  Relativistic corrections have been made in the non-relativistic
antisymmetrized molecular dynamics (AMD) simulations to apply to the high
energy neutron production in the $^{12}$C+$^{12}$C and $^{16}$O+$^{12}$C
collisions at incident energies of 290 and 400 MeV/nucleon. The corrections are
made in kinematics alone and no nucleon-nucleon inelastic scatterings nor meson
productions are taken into account, and AMD with the relativistic corrections
is called semi-relativistic AMD. The three-nucleon collision (3NC) and Fermi
boost in the collision processes are taken into account in the non-relativistic
AMD. Since the relativistic corrections tend to compensate in each other, the
difference between the semi-relativistic and non-relativistic results become
small. High energy tails of the available experimental neutron double
differential cross sections, especially at larger angles, are well reproduced
by AMD with the 3NC term both with non-relativistic and semi-relativistic
simulations. These results indicate that the high energy neutrons are
dominantly produced by the 3NC process in this incident energy range.
