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Any satisfiability problem in conjunctive normal form can be solved inpolynomial time by reducing it to a 3-sat formulation and transforming this toa Linear Complementarity problem (LCP) which is then solved as a linear program(LP). Any instance in this problem class, reduced to a LCP may be solved,provided certain necessary and sufficient conditions hold. The proof that theseconditions will be satisfied for all problems in this class is the contributionof this paper and this derivation requires a nonlinear Instrumentalistmethodology rather than a Realistic one and confirms the advantages of aVariational Inequalities implementation.

A Linear Complementarity Theorem to solve any Satisfiability Problem in conjunctive normal form in polynomial time