I'm just jumping in without any clue about the conversation but the INTP 2 INTP reminded me of a confrontation of two INTP's I witnessed at work for quite while ago. The other INTP was a male of his fifties and the other one a male in his forties.
(I don't know if the age is relevant here but anyways..)
I'll have to say that the confrontation was terrible to watch. It seems that nobody could crush the other person as bad as the same personality type can. Because if the other person is a bit more skilled in your own logic and plays with your mind even if you think you can play with the mind of other people.....that means only someting bad.
(And in this case, the older INTP is a bit messed up person whose biggest enjoyment seems to be bringing misery to everybody just for the fun of it
.)
So in this case, the older, more experienced guy crushed the younger INTP totally with the logic of the younger INTP. I witnessed the younger INTP (who was very arrogant in his ways but not mean in any way) almost in tears. It was very strange to see that because normally he was very cool, very distant and very controlled. I tried to make him feel better by saying it's the normal behavior of the older INTP and after some conversation the younger INTP seemed to cheer up a bit.
But thats INTP 2 INTP to you. I wouldn't recommend and I wouldn't want to try it out. I'm not saying here that it's normal behavior of INTP I'm just telling about something I saw happening.