Story highlights "Cutting torches and angle grinders" are being used to destroy the weapons

"Missile warheads, aerial bombs and mixing and filling equipment" are being destroyed

A U.N. team is "monitoring, verifying and reporting" on Syria's compliance with a resolution

"The process will continue in the coming days," the U.N. says

Syrians began destroying their country's chemical weapons program Sunday, according to an international team tasked with overseeing the effort.

Syrian personnel are using "cutting torches and angle grinders to destroy or disable a range of items," a news release from the Organisation for the Prohibition of Chemical Weapons said Sunday. "This included missile warheads, aerial bombs and mixing and filling equipment."

The OPCW team, which arrived in Damascus on Tuesday, "are monitoring, verifying and reporting on Syria's compliance with international demands to destroy chemical weapons stockpiles and production facilities," the release said.

"The process will continue in the coming days," it said. The inspectors plan to visit nearly 50 sites as part of the mission, the OPCW said.

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Some are not convinced the plan will work.

A defected Syrian general told CNN's Christiane Amanpour on Tuesday that the government of Syrian President Bashar al-Assad will never give up its chemical stockpile.

"The locations of most of the scientific research centers in Syria and the storage facilities are known and under surveillance, thus, he will give up those centers and facilities for sure without lying. That said, however, Bashar al-Assad will not give up the chemical stockpile," said Syrian Brig. Gen. Zaher al-Sakat.

Al-Sakat said that he defected from the Syrian military after he was ordered to use chemical agents. He said he swapped the chemicals out for something non-toxic to fool his commanders.

The general said that in addition to four secret locations within Syria, the regime is currently transferring chemical weapons to Iraq and Lebanon, an allegation that the commander of the opposition Free Syrian Army, Gen. Salim Idriss, also recently made to Amanpour.

Lebanon and Iraq denied the claims at the time, and CNN's Barbara Starr reported that, if true, the claim would fundamentally shift the assessments of U.S. intelligence officials.

The U.N. Security Council, capping a dramatic month of diplomacy, voted unanimously September 27 to require Syria to eliminate its arsenal of chemical weapons -- or face consequences.

"Today's resolution will ensure that the elimination of the Syrian chemical weapons program happens as soon as possible and with the utmost transparency and accountability," Secretary-General Ban Ki-moon said.

The U.N. resolution was based on a deal struck this month between the United States and Russia that averted an American military strike over allegations the Syrian government used sarin nerve gas in an August 21 attack on a Damascus suburb. U.S. officials said it left at least 1,400 people dead.