On March 8, 1995, was found the following nontrivial single axiomschema characteristic of Leśniewski-Ishimoto's propositional ontologyIn this paper, we shall present the progress about the above axiomschema from 1995 and conjectures about it. Here we shall give two criteria nontiriviality and quasi-nontriviality in order to distinguish two axiom-schemata.