Conjecture on two-parameter contact inequivalence in characteristic p

Let $F$ be an algebraically closed field with characteristic $p$. Consider the isolated complete intersection singularities

$$(x^2+y^4,y^{5}+\lambda xy^3+axy^{p+3}+xy^{4+p}+bxy^{2p+3})$$

and

$$(x^2+y^4,y^{5}+\lambda xy^3+cxy^{p+3}+xy^{4+p}+dxy^{2p+3}).$$

Contact-inequivalence conjecture. For general $a,b,c,d a\in F$, these singularities are not contact equivalent.

The conjecture would establish that the displayed family contributes two independent moduli parameters and would support the claimed classification of unimodal isolated complete intersection singularities. Its status is unresolved in the source.