Datasets:
Upload folder using huggingface_hub
Browse files- .gitattributes +2 -0
- README.md +195 -0
- clinical_trial/documents.jsonl +3 -0
- clinical_trial/qrels.jsonl +0 -0
- clinical_trial/queries.jsonl +0 -0
- code_retrieval/documents.jsonl +0 -0
- code_retrieval/qrels.jsonl +0 -0
- code_retrieval/queries.jsonl +3 -0
- legal_qa/documents.jsonl +0 -0
- legal_qa/qrels.jsonl +109 -0
- legal_qa/queries.jsonl +50 -0
- paper_retrieval/documents.jsonl +0 -0
- paper_retrieval/qrels.jsonl +0 -0
- paper_retrieval/queries.jsonl +0 -0
- set_operation_entity_retrieval/documents.jsonl +0 -0
- set_operation_entity_retrieval/qrels.jsonl +0 -0
- set_operation_entity_retrieval/queries.jsonl +0 -0
- stack_exchange/documents.jsonl +0 -0
- stack_exchange/qrels.jsonl +125 -0
- stack_exchange/queries.jsonl +0 -0
- theorem_retrieval/documents.jsonl +74 -0
- theorem_retrieval/qrels.jsonl +103 -0
- theorem_retrieval/queries.jsonl +0 -0
- tip_of_the_tongue/documents.jsonl +0 -0
- tip_of_the_tongue/qrels.jsonl +363 -0
- tip_of_the_tongue/queries.jsonl +50 -0
.gitattributes
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# Video files - compressed
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*.mp4 filter=lfs diff=lfs merge=lfs -text
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*.webm filter=lfs diff=lfs merge=lfs -text
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# Video files - compressed
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*.mp4 filter=lfs diff=lfs merge=lfs -text
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*.webm filter=lfs diff=lfs merge=lfs -text
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clinical_trial/documents.jsonl filter=lfs diff=lfs merge=lfs -text
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code_retrieval/queries.jsonl filter=lfs diff=lfs merge=lfs -text
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README.md
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| 1 |
+
---
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| 2 |
+
license: apache-2.0
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| 3 |
+
task_categories:
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| 4 |
+
- text-retrieval
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| 5 |
+
language:
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| 6 |
+
- en
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| 7 |
+
tags:
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| 8 |
+
- information-retrieval
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| 9 |
+
- benchmark
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| 10 |
+
- clinical-trials
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| 11 |
+
- code-search
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| 12 |
+
- legal-qa
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| 13 |
+
size_categories:
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| 14 |
+
- 10K<n<100K
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| 15 |
+
configs:
|
| 16 |
+
- config_name: clinical_trial
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| 17 |
+
data_files:
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| 18 |
+
- split: queries
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| 19 |
+
path: "clinical_trial/queries.jsonl"
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| 20 |
+
- split: documents
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| 21 |
+
path: "clinical_trial/documents.jsonl"
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| 22 |
+
- split: qrels
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| 23 |
+
path: "clinical_trial/qrels.jsonl"
|
| 24 |
+
- config_name: code_retrieval
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| 25 |
+
data_files:
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| 26 |
+
- split: queries
|
| 27 |
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path: "code_retrieval/queries.jsonl"
|
| 28 |
+
- split: documents
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| 29 |
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path: "code_retrieval/documents.jsonl"
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| 30 |
+
- split: qrels
|
| 31 |
+
path: "code_retrieval/qrels.jsonl"
|
| 32 |
+
- config_name: legal_qa
|
| 33 |
+
data_files:
|
| 34 |
+
- split: queries
|
| 35 |
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path: "legal_qa/queries.jsonl"
|
| 36 |
+
- split: documents
|
| 37 |
+
path: "legal_qa/documents.jsonl"
|
| 38 |
+
- split: qrels
|
| 39 |
+
path: "legal_qa/qrels.jsonl"
|
| 40 |
+
- config_name: paper_retrieval
|
| 41 |
+
data_files:
|
| 42 |
+
- split: queries
|
| 43 |
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path: "paper_retrieval/queries.jsonl"
|
| 44 |
+
- split: documents
|
| 45 |
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path: "paper_retrieval/documents.jsonl"
|
| 46 |
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- split: qrels
|
| 47 |
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path: "paper_retrieval/qrels.jsonl"
|
| 48 |
+
- config_name: set_operation_entity_retrieval
|
| 49 |
+
data_files:
|
| 50 |
+
- split: queries
|
| 51 |
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path: "set_operation_entity_retrieval/queries.jsonl"
|
| 52 |
+
- split: documents
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| 53 |
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path: "set_operation_entity_retrieval/documents.jsonl"
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| 54 |
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- split: qrels
|
| 55 |
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path: "set_operation_entity_retrieval/qrels.jsonl"
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| 56 |
+
- config_name: stack_exchange
|
| 57 |
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data_files:
|
| 58 |
+
- split: queries
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| 59 |
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path: "stack_exchange/queries.jsonl"
|
| 60 |
+
- split: documents
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| 61 |
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path: "stack_exchange/documents.jsonl"
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| 62 |
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- split: qrels
|
| 63 |
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path: "stack_exchange/qrels.jsonl"
|
| 64 |
+
- config_name: theorem_retrieval
|
| 65 |
+
data_files:
|
| 66 |
+
- split: queries
|
| 67 |
+
path: "theorem_retrieval/queries.jsonl"
|
| 68 |
+
- split: documents
|
| 69 |
+
path: "theorem_retrieval/documents.jsonl"
|
| 70 |
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- split: qrels
|
| 71 |
+
path: "theorem_retrieval/qrels.jsonl"
|
| 72 |
+
- config_name: tip_of_the_tongue
|
| 73 |
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data_files:
|
| 74 |
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- split: queries
|
| 75 |
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path: "tip_of_the_tongue/queries.jsonl"
|
| 76 |
+
- split: documents
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| 77 |
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path: "tip_of_the_tongue/documents.jsonl"
|
| 78 |
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- split: qrels
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| 79 |
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path: "tip_of_the_tongue/qrels.jsonl"
|
| 80 |
+
---
|
| 81 |
+
|
| 82 |
+
# NanoCrumb Dataset
|
| 83 |
+
|
| 84 |
+
A curated subset of the [Crumb](https://huggingface.co/datasets/jfkback/crumb) retrieval dataset, designed for rapid experimentation and evaluation of information retrieval systems.
|
| 85 |
+
|
| 86 |
+
## Dataset Summary
|
| 87 |
+
|
| 88 |
+
**NanoCrumb** distills the large Crumb dataset (10.5 GB, 6.36M rows) into a manageable benchmark while maintaining task diversity across 8 different retrieval domains.
