I am following the rules outlined in these slides: https://www.csie.ntu.edu.tw/~lyuu/complexity/2011/20111018.pdf
The rules for converting the graph to CNF and the proof are in the first few slides.
So far I have the following for the CNF:
(x11 V x12 V x13 V ¬x21 V¬x31 V ¬x22 V¬x32 V ¬x23 V¬x33 ) ^ (x21 V x22 V x23 V ¬x11 V¬x31 V ¬x12 V¬x32 V ¬x13 V¬x33) ^ (x31 V x32 V x33 V ¬x11 V¬x21 V ¬x12 V¬x22 V ¬x13 V¬x23) ^ (¬x11 V ¬x23) ^ (¬x21 V ¬x33) ^ (¬x12 V ¬x23) ^ (¬x22 V ¬x33)
My first question is if I converted it correctly.
My next question is how to show that T entails R(G) where R(G) is the CNF.
I understand that this graph there is no hamiltonian path and I would like to somehow prove that.