You're in negotiations and the other side gives you inconsistent information that leads you to believe they're lying. Do you point this out to them?

Thanks 

Yes, I would inform them, in order let them know I am full awaking and I know they want to mislead me 

Definitely but not immediately. There is always a right timing for everything. But I will be cautious though with my words and my way of telling them. For example, I will not say to their faces that they are lying instead I will prove to them that I cannot be fooled.

thanks!

I would rather like to prove it by counter facts. I would not say they are lying, i will prove it through data, politely. 

thanks

yes i would  point this for them

A negotiation session must be covered by an ethical behavior.  This means that I cannot say they are lying but I can say with my eyes or body language.

For me, it depends on the situation. Actually, I can image situations where I simply refuse to continue negotiations with a lying party. Some business needs trust!

When continuing is in my interest, I would not outright say "you are lying". I would rather ask questions, indicating that I do not understand their arguments or logic, thus giving them a chance to explain or correct themselves.

Thanks for invitation,

Yes of course, but in indirectly just to prove to him that I have catched the point, and stop trying this again.