Eos3.32 is the modification of Eos3.31 to cope with the upgrade of Mathematica from version 12.1 to version  12.2.0.  The reasons that Eos3.31 do not work come from the changes of implementation of the Notation package and the Exists function.  Especially, the change of Exists posed challenges.  I treat Exists differently than the way implemented in the new Mathematica 12.2.  I also used a different notation for existentially (and universally) quantified formulas.  The use of the Notation package realized my notation.  Since the Notation command with non-trivial external expression does not seem to work as it worked in Mathematica 12.1 and earlier versions.  It took me more time than I expected.