Complex sentence: Its correctness follows from the more general correctness of the Davis-Putnam algorithm, and its polynomial time bound is clear since each resolution step increases the number of clauses in the instance, which is upper bounded by a quadratic function of the number of variables.
Split into simpler sentences: Its correctness follows from the more general correctness of the Davis-Putnam algorithm. Its polynomial time bound follows from the fact that each resolution step increases the number of clauses in the instance, which is upper bounded by a quadratic function of the number of variables.