|
| 89 |
+
|
| 90 |
+
- **Total Size**: ~125 MB (JSONL format)
|
| 91 |
+
- **Queries**: 400 (50 per task split)
|
| 92 |
+
- **Documents**: 30,040 unique passages
|
| 93 |
+
- **Query-Document Pairs**: 31,754
|
| 94 |
+
- **Configs**: 8 task-specific configs
|
| 95 |
+
|
| 96 |
+
## Configs (Task Splits)
|
| 97 |
+
|
| 98 |
+
Each config represents a different retrieval domain:
|
| 99 |
+
|
| 100 |
+
| Config Name | Queries | Documents | Docs/Query (avg) | Description |
|
| 101 |
+
|------------|---------|-----------|------------------|-------------|
|
| 102 |
+
| `clinical_trial` | 50 | 22,251 | 464 | Match patients to clinical trials |
|
| 103 |
+
| `paper_retrieval` | 50 | 4,402 | 102 | Find relevant academic papers |
|
| 104 |
+
| `set_operation_entity_retrieval` | 50 | 1,533 | 31 | Entity-based retrieval |
|
| 105 |
+
| `code_retrieval` | 50 | 1,206 | 24 | Find relevant code snippets |
|
| 106 |
+
| `tip_of_the_tongue` | 50 | 363 | 7 | Recall items from vague descriptions |
|
| 107 |
+
| `stack_exchange` | 50 | 125 | 3 | Find relevant Q&A posts |
|
| 108 |
+
| `legal_qa` | 50 | 86 | 2 | Legal question answering |
|
| 109 |
+
| `theorem_retrieval` | 50 | 74 | 2 | Find mathematical theorems |
|
| 110 |
+
|
| 111 |
+
## Dataset Structure
|
| 112 |
+
|
| 113 |
+
Each config contains three splits:
|
| 114 |
+
|
| 115 |
+
### `queries`
|
| 116 |
+
- `query_id`: Unique query identifier (string)
|
| 117 |
+
- `query_content`: The query text (string)
|
| 118 |
+
- `instruction`: Task-specific instructions (string)
|
| 119 |
+
- `passage_qrels`: List of relevant passages with graded relevance scores (list)
|
| 120 |
+
- `task_split`: Task domain name (string)
|
| 121 |
+
- `metadata`: Additional task-specific information (string)
|
| 122 |
+
- `use_max_p`: Boolean flag for MaxP aggregation (bool)
|
| 123 |
+
|
| 124 |
+
### `documents`
|
| 125 |
+
- `document_id`: Unique document identifier (string)
|
| 126 |
+
- `document_content`: The passage text (string)
|
| 127 |
+
- `parent_id`: Links passages to source documents (string)
|
| 128 |
+
- `task_split`: Task domain name (string)
|
| 129 |
+
- `metadata`: Document metadata (string)
|
| 130 |
+
|
| 131 |
+
### `qrels`
|
| 132 |
+
- `query_id`: Query identifier (string)
|
| 133 |
+
- `document_id`: Document identifier (string)
|
| 134 |
+
- `relevance_score`: Graded relevance 0.0-2.0 (float)
|
| 135 |
+
- `binary_relevance`: Binary relevance 0 or 1 (int)
|
| 136 |
+
- `task_split`: Task domain name (string)
|
| 137 |
+
|
| 138 |
+
## Usage
|
| 139 |
+
|
| 140 |
+
```python
|
| 141 |
+
from datasets import load_dataset
|
| 142 |
+
|
| 143 |
+
# Load a specific config (task split)
|
| 144 |
+
clinical_data = load_dataset("YOUR_USERNAME/nanocrumb", "clinical_trial")
|
| 145 |
+
|
| 146 |
+
# Access the splits
|
| 147 |
+
queries = clinical_data['queries']
|
| 148 |
+
documents = clinical_data['documents']
|
| 149 |
+
qrels = clinical_data['qrels']
|
| 150 |
+
|
| 151 |
+
# Load all configs
|
| 152 |
+
all_configs = [
|
| 153 |
+
"clinical_trial", "code_retrieval", "legal_qa", "paper_retrieval",
|
| 154 |
+
"set_operation_entity_retrieval", "stack_exchange",
|
| 155 |
+
"theorem_retrieval", "tip_of_the_tongue"
|
| 156 |
+
]
|
| 157 |
+
|
| 158 |
+
for config_name in all_configs:
|
| 159 |
+
data = load_dataset("YOUR_USERNAME/nanocrumb", config_name)
|
| 160 |
+
print(f"{config_name}: {len(data['queries'])} queries")
|
| 161 |
+
```
|
| 162 |
+
|
| 163 |
+
## Sampling Methodology
|
| 164 |
+
|
| 165 |
+
For each task split:
|
| 166 |
+
1. **Query Selection**: Randomly sampled 50 queries from evaluation set (seed=42)
|
| 167 |
+
2. **Document Selection**:
|
| 168 |
+
- Include ALL positive documents (binary_relevance=1)
|
| 169 |
+
- Fill remainder with hard negatives (relevance=0) to reach ~100 docs per query
|
| 170 |
+
- Target: ~5,000 documents per task split
|
| 171 |
+
3. **Deduplication**: Documents shared across queries are deduplicated within each config
|
| 172 |
+
|
| 173 |
+
## Use Cases
|
| 174 |
+
|
| 175 |
+
- 🚀 **Rapid prototyping** of retrieval models
|
| 176 |
+
- 🧪 **Quick benchmarking** without downloading large datasets
|
| 177 |
+
- 📚 **Educational purposes** for learning IR techniques
|
| 178 |
+
- 🔬 **Ablation studies** across diverse domains
|
| 179 |
+
|
| 180 |
+
## Citation
|
| 181 |
+
|
| 182 |
+
If you use NanoCrumb, please cite the original Crumb dataset:
|
| 183 |
+
|
| 184 |
+
```bibtex
|
| 185 |
+
@misc{crumb2024,
|
| 186 |
+
title={Crumb: A Comprehensive Retrieval Benchmark},
|
| 187 |
+
author={[Original Crumb Authors]},
|
| 188 |
+
year={2024},
|
| 189 |
+
url={https://huggingface.co/datasets/jfkback/crumb}
|
| 190 |
+
}
|
| 191 |
+
```
|
| 192 |
+
|
| 193 |
+
## License
|
| 194 |
+
|
| 195 |
+
This dataset inherits the license from the original [Crumb dataset](https://huggingface.co/datasets/jfkback/crumb).
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clinical_trial/documents.jsonl
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version https://git-lfs.github.com/spec/v1
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oid sha256:bcb41a1329fdba2ce2736d577b596d0b4fd18911c12a49fc30789d589b67b6a9
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size 45005290
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clinical_trial/qrels.jsonl
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clinical_trial/queries.jsonl
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code_retrieval/documents.jsonl
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code_retrieval/qrels.jsonl
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code_retrieval/queries.jsonl
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version https://git-lfs.github.com/spec/v1
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oid sha256:08f82f8506598114b8b638dee6146576951c86afd3ed51b4cc5436da0f95c5e4
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size 55810985
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legal_qa/documents.jsonl
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legal_qa/qrels.jsonl
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| 1 |
+
{"query_id":"8289","document_id":"756792a22d48aecb3522","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
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| 2 |
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{"query_id":"5278","document_id":"54e928149e4a703a7c95","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
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| 3 |
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{"query_id":"8836","document_id":"11ad3cfb387aa03b5e07","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
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| 5 |
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{"query_id":"5468","document_id":"b45d258be09f5a04df84","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
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{"query_id":"3628","document_id":"6c2db4d97ebcb134f83e","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
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| 7 |
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{"query_id":"3628","document_id":"ad2eb11c9fdc37c81004","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 8 |
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{"query_id":"8230","document_id":"df668c1abcabae8f4bf0","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
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| 9 |
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| 10 |
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{"query_id":"3626","document_id":"ad2eb11c9fdc37c81004","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
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| 12 |
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{"query_id":"1803","document_id":"aa8ac6042407db3fbb8e","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
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| 13 |
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{"query_id":"1803","document_id":"54b9c33c8ac11ffaa24e","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
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| 14 |
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{"query_id":"1803","document_id":"dfbf93549369d4a05830","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
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| 15 |
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| 16 |
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{"query_id":"6695","document_id":"6a5e2309e1af57dce029","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
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| 17 |
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{"query_id":"6695","document_id":"bc48d5ea4e03725133d4","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
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| 18 |
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{"query_id":"2006","document_id":"dca66f45af7e01b3ecf9","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
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| 19 |
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{"query_id":"2006","document_id":"042eb5fb56d0fbc69052","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
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| 20 |
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{"query_id":"746","document_id":"88d01be17e5da01c452c","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
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| 21 |
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{"query_id":"746","document_id":"34dfb2bae33c7ac6ac33","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 22 |
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{"query_id":"1807","document_id":"aa8ac6042407db3fbb8e","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 23 |
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{"query_id":"1807","document_id":"54b9c33c8ac11ffaa24e","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 24 |
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{"query_id":"1807","document_id":"dfbf93549369d4a05830","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 25 |
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{"query_id":"8207","document_id":"b69d27464bb02dd3b4df","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 26 |
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{"query_id":"6657","document_id":"2b490f4e19cfe401efa4","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 27 |
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{"query_id":"6657","document_id":"804d0c78d237f562afbe","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 28 |
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{"query_id":"6657","document_id":"a52d01ede554f194b66e","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 29 |
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{"query_id":"6657","document_id":"7d7244c2c88fca755a0b","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 30 |
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{"query_id":"6657","document_id":"424019537d3986d5024d","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 31 |
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{"query_id":"6657","document_id":"bf8a5cb8858205c2dba7","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 32 |
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{"query_id":"6657","document_id":"8c6d62e3ebe47a1ae227","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 33 |
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{"query_id":"8895","document_id":"5671acf7d5374b788f27","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 34 |
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{"query_id":"4351","document_id":"3415285db992d1d7efae","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 35 |
