A Counterexample to a Proposed Proof of P=NP by S. Gubin

In [1], the claim is put forth that P=NP; the form of this claim is an algorithm which purportedly can solve the 3SAT problem in O(n) time. The 3SAT problem (or “3-SAT problem,” as it is refered to in [1]) is to determine if the formula d1 ∧ d2 ∧ · · · ∧ dm (1) is satisfiable, where each clause dk with 1 ≤ k ≤ m is a disjunction of at most three variables or their negations from the set B = {b1, b2, . . . , bn}. (2) The validity of the algorithm rests on the following claim: Claim 1 Let (1) and (2) be the given instance of 3SAT. Let C be the set of clauses of the instance: C = {d1, d2, . . . , dm}. The instance is non-satisfiable if and only if at least one of the following is true: Pattern 1. There is α ∈ B: {α, ᾱ} ⊆ C; Pattern 2. There are different α, β ∈ B: {α ∨ β, α ∨ β̄, ᾱ ∨ β, ᾱ ∨ β̄} ⊆ C;