Lateran IV leads to the inquisition and the RCC itself uses the term "exterminate" for actions that follow where people were being killed.
It is their own Jesuit Fordham University that says it is in fact "exterminate"
Lateran IV calls for the "extermination of heretics" -- it is a supposedly infallible ecumenical council.
Fordham - a Jesuit web site and university.
FORDHAM – (Jesuit)
The Fourth Lateran Council, the council that dogmatized transubstantiation, offered indulgences to those who would "exterminate heretics" and participate in a Crusade. Since this council refers to the RCC's influence over the state (John 19:11), it points to the fact that the state was acting at the command of the RCC. The council declared (
http://legacy.fordham.edu/halsall/basis/lateran4.asp
Internet History Sourcebooks Project
CANON 3
“Secular authorities, whatever office they may hold, shall be admonished and induced and if necessary compelled by ecclesiastical censure, that as they wish to be esteemed and numbered among the faithful, so
for the defense of the faith they ought publicly to take an oath that they will
strive in good faith and to the best of their ability to exterminate in the territories subject to their jurisdiction all heretics pointed out by the Church; so that whenever anyone shall have assumed authority, whether spiritual or temporal, let him be bound to confirm this decree by oath. But if a temporal ruler, after having been requested and admonished by the Church,
should neglect to cleanse his territory of this heretical foulness, let him be excommunicated by the metropolitan and the other bishops of the province. If he refuses to make satisfaction within a year, let the matter be made known to the supreme pontiff [the Pope], that he may declare
the ruler's vassals absolved from their allegiance and may offer the territory to be ruled lay Catholics, who on the extermination of the heretics may possess it without hindrance and preserve it in the purity of faith; the right, however, of the chief ruler is to be respected as long
as he offers no obstacle in this matter and permits freedom of action. The same law is to be observed in regard to those
who have no chief rulers (that is, are independent). Catholics
who have girded themselves with the cross for the extermination of the heretics, shall enjoy the indulgences and privileges granted to those who go in defense of the Holy Land.”