Synthetic Tableaux: Minimal Tableau Search Heuristics.

We discuss the results of our work on heuristics for generating minimal synthetic tableaux. We present this proof method for classical propositional logic and its implementation in Haskell. Based on mathematical insights and exploratory data analysis we define heuristics that allows building a tableau of optimal or nearly optimal size. The proposed heuristics has been first tested on a data set with over 200,000 short formulas (length 12), then on 900 formulas of length 23. We describe the results of data analysis and examine some tendencies. We also confront our approach with the pigeonhole principle.