## Line Chart: pass@1-with-n-queries
### Overview
The image is a line chart comparing the performance of two automated theorem-proving systems. The chart plots the cumulative number of theorems successfully proved against the number of queries (attempts) made by each system. The title is "pass@1-with-n-queries".
### Components/Axes
* **Chart Title:** `pass@1-with-n-queries`
* **X-Axis:**
* **Label:** `Number of Queries (n)`
* **Scale:** Linear, ranging from 0 to 60, with major tick marks every 10 units (0, 10, 20, 30, 40, 50, 60).
* **Y-Axis:**
* **Label:** `Number of Theorems Proved`
* **Scale:** Linear, ranging from 0 to approximately 58, with major tick marks every 10 units (0, 10, 20, 30, 40, 50).
* **Legend:** Located in the bottom-right corner of the plot area.
* **Orange Line:** `COPRA (GPT-4-turbo) (with retrieval)`
* **Blue Line:** `Proverbot9001`
### Detailed Analysis
The chart displays two step-like, monotonically increasing lines, indicating cumulative success.
**1. COPRA (GPT-4-turbo) (with retrieval) - Orange Line:**
* **Trend:** Exhibits a very steep initial ascent, followed by a rapid deceleration and eventual plateau.
* **Data Points (Approximate):**
* Starts at (0, 0).
* Shows a dramatic increase between 0 and 5 queries, reaching approximately 35 theorems proved.
* Continues to climb steeply until about 10 queries, reaching ~45 theorems.
* The rate of increase slows significantly after 10 queries.
* Reaches a plateau of approximately 56-57 theorems proved by around 20 queries.
* The line remains flat (plateaued) from ~20 queries to the end of the chart at 60 queries.
**2. Proverbot9001 - Blue Line:**
* **Trend:** Shows a steadier, more gradual, and sustained increase compared to the orange line.
* **Data Points (Approximate):**
* Starts at (0, 0).
* Increases steadily, reaching ~10 theorems by 5 queries and ~25 theorems by 10 queries.
* Continues a consistent upward climb, crossing 40 theorems at approximately 30 queries.
* Reaches approximately 50 theorems by 40 queries.
* The line ends at approximately 54 theorems proved at 60 queries. A short dotted blue line extends horizontally to the right from the final point, suggesting the process may continue beyond the plotted range.
### Key Observations
1. **Performance Divergence:** The two systems have markedly different performance profiles. COPRA demonstrates high early efficiency, proving a large number of theorems with very few queries. Proverbot9001 is slower to start but maintains a more consistent rate of proving over a longer sequence of queries.
2. **Crossover Point:** The orange line (COPRA) is above the blue line (Proverbot9001) for the entire visible range of the chart. COPRA maintains a lead in theorems proved at every query count from 1 to 60.
3. **Plateau vs. Continued Growth:** COPRA's performance plateaus after ~20 queries, suggesting it may have exhausted the "easier" theorems in the dataset or reached a capability limit. Proverbot9001 shows no sign of plateauing within the 60-query window, indicating it might continue to prove more theorems if given more queries.
4. **Final Values:** At the 60-query mark, COPRA has proved approximately 56-57 theorems, while Proverbot9001 has proved approximately 54. The gap between them narrows significantly from a peak of ~20 theorems (at ~10 queries) to only ~2-3 theorems at 60 queries.
### Interpretation
This chart illustrates a classic trade-off between **initial efficiency** and **sustained performance** in automated reasoning tasks.
* **COPRA (with retrieval)** appears to be highly optimized for quickly solving a subset of problems, likely leveraging its retrieval mechanism and the powerful GPT-4-turbo model to identify and prove theorems that are more straightforward or closely match patterns in its knowledge base. Its rapid plateau suggests it may struggle with more complex or novel theorems that require deeper, sequential reasoning beyond its initial retrieval-augmented approach.
* **Proverbot9001** exhibits the behavior of a more traditional, possibly search-based or iterative theorem prover. It makes slower but steady progress, systematically working through problems. Its lack of a plateau within the observed window implies it has a more robust mechanism for tackling difficult problems, albeit at a higher computational cost (more queries).
The data suggests that for scenarios requiring quick results on a limited budget of attempts, COPRA is superior. However, for maximizing the total number of proven theorems given a larger allowance of queries, Proverbot9001 may ultimately be more effective, as indicated by its continuing upward trend and the narrowing performance gap. The "pass@1" metric in the title implies this measures success on the first attempt per query, highlighting COPRA's strength in single-shot accuracy.
