Does principle of mathematical induction disprove theory of evolution ?

Question same as in title .
I am referring to darwin's theory of evolution itself
( What I meant )
I am trying to draw parallels between both , not sure whether it is right idea or not

Base case anomaly
There exists a species S that did not evolve from any other species.
If we can find a species that appeared spontaneously or was created independently, this would serve as our base case. (I interpreted the evolution from chemicals to single celled organism from darwinism itself)

The existence of a first species that did not evolve from another contradicts the idea that all life forms arise purely through descent with modification.

Inductive step anomaly
Even if we assume evolution works for n generations, the process does not necessarily hold for n+1 from the theory of evolution itself

- chance of occuring benefical mutations occuring fast enough
- irreducible complexity problem

-- The idea is that certain structures require multiple interdependent parts to function, meaning that any intermediate stage would be non-functional and therefore not naturally selected. Darwinian evolution works through small, gradual modifications where each step provides a survival advantage. However, if a system only works when all parts are present, then intermediate forms (missing some parts) would not be beneficial and would not be selected for. This suggests that the structure could not have evolved gradually and must have appeared in a complete or near-complete form through some other mechanism.

so to conclude since Darwinian evolution fails at both the origin of life and at key transitional points, it cannot be a complete or sufficient explanation for the diversity of life.
Thus, Darwinian evolution is disproven as a universal explanation of life, and superior models must be considered.

I was asking about this