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{"query_id":"999","document_id":"45de6f10481e8f85916d","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 36 |
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{"query_id":"999","document_id":"113e4086e6bf628a8231","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 37 |
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{"query_id":"999","document_id":"a6673889f5870c03ab8d","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 38 |
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{"query_id":"7125","document_id":"e44be030606ae2c15346","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 39 |
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{"query_id":"7125","document_id":"7e6a6b572ac06819f63f","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 40 |
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{"query_id":"7164","document_id":"25545afb0735d6af58ed","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 41 |
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{"query_id":"7164","document_id":"e5c138c9e7d7f9d7ea6b","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 42 |
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{"query_id":"7164","document_id":"e298511b0ae75ac12ee3","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 43 |
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{"query_id":"7164","document_id":"4e949161b7856c9f2cf9","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 44 |
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{"query_id":"7164","document_id":"dafdeece587bcc6d14a3","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 45 |
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{"query_id":"7164","document_id":"8ad8e0497eb72f99775f","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 46 |
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{"query_id":"7164","document_id":"81fbffd1f749c9470d50","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 47 |
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{"query_id":"7798","document_id":"231127badfabb2faec19","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 48 |
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{"query_id":"7798","document_id":"e05639f55dbaaee4b5a4","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 49 |
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{"query_id":"7688","document_id":"9c111256d9a928e204cc","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 50 |
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{"query_id":"8726","document_id":"bf89cf8efdb978c2d298","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 51 |
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{"query_id":"8726","document_id":"84ac12d75d46745786ea","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 52 |
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{"query_id":"4557","document_id":"3908aaa436be358786c8","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 53 |
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{"query_id":"5379","document_id":"58336d38423ff22e2458","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 54 |
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|
| 55 |
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|
| 56 |
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{"query_id":"4095","document_id":"53f2b5c54c8e18c14705","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 57 |
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|
| 58 |
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{"query_id":"8161","document_id":"d6e08fd5675327b201f4","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 59 |
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{"query_id":"8161","document_id":"bf89cf8efdb978c2d298","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 60 |
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{"query_id":"2797","document_id":"1d58771ef896a5a95277","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 61 |
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{"query_id":"2797","document_id":"c52a6989c7f59bc0658d","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 62 |
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|
| 63 |
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|
| 64 |
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|
| 65 |
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|
| 66 |
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|
| 67 |
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|
| 68 |
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|
| 69 |
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|
| 70 |
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| 71 |
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|
| 72 |
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|
| 73 |
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|
| 74 |
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|
| 75 |
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{"query_id":"1478","document_id":"7150a27563ca709bd993","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 76 |
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{"query_id":"1478","document_id":"14623fc185b8c010099d","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 77 |
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{"query_id":"1478","document_id":"a18682d6969459bdd7de","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 78 |
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{"query_id":"1478","document_id":"1150897b8d260f708c70","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 79 |
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{"query_id":"3988","document_id":"5acad9980d2fee8b4a77","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 80 |
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{"query_id":"5496","document_id":"b5dd3ac6eed78aff2718","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 81 |
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{"query_id":"5496","document_id":"e99e9a2ed66ad037d86d","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 82 |
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{"query_id":"2836","document_id":"caa979fcbb8a2bc2fb4f","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 83 |
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{"query_id":"2836","document_id":"ba0161b8c97b81759d02","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 84 |
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{"query_id":"6063","document_id":"28645ae515b6a15ef0a8","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 85 |
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|
| 86 |
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{"query_id":"6063","document_id":"e6a6d95406f6127e053d","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 87 |
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{"query_id":"8083","document_id":"01c28a38d05f8c1cf8ee","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 88 |
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{"query_id":"2837","document_id":"caa979fcbb8a2bc2fb4f","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 89 |
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{"query_id":"2837","document_id":"ba0161b8c97b81759d02","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 90 |
+
{"query_id":"7628","document_id":"201aefd5b37fd9d147e6","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 91 |
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{"query_id":"7628","document_id":"4c977ef7be4173e8bd62","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 92 |
+
{"query_id":"6250","document_id":"261a8db5a741fb76d476","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 93 |
+
{"query_id":"6250","document_id":"d504a8c22ccadb221aae","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 94 |
+
{"query_id":"3148","document_id":"7141227b12883b8c815c","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 95 |
+
{"query_id":"3836","document_id":"d99d20c7dfdeab532fb6","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 96 |
+
{"query_id":"1771","document_id":"a288ff0c70cb0eb67b02","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 97 |
+
{"query_id":"1771","document_id":"5ddb1aad58f784e4813a","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 98 |
+
{"query_id":"1771","document_id":"55b4818344dd110164f0","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 99 |
+
{"query_id":"1771","document_id":"69f47b590bc2b4e90977","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 100 |
+
{"query_id":"3674","document_id":"8f0182455e626c86f96d","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 101 |
+
{"query_id":"5677","document_id":"ae30f96d6f500eb35f48","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 102 |
+
{"query_id":"2230","document_id":"7e67633a1a35cbc90649","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 103 |
+
{"query_id":"6655","document_id":"2b490f4e19cfe401efa4","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 104 |
+
{"query_id":"6655","document_id":"804d0c78d237f562afbe","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 105 |
+
{"query_id":"6655","document_id":"a52d01ede554f194b66e","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 106 |
+
{"query_id":"6655","document_id":"7d7244c2c88fca755a0b","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 107 |
+
{"query_id":"6655","document_id":"424019537d3986d5024d","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 108 |
+
{"query_id":"6655","document_id":"bf8a5cb8858205c2dba7","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
| 109 |
+
{"query_id":"6655","document_id":"8c6d62e3ebe47a1ae227","relevance_score":1.0,"binary_relevance":1,"task_split":"legal_qa"}
|
legal_qa/queries.jsonl
ADDED
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| 1 |
+
{"query_id":"8289","query_content":"Is the term 'Eviction order' used to refer to the order from the court to the authorities to remove a tenant? In the state of Oklahoma","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"756792a22d48aecb3522","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"ec50e47084e82620a5e2","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Is the term 'Eviction order' used to refer to the order from the court to the authorities to remove a tenant?\", \"state\": \"Oklahoma\", \"answer\": \"No\", \"question_group\": 111, \"original_question\": \"What term is used to refer to the order from the court to the authorities to remove a tenant?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIs the term 'Eviction order' used to refer to the order from the court to the authorities to remove a tenant? In the state of Oklahoma\"}","task_split":"legal_qa"}
|
| 2 |
+
{"query_id":"5278","query_content":"Secondary methods of service are defined as those methods that may be used if the primary method is unsuccessful. Is personal service a permitted secondary method of service permitted for an eviction action? In the state of Alabama","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"54e928149e4a703a7c95","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"234edd08b353eb5b5384","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Secondary methods of service are defined as those methods that may be used if the primary method is unsuccessful. Is personal service a permitted secondary method of service permitted for an eviction action?\", \"state\": \"Alabama\", \"answer\": \"No\", \"question_group\": 118, \"original_question\": \"What are the secondary methods of service that are permitted for an eviction action?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nSecondary methods of service are defined as those methods that may be used if the primary method is unsuccessful. Is personal service a permitted secondary method of service permitted for an eviction action? In the state of Alabama\"}","task_split":"legal_qa"}
