<p>May I suggest you read my paper <a href="http://arxiv.org/ftp/arxiv/papers/1411/1411.2901.pdf" rel="nofollow">http://arxiv.org/ftp/arxiv/papers/1411/1411.2901.pdf</a> 
There you will find a common splitting mechanism to determine satisfiability which apparently is similar to your procedure. The procedure is polynomial (actually linear) in each step but the problem is that the formula length blows up in each step. (As pointed out in one of the answers to your question). In the paper I have addressed the question whether and under which circumstances this blow up is prevented systematically.</p>
3 SAT algorithm's complexity?
<p>I have an interesting algorithm for 3SAT in mind that I wanted to implement but was not able to code for the same so unable to see if it really works.
The algorithm is defined in a Microsoft Word file here:
<a href="https://www.dropbox.com/s/7j1mvt7jubf2vb1/3SAT%20algorithm.docx?dl=0" rel="nofollow">DropBox Link for 3SAT algorithm</a>
I do not know if this algorithm really works and if it does what is its complexity. I would really like to know about its complexity though. Please help me regarding this as if it is in polynomial time then I would have proved P=NP!</p>