Statement I: Nuclear fission is a spontaneous process i.e. there is no need for external energy supply for this to happen.
Statement II: In a nuclear fission reaction, the rest mass energy of the parent nucleus is more than the combined rest mass energy of two daughter fragments and neutrons.
In a nuclear fission reaction, a heavy nucleus breaks into two middleweight nuclei of comparable masses. Only unstable nuclei undergo fission. A stable nucleus may require energy to become unstable but once unstable it doesn't require any further energy to fission.
For example, U-235 is a Uranium isotope which is relatively stable, but when bombarded with neutrons (this is how we supply energy to it), it absorbs the extra energy and becomes U-236. Now U-236 is a quite unstable nuclide and undergoes fission spontaneously giving daughter nuclei with lesser rest mass energy.
Hence, both the statements are correct and statement II infers statement I.