from lemsynth.lemsynth_engine import solveProblem
# Declarations
x = Var('x', fgsort)
y, nil = Consts('y nil', fgsort)
k = Const('k', intsort)
key = Function('key', fgsort, intsort)
lft = Function('lft', fgsort, fgsort)
rght = Function('rght', fgsort, fgsort)
minr = Function('minr', fgsort, intsort)
maxr = Function('maxr', fgsort, intsort)
bst = RecFunction('bst', fgsort, boolsort)
hbst = RecFunction('hbst', fgsort, fgsetsort)
AddRecDefinition(minr, x, If(x == nil, 100, min_intsort(key(x), minr(lft(x)), minr(rght(x)))))
AddRecDefinition(maxr, x, If(x == nil, -1, max_intsort(key(x), maxr(lft(x)), maxr(rght(x)))))
AddRecDefinition(bst, x, If(x == nil, True,
And(0 < key(x),
And(key(x) < 100,
And(bst(lft(x)),
And(bst(rght(x)),
And(maxr(lft(x)) <= key(x),
key(x) <= minr(rght(x)))))))))
AddRecDefinition(hbst, x, If(x == nil, fgsetsort.lattice_bottom,
SetAdd(SetUnion(hbst(lft(x)), hbst(rght(x))), x)))
AddAxiom((), lft(nil) == nil)
AddAxiom((), rght(nil) == nil)
# Problem parameters
goal = Implies(bst(x), Implies(And(x != nil,
And(IsMember(y, hbst(x)),
# declarations
x = Var('x', fgsort)
y, nil = Consts('y nil', fgsort)
k = Const('k', intsort)
key = Function('key', fgsort, intsort)
lft = Function('lft', fgsort, fgsort)
rght = Function('rght', fgsort, fgsort)
minr = RecFunction('minr', fgsort, intsort)
maxr = RecFunction('maxr', fgsort, intsort)
bst = RecFunction('bst', fgsort, boolsort)
hbst = RecFunction('hbst', fgsort, fgsetsort)
AddRecDefinition(
minr, x, If(x == nil, 100, min_intsort(key(x), minr(lft(x)),
minr(rght(x)))))
AddRecDefinition(
maxr, x, If(x == nil, -1, max_intsort(key(x), maxr(lft(x)),
maxr(rght(x)))))
AddRecDefinition(
bst, x,
If(
x == nil, True,
And(
0 < key(x),
And(
key(x) < 100,
And(
bst(lft(x)),
And(
bst(rght(x)),
And(
maxr(lft(x)) <= key(x),
And(
