## Line Chart: Cumulative solving + checking time
### Overview
The chart displays the cumulative time (in seconds) required to solve and check benchmarks across three solver combinations. The y-axis uses a logarithmic scale (10^-1 to 10^5 seconds), while the x-axis represents the number of benchmarks (0 to 7000). Three data series are plotted, showing divergent performance trends.
### Components/Axes
- **X-axis**: Number of benchmarks (0–7000, linear scale)
- **Y-axis**: Time (s) (10^-1 to 10^5, logarithmic scale)
- **Legend**: Located in the bottom-right corner, with three entries:
- Blue: `cvc5+Ethos`
- Orange: `cvc5+Lean-SMT`
- Green: `veriT+SMTCoq`
### Detailed Analysis
1. **Initial Behavior**: All three lines originate from the same point near (0, 10^0) and rise sharply in the first 1000 benchmarks.
2. **Divergence**:
- **Orange (`cvc5+Lean-SMT`)**: Steepest ascent, reaching ~10^5 seconds at ~5000 benchmarks.
- **Green (`veriT+SMTCoq`)**: Intermediate growth, peaking at ~10^4 seconds at ~4000 benchmarks.
- **Blue (`cvc5+Ethos`)**: Slowest growth, reaching ~10^4 seconds at ~7000 benchmarks.
3. **Final Values** (approximate):
- At 7000 benchmarks:
- `cvc5+Lean-SMT`: ~10^5 seconds
- `veriT+SMTCoq`: ~10^4 seconds
- `cvc5+Ethos`: ~10^3.5 seconds
### Key Observations
- **Performance Hierarchy**: `cvc5+Lean-SMT` outperforms others by ~10x at 7000 benchmarks.
- **Exponential Scaling**: Time increases exponentially with benchmarks, especially for `cvc5+Lean-SMT`.
- **Logarithmic Compression**: The y-axis emphasizes differences in growth rates between solvers.
### Interpretation
The data suggests that solver combinations significantly impact efficiency. `cvc5+Lean-SMT` achieves the fastest cumulative time, likely due to optimized checking mechanisms. `cvc5+Ethos` lags, possibly due to Ethos's stricter verification requirements. The logarithmic scale highlights how time complexity escalates with problem size, emphasizing the need for scalable solver architectures. The divergence at higher benchmarks indicates that Lean-SMT's incremental gains compound more effectively than other combinations.
