Note that the infallible documents are not necessarily limited to those in this list, but this list is considered infallible by several sources:
1. All Dogmatic decrees of the Councils.
2. Unanimous opinion of the Fathers of the Church
3. Pope Leo I Lectix Dilectionis Tuae
4. Pope Agatho: Omnium Bonorum Spes DZ 288 (Notes references are to Denzinger's Enchiridion Symbolorum)
6. Pope Benedict XII: Benedictus Deus DZ 530
7. Pope Leo X: Exsurge Domine DZ 741-781
8. Pope Innocent X: Cum Occassione DZ 1092-1096
9. Pope Innocent XI: Coelestis Pater DZ 1221-1288
10. Pope Clement XI: Unigenitus DZ 1351-1451
11. Pope Pius VI Auctorem Fidei DZ 1501-1599
12. Pope Pius IX Ineffabilis Dei DZ 1967-1978
13. Pope Pius IX Quanta Cura DZ 1688-1699
14. Pope Leo XIII Apostolicae Curae DZ 1963-1966
15. Pope Leo XIII Testem Benevolentiae DZ 1967-1976
16. Pope Pius X Lamentabili DZ 2239-2250
17. Pope Pius X Pascendi, DZ 2253-2333
18. Pope Pius XI Casti Conubii
19. Pope Pius XI Quadragesimo Anno
20. Pope Pius XII Munificentissiums Deus DZ 2331-2333
21. And many more not on this list.
Nor must it be thought that what is expounded in encyclical letters does not itself demand consent, on the pretext that in writing such letters the popes do not exercise the supreme power of their teaching authority. For these matters are taught with the ordinary teaching authority, of which it is true to say: 'He who heareth you, heareth Me'; and generally what is expounded and inculcated in encyclical letters already for other reasons appertains to Catholic doctrine. But if the supreme pontiffs in their official documents purposely pass judgment on a matter up to that time under dispute, it is obvious that the matter, according to the mind and will of the same pontiffs, cannot be any longer considered a question open to discussion among theologians. Humani Generis, Pope Pius XII, August 12, 1950.
We must therefore conclude that is a Pope decides a matter in an EncyclicaL, he does so infallibly.