Proving SAT does not have small circuits with an application to the two queries problem

We show that if SAT does not have small circuits, then there must exist a small number of formulas such that every small circuit fails to compute satisfiability correctly on at least one of these formulas. We use this result to show that if P^NP[1]=P^NP[2], then the polynomial-time hierarchy collapses to S₂^P⊆Σ₂^p∩Π₂^p. Even showing that the hierarchy collapsed to Σ₂^p remained open.