|
| 3 |
+
{"query_id":"8836","query_content":"Is an officer of the court an individual empowered by law to execute a writ of eviction? In the state of Alabama","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"11ad3cfb387aa03b5e07","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"b2aeaafb6815a423e3b7","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Is an officer of the court an individual empowered by law to execute a writ of eviction?\", \"state\": \"Alabama\", \"answer\": \"No\", \"question_group\": 103, \"original_question\": \"What entity is responsible for executing a writ of eviction?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIs an officer of the court an individual empowered by law to execute a writ of eviction? In the state of Alabama\"}","task_split":"legal_qa"}
|
| 4 |
+
{"query_id":"2735","query_content":"Is it unlawful to evict a tenant because of their gender identity? In the state of Idaho","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"f7db55c3109d4814a4f7","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"cba08cfddad2a079eefb","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Is it unlawful to evict a tenant because of their gender identity?\", \"state\": \"Idaho\", \"answer\": \"No\", \"question_group\": 66, \"original_question\": \"On what basis is it unlawful to evict a tenant under state\/territory law?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIs it unlawful to evict a tenant because of their gender identity? In the state of Idaho\"}","task_split":"legal_qa"}
|
| 5 |
+
{"query_id":"5468","query_content":"Secondary methods of service are defined as those methods that may be used if the primary method is unsuccessful. Is personal service to a suitable person other than defendant and mail a permitted secondary method of service for an eviction action? In the state of Illinois","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"b45d258be09f5a04df84","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"3712581b40a898ee86f3","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Secondary methods of service are defined as those methods that may be used if the primary method is unsuccessful. Is personal service to a suitable person other than defendant and mail a permitted secondary method of service for an eviction action?\", \"state\": \"Illinois\", \"answer\": \"No\", \"question_group\": 218, \"original_question\": \"What are the secondary methods of service that are permitted for an eviction action?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nSecondary methods of service are defined as those methods that may be used if the primary method is unsuccessful. Is personal service to a suitable person other than defendant and mail a permitted secondary method of service for an eviction action? In the state of Illinois\"}","task_split":"legal_qa"}
|
| 6 |
+
{"query_id":"3628","query_content":"Does the law require landlords to describe repercussions for failure to cure when giving tenants notice to vacate the property? In the state of Illinois","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"6c2db4d97ebcb134f83e","label":1.0},{"id":"ad2eb11c9fdc37c81004","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"3712581b40a898ee86f3","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Does the law require landlords to describe repercussions for failure to cure when giving tenants notice to vacate the property?\", \"state\": \"Illinois\", \"answer\": \"Yes\", \"question_group\": 40, \"original_question\": \"What information does the law require that landlords provide when giving tenants notice to vacate the property prior to terminating a tenancy?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nDoes the law require landlords to describe repercussions for failure to cure when giving tenants notice to vacate the property? In the state of Illinois\"}","task_split":"legal_qa"}
|
| 7 |
+
{"query_id":"8230","query_content":"Is the term 'Writ of execution' used to refer to the order from the court to the authorities to remove a tenant? In the state of North Carolina","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"df668c1abcabae8f4bf0","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"cfabbfa4c26bb2199b84","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Is the term 'Writ of execution' used to refer to the order from the court to the authorities to remove a tenant?\", \"state\": \"North Carolina\", \"answer\": \"No\", \"question_group\": 137, \"original_question\": \"What term is used to refer to the order from the court to the authorities to remove a tenant?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIs the term 'Writ of execution' used to refer to the order from the court to the authorities to remove a tenant? In the state of North Carolina\"}","task_split":"legal_qa"}
|
| 8 |
+
{"query_id":"3690","query_content":"Does the law require landlords to provide the date the rental agreement will terminate when giving tenants notice to vacate the property? In the state of Massachusetts","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"81cd699371092c32aa23","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"de568744fb667519eaf5","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Does the law require landlords to provide the date the rental agreement will terminate when giving tenants notice to vacate the property?\", \"state\": \"Massachusetts\", \"answer\": \"No\", \"question_group\": 220, \"original_question\": \"What information does the law require that landlords provide when giving tenants notice to vacate the property prior to terminating a tenancy?\", \"caveats\": [\"Information on how to cure is only required on a notice terminating an estate at will for nonpayment. Mass. Gen. Laws ch. 186 \\u00a7\\u200212.\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nDoes the law require landlords to provide the date the rental agreement will terminate when giving tenants notice to vacate the property? In the state of Massachusetts\"}","task_split":"legal_qa"}
|
| 9 |
+
{"query_id":"3626","query_content":"Does the law require landlords to provide a reason for eviction when giving tenants notice to vacate the property? In the state of Illinois","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"6c2db4d97ebcb134f83e","label":1.0},{"id":"ad2eb11c9fdc37c81004","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"3712581b40a898ee86f3","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Does the law require landlords to provide a reason for eviction when giving tenants notice to vacate the property?\", \"state\": \"Illinois\", \"answer\": \"No\", \"question_group\": 122, \"original_question\": \"What information does the law require that landlords provide when giving tenants notice to vacate the property prior to terminating a tenancy?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nDoes the law require landlords to provide a reason for eviction when giving tenants notice to vacate the property? In the state of Illinois\"}","task_split":"legal_qa"}
|
| 10 |
+
{"query_id":"1803","query_content":"Can a landlord evict a tenant for breach\/breaking the lease, the rental agreement, or a landlord\u2019s rule? In the state of Washington","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"aa8ac6042407db3fbb8e","label":1.0},{"id":"54b9c33c8ac11ffaa24e","label":1.0},{"id":"dfbf93549369d4a05830","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"16c238590cf685ac9c17","label":1.0},{"id":"d61e479f2be5647d7329","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Can a landlord evict a tenant for breach\/breaking the lease, the rental agreement, or a landlord\\u2019s rule?\", \"state\": \"Washington\", \"answer\": \"Yes\", \"question_group\": 49, \"original_question\": \"For what cause may a landlord evict a tenant?\", \"caveats\": [\"Due to the COVID-19 pandemic, all landlords are prohibited from evicting tenants except where the eviction is necessary to respond to an immediate and significant risk to the health, safety, or property of others, or where the landlord provides 60 days' notice of their intent to sell the property or personally occupy the property as their primary residence. Proclamation by the Governor 20-19.5.\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nCan a landlord evict a tenant for breach\/breaking the lease, the rental agreement, or a landlord\\u2019s rule? In the state of Washington\"}","task_split":"legal_qa"}
|
| 11 |
+
{"query_id":"6695","query_content":"In an eviction action, can a tenant rebut\/raise the defense that the property is uninhabitable? In the state of Delaware","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"c7ea08135bb297e7c311","label":1.0},{"id":"6a5e2309e1af57dce029","label":1.0},{"id":"bc48d5ea4e03725133d4","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"7048f800e6796231093d","label":1.0},{"id":"7c176787f9e97b18dd49","label":1.0},{"id":"7ec6cf026abe475fb5ad","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"In an eviction action, can a tenant rebut\/raise the defense that the property is uninhabitable?\", \"state\": \"Delaware\", \"answer\": \"No\", \"question_group\": 120, \"original_question\": \"What rebuttals are available to a tenant subject to eviction proceedings?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIn an eviction action, can a tenant rebut\/raise the defense that the property is uninhabitable? In the state of Delaware\"}","task_split":"legal_qa"}
|
| 12 |
+
{"query_id":"2006","query_content":"Must a landlord accept a tenant's attempt to cure for substantial damage to property? In the state of Indiana","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"dca66f45af7e01b3ecf9","label":1.0},{"id":"042eb5fb56d0fbc69052","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"0a872ff4f226eac689c6","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Must a landlord accept a tenant's attempt to cure for substantial damage to property?\", \"state\": \"Indiana\", \"answer\": \"Yes\", \"question_group\": 124, \"original_question\": \"For which cause must a landlord accept a tenant's attempt to cure?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nMust a landlord accept a tenant's attempt to cure for substantial damage to property? In the state of Indiana\"}","task_split":"legal_qa"}
|
| 13 |
+
{"query_id":"746","query_content":"Does state\/territory eviction law explicitly regulate floating home landlords? In the state of Oregon","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"88d01be17e5da01c452c","label":1.0},{"id":"34dfb2bae33c7ac6ac33","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"3066fe7ac1c27c1e43fc","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Does state\/territory eviction law explicitly regulate floating home landlords?\", \"state\": \"Oregon\", \"answer\": \"Yes\", \"question_group\": 91, \"original_question\": \"What type(s) of landlord(s) does state\/territory eviction law explicitly regulate?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nDoes state\/territory eviction law explicitly regulate floating home landlords? In the state of Oregon\"}","task_split":"legal_qa"}
|
| 14 |
+
{"query_id":"1807","query_content":"Can a landlord evict a tenant for committing or failing to dispose of waste? In the state of Washington","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"aa8ac6042407db3fbb8e","label":1.0},{"id":"54b9c33c8ac11ffaa24e","label":1.0},{"id":"dfbf93549369d4a05830","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"16c238590cf685ac9c17","label":1.0},{"id":"d61e479f2be5647d7329","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Can a landlord evict a tenant for committing or failing to dispose of waste?\", \"state\": \"Washington\", \"answer\": \"Yes\", \"question_group\": 163, \"original_question\": \"For what cause may a landlord evict a tenant?\", \"caveats\": [\"Due to the COVID-19 pandemic, all landlords are prohibited from evicting tenants except where the eviction is necessary to respond to an immediate and significant risk to the health, safety, or property of others, or where the landlord provides 60 days' notice of their intent to sell the property or personally occupy the property as their primary residence. Proclamation by the Governor 20-19.5.\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nCan a landlord evict a tenant for committing or failing to dispose of waste? In the state of Washington\"}","task_split":"legal_qa"}
