  In this paper we examine four-element and five-element digraphs for existence
of certain polymorphisms that imply congruence meet-semidistributivity in a
locally finite variety. The results presented here occurred as an integral part
of my research for optimal strong Mal'cev conditions describing the property
mentioned. Most of the programming needed to obtain these results was done in C
programming language but for some results we also used the model builder
Paradox. The source codes and Paradox inputs will be presented here as well
(appendices one and two of this paper contain the source codes; an example of
Paradox input is given in section 6).
