Aulus Gellius, who preserves this paradox in Noctes Atticae, treats it as a genuine antinomy precisely because neither horn of the dilemma yields a determinate legal obligation, suggesting the contract is indeterminate rather than doubly binding.

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Antinomy(Central structure of the middle section of Kant's Transcendental Dialectic): A conflict of reason with itself in which both a thesis and its antithesis appear to follow from apparently valid arguments, arising when reason attempts to apply its principles beyond the bounds of possible experience
Aulus Gellius(as the ancient source preserving this paradox): A Roman writer from the 2nd century CE who collected interesting philosophical puzzles and stories in a book called Noctes Atticae.
Determinate legal obligation(as what is supposedly missing in this problematic contract): A clear, specific requirement or duty created by a contract that is definite and unambiguous.
Doubly binding(as the alternative problem if the contract were not indeterminate): Obligation in two directions at once—where both parties would be bound simultaneously by contradictory requirements.

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Horn of the dilemma(as each possible legal interpretation mentioned here)

Each of the two opposing options or sides of a contradictory problem—like the two branches of a dilemma.

Indeterminate(Reichenbach's three-valued quantum logic)

The value of propositions that quantum theory implies cannot be assessed to be either true or false

Noctes Atticae(as the book where this paradox is documented)

A collection of miscellaneous essays and notes written by Aulus Gellius; the title means 'Attic Nights' in Latin.

dilemma(Used in classical rhetoric and logic; discussed by Valla in the context of the Protagoras–Euathlus lawsuit.)

An argument structured so that two mutually exhaustive alternatives each independently entail the same conclusion, leaving the opponent no escape.

paradox(R. M. Sainsbury's definition, presented as a target of criticism)

An apparently unacceptable conclusion derived by apparently acceptable reasoning from apparently acceptable premises

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