When a theorem is proven, the system produces a verifiable proof, which validates both the clausification phase and the refutation of the conjunctive normal form.
The adverbs and adverbial phrases that fit the criteria for a conjunctive adverb are always modifiers of the predicate in the first independent clause.
Since all logical formulae can be converted into an equivalent formula in conjunctive normal form, proofs are often based on the assumption that all formulae are CNF.