from z3 import *

# lecture 15, slide 36 and on

# declare the variables x and y
x = Bool('x')
y = Bool('y')

# declare the 'next state' variables x_ and y_
x_ = Bool('x_')
y_ = Bool('y_')

# define R as manually computed
R = Or(And(x_ == x, y_ != y), And(x_ != x, y_ == y)) 

# define the property we are interested in
phi = And(x, y)

# substitute the 'next state' variables
phi_ = substitute(phi, (x, x_), (y, y_))

# define EX_phi using the definition
EX_phi = Exists([x_, y_], And(R, phi_)) 

# use the quantifier elimination 'tactic'
quant_elim = Tactic('qe')

# apply the qe tactic
result = quant_elim(EX_phi)[0][0]

#print the result
print(result)