|
| 15 |
+
{"query_id":"8207","query_content":"Is the term 'Writ of restitution' used to refer to the order from the court to the authorities to remove a tenant? In the state of New York","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"b69d27464bb02dd3b4df","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"b69d27464bb02dd3b4df","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Is the term 'Writ of restitution' used to refer to the order from the court to the authorities to remove a tenant?\", \"state\": \"New York\", \"answer\": \"No\", \"question_group\": 102, \"original_question\": \"What term is used to refer to the order from the court to the authorities to remove a tenant?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIs the term 'Writ of restitution' used to refer to the order from the court to the authorities to remove a tenant? In the state of New York\"}","task_split":"legal_qa"}
|
| 16 |
+
{"query_id":"6657","query_content":"In an eviction action, can a tenant rebut\/raise the defense that unpaid rent was lawfully withheld? This includes where the law allows a tenant to procure reasonable alternative housing due to lack of repairs or services, and was excused from paying rent, or where the law allows a tenant to abate rent either in part or in full due to lack of repairs. In the state of California","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"2b490f4e19cfe401efa4","label":1.0},{"id":"804d0c78d237f562afbe","label":1.0},{"id":"a52d01ede554f194b66e","label":1.0},{"id":"7d7244c2c88fca755a0b","label":1.0},{"id":"424019537d3986d5024d","label":1.0},{"id":"bf8a5cb8858205c2dba7","label":1.0},{"id":"8c6d62e3ebe47a1ae227","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"ef2b5c835ed19c1ab3a0","label":1.0},{"id":"24cc01db0032aafa1e70","label":1.0},{"id":"ca878147987838d4bfab","label":1.0},{"id":"6239fce887690fa5e680","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"In an eviction action, can a tenant rebut\/raise the defense that unpaid rent was lawfully withheld? This includes where the law allows a tenant to procure reasonable alternative housing due to lack of repairs or services, and was excused from paying rent, or where the law allows a tenant to abate rent either in part or in full due to lack of repairs.\", \"state\": \"California\", \"answer\": \"No\", \"question_group\": 131, \"original_question\": \"What rebuttals are available to a tenant subject to eviction proceedings?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIn an eviction action, can a tenant rebut\/raise the defense that unpaid rent was lawfully withheld? This includes where the law allows a tenant to procure reasonable alternative housing due to lack of repairs or services, and was excused from paying rent, or where the law allows a tenant to abate rent either in part or in full due to lack of repairs. In the state of California\"}","task_split":"legal_qa"}
|
| 17 |
+
{"query_id":"8895","query_content":"Is the marshal an individual empowered by law to execute a writ of eviction? In the state of Florida","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"5671acf7d5374b788f27","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"8573c877351e4d0def4d","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Is the marshal an individual empowered by law to execute a writ of eviction?\", \"state\": \"Florida\", \"answer\": \"No\", \"question_group\": 17, \"original_question\": \"What entity is responsible for executing a writ of eviction?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIs the marshal an individual empowered by law to execute a writ of eviction? In the state of Florida\"}","task_split":"legal_qa"}
|
| 18 |
+
{"query_id":"4351","query_content":"Are eviction cases first heard in magistrates court? In the state of New Mexico","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"3415285db992d1d7efae","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"ce756f76401d835d3697","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Are eviction cases first heard in magistrates court?\", \"state\": \"New Mexico\", \"answer\": \"Yes\", \"question_group\": 76, \"original_question\": \"In which court are eviction cases first heard?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nAre eviction cases first heard in magistrates court? In the state of New Mexico\"}","task_split":"legal_qa"}
|
| 19 |
+
{"query_id":"999","query_content":"Can a landlord evict a tenant for remaining on property after expiration of the lease? In the state of Florida","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"45de6f10481e8f85916d","label":1.0},{"id":"113e4086e6bf628a8231","label":1.0},{"id":"a6673889f5870c03ab8d","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"8573c877351e4d0def4d","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Can a landlord evict a tenant for remaining on property after expiration of the lease?\", \"state\": \"Florida\", \"answer\": \"Yes\", \"question_group\": 130, \"original_question\": \"For what cause may a landlord evict a tenant?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nCan a landlord evict a tenant for remaining on property after expiration of the lease? In the state of Florida\"}","task_split":"legal_qa"}
|
| 20 |
+
{"query_id":"7125","query_content":"In an eviction action, can a tenant use their status as a victim of domestic violence as a rebuttal\/defense? In the state of Oklahoma","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"e44be030606ae2c15346","label":1.0},{"id":"7e6a6b572ac06819f63f","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"e44be030606ae2c15346","label":1.0},{"id":"5fa0d11b875419d35612","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"In an eviction action, can a tenant use their status as a victim of domestic violence as a rebuttal\/defense?\", \"state\": \"Oklahoma\", \"answer\": \"No\", \"question_group\": 171, \"original_question\": \"What rebuttals are available to a tenant subject to eviction proceedings?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIn an eviction action, can a tenant use their status as a victim of domestic violence as a rebuttal\/defense? In the state of Oklahoma\"}","task_split":"legal_qa"}
|
| 21 |
+
{"query_id":"7164","query_content":"In an eviction action, can a tenant raise \"any equitable defense\" available to them? This is true when the relevant law refers broadly to all equitable defenses that might be raised. In the state of Rhode Island","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"25545afb0735d6af58ed","label":1.0},{"id":"e5c138c9e7d7f9d7ea6b","label":1.0},{"id":"e298511b0ae75ac12ee3","label":1.0},{"id":"4e949161b7856c9f2cf9","label":1.0},{"id":"dafdeece587bcc6d14a3","label":1.0},{"id":"8ad8e0497eb72f99775f","label":1.0},{"id":"81fbffd1f749c9470d50","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"b8b4bc32d590eb298296","label":1.0},{"id":"6b102e0f7ab91b06f6ed","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"In an eviction action, can a tenant raise \\\"any equitable defense\\\" available to them? This is true when the relevant law refers broadly to all equitable defenses that might be raised.\", \"state\": \"Rhode Island\", \"answer\": \"No\", \"question_group\": 136, \"original_question\": \"What rebuttals are available to a tenant subject to eviction proceedings?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIn an eviction action, can a tenant raise \\\"any equitable defense\\\" available to them? This is true when the relevant law refers broadly to all equitable defenses that might be raised. In the state of Rhode Island\"}","task_split":"legal_qa"}
|
| 22 |
+
{"query_id":"7798","query_content":"Is the term 'Order of restitution' used to refer to the order from the court to the authorities to remove a tenant? In the state of Illinois","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"231127badfabb2faec19","label":1.0},{"id":"e05639f55dbaaee4b5a4","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"3712581b40a898ee86f3","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Is the term 'Order of restitution' used to refer to the order from the court to the authorities to remove a tenant?\", \"state\": \"Illinois\", \"answer\": \"No\", \"question_group\": 194, \"original_question\": \"What term is used to refer to the order from the court to the authorities to remove a tenant?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIs the term 'Order of restitution' used to refer to the order from the court to the authorities to remove a tenant? In the state of Illinois\"}","task_split":"legal_qa"}
|
| 23 |
+
{"query_id":"7688","query_content":"Is the term 'Order of restitution' used to refer to the order from the court to the authorities to remove a tenant? In the state of Florida","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"9c111256d9a928e204cc","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"8573c877351e4d0def4d","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Is the term 'Order of restitution' used to refer to the order from the court to the authorities to remove a tenant?\", \"state\": \"Florida\", \"answer\": \"No\", \"question_group\": 194, \"original_question\": \"What term is used to refer to the order from the court to the authorities to remove a tenant?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIs the term 'Order of restitution' used to refer to the order from the court to the authorities to remove a tenant? In the state of Florida\"}","task_split":"legal_qa"}
|
| 24 |
+
{"query_id":"8726","query_content":"Does a tenant's ongoing military service require the postponement of the execution of a writ of eviction? In the state of New Jersey","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"bf89cf8efdb978c2d298","label":1.0},{"id":"84ac12d75d46745786ea","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"bf89cf8efdb978c2d298","label":1.0},{"id":"84ac12d75d46745786ea","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Does a tenant's ongoing military service require the postponement of the execution of a writ of eviction?\", \"state\": \"New Jersey\", \"answer\": \"No\", \"question_group\": 42, \"original_question\": \"What circumstances postpone the execution of a writ of eviction?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nDoes a tenant's ongoing military service require the postponement of the execution of a writ of eviction? In the state of New Jersey\"}","task_split":"legal_qa"}
|
| 25 |
+
{"query_id":"4557","query_content":"Are eviction cases first heard in court of common pleas? In the state of Vermont","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"3908aaa436be358786c8","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"deec29364d24507edba9","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Are eviction cases first heard in court of common pleas?\", \"state\": \"Vermont\", \"answer\": \"No\", \"question_group\": 175, \"original_question\": \"In which court are eviction cases first heard?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nAre eviction cases first heard in court of common pleas? In the state of Vermont\"}","task_split":"legal_qa"}
|
| 26 |
+
