Drawbacks to resolution theorem:

Thus the underlining here identifies some drawbacks to resolution theorem proving:

• It only works for true theorems that can be expressed in first order logic:

Just cannot to check at the same time where a conjecture is true or false, but it can't work in higher order logics. So if there are related techniques which address these problems, than to varying degrees of success. 

• While it is proven such the method will find the solution, there in practice the search space is often too large to find one in a reasonable amount of time, so even for fairly simple theorems.

So notwithstanding these drawbacks, there resolution theorem proving is a complete method: but if your theorem does follow from the axioms of a domain so such resolution can prove it. However, it only uses one rule of deduction the resolution but the multitude we saw in the last lecture. Thus it is comparatively simple to understand how resolution theorem provers work. Here for these reasons and the development of the resolution method was a major accomplishment in logic in which with serious implications to "Artificial Intelligence" research. 

There resolution works by taking two sentences and resolving them with one ultimately resolving two sentences to produce the False statement. So we can say that the resolution rule is more complicated other than the rules of inference we've seen before we require  to cover some preparatory notions before we can understand how it works. Now here in particularly we use to look at conjunctive normal form and unification before we can state the full resolution rule at the heart of the resolution method to justified.