IPA: /ɪˈrɛfrəɡəbli/
KK: /ɪˈrɛfrəgəbli/
In a way that cannot be refuted or disproven; undeniably.
The evidence presented in court proved the defendant's guilt irrefragably.
Irrefragably → It is formed from "in-" (meaning not), "refragari" (meaning to refute or oppose), and "-ably" (meaning in a manner). The word means in a manner that cannot be refuted or opposed.
Think of something that cannot be 'refuted' ('refragari') — the 'in-' means not, so 'irrefragably' describes something that cannot be opposed.