I'd say LII > ILE, though on JCF:

I do not nor cannot ignore data (objective data which has proven some connection with facts) that disagree with me only for feeling comfortable. But I do not feel comfortable with contradictions, feeling them as a insufficient knowledge or concept misunderstanding. While I'm not able to solve them I do not feel that the task of "understanding" is complete.
This actually sounds like extroversion > Ti, so I'd go with ENTP over INTP.

5w6 sounds very much right.