In their answer, Janoma proves that $\{a^ib^jc^k:i\neq j,j\neq k,i\neq k\}$ is not context-free using Ogden's lemma, but I haven't learned about Ogden's lemma yet. I wanted to know whether Ogden's lemma can be dispensed with.
This could be interpretted as $\{a^ib^jc^k: i,j,k\text{ are not all equal}\}$ correct? Can someone show that this is context-free without a lemma? Like making a CFG or PDA?
This is just for my own reference for learning.
