## Line Chart: Relationship Between Clauses in Formula and Clauses Stored ### Overview The chart illustrates the relationship between the number of clauses in a formula and the number of clauses stored, across three distinct scenarios defined by the parameters `p1=p2=0.1`, `p1=p2=0.2`, and `p1=p2=0.3`. Each scenario is represented by a distinct line with unique markers and colors. The y-axis represents the "Number of clauses stored," while the x-axis represents the "Number of clauses in the formula." ### Components/Axes - **X-Axis (Horizontal)**: Labeled "Number of clauses in the formula," ranging from 0 to 200 in increments of 20. - **Y-Axis (Vertical)**: Labeled "Number of clauses stored," ranging from 0 to 1300 in increments of 100. - **Legend**: Positioned in the top-right corner, with three entries: - **Black circles**: `p1=p2=0.1` - **Dark gray squares**: `p1=p2=0.2` - **Light gray triangles**: `p1=p2=0.3` ### Detailed Analysis 1. **`p1=p2=0.1` (Black Circles)**: - Starts at (0, 0) and increases steadily. - Approximate values: - At x=20: ~50 - At x=100: ~300 - At x=200: ~580 2. **`p1=p2=0.2` (Dark Gray Squares)**: - Starts at (0, 0) with a steeper slope than `p1=p2=0.1`. - Approximate values: - At x=20: ~70 - At x=100: ~450 - At x=200: ~540 3. **`p1=p2=0.3` (Light Gray Triangles)**: - Starts at (0, 0) with the steepest slope. - Approximate values: - At x=20: ~90 - At x=100: ~600 - At x=200: ~1280 (near the y-axis maximum of 1300) ### Key Observations - The `p1=p2=0.3` series (light gray triangles) exhibits the fastest growth, surpassing all other series by x=200. - The `p1=p2=0.2` series (dark gray squares) initially grows faster than `p1=p2=0.1` but falls below it at x=200, suggesting an anomaly or non-linear behavior. - All series begin at (0, 0), indicating no stored clauses when no clauses are in the formula. ### Interpretation The data suggests a direct proportionality between the number of clauses in the formula and the number stored, with higher `p1=p2` values generally leading to greater storage efficiency. However, the `p1=p2=0.2` series deviates from this trend at higher x-values, potentially indicating: 1. A data collection error or mislabeling in the legend. 2. A non-linear relationship not captured by the linear model. 3. A threshold effect where `p1=p2=0.3` becomes disproportionately effective. The legend’s placement and color coding enhance clarity, but the inconsistency in the `p1=p2=0.2` series warrants further investigation to validate the underlying assumptions or data accuracy.