Context Free Grammar for $a^*b^*c^* - \{a^n b^n c^n \mid n \geq 0 \}$
This question has been answered before, but let me summarize the answer:
$$
a^*b^*c^* \setminus \{ a^n b^n c^n \} = \\
\{ a^{n+1+m} b^n c^p \} \cup \{ a^n b^{n+1+m} c^p \} \cup \\
\{ a^{n+1+m} b^p c^n \} \cup \{ a^n b^p c^{n+1+m} \} \cup \\
\{ a^p b^{n+1+m} c^n \} \cup \{ a^p b^n c^{n+1+m} \}.
$$
All parameters $n,m,p$ are assumed to be non-negative.