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If an ability would produce one or more mana of an undefined type, it produces no mana instead.

Some abilities produce mana based on the type of mana another permanent or permanents “could produce.” The type of mana a permanent could produce at any time includes any type of mana that an ability of that permanent would produce if the ability were to resolve at that time, taking into account any applicable replacement effects in any possible order. Ignore whether any costs of the ability could or could not be paid. If that permanent wouldn’t produce any mana under these conditions, or no type of mana can be defined this way, there’s no type of mana it could produce.

To “tap [a permanent] for mana” is to activate a mana ability of that permanent that includes the {T} symbol in its activation cost. See rule 605, “Mana Abilities.”

An ability that triggers whenever a permanent “is tapped for mana” or is tapped for mana of a specified type triggers whenever such a mana ability resolves and produces mana or the specified type of mana.

A replacement effect that applies if a permanent “is tapped for mana” or tapped for mana of a specific type and/or amount modifies the mana production event while such an ability is resolving and producing mana or the specified type and/or amount of mana.

If an object’s enters-the-battlefield triggered ability or replacement effect refers to X, and the spell that became that object as it resolved had a value of X chosen for any of its costs, the value of X for that ability is the same as the value of X for that spell, although the value of X for that permanent is 0. This is an exception to rule 107.3i.

The tap symbol is {T}. The tap symbol in an activation cost means “Tap this permanent.” A permanent that’s already tapped can’t be tapped again to pay the cost. A creature’s activated ability with the tap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

The untap symbol is {Q}. The untap symbol in an activation cost means “Untap this permanent.” A permanent that’s already untapped can’t be untapped again to pay the cost. A creature’s activated ability with the untap symbol in its activation cost can’t be activated unless the creature has been under its controller’s control continuously since their most recent turn began. See rule 302.6.

If the card you cast without paying its mana cost has an X in its mana cost, you must choose 0 as its value.

If multiple Knowledge Pools are on the battlefield, keep track of which cards are exiled by each of them. Whenever a player casts a spell from their hand: -- If all Knowledge Pools are controlled by the same player, that player chooses the order in which the triggered abilities are put onto the stack. The last one put onto the stack will be the first to resolve. -- If multiple players each control one or more Knowledge Pools, the active player put their triggered abilities on the stack in any order, then each other player in turn order does the same. The last ability put onto the stack this way will be the first to resolve. -- The first triggered ability to resolve will exile the original spell, then the player who cast that spell may cast one of the nonland cards exiled by the Knowledge Pool that generated that triggered ability. The abilities of other Knowledge Pools will do nothing when they resolve, as the original spell will already have been exiled.

If the card has any mandatory additional costs, as Kuldotha Rebirth does, you must pay them in order to cast the spell.

Any other abilities that trigger when you cast the original spell (for example, if you cast Emrakul, the Aeons Torn) will still trigger and go on the stack.

Timing restrictions based on the card's type are ignored. For example, you can cast an exiled creature card this way. Other restrictions, such as Spinal Embrace's "Cast Spinal Embrace only during combat" are not ignored.

The spell a player casts from their hand won't resolve if it's exiled, even if that spell can't be countered by spells or abilities.

If the original spell isn't exiled (perhaps because it's countered by another spell or ability before Knowledge Pool's second triggered ability resolves), the rest of the ability does nothing. The player doesn't get to cast an exiled card.

You may cast any other card exiled by Knowledge Pool, including one owned by an opponent. Any card exiled by Knowledge Pool's "enters" ability or its other triggered ability may be cast.

If there are no nonland cards exiled by Knowledge Pool, the original spell is still exiled.

You may pay additional costs, such as kicker costs, of the exiled card.