Because there is no dedicated caretaker of the company's legacy, this statement has never been proved or disproved.

The statement for algebraic curves can be proved using Serre duality.

The statement can be proved using Zorn's lemma, which is equivalent to the axiom of choice.

Thought is required wherever a statement is proved, or, it may be, a general truth enunciated.

Completeness: a proof that all true mathematical statements can be proved in the formalism.

The statement made in the same source, that Linus suffered martyrdom, cannot be proved and is improbable.

Moreover, this stronger statement can be proved as well to be accomplished by means of translations only.

That is, their statements couldn't be proved or disproved.

If the statements are proved untrue, the condition of contract is broken.

(The last statement has not been proved historical).