Context Free Grammar for $a^*b^*c^* - \{a^n b^n c^n \mid n \geq 0 \}$ I'm having trouble constructing a Context Free Grammar for the following language: 
$$a^{\ast}b^{\ast}c^{\ast} - \{a^{n} b^{n} c^{n} \mid n \geq 0 \}$$

I believe it's telling me that no string can be generated that has the same number of of $a$'s $b$'s and $c$'s.  This is due to the subtraction of the second set.  

A good string from a newly formed language should be something like $aaabbc$ or $abbbcc$ and so on.

So I tried breaking the problem into three parts...


Single states:

$S_{1} \rightarrow aS_{1} \mid a \mid \lambda$
$S_{2} \rightarrow bS_{2} \mid b \mid \lambda$
$S_{3} \rightarrow cS_{2} \mid b \mid \lambda$

Two States

$S_{4} \rightarrow aS_{4}b \mid S_{1} \mid S_{2}$
$S_{5} \rightarrow bS_{5}c \mid S_{2}$
$S_{6} \rightarrow aS_{6}c \mid S_{3} \mid S_{1}$

States w/AB states

$S_{7} \rightarrow S_{1} \mid S_{4}S_{6}$
$S_{8} \rightarrow S_{2} \mid S_{5}S_{6}$
$S_{9} \rightarrow S_{3} \mid S_{6}S_{3}$



with an orginal start state of   ...

$$
S \rightarrow  S_{7} \mid S_{8} \mid S_{9}
$$

However I'm having problems building strings like $aaaabbbcc$ ...

Am I forming CFG's incorrectly?  I felt like I was on the right track but now I'm quite lost.
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.