Is the language {$a^{i}b^{j}c^{k} ~|~ i \neq j, i \neq k, j \neq k$} context-free or not?
I realized that I have encountered almost all variants of this question with different conditions about the relationship between i, j, and k, but not this one.
My guess is that it is not context-free, but do you have a proof?