Well, I haven't seen any "duplicate formula" warning so what you deleted worked.
Just for reference, here's what "duplicate formulas" are usually about. When asset creators create morphs, they have to name them. One of the kind of morphs is a "Joint Controlled Morph". When a character's knee bends, for example, it's possible for the mesh points on the inside of the knee not to work correctly. So, what the creator will do is to create a morph that fixes that, and then arrange for it to be "invoked" as the character's knee bends. So the application of the morph is controlled by the joint. Hence "Joint Controlled Morph." Note that these morphs are normally hidden - you never see them, but they're there. The problem comes because these morphs still have to be named, and it's possible for two different artists to choose the same name for their JCM. Then Daz finds out that there are two different places where "knee joint causes JCM named 'x' to be invoked", and complains about "duplicate formula," because it only expects there to be one of these.
For stuff sold thru the Daz store, Daz usually either ensures that the JCM's are named uniquely, or else when one slips thru, they have the creator do an update to the package and re-release it to fix the issue. But sometimes people end with and old version, not the updated version. Alternately, if you get content from non-Daz locations, there's always the possibility that two different vendors selling on two different stores may "collide." Again, frequently they get updated, but not always.
JCM's aren't the only place that something like this can happen, but it's an example of what's going on.
Usually, you can still use the asset even so, but, as was pointed out, it can sometimes be a problem if you were going to try to do batch rendering or something like that.
As for the multiple errors you have of "Could not find output property for formula: ...", I'm not 100% sure but I think they are warnings that what you try to load (in this case the base figure Genesis 8 Female) has links to certain morphs that you don't have installed, and warns you, but you can work without problem.
These are completely normal, and can be ignored. As was pointed out, this is a situation in which an asset you have references an asset you don't. It frequently happens with morph packs. If, for example, I install a morph pack that has morphs for both G3 and G8 and I don't actually have G8 installed, Daz will complain about morphs that reference the G8 properties because it can't find the G8 properties that are reference. Usually it's not that gross, but it's not uncommon for morph packs and things like that to have special versions for specific characters, and if you don't have that character installed, you get the warning. Hopefully you see what I mean.
Basically, there is a LOT of cruft in the log file. I wish Daz would do something to help clean it up, but it is what it is.
So "Could not find output property" - ignore. "Duplicate formula" - worth investigating to find which pair of assets are conflicting and see if there's an update that fixes it.
