  A fully invarient congruence relations on the free algebra on a given type
induces a variety of the given type. In contrast, a congruence relation of the
free algebra provides algebra of that type. This algebra is given by a
so-called presentation. In the present paper, we deal with an important class
of algebras of type $(2)$, namely with semigroups of transformations on a
finite set. Here, we are particularly interested in a presentation of a
submonoid of the symmetric inverse monoid $I_n$. Our main result is a
presentations for $IOF_n^{par}$, the monoid of all order-preserving,
fence-preserving, and parity-preserving transformations on an $n$-element set.
