Recall Dalton’s atomic theory

Dalton proposed that:

• Matter is made of indivisible atoms.
• Atoms of the same element are identical in mass and properties.
• Atoms of different elements differ in mass and properties.
• Chemical reactions involve only the rearrangement of atoms.
• Atoms are neither created nor destroyed in chemical reactions.
• Compounds are formed when atoms combine in simple whole-number ratios.

Check each option

Option A: "Matter consists of indivisible atoms..."

• This is a direct part of Dalton’s theory.
• So, A was proposed by Dalton.

Option B: "Chemical reactions involve reorganization of atoms. These are neither created nor destroyed in a chemical reaction."

• This is also a direct part of Dalton’s theory.
• So, B was proposed by Dalton.

Option C: "When gases combine or are produced in a chemical reaction they do so in a simple ratio by volume provided all gases are at the same $T$ and $P$."

• This is Gay-Lussac’s law of combining volumes, not Dalton’s atomic theory.
• So, C was not proposed by Dalton.

Option D: "Atoms of a given element have identical properties including identical mass. Atoms of different elements differ in mass."

• This is again a statement from Dalton’s atomic theory.
• So, D was proposed by Dalton.

Conclusion

The statement not proposed by Dalton is: $\boxed{\text{C}}$

Comparison with stored correct answer

Stored correct answer = C.

My derived answer also = C. Hence, they agree.