Look for a counterexample for a conjecture regarding Level Set Integrals

lsi.py

from random import *

pa = 0.25
pb = 0.25

def E(f): 
    fa,fb = f
    return fa + (fb-fa) * pb if fa < fb else fb + (fa-fb) * pa
    
def r():
    return (randint(0,3),randint(0,3))
    
def test():
    while True:
        A = r()
        A_ = r()
        
        if E(A)<E(A_):
            A,A_ = A_,A
            
        if E(A)>E(A_):
            break
       
    while True:
        B = r()
        B_ = r()
        AB = (A[0]+B[0],A[1]+B[1])
        A_B_ = (A_[0]+B_[0],A_[1]+B_[1])
        AB_ = (A[0]+B_[0],A[1]+B_[1])
        if E(AB) > E(AB_):
            break
            
    if A_B_[0] > AB[0] and A_B_[1] > AB[1]:
        print(A,A_,B,B_)
        
for i in range(1000000):
    test()