Parsing permutations of first-order propositional logic formulas

In this work, we wish to determine the complexity of deciding whether a given multiset of symbols, chosen from some finite set of symbols, can be derived according to the rules of a given context-free grammar. Providing an upper bound for this problem is of interest to computational linguistics, one goal of which is to classify the complexity of parsing and understanding natural language. We consider a simplified subset of fist-order propositional logic consisting of only those formulas containing universal quantification, conjunction operations, and equality relations. Variables xi will be represented as i repetitions of the symbol x (for example, x3 becomes xxx).