Pot of Duality

Being the most commonly played card currently, with most decks
running the maximum of three, Pot of Duality is quickly becoming one of
the most misplayed card.

The most common misplay with Pot of Duality is whether a player can
or cannot activate this card after a Special Summon was negated.
Essentially this article will explain the difference in various Special
Summoning negation, using Pot of Duality as the example.



Contractual Effect
Contractual Effect (誓約効果) is an unofficial term to refer to the
condition that restricts the usage of a card or effect. For Pot of
Duality, both “You can only activate 1 “Pot of Duality” per turn” and
“You cannot Special Summon a monster(s) during the turn you activate
this card” are Contractual Effects.

Contractual Effect is not an actual effect like Ignition Effect,
Trigger Effect, etc. As implied in its name, a Contractual Effect works
like a contract. If you activate this card, then you cannot perform the
action restricted by the Contractual Effect. Conversely, if you had
perform the action restricted by the Contractual Effect (breaking the
contract), then you cannot activate the card with said Contractual
Effect. Using Pot of Duality as an example, if you activate Pot of
Duality this turn, then you cannot cannot Special Summon a monster(s)
this turn. Conversely, if you Special Summoned a monster(s) this turn,
then you cannot activate Pot of Duality.

An action restricted by the Contractual Effect do not limit you from
playing another card with the same Contractual Effect. For example, Soul
Exchange and Cards from the Sky have the same Contractual Effect of not
allowing the player to conduct his/her Battle Phase this turn. You may
play both cards in the same turn.

Since Contractual Effect is not an actual effect, it does not get
negated or redirected. Once the card has resolved, the action restricted
by the Contractual Effect can no longer be performed.

Activation Negation vs Effect Negation
Activation Negation (発動の無効) means that the card was not activated, and you do not resolve its effect.

Effect Negation (効果の無効) means that the card is activated, and you resolve but do not apply its effect.

If your first Pot of Duality’s activation was negated (i.e. Horus the Black Flame Dragon LV8), then you are considered to have not activated Pot of Duality this turn. You can either activate your second Pot of Duality or perform a Special Summon this turn.

However, if your first Pot of Duality’s effect was negated
(i.e. Silent Swordsman LV7), then you are considered to have activated
Pot of Duality this turn. Although the effect of Pot of Duality is not
applied, the Contractual Effect is still applied. You cannot activate your second Pot of Duality nor perform a Special Summon this turn.

Negation of a Monster Effect that Special Summon
Negation of a Monster Effect comes in the form of Activation Negation
and Effect Negation, similar to the Negation of a Spell or Trap.

If the Activation of your Blackwing – Blizzard the Far North’s effect was negated (i.e. Divine Wrath), then you can activate Pot of Duality in the same turn.

However, if the Effect of your Blackwing – Blizzard the Far North’s effect was negated (i.e. Skill Drain), then you cannot activate Pot of Duality in the same turn.

Negation of a Built-In Special Summon
A Built-In Special Summon (also known as Inherent Special Summon) is a
Special Summon of an Effect Monster through its own Summoning Condition.
A Summoning Condition is not an actual Monster Effect (i.e. Ignition
Effect, Trigger Effect, etc), as it does not use the Chain Block.

Examples of Built-In Special Summon:

• Black Luster Soldier – Envoy of the Beginning
  Summoning Conidtion: Banishing 1 LIGHT and 1 DARK monster in your Graveyard
  
• Machina Fortress
  Summoning Condition: Discard Machine-Type monster(s) whose total Levels equal 8 or more
  
• Grapha, Dragon God of Dark World
  Summoning Condition: Return 1 face-up “Dark World” monster you control to the hand, except “Grapha, Dragon God of Dark World”
  

If a Built-In Special Summon was negated, you cannot activate Pot of Duality. This also applies to Contact Fusion Summon, Synchro Summon and Xyz Summon.

Side Note: This was ruled otherwise in the World Championship 2011, as seen in the Semi-Final Game 2.

Conclusion
If the Activation of a Special Summon Effect was negated, you can activate Pot of Duality.

If the Effect of a Special Summon Effect was negated or a Built-In Special Summon was negated, you cannot activate Pot of Duality.

Rulings are from 《強欲で謙虚な壺》 -遊戯王カードWiki, correct as at 1st September 2011.