  Exact four-body equations of Alt, Grassberger and Sandhas are solved for
neutron-${}^3\mathrm{He}$ and proton-${}^3\mathrm{H}$ scattering in the energy
regime above the four-nucleon breakup threshold. Cross sections and spin
observables for elastic, transfer, charge-exchange, and breakup reactions are
calculated using realistic nucleon-nucleon interaction models, including the
one with effective many-nucleon forces due to explicit $\Delta$-isobar
excitation. The experimental data are described reasonably well with only few
exceptions such as vector analyzing powers.
