now in charge, but they would still own a small piece of the pie, which is fair considering their contribution to build the product.
I think Alain is right. You have agreements in place that prevent you from doing this as-is.
If I were in that situation, I'd see if I could come to some other arrangement that everyone else could agree to. What I'd probably do is set up a meeting with them and say, "Look, you two have clearly quit, and I'm not interested in staying in this alone, while you keep your equity. It's dead weight that the company can't afford to keep pulling. I'm prepared to walk away from what we've built so far and start a new business from the ground up, unless we can come to another arrangement. The default buyout price is way more than the company is currently worth, but each of our shares are worth $X at the moment, and that's what I'm willing to pay for it. I'll give you the option of buying my share from me for that much, or selling your share of the company to me for that much. Otherwise, I'll just walk away and the business will just drift away into nothingness."
This is effectively a shotgun clause (which is basically the idea behind somebody cutting a cake in two pieces and letting the other person choose their half). Your contract doesn't seem to specifically allow this (it uses a fixed buyout amount, for some reason) but I think it's a viable strategy here. If you don't come to some sort of alternative agreement, your best bet might be to just walk away like they've done. You'll be doing quite a bit more than simply reinventing your image or rebranding if you start over, but it frees you from the dead weight. (Hopefully your agreement didn't prevent you from quitting and starting a competing company too.)
In the future, take Alain's advice and only give out equity that vests over time, preferably with a 1-year cliff at the beginning.