I faced with that error on 11.2.0.2 db on AIX 6.1 system.

During export an error message EXP-113 is raised:
EXP-00113: Feature New Composite Partitioning Method is unsupported. Table MYTABLE could not be exported
But the export would still complete and also there are some addition error messages are raised:
EXP-00006: internal inconsistency error
EXP-00000: Export terminated unsuccessfully

Complete error is:

. . exporting table XX
. . exporting table XX
. . exporting table XX
. . exporting table XX
. about to export X’s tables via Direct Path …
. about to export X’s tables via Direct Path …
. about to export X’s tables via Direct Path …
. about to export X’s tables via Direct Path …
. about to export X’s tables via Direct Path …
. about to export X’s tables via Direct Path …
. about to export X’s tables via Direct Path …
EXP-00113: Feature New Composite Partitioning Method is unsupported. Table X could not be exported
. . exporting table XX
. . exporting table XX
. . exporting table XX
. . exporting table XX
. . exporting table XX
. . exporting table XX
. . exporting table XX
. . exporting table XX
. . exporting table XX
. . exporting table XX
EXP-00006: internal inconsistency error
EXP-00000: Export terminated unsuccessfully

After make search at metalink, I noticed that; I met one bug.. Bug 7834212

From note:
Bug 7834212 has been filed regarding this problem. However, it should be noted that the new composite partitioning and system partitioning is a 11g feature.
Classic Export does not support this. When a table with this feature is exported, an error message EXP-113 is raised.But if the table partition has split or added a new partition, it will now generate the EXP-6 and EXP-0 errors and fail to complete.

So what is solution? Here is the answer:
Use DataPump to perform exports of composite partitioning and system partitioned tables as this is the recommended method.

Reference:
Exporting System or Composite Partitioned Table Using Classic Export Gives EXP-6 AND EXP-0 (Doc ID 762774.1)

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