TULIP is a mnemonic of American origin, not older than the early twentieth century, for the canons the Synod of Dort issued in 1619. Dort was convened to answer the five articles the Dutch Remonstrants had published in 1610 after the death of Arminius, and its five heads of doctrine are replies, taken in the Remonstrants' order. Reading them as a summary of Calvin's theology inverts the relationship: Calvin never produced such a list, and the doctrine of election occupies a modest place in the Institutes.
Total depravity does not claim that people are as bad as they could be. It claims that sin has affected every faculty, including the will and the understanding, so that no part of the person remains capable of initiating a turn to God. Moral achievement in ordinary human terms is not denied.
Unconditional election holds that God's choice rests on his own purpose and not on anything foreseen in the elect, faith included.
Limited atonement, better named particular redemption, holds that Christ died with the intention of actually securing the salvation of the elect rather than making salvation possible for everyone. The argument is about the design and efficacy of the atonement, not its sufficiency: the tradition's own formula is that the death of Christ is sufficient for all and efficient for the elect.
Irresistible grace, better named effectual calling, holds that when God calls a person to himself the call achieves what it intends. It does not claim that grace is never resisted, only that the inward effectual call is not finally refused.
Perseverance of the saints holds that those truly regenerate will be preserved to the end, and Dort coupled it with a frank acknowledgement that believers fall into serious sin.