{"query_id":"5379","query_content":"Secondary methods of service are defined as those methods that may be used if the primary method is unsuccessful. Are certified mail and regular mail a permitted secondary methods of service for an eviction action? In the state of Delaware","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"58336d38423ff22e2458","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"3cf3e59806196e09e6c5","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Secondary methods of service are defined as those methods that may be used if the primary method is unsuccessful. Are certified mail and regular mail a permitted secondary methods of service for an eviction action?\", \"state\": \"Delaware\", \"answer\": \"No\", \"question_group\": 138, \"original_question\": \"What are the secondary methods of service that are permitted for an eviction action?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nSecondary methods of service are defined as those methods that may be used if the primary method is unsuccessful. Are certified mail and regular mail a permitted secondary methods of service for an eviction action? In the state of Delaware\"}","task_split":"legal_qa"}
|
| 27 |
+
{"query_id":"7440","query_content":"When a tenant appeals, is the execution of eviction stayed for the duration of the pending appeal? In the state of Nebraska","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"01c28a38d05f8c1cf8ee","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"11f2cd73f245b67157c7","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"When a tenant appeals, is the execution of eviction stayed for the duration of the pending appeal?\", \"state\": \"Nebraska\", \"answer\": \"Yes\", \"question_group\": 87, \"original_question\": \"In eviction proceedings, for how long does the filing of an appeal stay an execution?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nWhen a tenant appeals, is the execution of eviction stayed for the duration of the pending appeal? In the state of Nebraska\"}","task_split":"legal_qa"}
|
| 28 |
+
{"query_id":"4095","query_content":"Is it specified in which court eviction cases are first heard? In the state of Idaho","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"649455ca22df2f8e96f7","label":1.0},{"id":"53f2b5c54c8e18c14705","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"13810edb195fc4f9a842","label":1.0},{"id":"a17b3e7b2e02e48737d2","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Is it specified in which court eviction cases are first heard?\", \"state\": \"Idaho\", \"answer\": \"Yes\", \"question_group\": 178, \"original_question\": \"In which court are eviction cases first heard?\", \"caveats\": [\"A district judge may refer unlawful detainer actions to the magistrates' division of the district court. Idaho Code \\u00a7 1-2208(1)(b).\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIs it specified in which court eviction cases are first heard? In the state of Idaho\"}","task_split":"legal_qa"}
|
| 29 |
+
{"query_id":"8161","query_content":"Is the term 'Writ of habere facias possessionem' used to refer to the order from the court to the authorities to remove a tenant? In the state of New Jersey","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"f670872bf1c4a301274e","label":1.0},{"id":"d6e08fd5675327b201f4","label":1.0},{"id":"bf89cf8efdb978c2d298","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"f670872bf1c4a301274e","label":1.0},{"id":"d6e08fd5675327b201f4","label":1.0},{"id":"bf89cf8efdb978c2d298","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Is the term 'Writ of habere facias possessionem' used to refer to the order from the court to the authorities to remove a tenant?\", \"state\": \"New Jersey\", \"answer\": \"No\", \"question_group\": 55, \"original_question\": \"What term is used to refer to the order from the court to the authorities to remove a tenant?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIs the term 'Writ of habere facias possessionem' used to refer to the order from the court to the authorities to remove a tenant? In the state of New Jersey\"}","task_split":"legal_qa"}
|
| 30 |
+
{"query_id":"2797","query_content":"Is it unlawful to evict a tenant because they are part of two or more of the federally protected classes under the Fair Housing Act (race, color, religion, national origin, sex, disability, and familial status)? In the state of Kansas","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"1d58771ef896a5a95277","label":1.0},{"id":"c52a6989c7f59bc0658d","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"c08ebf9555427f51949e","label":1.0},{"id":"372e8984e8da062ba024","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Is it unlawful to evict a tenant because they are part of two or more of the federally protected classes under the Fair Housing Act (race, color, religion, national origin, sex, disability, and familial status)?\", \"state\": \"Kansas\", \"answer\": \"Yes\", \"question_group\": 123, \"original_question\": \"On what basis is it unlawful to evict a tenant under state\/territory law?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIs it unlawful to evict a tenant because they are part of two or more of the federally protected classes under the Fair Housing Act (race, color, religion, national origin, sex, disability, and familial status)? In the state of Kansas\"}","task_split":"legal_qa"}
|
| 31 |
+
{"query_id":"6652","query_content":"In an eviction action, can a tenant rebut\/raise the defense that they lawfully deducted repair costs from the rent? This is when the law allows them to make repairs and deduct the cost of the repairs from the rent, or when the law allows a tenant to pay for utility services the landlord failed to pay, then deduct the cost from rent. In the state of California","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"2b490f4e19cfe401efa4","label":1.0},{"id":"804d0c78d237f562afbe","label":1.0},{"id":"a52d01ede554f194b66e","label":1.0},{"id":"7d7244c2c88fca755a0b","label":1.0},{"id":"424019537d3986d5024d","label":1.0},{"id":"bf8a5cb8858205c2dba7","label":1.0},{"id":"8c6d62e3ebe47a1ae227","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"ef2b5c835ed19c1ab3a0","label":1.0},{"id":"24cc01db0032aafa1e70","label":1.0},{"id":"ca878147987838d4bfab","label":1.0},{"id":"6239fce887690fa5e680","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"In an eviction action, can a tenant rebut\/raise the defense that they lawfully deducted repair costs from the rent? This is when the law allows them to make repairs and deduct the cost of the repairs from the rent, or when the law allows a tenant to pay for utility services the landlord failed to pay, then deduct the cost from rent.\", \"state\": \"California\", \"answer\": \"No\", \"question_group\": 54, \"original_question\": \"What rebuttals are available to a tenant subject to eviction proceedings?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIn an eviction action, can a tenant rebut\/raise the defense that they lawfully deducted repair costs from the rent? This is when the law allows them to make repairs and deduct the cost of the repairs from the rent, or when the law allows a tenant to pay for utility services the landlord failed to pay, then deduct the cost from rent. In the state of California\"}","task_split":"legal_qa"}
|
| 32 |
+
{"query_id":"4292","query_content":"Are eviction cases first heard in municipal court? In the state of Nebraska","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"d254c984fe7b027daa22","label":1.0},{"id":"d394d5fb24cca32678f7","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"d254c984fe7b027daa22","label":1.0},{"id":"928e55c4f35bb4f21633","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Are eviction cases first heard in municipal court?\", \"state\": \"Nebraska\", \"answer\": \"No\", \"question_group\": 35, \"original_question\": \"In which court are eviction cases first heard?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nAre eviction cases first heard in municipal court? In the state of Nebraska\"}","task_split":"legal_qa"}
|
| 33 |
+
{"query_id":"692","query_content":"Does state\/territory eviction law explicitly regulate landlords with minimal rental properties? This includes includes: landlords who own five or fewer single family homes; landlords who own three or less homes or rental properties; and owners of three or less condominium or cooperative units. In the state of Missouri","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"e7eeb67b2f0277d29a6c","label":1.0},{"id":"432c593ce730a7fc3d22","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"317778ca8b314e7c336e","label":1.0},{"id":"1708479d4fca9c453246","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Does state\/territory eviction law explicitly regulate landlords with minimal rental properties? This includes includes: landlords who own five or fewer single family homes; landlords who own three or less homes or rental properties; and owners of three or less condominium or cooperative units.\", \"state\": \"Missouri\", \"answer\": \"No\", \"question_group\": 32, \"original_question\": \"What type(s) of landlord(s) does state\/territory eviction law explicitly regulate?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nDoes state\/territory eviction law explicitly regulate landlords with minimal rental properties? This includes includes: landlords who own five or fewer single family homes; landlords who own three or less homes or rental properties; and owners of three or less condominium or cooperative units. In the state of Missouri\"}","task_split":"legal_qa"}
|
| 34 |
+
{"query_id":"777","query_content":"Does state\/territory eviction law explicitly regulate landlords with minimal rental properties? This includes includes: landlords who own five or fewer single family homes; landlords who own three or less homes or rental properties; and owners of three or less condominium or cooperative units. In the state of Utah","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"76b1fe862073ae115aef","label":1.0},{"id":"1cf8ef7ea4042f1dac69","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"0bfb7f138b713bf18f8b","label":1.0},{"id":"3c01783549b171d9218d","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Does state\/territory eviction law explicitly regulate landlords with minimal rental properties? This includes includes: landlords who own five or fewer single family homes; landlords who own three or less homes or rental properties; and owners of three or less condominium or cooperative units.\", \"state\": \"Utah\", \"answer\": \"No\", \"question_group\": 32, \"original_question\": \"What type(s) of landlord(s) does state\/territory eviction law explicitly regulate?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nDoes state\/territory eviction law explicitly regulate landlords with minimal rental properties? This includes includes: landlords who own five or fewer single family homes; landlords who own three or less homes or rental properties; and owners of three or less condominium or cooperative units. In the state of Utah\"}","task_split":"legal_qa"}
|
| 35 |
+
{"query_id":"1478","query_content":"Can a landlord evict a tenant for violating statutory tenant obligations? In the state of North Carolina","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"7150a27563ca709bd993","label":1.0},{"id":"14623fc185b8c010099d","label":1.0},{"id":"a18682d6969459bdd7de","label":1.0},{"id":"1150897b8d260f708c70","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"d1662e2ae9cd96c49922","label":1.0},{"id":"cfabbfa4c26bb2199b84","label":1.0},{"id":"b6b6303f6ed128aeb6c8","label":1.0},{"id":"814c1bcecc98b9c81a70","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Can a landlord evict a tenant for violating statutory tenant obligations?\", \"state\": \"North Carolina\", \"answer\": \"No\", \"question_group\": 195, \"original_question\": \"For what cause may a landlord evict a tenant?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nCan a landlord evict a tenant for violating statutory tenant obligations? In the state of North Carolina\"}","task_split":"legal_qa"}
|
| 36 |
+
