Ah see, there's the problem. I don't think it's like Newton's Theory of Gravitation. The rate of profit to fall isn't some ironclad law that's applicable in all cases 100% of the time. Cowbee already conceded various ways it could not be true (lack of competition such as through monopoly, exploitation of workers, globalization and imperialism, cartels, trusts, etc).

It seems to describe the natural tendency of a system-wide phenomenon (assuming increasing automation and existing competition in capitalism but nothing really else), so you'd have to consider a macro view of the entire system over a long period of time for it to work. It's like how you can't say one section of the world has been getting colder or staying the same for a couple years and thus climate change has been debunked, as you not only need to look at the whole planet but then the next couple decades as well.

So the next company has a brief increase in rate of profit, but then taking a more extended look at the system, everyone will probably switch suppliers to the cheaper wood and someone is going to lower their prices, forcing everyone else to (barring one of the scenarios above).