If an argument adheres to the rules of logic without exception, it's said to be logically complete, inferentially true, or logically valid.

Whether or not the premises are true is a separate issue, but if they are, one could say that the argument's ground-truths are valid, or that the premises are confirmed (confirmed analytically or confirmed empirically).

The argument has 'unbreakable reasoning'.
would be synonymous with
The argument has valid ground truths and is logically complete.

One word answer(s): indisputable, incontrovertible, self-evident.

Actual answer:

If an argument adheres to the rules of logic without exception, it's said to be logically complete, inferentially true, or logically valid.

Whether or not the premises are true is a separate issue, but if they are, one could say that the argument's ground-truths are valid, or that the premises are confirmed (confirmed analytically or confirmed empirically).

The argument has 'unbreakable reasoning'.
would be synonymous with
The argument has valid ground truths and is logically complete.