You can't prove something that's not true.
Evolution is just a belief of naturalistic philosophy according to which new functional genes for structures and processes of living organisms can result from errors during DNA replication that are then selected in a specific environment. All knowledge gained through observation and experimentation completely refutes this belief.
For example, according to the most generous interpretations of the fossil record, the longest possible time frame for the theorized evolution of a land dwelling animal into a whale is 9 million years. Now just imagine how many new genes is needed in order to transform a four legged terrestrial mammal the size of a wolf or sheep,into a fully aquatic mammal like a whale. The scale of these adaptations would have to be massive: a remodel of the skull and muscles to move the nostrils to the top of the head, the conversion of front legs into flippers, a reconstruction of the skeleton including a ball joint that allow the tail to move up and down, reorganization of kidney tissues to accommodate the intake of salt water, lungs dramatically enlarged and renovated to withstand the intense pressure of deep dives, the inclusion of a blubber layer for insulation in cold water, reproductive organs would have to move from the exterior of the animal's torso to inside, and many many more.
Now, lets go to the biggest observation of evolution in action - Lenski's E.coli experiment. After more than 67.000 generations, which translated into whale generations is equivalent to around one million years, this experiment resulted in 0 - zero new genes. Most of the changes in this experiment involved streamlining the genome, deleting genes no longer needed, or reducing protein expression. One of the changes involved something that proponents of evolution refers to as evidence for bacteria evolving a "key innovation" But, nothing structurally new evolved. After about 31,000 generations there was a mutational transfer of one pre-existing gene(citT) from one location to another which resulted in the ability of E.coli to grow on citrate under the oxygen-rich conditions. Hence, according to naturalistic belief, evolution must have produced hundreds and hundreds...even...thousands of new genes in 9 million years . But, the observation shows that in the equivalent of 1/10th of that time, evolution can produce zero new genes.
How can we explain this fact of impotence of evolution? Well, quite simple. The total number of mutations in the history of life is estimated at 10^43(1), while the length of an average eukaryotic gene is 1346 bp, which gives a library of 10^802 DNA seqeunces. Meaning, even with all evolutionary mutations spent, and with a functional landscape of size 10^200, still there is a 559 orders of magnitude lack of mutational resources to explore this library and find new functional landscapes.
This mathematical problem is either denied or ignored through the appeals to natural selection(NS). But such appeals are completely flawed. For e.g., we all know that humans are unable to breathe under water. We also know that there’s tons of mutations in the human gene pool in every generation. Thus, large amounts of mutations have been spent in the last 5 million years and no trait for breathing underwater has entered the human gene pool. It can be shown mathematically that this won't happen even if we spent all the mutations that occured in the history of life. IOWs, NS cannot change the fact that mutations didn't result in a trait for breathing under water. NS can act only when such trait entered the gene pool, by increasing or decreasing its frequency. Thus, NS is completely unrelated to the question of mutational resources required to find adaptive traits.
The second kind of responses assert that new functions come out of pre-existing functions or IOWs, that nothing in evolution starts out from scratch. Such responses are also flawed. Here is why. If these DNA sequences: ATT, CGC and ACA are something that is functional in the environment A, while these DNA sequences: TAC, AAA and CCC are required for adaptation to environment B, then the first three sequences are equally junk as all ‘non-TAC, AAA and CCC’ sequences. IOWs, in the environment where pathway for metabolism of galactose is required as an adaptation, DNA that codes for gears in jumping insects(pre-existing function) is equally junk as any random sequence of nucleotides. The mere fact that some sequence codes for pre-existing function cannot chage the ratio between non-adaptive and adaptive DNA sequences in the context of a specific environment. That is why every new adaptation starts out from scratch.
Thus, due to the enormous lack of mutational resources it is mathematically impossible for bio-structures and processes to emerge from errors during DNA replication and enter the gene pool of a population so that natural selection can do its work. That is why living organisms are not the product of evolution. And that's why evolutionary scientists are unable to prove Darwinism.
(2)The length of an average eukaryotic gene is 1346 bp. A gene consists of four different bases. Any base can assume one of four values (ATCG). A sequence of L basis can therefore assume one out of 4^L values, which gives library of 4^1346 or 10^810 sequences.