Filling gaps in a concrete floor

Our 1950’s brick two story, three bedroom with a basement is a pretty common type around Toronto. We’re doing some demolition and cleaning up in the basement. We are fairly sure we want to sell; our original plan was not to finish the basement, but to take it down to "clean"; painted cement floors, painted concrete block walls.

The basement was finished to a certain extent by a former owner.

• Part of the basement floor looks like "normal painted concrete basement floor". Mostly smooth, painted with a kind of thick paint.
• Another part of the basement had carpet. This carpet was sitting on plywood, that we thought was sitting on the same kind of smooth painted concrete.

However, we just pulled up the carpet and plywood subfloor, and as we do it, we’re finding that this area does not have smooth concrete under it. It has rough concrete instead, looks like it was not finished.

More confusingly, that concrete appears to have been poured between 2×4’s, so each strip of concrete is about 8 feet long and 18 inches wide. Now 70 years later now, many of those 2×4’s have rotted, and for those we can look down and see soil!

I’ve had a recommendation to pull up all the 2×4’s and just pour self leveling concrete in the gaps. Is that the right direction? If not, what other directions would be good?

Note: as you can see in the image, some of the "2×4’s" appear to be two separate studs that are 1" wide, not 2×4’s.