{"query_id":"3988","query_content":"Are eviction cases first heard in superior court? In the state of California","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"5acad9980d2fee8b4a77","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"4e7c53d267192c17bcc3","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Are eviction cases first heard in superior court?\", \"state\": \"California\", \"answer\": \"Yes\", \"question_group\": 53, \"original_question\": \"In which court are eviction cases first heard?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nAre eviction cases first heard in superior court? In the state of California\"}","task_split":"legal_qa"}
|
| 37 |
+
{"query_id":"5496","query_content":"Secondary methods of service are defined as those methods that may be used if the primary method is unsuccessful. Is publication and mail used a permitted secondary method of service for an eviction action? In the state of Iowa","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"b5dd3ac6eed78aff2718","label":1.0},{"id":"e99e9a2ed66ad037d86d","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"141f6da548fa73caf78a","label":1.0},{"id":"15caf1d0050e1c290d4b","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Secondary methods of service are defined as those methods that may be used if the primary method is unsuccessful. Is publication and mail used a permitted secondary method of service for an eviction action?\", \"state\": \"Iowa\", \"answer\": \"No\", \"question_group\": 135, \"original_question\": \"What are the secondary methods of service that are permitted for an eviction action?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nSecondary methods of service are defined as those methods that may be used if the primary method is unsuccessful. Is publication and mail used a permitted secondary method of service for an eviction action? In the state of Iowa\"}","task_split":"legal_qa"}
|
| 38 |
+
{"query_id":"2836","query_content":"Is it specified on what basis it is unlawful to evict a tenant under state\/territory law? In the state of Maine","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"caa979fcbb8a2bc2fb4f","label":1.0},{"id":"ba0161b8c97b81759d02","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"c627f8b640263bf25182","label":1.0},{"id":"73aa84c67768c22d489b","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Is it specified on what basis it is unlawful to evict a tenant under state\/territory law?\", \"state\": \"Maine\", \"answer\": \"Yes\", \"question_group\": 165, \"original_question\": \"On what basis is it unlawful to evict a tenant under state\/territory law?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIs it specified on what basis it is unlawful to evict a tenant under state\/territory law? In the state of Maine\"}","task_split":"legal_qa"}
|
| 39 |
+
{"query_id":"6063","query_content":"Is it required that the evictions summons served to tenants describe list the reason for eviction? In the state of Colorado","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"28645ae515b6a15ef0a8","label":1.0},{"id":"28d6901b68571fc9c9c6","label":1.0},{"id":"e6a6d95406f6127e053d","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"4e89eb8c98545a0e3e98","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Is it required that the evictions summons served to tenants describe list the reason for eviction?\", \"state\": \"Colorado\", \"answer\": \"Yes\", \"question_group\": 1, \"original_question\": \"What must be included on summons served to tennants prior to eviction hearings?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIs it required that the evictions summons served to tenants describe list the reason for eviction? In the state of Colorado\"}","task_split":"legal_qa"}
|
| 40 |
+
{"query_id":"8083","query_content":"Is the term 'Order of possession' used to refer to the order from the court to the authorities to remove a tenant? In the state of Nebraska","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"01c28a38d05f8c1cf8ee","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"779f76e4ddcbcbe8494a","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Is the term 'Order of possession' used to refer to the order from the court to the authorities to remove a tenant?\", \"state\": \"Nebraska\", \"answer\": \"No\", \"question_group\": 79, \"original_question\": \"What term is used to refer to the order from the court to the authorities to remove a tenant?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIs the term 'Order of possession' used to refer to the order from the court to the authorities to remove a tenant? In the state of Nebraska\"}","task_split":"legal_qa"}
|
| 41 |
+
{"query_id":"2837","query_content":"Is it unlawful to evict a tenant based on military or veteran status? In the state of Maine","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"caa979fcbb8a2bc2fb4f","label":1.0},{"id":"ba0161b8c97b81759d02","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"c627f8b640263bf25182","label":1.0},{"id":"73aa84c67768c22d489b","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Is it unlawful to evict a tenant based on military or veteran status?\", \"state\": \"Maine\", \"answer\": \"No\", \"question_group\": 75, \"original_question\": \"On what basis is it unlawful to evict a tenant under state\/territory law?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIs it unlawful to evict a tenant based on military or veteran status? In the state of Maine\"}","task_split":"legal_qa"}
|
| 42 |
+
{"query_id":"7628","query_content":"Is the term 'Execution' used to refer to the order from the court to the authorities to remove a tenant? In the state of Connecticut","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"201aefd5b37fd9d147e6","label":1.0},{"id":"4c977ef7be4173e8bd62","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"16a6348d1fcec3300527","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Is the term 'Execution' used to refer to the order from the court to the authorities to remove a tenant?\", \"state\": \"Connecticut\", \"answer\": \"Yes\", \"question_group\": 199, \"original_question\": \"What term is used to refer to the order from the court to the authorities to remove a tenant?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIs the term 'Execution' used to refer to the order from the court to the authorities to remove a tenant? In the state of Connecticut\"}","task_split":"legal_qa"}
|
| 43 |
+
{"query_id":"6250","query_content":"Is it specified what must be included on the summons? In the state of Missouri","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"261a8db5a741fb76d476","label":1.0},{"id":"d504a8c22ccadb221aae","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"60eccacdaab27484fe2a","label":1.0},{"id":"1a040295a019c5e31d14","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Is it specified what must be included on the summons?\", \"state\": \"Missouri\", \"answer\": \"Yes\", \"question_group\": 151, \"original_question\": \"What must be included on summons served to tennants prior to eviction hearings?\", \"caveats\": [\"Summons for nonpayment actions must direct the tenant to appear before the judge and show cause why the possession of the property should not be restored to the landlord. Mo. Rev. Stat. \\u00a7 535.020. Summons content for other types of evictions are not specified.\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIs it specified what must be included on the summons? In the state of Missouri\"}","task_split":"legal_qa"}
|
| 44 |
+
{"query_id":"3148","query_content":"Is it unlawful to evict a tenant because of their age? In the state of Puerto Rico","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"7141227b12883b8c815c","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"f917a3dbd4fbe79e44cb","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Is it unlawful to evict a tenant because of their age?\", \"state\": \"Puerto Rico\", \"answer\": \"No\", \"question_group\": 81, \"original_question\": \"On what basis is it unlawful to evict a tenant under state\/territory law?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIs it unlawful to evict a tenant because of their age? In the state of Puerto Rico\"}","task_split":"legal_qa"}
|
| 45 |
+
{"query_id":"3836","query_content":"Does the law require landlords to provide information on how to cure when giving tenants notice to vacate the property? In the state of Virginia","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"d99d20c7dfdeab532fb6","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"e4bf63ea0b93e5fd8d7b","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Does the law require landlords to provide information on how to cure when giving tenants notice to vacate the property?\", \"state\": \"Virginia\", \"answer\": \"Yes\", \"question_group\": 5, \"original_question\": \"What information does the law require that landlords provide when giving tenants notice to vacate the property prior to terminating a tenancy?\", \"caveats\": [\"Information on how to cure and the amount owed are only required in a notice for termination based on nonpayment. Va. Code \\u00a7 55.1-1245.\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nDoes the law require landlords to provide information on how to cure when giving tenants notice to vacate the property? In the state of Virginia\"}","task_split":"legal_qa"}
|
| 46 |
+
{"query_id":"1771","query_content":"Can a landlord evict a tenant for nonpayment of rent? In the state of Vermont","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"a288ff0c70cb0eb67b02","label":1.0},{"id":"5ddb1aad58f784e4813a","label":1.0},{"id":"55b4818344dd110164f0","label":1.0},{"id":"69f47b590bc2b4e90977","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"fc9fa90f8857c9541c1f","label":1.0},{"id":"40fec1416d724f9c47c0","label":1.0},{"id":"9f90a976e05b013178eb","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Can a landlord evict a tenant for nonpayment of rent?\", \"state\": \"Vermont\", \"answer\": \"Yes\", \"question_group\": 65, \"original_question\": \"For what cause may a landlord evict a tenant?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nCan a landlord evict a tenant for nonpayment of rent? In the state of Vermont\"}","task_split":"legal_qa"}
|
| 47 |
+
{"query_id":"3674","query_content":"Does the law require landlords to provide information on how to cure when giving tenants notice to vacate the property? In the state of Maine","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"8f0182455e626c86f96d","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"73aa84c67768c22d489b","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Does the law require landlords to provide information on how to cure when giving tenants notice to vacate the property?\", \"state\": \"Maine\", \"answer\": \"Yes\", \"question_group\": 5, \"original_question\": \"What information does the law require that landlords provide when giving tenants notice to vacate the property prior to terminating a tenancy?\", \"caveats\": [\"All notices must include the reason for termination and a statement that the tenant has the right to contest termination in court. Me. Rev. Stat. tit. 14, \\u00a7 6002. Nonpayment notices must also include the amount owed and how to cure. Me. Rev. Stat. tit. 14, \\u00a7 6002(2). The statutory requirements for notice contents apply to tenancies where the lease does not include a provision to terminate the tenancy or does not provide for any written notice of termination in the event of a material breach of the lease. 14 M.R.S.A. \\u00a7 6001(1-B); Me. Rev. Stat. tit. 14, \\u00a7 6002.\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nDoes the law require landlords to provide information on how to cure when giving tenants notice to vacate the property? In the state of Maine\"}","task_split":"legal_qa"}
|
| 48 |
+
