  Discovering Dirac fermions with novel properties has become an important
front in condensed matter and materials sciences. Here, we report the
observation of unusual Dirac fermion states in a strongly-correlated electron
setting, which are uniquely distinct from those of graphene and conventional
topological insulators. In strongly-correlated cerium monopnictides, we find
two sets of highly anisotropic Dirac fermions that interpenetrate each other
with negligible hybridization, and show a peculiar four-fold degeneracy where
their Dirac nodes overlap. Despite the lack of protection by crystalline or
time-reversal symmetries, this four-fold degeneracy is robust across magnetic
phase transitions. Comparison of these experimental findings with our
theoretical calculations suggests that the observed surface Dirac fermions
arise from bulk band inversions at an odd number of high-symmetry points, which
is analogous to the band topology which describes a
$\mathbb{Z}_{2}$-topological phase. Our findings open up an unprecedented and
long-sought-for platform for exploring novel Dirac fermion physics in a
strongly-correlated semimetal.
