Four derivations from formula of universal law of nature

In Groundwork of the metaphysics of moral, KANT puts forth a general formulation of categorical imperative: act on that maxim through which at the same time you can always will that it will become a universal law. Only passes this test, a maxim will be permissible. Besides the general one, there are still three variants, as follows: formula of universal law of nature, formula of humanity as the end in itself, and the formula of autonomy. Today I will review the first variant. 

The first variant is similar to the general imperative but emphasize the role of nature. Kant offers four examples to illustrate the formula. The first derivation is concerned with suicide. When one wants to shorten her life to avoid troubles in life on the basis of self love, she will come into contradiction because the the maxim of self love given by nature is on sake of furthering life. Therefore, the maxim of self love in the case is self defeated. The second derivation is about false promise. When one acts on a maxim which admits that one can make false promise in order to get money when he is in need but knows that he will not pay back, the maxim will be contradictory when it is universalized because no promise is possible in such a world. The third derivation is the development of one's talent. One may claim that he will neglect his talent given by nature but at the same he also claims to enjoy his life while achieving enjoyment absolutely bases on the development of one's talent. The will will be in contradiction. The fourth derivation refer to beneficence. One may claim to be indifferent to others' suffering and refuse to offer help but when he is in such a situation, he will expect help from others. This is conflict in his will. 

There four derivations are very complicated and vague, so I need do more effort to clarify them with a critical eye.