It should already be difficult to define knowledge for non-humans.
Not really. Here's the definition of knowledge that I use for my "proof" that axiom 8 is inconsistent. If you disagree with this definition, I'll use a different word.
You know a statement is true if the truth of that statement has somehow revealed itself to you (through logic/observation) and you
can have no doubt about its truth. Note, that's different from, "you have no doubt about its truth". Rocks clearly don't know anything. Most computer programs will believe anything a human tells them, so you could say they don't really know anything. But you could also say they know that "we told them this", and they know that "If all their input is correct, then their output is true". A more sophisticated program would take input from other sources, and develop knowledge just like a human.
A more common definition would be something like "if you believe it, and it's true, then you know it." But this makes it impossible to verify knowledge, as well as assuming the existence of an objective truth (which I do, but many don't).
We don't need to define "observation" and "feel". But we can assume that any entity can make an observation, but only a conscious entity can "feel" something.
Here comes again into play the I may perceive something about the knowledge of an other person, if I can in some kind connect/communicate with a system. But its already difficult if the other system speaks another language and it depends on the observer (for example if he speaks the language).
To be true, axiom 8c has to apply for every pair of conscious entities. Thus, all we need to do to prove it false is to find a single counterexample. So you might say, "what if they speak different languages", but I say "what if they don't?".
I might try to put my objection another way. You claim that you know that you're conscious, because you feel things in a way that a robot wouldn't. Furthermore, I can never know that you're conscious, because I can't prove that you feel things in this way. Even if you tell me, for all I know you could be lying, or just programmed to tell me that.
But do you know that you were conscious 10 minutes ago? The only proof you have is a memory of feeling something 10 minutes ago. But for all you know, that memory could have been implanted there. Furthermore, if I could somehow extract your memory, you would have no more evidence for consciousness than I do. If you decide that a memory is sufficient evidence, then I can prove you are conscious.
Now there's nothing special about memory, it's just easier to understand here. My argument works just as well for one second ago, or right now. Simply replace "memory" with "experience". Note that your argument depended on the idea that we "feel" our "observations", but my argument depends on the fact that we must also "observe" our "feelings".