The phrase "show once and for all" implies proving something conclusively or definitively. Antonyms for this phrase could include "unclear," "ambiguous," "inconclusive," "doubtful," "uncertain," or "unverifiable." These words suggest a lack of evidence or proof to settle an issue or answer a question definitively. Other antonyms may include "unproven," "untested," "unconfirmed," "speculative," or "unreliable," which suggest a lack of evidence or support for a particular claim or assertion. Whatever the antonym, it represents a lack of certainty or proof and an inability to definitively determine the truth of a matter.