  We present an exactly solvable model of a spin-triplet $f$-wave topological
superconductor on the honeycomb lattice in the presence of the Hubbard
interaction for arbitrary interaction strength. First we show that the
Kane-Mele model with the corresponding spin-triplet $f$-wave superconducting
pairings becomes a full-gap topological superconductor possessing the
time-reversal symmetry. We then introduce the Hubbard interaction. The exactly
solvable condition is found to be the emergence of perfect flat bands at zero
energy. They generate infinitely many conserved quantities. It is intriguing
that the Hubbard interaction breaks the time-reversal symmetry spontaneously.
As a result, the system turns into a trivial superconductor. We demonstrate
this topological property based on the topological number and by analyzing the
edge state in nanoribbon geometry.
