I'd like your help with understanding whether the following problem is in $P$, $NP$, $NPC$.
The problem $B$:
Input: a $3CNF$ formula which contains more than one clause.
output: Can we divide the formula to two $3CNF$ satisﬁable clauses?
I'd really like to learn how to analyze this kind of questions.
First I know that in order that the problem would be in $NP$ I need to find a polynomial verifier to the problem, so I can check all the options for partitions and see if it's satisfies the problem. so the problem is probably in $NP$, in order to know whether it is complete, I need to find a reduction from a NP-hard problem, first one came to my head is $3SAT$, but how a suitable reduction would look like? or maybe it is simply in $P$? what is the way for deciding this?
I'd really appreciate some explanations.
Thanks a lot!