Challenge Meaning System Directly Pleads Ignorance Disputed Imply

The meaning of "challenged somebody to do something" is not quite suggested that somebody do something, nor is it at all disputed that somebody did something. The meaning is more like, daring somebody to do something. By challenging somebody to do something, you imply that the person is afraid to do the thing and, further, that they ought to do it, but might not. 

The "dispute" meaning of challenge is when it is used followed by, not an infinitive, but a noun or noun phrase like, "We challenged the company's proof that its system was safe" means we disputed that the proof was accurate. In this case the company is inferred to have already given a proof, but one that may be inadequate. If "we challenged the company to prove that its system was safe" then they have not yet provided a proof, we think they should, but we also imply that they are afraid that they can't prove their system to be safe.