Exclusion of nondegenerate sextuples with exactly two small entries

Let K be an imaginary quadratic number field, let phi be a complex embedding, and let t be a Diophantine sextuple in its full ring of integers. Assume that the absolute values of the images of its entries are nondecreasing. Such a sextuple is impossible if the second absolute value is below 3, the third is at least 3, and the product of the first two entries plus one is nonzero.

The sextuple consists of distinct nonzero algebraic integers, and the product of any two distinct entries plus one is a square in the full ring of integers. Equal absolute values are permitted. This is one of the exhaustive branches used to establish the cardinality bound.