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(B and C) or (not B and not C) or (A and (not B) and not C)

I get two different answers depending on the order I do the simplification.

1. If I factor C out of the first and third terms I get (B and C) or (A and C) or (not B and not C)

2. If I factor not B out of the second and third terms I get (B and C) or (A and not B) or (not B and not C)

The second version is wrong according to several people and the Wolfram Boolean calculator but I can't see my mistake. Here are the steps.

(B and C) or (not B and not C) or (A and (not B) and not C) ; problem as stated

(B and C) or ((not B) and (not C or (C and A)) ; factored out (not B)

(not C or (C and A)) becomes (not C or A)

(B and C) or ((not B) and (not C or A))

(B and C) or (not B and not C) or (not B and A) ; distribute (not B).

Can anyone point out my error?

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# Boolean Algebra - Simplifying to two different expressions

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