So, when we take more premises, we get less models for the premises. When we take more premises, we intersect their models. A key part of doing relational resolution is negating a relational sentence. There is a problem, however, when we try to negate a sentence with free variables. Everything is beautiful.
Nothing is beautiful.
Remember this trick when you start negating goals for relational resolution . Doing so will save you a lot of skull sweat. Here is a faulty proof for the statement. As a counterexample, consider the sentence from above. We can imagine an interpretation i for this sentence where some things in the universe are beautiful, and some things are not.