  The isobar model and the resonance model are applied for the first analysis
of the subthreshold $K^+$-meson production in proton-carbon collisions, which
was perfomed at GSI at an emission angle of 40 degrees and a bombarding energy
of 1.2 GeV. In this study, we focus on the role of the secondary processes $\pi
N \to K^+ Y$ in normal nuclear matter density. It turns out that the present
approach can reproduce very well both the $\pi^+$- and $K^+$- meson spectra. It
is also demonstrated that the different kinds of descriptions for the $\pi N
\to K^+ \Lambda$ reactions substantially differentiate the calculated results
for the $p A \to K^+ X$ differential cross sections.
