Barrier in-and-out parity

If we buy an up-and-out European call and an up-and-in European call, then the following parity should hold good:

The logic is very simple—if the stock price reaches the barrier, then the first call is worthless and the second call will be activated. If the stock price never touches the barrier, the first call will remain active, while the second one is never activated. Either way, one of them is active. The following Python program illustrates such scenarios:

def upCall(s,x,T,r,sigma,nSimulation,barrier):
    import scipy as sp
    import p4f 
    n_steps=100
    dt=T/n_steps 
    inTotal=0 
    outTotal=0
    for j in range(0, nSimulation): 
        sT=s
        inStatus=False 
        outStatus=True
        for i in range(0,int(n_steps)):
            e=sp.random.normal()
            sT*=sp.exp((r-0.5*sigma*sigma)*dt+sigma*e*sp.sqrt(dt)) 
            if sT>barrier:
                outStatus=False 
                inStatus=True
        if outStatus==True...