What happens when the {X} in Mind Grind *is* zero?
You must choose zero for X, but you can't choose zero for X, so you can't cast the spell. Epic Experiment doesn't force you to cast anything ("may cast"), so it will be moved to the graveyard by the later part of Epic Experiment's effect.


  107.3b If a player is casting a spell that has an {X} in its mana cost, the value of X isn’t defined by the text of that spell, and an effect lets that player cast that spell while paying neither its mana cost nor an alternative cost that includes X, then the only legal choice for X is 0. This doesn’t apply to effects that only reduce a cost, even if they reduce it to zero. See rule 601, “Casting Spells.”
  
  101.2. When a rule or effect allows or directs something to happen, and another effect states that it can’t happen, the “can’t” effect takes precedence.
  
  601.2. To cast a spell is to take it from where it is (usually the hand), put it on the stack, and pay its costs, so that it will eventually resolve and have its effect. Casting a spell follows the steps listed below, in order. If, at any point during the casting of a spell, a player is unable to comply with any of the steps listed below, the casting of the spell is illegal; the game returns to the moment before that spell started to be cast (see rule 717, “Handling Illegal Actions”). Announcements and payments can’t be altered after they’ve been made.


You can see these rules applied by an official source in the Oracle rulings for Ertai's Meddling:


  10/4/2004     Ertai's Meddling can't be cast through any way that doesn't
  pay its mana cost. This is because the X in the Meddling's mana cost
  can't be 0, but effects that allow spells to be cast without paying
  their mana costs set X to 0.