  Intermediate energy (p,p$'$x) reaction is studied with antisymmetrized
molecular dynamics (AMD) in the cases of $^{58}$Ni target with $E_p = 120$ MeV
and $^{12}$C target with $E_p = $ 200 and 90 MeV. Angular distributions for
various $E_{p'}$ energies are shown to be reproduced well without any
adjustable parameter, which shows the reliability and usefulness of AMD in
describing light-ion reactions. Detailed analyses of the calculations are made
in the case of $^{58}$Ni target and following results are obtained: Two-step
contributions are found to be dominant in some large angle region and to be
indispensable for the reproduction of data. Furthermore the reproduction of
data in the large angle region $\theta \agt 120^\circ$ for $E_{p'}$ = 100 MeV
is shown to be due to three-step contributions. Angular distributions for
$E_{p'} \agt$ 40 MeV are found to be insensitive to the choice of different
in-medium nucleon-nucleon cross sections $\sigma_{NN}$ and the reason of this
insensitivity is discussed in detail. On the other hand, the total reaction
cross section and the cross section of evaporated protons are found to be
sensitive to $\sigma_{NN}$. In the course of the analyses of the calculations,
comparison is made with the distorted wave approach.
