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symbolic n,m,B;
{ [max_diff] :
forall (m :
(not exists (z1,z2 : 0<=z1<n && z1<=z2<m+z1 && z2 = m))
or
(forall (minX,minY :
(not (forall (x1,x2 : (not (0<=x1<n && x1<=x2<m+x1 && m-B+1 <= x2 <= m)) or (x1+x2 >= minX)) &&
exists (x1,x2 : 0<=x1<n && x1<=x2<m+x1 && m-B+1 <= x2 <= m && x1+x2 = minX) &&
forall (y1,y2 : (not (0<=y1<n && y1<=y2<=m+y1 && m+1 <= y2 <= m+B)) or (y1+y2 >= minY)) &&
exists (y1,y2 : 0<=y1<n && y1<=y2<=m+y1 && m+1 <= y2 <= m+B && y1+y2 = minY)))
or
(minY-minX <= max_diff)))) &&
exists (m,z1,z2,minX,minY :
0<=z1<n && z1<=z2<=m+z1 && z2 = m &&
forall (x1,x2 : (not (0<=x1<n && x1<=x2<m+x1 && m-B+1 <= x2 <= m)) or (x1+x2 >= minX)) &&
exists (x1,x2 : 0<=x1<n && x1<=x2<m+x1 && m-B+1 <= x2 <= m && x1+x2 = minX) &&
forall (y1,y2 : (not (0<=y1<n && y1<=y2<=m+y1 && m+1 <= y2 <= m+B)) or (y1+y2 >= minY)) &&
exists (y1,y2 : 0<=y1<n && y1<=y2<=m+y1 && m+1 <= y2 <= m+B && y1+y2 = minY) &&
minY-minX = max_diff)};
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