Hindman's conjecture on monochromatic products and sums

Let $\mathbb{N}$ be the set of positive integers, and let a finite coloring assign one of finitely many colors to each element of $\mathbb{N}$. A set is monochromatic if all of its elements have the same color. Hindman's conjecture. Any finite coloring of $\mathbb{N}$ contains monochromatic sets of the form

$$\{x,y,xy,x+y\}.$$

The conjecture concerns the interaction between additive and multiplicative structure in finite colorings of the natural numbers. The source's abstract states a stronger result for $2$-colorings, namely that infinitely many such monochromatic sets exist; this resolves the stated conjecture in the two-color case, while the finite-color formulation itself is presented here without a resolution status.