What's to disprove? They are prima facie false, not just formally (because "ever" and "effectively infinite" are obviously exaggerations), but also empirically, here and now - mankind already needs more land than Earth has, and more energy than Earth can spare.
"The Earth has more land than mankind will ever need."
"The Earth has effectively infinite energy from the Sun.
> "ever" and "effectively infinite" are obviously exaggerations
I see no exaggeration, obvious or otherwise. Scientific consensus is that mankind's population is going to peak in the next century.
> mankind already needs more land than Earth has
By what basis? There's no shortage of land. There's a shortage of land close to popular population centers, and that tends to be the land that people want to live on most. But that's an inherent geometric and social problem which outer space definitely doesn't solve, in fact it makes it worse.
> more energy than Earth can spare
Earth doesn't provide energy, the sun does. Even fossil fuels, biomass and wind power were all originally energy from the sun. The exception is nuclear - Earth does have an unusually high concentration of heavily elements like uranium and plutonium.
The bottleneck has always been development and delivery, not availability of energy itself. On just the land the US currently uses to grow corn for ethanol gasoline, we could build enough solar panels to power the entire US. And I certainly don't need to tell you about nuclear - the only reason entire civilizations aren't already powered by it is the time and expense and risk of building the plants.
What energy does outer space provide? You have solar, which we have here, and nuclear, which we have here. (You also have a variety of ideas that exist in science fiction but not the real world, like dyson spheres - I surely hope you aren't referring to such as the basis of your arguments.) None of this is new, and none of this solves the problems of development and delivery, in fact it makes both problems significantly worse.
Not to mention that it seems more healthy to have a far off frontier for a human civilization. It makes it possible for people to try something new, something different, brings innovation, etc. Without it, some people might just be too unhappy in the regular society.
I get it though. This is just how naturalism looks like when runs out of arguments in its favor.