Show me this proof. I think you are talking big. The math is the math. Oh wait, are you using the new shape of the earth as explained by Neil DeGrasse Tyson? It's spheroid, pear shaped, chubby thing. Bullshit, the lighthouse proof is solid and if you studied it you know that.
At least be honest like the textbook writers and admit you don't know. SHOW ME these proofs you speak of.
Here is a plot of lighthouse visibility versus height of the light above sea level, taking into account standard correction for refraction and a bridge height of 30 ft above the water line.

The formula for calculating distance to the horizon, including refraction correction for standard atmosphere is D = 3.86 * sqrt ( h ) h = height in meters, D = distance in km.
The Planier lighthouse is 66 meters asl, and is visible for 43 km, calculated distance is 43 km, Flat Earthers claim the calculated value is 29 km
The Jeddah lighthouse is 113 meters asl, and is visible for 46 km, calculated distance is 53 km, Flat Earthers claim the calculated value is 38 km
The Ile Vierge lighthouse is 82.5 meters asl, and is visible for 50 km, calculated distance is 47 km, Flat Earthers claim the calculated value is 33 km
The Genoa lighthouse is 76 meters asl, and is visible for 46 km, calculated distance is 45 km, Flat Earthers claim the calculated value is 31 km
The conclusion is that if you do the calculations properly, the flat earth argument, falls flat on its face ( once again )
For details of the formula derivation go to ...
http://www-rohan.sdsu.edu/~aty/explain/atmos_refr/horizon.htmlCalculation of ducting effects.
http://www-rohan.sdsu.edu/~aty/explain/atmos_refr/bending.html