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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.

Any power- or toughness-modifying effects (those that give +N/+N, for example) and counters will apply to the creature's new base power and toughness, even if they started to apply before Vedalken Humiliator's ability resolved.

If you don't control three artifacts as Vedalken Humiliator's ability resolves, it has no effect. If you do, the effect continues to apply even if you lose control of Vedalken Humiliator or your artifacts later in the turn.

Vedalken Humiliator's ability overwrites all previous effects that set an affected creature's base power and toughness to specific values. Any power- or toughness-setting effects that start to apply to a creature after the ability resolves will overwrite this effect.

Vedalken Humiliator's ability affects only creatures your opponents control at the time it resolves. Creatures they begin to control later in the turn won't lose power, toughness, or abilities.

All creatures your opponents control are affected by Vedalken Humiliator's ability, not just those controlled by the player it's attacking.