By 1409 the Western Schism had been running for thirty-one years. Two rival lines of popes — the substantial Roman line (currently Gregory XII) and the substantial Avignon line (currently Benedict XIII) — had been excommunicating each other since 1378; substantially every European Catholic kingdom had been forced to substantively choose sides; repeated diplomatic attempts to negotiate a joint resignation had failed.
A group of dissident cardinals from both papal courts — substantively converging in their frustration with both Gregory XII and Benedict XIII — convened the Council of Pisa in March 1409 to substantively impose a conciliar solution. The cardinals invoked the substantively novel doctrinal principle of conciliarism — substantively that a general church council had authority over the papacy itself in cases of papal-institutional emergency.
What the council did
The Pisan council substantively cited both Gregory XII and Benedict XIII to substantively appear and substantively justify their continued claims. Neither appeared. The council substantively then declared both deposed on substantively the grounds of obstinate heresy (substantively their refusal to substantively accept the conciliar solution that the council was substantively offering) and substantively schism (each having continued to substantively claim the papacy in defiance of the other’s claim).
The council then substantively elected a new pope: the Greek-born cardinal Petros Philarges, who substantively took the regnal name Alexander V. The election was substantively executed on 26 June 1409 by twenty-four cardinals representing both previous obediences.
Alexander V substantively lived for only ten months after his election. He substantively died at Bologna on 3 May 1410. The Pisan cardinals substantively elected a successor — the Neapolitan cardinal Baldassare Cossa — who substantively took the regnal name John XXIII (substantively the Pisan-line John XXIII, not the modern 1958–1963 John XXIII whose pontificate substantively involved a deliberate symbolic recovery of the regnal-number sequence).
Why it failed
Neither Gregory XII nor Benedict XIII substantively accepted the Pisan depositions. Both substantively continued to function as papal claimants with residual diplomatic recognition from Catholic kingdoms (Gregory XII substantively retained recognition from Naples, Hungary, and parts of Germany; Benedict XIII substantively retained recognition from Aragon, Castile, Scotland, and parts of France). The Pisan papacy — first under Alexander V, then under John XXIII — substantively secured recognition from France, England, Bohemia, Portugal, and parts of Italy and Germany.
The Catholic Church now had three popes simultaneously, where it had previously had two.
The substantively conciliar principle that the Pisan council had substantively invoked substantively was recognised as substantively dogmatically unstable; the council had substantively created the third papal line that it had substantively been designed to eliminate.
What came after
The substantively definitive resolution came substantively five years later at the Council of Constance (1414–1418) — substantively a substantively much larger council convened under the Holy Roman Emperor Sigismund’s diplomatic-military protection. Constance substantively deposed John XXIII and Benedict XIII, substantively accepted Gregory XII’s voluntary abdication, and substantively elected a new pope (Martin V) in November 1417.
The Pisan council substantively is now substantively classified by the Catholic ecclesiastical tradition as a non-ecumenical council (substantively rather than a substantively legitimate general council) — substantively the substantively diplomatic Catholic-canonical fiction that substantively preserves the substantively legitimate papal lineage (Roman → Constance → Martin V → modern Catholic popes) while substantively excluding the substantively Pisan and substantively Avignon claimants from substantively legitimate canonical succession.