Solving the Cubic Monotone 1-in-3 SAT Problem in Polynomial Time

Abstract

The exact 3-satisfiability problem (X3SAT) is known to remain NP-complete when restricted to expressions where every variable has exactly three occurrences, even in the absence of negated variables (Cubic Monotone 1-in-3 SAT Problem). The present paper shows that the Cubic Monotone 1-in-3 SAT Problem can be solved in polynomial time and, therefore prove that the conjecture P=NP holds.