In several articles, Mumma has presented a formal diagrammatic system Eu meant to give an account of one way in which Euclid's use of diagrams in the Elements could be formalized. However, largely because of the way in which it tries to limit case analysis, this system ends up being inconsistent, as shown here. Eu also suffers from several other problems: it is unable to prove several wide classes of correct geometric claims and contains a construction rule that is probably computationally intractable and that may not even be decidable.
"On the Inconsistency of Mumma's Eu." Notre Dame J. Formal Logic 53 (1) 27 - 52, 2012. https://doi.org/10.1215/00294527-1626509