The conjecture that $K_6$ is not reducible for the first Symanzik polynomial

A graph is reducible with respect to the first Symanzik polynomial when it has the corresponding reducibility property for that polynomial. The $K_6$ irreducibility conjecture. The graph $K_6$ is not reducible with respect to the first Symanzik polynomial. This is proposed as a starting point for determining the full forbidden minor set for reducibility with respect to the first Symanzik polynomial; the source gives no resolution.