Show that the Pumping Lemma for CFLs is not powerful enough to prove that the language L = {aibjck |i ≠j ≠ k ≠ i } is not context free
The Pumping Lemma states: "... there exists a constant $p$ such that for each word $w\in L$ with $|w|\ge p$ there exists a decomposition $w = uvxyz$ such that ...", where $p$ is the pumping constant.

You have chosen your own decomposition, and shown it not fit the pumping property. Perhaps there is another decomposition that will work?

And even in the case your example would work, I can claim that the pumping is larger than 6.