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Here is an interesting article in russian (googletranslate it) about real life firing practice:
2 Mig-31 + A-50 + ground control radars vs 1 SS-N-19 cruise missile

The target is rather tough (low RCS, supersonic).
The cruise missile got detected at 80km. Survived long range anti-air missile hit and did not even change its course. Got destroyed by another 2 AA missiles.

You have to hand it to the MiG-31 though - as far as this kind of interception goes, it really is an excellent platform.

One small clarification. P-700 survived after 2 first AA missiles (probably R-33 or R-37).
Food for meditation. In CMANO P-700 was hit by one SM-2 family missile.

I'd take this story with a (huge) grain of salt. Especially the part about P-700 survived two hits of 55kg warheads. The only realistic explanation - the first two R-33 simply missed the target.

Density of P-700 (10.1 m - length) is 7000 kg / 22.7 m^3 = 308.37 kg/m^3
Density of Mig-15 (8.6 m - length of fuselage) if 3382 (weight of empty plane) + 1210 kg (weight of fuel) / 52.95 m^3 = 86.72 kg/m^3 (the value of volume is took only for fuselage without wings and tail)

Why do not we assume that the difference in density can be explained by armor?

Because this means and tells nothing, especially in comparison to 55kg warhead. And BTW, don't forget about the huge penetrator made of hardened steel in the warhead and booster stage, which are included in these 7000kg.