Shortly after the death of James Arminius in 1609, his followers summarized his views into the five points of the remonstrants. At Dort, the Calvinists requested a clarification of the remonstrants views. Lead by Episcopius, they drafted the Opinions of the Remonstrants, which expand on the five points. They are organized under the original five points (conditional election, unlimited atonement, total depravity, resistible grace and perseverance) and should be seen as sub-points under the five points of the remonstrants.
On election, they have three subpoints objecting to supra-lapsarianism, one objecting to infra-lapsarianism and three more subpoints defining conditional election. Additionally, they added two points rejecting the damnation of children of believers, if the children die in infancy.
On the atonement they affirm that Christ died for all men, such that salvation is possible for all men and God desires all men to believe and be saved, but He only saves believers. In the last subpoint the remonstrants rejected the idea that someone might be required to believe Christ died for him even though Christ did not die for him.
On depravity and resistible grace, they affirm total depravity, to the extent that man cannot believe without God drawing and enabling them and without grace they cannot do anything good or pleasing to God. On grace, they affirm that it is resistible and while God gives some men more grace than others, He gives all men sufficient grace to be saved. They affirm that the God’s call is serious and He desires the conversion of those He calls. They reject the idea that God calls some people for the purpose of making their punishment more severe and they reject the idea that God has two contradictory wills regarding His call of the reprobate. They strongly rejected the idea that sins are necessary with respect to God’s decree.
On perseverance, they hold that God provides all true believers with sufficient grace to preservere. Regarding apostasy they said people can fall away and ultimately perish and that true belivers cannot have assurance that God will certainly bring them to repentance from serious sin. Some would read this to imply that some true believers actually do fall away and ultimately perish. But the Remosntrants do not explicitly say that here. In my opinion, they are saying that people sometimes temporarily lose their salvation, that true believers can fall away and ultimately perish without implying that this actually happens, and that apostates have no assurance they will be re-converted. However, in their confession of 1621, the Remonstrants do firmly state that some true believers actually do fall away and ultimately perish.