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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 a cost includes life gain (like Invigorate's alternative cost does), that cost can't be paid.

Effects that would replace gaining life with some other effect won't be able to do anything because it's impossible for players to gain life.

Spells and abilities that replace or redirect damage aren't affected by Everlasting Torment's second ability. They'll work as normal.

The last ability affects all damage, whether it's dealt by creatures, other permanents, spells, or cards that aren't on the battlefield. Wither works everywhere.

If an effect says to set your life total to a certain number, and that number is higher than your current life total, that effect will normally cause you to gain life equal to the difference. With Everlasting Torment on the battlefield, that part of the effect won't do anything. (If the number is lower than your current life total, the effect will work as normal.)

Effects that replace an event with gaining life (like Words of Worship's effect does) will end up replacing the event with nothing.

The "damage can't be prevented" statement overrides all forms of preventing damage, including protection abilities. Damage prevention spells and abilities can still be cast and played; they just don't do anything.

Spells and abilities that would normally cause a player to gain life still resolve, but the life-gain part simply has no effect.