Unresolved exponential variants of the Pairwise Sum-Product Theorem

Determine which of the formulas (−x + y = z) ∧ (xy = t), (−x + y = z) ∧ (y = tx), and (x + y = z) ∧ (y = tx) are Ramsey partition regular in (x, y) | z, t.

Background

The paper proves several failures of Ramsey partition regularity for configurations combining addition, multiplication, and exponentiation. It observes that variants of the Pairwise Sum-Product Theorem remain unresolved and identifies three formulas as the principal cases whose classification may complete the relevant picture. Ramsey partition regularity in (x, y) | z, t requires an infinite monochromatic set of pairs in the first block together with appropriately monochromatic witnesses for z and t.