I'm reading this paper, A simple NP-hard problem by Demontis, where he defines an interesting $NP$-hard set and finally he conclude with this theorem:Theorem: $P=NP$  if and only if it is possible to calculate in polynomial time all the  fundamental elements of any formula.The paper does not have an abstract and I'm kind of lost because of the new terminology used in the paper.Could you explain the significance of this paper? Do the fundamental elements of a formula represent the variables that have true value in every satisfying assignment? Does this theorem represent a new result? What are the insights into the $P$ vs $NP$ problem presented in the paper? ACM SIGACT News, Volume 40 Issue 2, June 2009
A simple NP-hard problem
cc.complexity theory