3SAT solved in polynomial time?

Question

I have seen few errors in the cnf files for both satisfiable and unsatisfiable clauses files SATLIB Benchmark Problems

To be more specific I have found out that the 1st file of the zip folder here: 20 variables, 91 clauses - 1000 instances, all satisfiable contains a file with the title of "uf20-01", the equation of which is unsatisfiable clearly as the 7th clause at the 15th line and the 87th clause at line number 4 are both exact inverse of each other!((5 19 17) and (-5 -19 -17))

Thus an AND operation having them at any point of time would result in equation to be unsatisfiable.

I have come to a conclusion that if two clauses are exact inverse of each other then and only then the equation is unsatisfiable, else the equation is satisfiable.. I have attempted another UNSAT file of the above link with trial and error and though the MINISAT browser version also says the same file to be unsatisified I have found out a solution for the same in 1's and 0's for every variable.

The algorithm above was posted to a journal by me but got rejected.

My question is : Can somebody give me an example of an unsatisfiable 3SAT equation that contains only 3 variables(or maybe a bit more..) without having any clause being an exact inverse of the other?

If I can get such a clause then the algorithm is wrong(but still it proves many SAT benchmark problems to be UNSAT) and it would not prove that many UNSAT problems in the 1st link are indeed SAT.

This is teasing my mind and hope you all can understand it, as if the algorithm above is right, then I have proved P=NP! It can start a revolution also..

BTW: I have sent email to SATLIB contact person also but still no reply after 2 days concerning the 2nd link file.

Answer 1

In the 3-Sat in CNF all clauses are OR-clauses and they are combined by AND. So the two lines you cite define the following two clauses

x5 or x17 or x19
(not x5) or (not x17) or (not x19)

which can both be satisfied, for example, by setting x5 to true, x17 to false, and x19 arbitrary.