I want to know if finding solution to a specific number of 2SAT equations sepearted by OR gate (DNF form as below) is in P or NP.
The equation has total n variables and each clause is a 2SAT equation in itself in a subset of variables from 1 to n. Example:
F = [(x1 || x2 ) && ( !x2 || x3) && (x3 || x4)] || [(x2 || x5) && (x3 || x6) && (!x4 || !x6)] || ….
The equation F is a DNF of 2SAT equations, which has say m clauses. Is finding a solution to this in NP? If yes how?
Also, specifically I also want to know if finding False instances of equation F is in P or NP as well.