  In experiments the two-dimensional systems are realized mainly on solid
substrates which introduce quenched disorder due to some inherent defects. The
defects of substrates influence the melting scenario of the systems and have to
be taken into account in the interpretation of the experimental results. We
present the results of the molecular dynamics simulations of the two
dimensional system with the core-softened potential in which a small fraction
of the particles is pinned, inducing quenched disorder.The potentials of this
type are widely used for the qualitative description of the systems with the
water-like anomalies. In our previous publications it was shown that the system
demonstrates an anomalous melting scenario: at low densities the system melts
through two continuous transition in accordance with the
Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory with the intermediate
hexatic phase, while at high densities the conventional first order melting
transition takes place. We find that the well-known disorder-induced widening
of the hexatic phase occurs at low densities, while at high density part of the
phase diagram random pinning transforms the first-order melting into two
transitions: the continuous KTHNY-like solid-hexatic transition and first-order
hexatic-isotropic liquid transition.
