How to prove:
Say you just crafted something and you collected it, theres 2 options:
1: it didn't up into your inventory, simple: just make ticket straight away and say you collected something, and it didnt show up in there. In logs we will be able to see a cost being deducted when you start a craft, or we will be able to see what was collected (including the vision vapor you got when collecting)
2: it did show up into your inventory, but a few days later you notice its suddenly gone, harder. You make a ticket straight away, explaining the item disappeared from your inventory, that you crafted hopefully not long ago so we can look that receiveing of the item in our logs. we chek if you actually got the item a few days ago and that you didnt use/disenchanted it yet.
If you suspect our logs would also remove items from itself, then there is no other choice then to just make a screenshot of the item in your inventory after you got it (with some kind of timestamp visible on the screenshot).
But being a programmer myself, I can assure you its pretty hard or work intensive to remove something from a database without there being any trace of it anywhere and it can almost always only be done by removing records manually. So the chances of our logs being wrong is pretty low (but not impossible).
Frankly i often have the same feeling about my bank account, "where did my money suddenly go to?", and only after carefully looking at my expenses i see my bank didn't steal from me but i actually spent it myself and forgot about it.