Assumption of Rankine Theory:
1. Vertical boundary formed by the vertical back of a smooth wall surface.
2. Soil is homogeneous and dry.
3. Soil is cohesive.
4. Semi-infinite mass of soil bound by a horizontal surface.

Explanation:
The Rankine theory is a classical method used to analyze the lateral earth pressure exerted on retaining structures, such as walls or sheet piles, when the soil is at rest. It makes several assumptions to simplify the analysis and provide approximate results. Let's discuss each assumption in detail:

1. Vertical boundary formed by the vertical back of a smooth wall surface:
This assumption implies that the retaining structure has a vertical back and is perfectly smooth. It helps in simplifying the analysis by assuming that the soil-wall interface is frictionless. In reality, walls may have rough surfaces or irregular shapes, but for the purpose of this theory, a smooth vertical boundary is considered.

2. Soil is homogeneous and dry:
The assumption of soil homogeneity means that the soil properties, such as density, cohesion, and friction angle, are constant throughout the soil mass. This assumption simplifies the analysis, as it eliminates the need to consider variations in soil properties with depth. Additionally, the assumption of dry soil implies that there is no presence of water influencing the soil behavior.

3. Soil is cohesive:
Cohesion refers to the shear strength exhibited by a soil due to attractive forces between its particles. The Rankine theory assumes that the soil is cohesive, meaning it possesses shear strength even in the absence of normal stress. This assumption allows for the consideration of cohesive forces in the calculation of lateral earth pressure.

4. Semi-infinite mass of soil bound by a horizontal surface:
This assumption assumes that the soil mass extends to infinity horizontally and is bounded by a horizontal surface. It implies that the soil mass is extensive enough to neglect any boundary effects. This assumption simplifies the analysis by considering an infinitely wide soil mass, which eliminates the need to consider edge effects.

Conclusion:
Out of the given options, the assumption that is NOT included in Rankine Theory is that the soil is cohesive (option C). The theory assumes that the soil is cohesive, meaning it possesses shear strength even in the absence of normal stress. This assumption allows for the consideration of cohesive forces in the calculation of lateral earth pressure.