I vibed a proof of Conway's conjecture

In a recent development, a non-expert in mathematics managed to create a Lean proof for a 50-year-old conjecture proposed by John Conway known as Conway's refinement conjecture. The conjecture states that omnific integers possess a refinement property: if ab = cd, then there exist integers e, f, g, h such that a = ef, b = gh, c = eg, and d = fh.

While the proof has not yet been independently verified by mathematicians, the author of the proof believes it to be correct and invites potential refutations. The proof has passed the mechanical checks from the Palomar registry and has been deemed likely accurate by some individuals familiar with both Lean and the field.