Doubt about Fall of the Empire's victory conditions

By Pretorian, in Twilight Imperium 3rd Edition

I was asked this question but I'm not sure of the answer.
Situation: at the end of turn 8 the Lazax (P1) win the game and the "Loyalist" (P2) win with him. Now happens that P3 has P1's (Lazax's) treaty card and P4 has P2's (Loyalist's) treaty card.

So who win the game? P1+P2+P3+P4 or just P1+P2+P3?
Is there any official rule or FAQ that solve this? If not what are yours interpretation?