This paper shows effectiveness of X3SAT in proving P = NP. This is due to the fact that it is easy to check unsatisfiability of a particular truth assignment. A truth assignment leads to some reductions of clauses by means of "exactly-1 disjunction". The reductions result in a conjunction of literals, called the scope of the assignment. It is proved that this particular truth assignment makes the formula unsatisfiable iff the scope_s is unsatisfiable for some s, which is trivial to check. Then, each literal such that its scope is unsatisfiable is removed from the formula. Therefore, the formula is satisfiable iff the scope of every literal is satisfied.

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关于不可满足性的可处理性

本文展示了 X3SAT 在证明 P = NP 方面的有效性。这是因为很容易检查特定真值分配的不满足性。真值赋值通过“exactly-1 析取”导致子句的一些减少。减少导致文字的连接，称为赋值的范围。证明了这个特殊的真值分配使得公式不可满足，当仅当 scope_s 对某些 s 是不可满足的，这是微不足道的检查。然后，从公式中删除其范围不可满足的每个文字。因此，当满足每个文字的范围时，该公式是可满足的。