Need help calculating Ur-Priest Caster Level

If a character is a Wizard 3/Ur-Priest 2/Mystic Theurge 8/Red Wizard 7

What would his Ur-Priest Caster Level be? Would the following be accurate?

Final Ur-Priest Caster Level = 2 (Base Ur-Priest Class Level) + 8 (Mystic Theurge bonus) + X

where X = ( 1/2 * (sum of his levels in other spellcasting classes) )

I assume that by levels they mean Class Levels in other spellcasting classes, not Caster Levels in other spellcasting classes.

But what exactly qualifies as a spellcasting class?

I have done some research on this and it seems that some players insist that only classes that have their own spell progression, such as Wizard, Sorcerer, Ranger, Cleric, Druid are spellcasting classes.

Those players do not count Prestige Classes (such as Mystic Theurge, Archmage, Red Wizard) that add +1 to caster level of another class, as true spellcasting classes since they lack their own spell progression.

So for this Wizard 3/Ur-Priest 2/Mystic Theurge 8/Red Wizard 7

would the Ur-Priest Caster Level be = 2 + 8 + ( 1/2 * (3 Wizard Levels) ) = roughly 11 Answer A

or
2 + 8 + (1/2 * ( 3 wiz lvls + 7 Red Wiz levels) = 10 + 5 = 15 levels Answer B

Some people would also add the Mystic Theurge in the calculations of 1/2 * (sum of other Spellcasting Class Levels)

Which would give us

2 + 8 + (1/2 * ( 3 wiz lvls + 7 Red Wiz levels + 8 mystic levels) = 10 + 9 = 19 levels Answer C

Which of the 3 answers is correct?
 

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