The fundamental conflict between both characters in Act III is one of belief. Abigail's ability to get people to believe in her accusations and her stories are of central importance. These are the reasons why the trial is being held. Proctor is trying to get the court and others to believe that her beliefs are fraudulent. This is where their conflict lies. Proctor and Abigail wage a sort of "chess match" of veracity whereby both are seeking to be seen as true and right. Only one of them can win. Both realize what is at stake. Proctor tries to follow the path of legal purpose. When this fails, he confesses to adultery, in the hopes of taking away the cloack of secrecy within which Abigail operates. When this fails, he hopes Mary Warren's testimony will assist. When Abigail conspires for this failure, she gives him an evil smile, small and creeping across her face, when Mary collapses in Abigail's arms. At this point, Proctor knows that Abigail has won. Their fundamental conflict in this scene resides in who is going to be accepted more and with "open arms" by the court and the people of Salem. In this, John loses, but ends up understanding and gaining more as a result.