The doctrine everyone associates with Calvinism was fixed by an argument that happened fifty years after Calvin died.
Jacobus Arminius, a Dutch Reformed minister, came to hold that God's election is conditional on foreseen faith and that grace can be resisted. After his death in 1609 his followers put their case in the Remonstrance of 1610, five articles asking the Dutch church to make room for it. The Synod of Dort, sitting from 1618 to 1619 with delegates from across Reformed Europe, rejected all five and answered them point for point.
Those answers are what later became TULIP, total depravity, unconditional election, limited atonement, irresistible grace, perseverance of the saints. The acronym is an English-language teaching device from the twentieth century and appears in none of the Reformed confessions, a small point worth keeping straight because the summary is often treated as though it were the confessional text itself.
What Dort actually holds is that fallen humanity cannot turn to God unaided; that God's choice of those who will be saved rests on his will and not on anything foreseen in them; that Christ's death is sufficient for all and effective for the elect; that saving grace is not finally refused; and that those God saves are kept. The tradition has argued internally about the middle point ever since, and Reformed bodies that hold a genuinely universal intent in the atonement exist and consider themselves entirely within the confessions.
Two other confessions carry most of the tradition's weight: the Heidelberg Catechism of 1563, warm and pastoral in tone, and the Westminster Confession of 1646, precise and legal. Which one a Reformed church teaches tells you a good deal about its temperament.