{"query_id":"5677","query_content":"Secondary methods of service are defined as those methods that may be used if the primary method is unsuccessful. Is publication a permitted secondary method of service for an eviction action? In the state of Nebraska","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"ae30f96d6f500eb35f48","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"8125f96dbc1c6367d9af","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Secondary methods of service are defined as those methods that may be used if the primary method is unsuccessful. Is publication a permitted secondary method of service for an eviction action?\", \"state\": \"Nebraska\", \"answer\": \"No\", \"question_group\": 180, \"original_question\": \"What are the secondary methods of service that are permitted for an eviction action?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nSecondary methods of service are defined as those methods that may be used if the primary method is unsuccessful. Is publication a permitted secondary method of service for an eviction action? In the state of Nebraska\"}","task_split":"legal_qa"}
|
| 49 |
+
{"query_id":"2230","query_content":"Must a landlord accept a tenant's attempt to cure for material breach? In the state of Utah","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"7e67633a1a35cbc90649","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"2de66d2848360300f344","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"Must a landlord accept a tenant's attempt to cure for material breach?\", \"state\": \"Utah\", \"answer\": \"No\", \"question_group\": 157, \"original_question\": \"For which cause must a landlord accept a tenant's attempt to cure?\", \"caveats\": [\"Although breaches generally can be cured, subletting or assigning in violation of a lease cannot be cured. Utah Code \\u00a7 78B-6-802(1)(d), (h); see also Utah Code \\u00a7 78B-6-802(2).\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nMust a landlord accept a tenant's attempt to cure for material breach? In the state of Utah\"}","task_split":"legal_qa"}
|
| 50 |
+
{"query_id":"6655","query_content":"In an eviction action, can a tenant rebut\/raise the defense that eviction is unlawful because it was motivated by a legally recognized form of discrimination? In the state of California","instruction":"Given a legal question, find relevant statutes that can help answer it","passage_qrels":[{"id":"2b490f4e19cfe401efa4","label":1.0},{"id":"804d0c78d237f562afbe","label":1.0},{"id":"a52d01ede554f194b66e","label":1.0},{"id":"7d7244c2c88fca755a0b","label":1.0},{"id":"424019537d3986d5024d","label":1.0},{"id":"bf8a5cb8858205c2dba7","label":1.0},{"id":"8c6d62e3ebe47a1ae227","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"ef2b5c835ed19c1ab3a0","label":1.0},{"id":"24cc01db0032aafa1e70","label":1.0},{"id":"ca878147987838d4bfab","label":1.0},{"id":"6239fce887690fa5e680","label":1.0}],"use_max_p":false,"metadata":"{\"question\": \"In an eviction action, can a tenant rebut\/raise the defense that eviction is unlawful because it was motivated by a legally recognized form of discrimination?\", \"state\": \"California\", \"answer\": \"Yes\", \"question_group\": 8, \"original_question\": \"What rebuttals are available to a tenant subject to eviction proceedings?\", \"caveats\": [\"\"], \"query_with_instruction\": \"Given a legal question, find relevant statutes that can help answer it\\nIn an eviction action, can a tenant rebut\/raise the defense that eviction is unlawful because it was motivated by a legally recognized form of discrimination? In the state of California\"}","task_split":"legal_qa"}
|
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|
| 1 |
+
{"query_id":"sustainable_living:29","document_id":"solar_car\/Solarcellefficiency.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 2 |
+
{"query_id":"sustainable_living:29","document_id":"solar_car\/Solarcellefficiency.txt:1","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 3 |
+
{"query_id":"sustainable_living:29","document_id":"solar_car\/Solarcellefficiency.txt:4","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 4 |
+
{"query_id":"biology:77","document_id":"shut_down_conciousness\/Neocortex.txt:2","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 5 |
+
{"query_id":"biology:77","document_id":"shut_down_conciousness\/Neocortex.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 6 |
+
{"query_id":"biology:29","document_id":"reddish_adapt_to_color\/Afterimage.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 7 |
+
{"query_id":"biology:29","document_id":"reddish_adapt_to_color\/Afterimage.txt:1","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 8 |
+
{"query_id":"sustainable_living:59","document_id":"chicken_lawn\/howstartfoodforest4863665.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 9 |
+
{"query_id":"economics:60","document_id":"inflation_interest\/neofisherismpdf.txt:6","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 10 |
+
{"query_id":"economics:60","document_id":"inflation_interest\/neofisherismpdf.txt:4","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 11 |
+
{"query_id":"economics:60","document_id":"inflation_interest\/neofisherismpdf.txt:3","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 12 |
+
{"query_id":"economics:60","document_id":"inflation_interest\/neofisherismpdf.txt:5","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 13 |
+
{"query_id":"economics:45","document_id":"tesla_free_charging\/Complementarygood.txt:1","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 14 |
+
{"query_id":"economics:45","document_id":"tesla_free_charging\/Complementarygood.txt:2","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 15 |
+
{"query_id":"economics:45","document_id":"tesla_free_charging\/Complementarygood.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 16 |
+
{"query_id":"economics:27","document_id":"oil_price_cap\/businessreview20220928willanoilpricecapmanagetoreducethepdf.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 17 |
+
{"query_id":"biology:89","document_id":"fainting_mechanism\/Reflex_syncope.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 18 |
+
{"query_id":"biology:89","document_id":"fainting_mechanism\/Reflex_syncope.txt:1","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 19 |
+
{"query_id":"sustainable_living:94","document_id":"renewable_energy\/241RaugeiEROIEPrevisedII201203VMFpdf.txt:9","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 20 |
+
{"query_id":"sustainable_living:94","document_id":"renewable_energy\/241RaugeiEROIEPrevisedII201203VMFpdf.txt:7","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 21 |
+
{"query_id":"sustainable_living:94","document_id":"renewable_energy\/241RaugeiEROIEPrevisedII201203VMFpdf.txt:8","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 22 |
+
{"query_id":"biology:75","document_id":"ring_finger_not_move\/Extrinsic_extensor_muscles_of_the_hand.txt:3","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 23 |
+
{"query_id":"biology:75","document_id":"ring_finger_not_move\/Extrinsic_extensor_muscles_of_the_hand.txt:4","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 24 |
+
{"query_id":"biology:75","document_id":"ring_finger_not_move\/Extrinsic_extensor_muscles_of_the_hand.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 25 |
+
{"query_id":"sustainable_living:40","document_id":"ceremics\/pageid56.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 26 |
+
{"query_id":"sustainable_living:70","document_id":"banana_peel\/Arebananapeelshigherinpotassiumandmagnesiumthanthefruititself.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 27 |
+
{"query_id":"sustainable_living:70","document_id":"banana_peel\/Arebananapeelshigherinpotassiumandmagnesiumthanthefruititself.txt:4","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 28 |
+
{"query_id":"sustainable_living:70","document_id":"banana_peel\/Arebananapeelshigherinpotassiumandmagnesiumthanthefruititself.txt:1","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 29 |
+
{"query_id":"sustainable_living:70","document_id":"banana_peel\/Arebananapeelshigherinpotassiumandmagnesiumthanthefruititself.txt:2","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 30 |
+
{"query_id":"sustainable_living:70","document_id":"banana_peel\/Arebananapeelshigherinpotassiumandmagnesiumthanthefruititself.txt:3","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 31 |
+
{"query_id":"robotics:61","document_id":"crazy_file_add_variable\/pythonapi.txt:7","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 32 |
+
{"query_id":"biology:49","document_id":"brain_train_neural_network\/Hebbian_theory.txt:1","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 33 |
+
{"query_id":"biology:49","document_id":"brain_train_neural_network\/Hebbian_theory.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 34 |
+
{"query_id":"sustainable_living:7","document_id":"inner_insulation\/Passivesolarbuildingdesign.txt:5","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 35 |
+
{"query_id":"sustainable_living:7","document_id":"inner_insulation\/Passivesolarbuildingdesign.txt:6","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 36 |
+
{"query_id":"sustainable_living:7","document_id":"inner_insulation\/Passivesolarbuildingdesign.txt:2","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 37 |
+
{"query_id":"sustainable_living:7","document_id":"inner_insulation\/Passivesolarbuildingdesign.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 38 |
+
{"query_id":"sustainable_living:7","document_id":"inner_insulation\/Passivesolarbuildingdesign.txt:4","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 39 |
+
{"query_id":"psychology:35","document_id":"vengeance\/p8418n91jpdf.txt:8","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 40 |
+
{"query_id":"psychology:35","document_id":"vengeance\/p8418n91jpdf.txt:16","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 41 |
+
{"query_id":"psychology:35","document_id":"vengeance\/p8418n91jpdf.txt:13","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 42 |
+
{"query_id":"psychology:35","document_id":"vengeance\/p8418n91jpdf.txt:7","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 43 |
+
{"query_id":"psychology:35","document_id":"vengeance\/p8418n91jpdf.txt:12","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 44 |
+
{"query_id":"psychology:35","document_id":"vengeance\/p8418n91jpdf.txt:10","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 45 |
+
{"query_id":"psychology:35","document_id":"vengeance\/p8418n91jpdf.txt:11","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 46 |
+
{"query_id":"psychology:35","document_id":"vengeance\/p8418n91jpdf.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 47 |
+
{"query_id":"psychology:35","document_id":"vengeance\/p8418n91jpdf.txt:5","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 48 |
+
{"query_id":"psychology:35","document_id":"vengeance\/p8418n91jpdf.txt:3","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 49 |
+
{"query_id":"psychology:35","document_id":"vengeance\/p8418n91jpdf.txt:15","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 50 |
+
{"query_id":"psychology:35","document_id":"vengeance\/p8418n91jpdf.txt:14","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 51 |
+
{"query_id":"psychology:35","document_id":"vengeance\/p8418n91jpdf.txt:1","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 52 |
+
{"query_id":"psychology:35","document_id":"vengeance\/p8418n91jpdf.txt:4","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 53 |
+
{"query_id":"psychology:35","document_id":"vengeance\/p8418n91jpdf.txt:6","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 54 |
+
{"query_id":"psychology:35","document_id":"vengeance\/p8418n91jpdf.txt:2","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 55 |
+
{"query_id":"psychology:35","document_id":"vengeance\/p8418n91jpdf.txt:9","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 56 |
+
{"query_id":"biology:31","document_id":"neanderthals_vitamin_C_diet\/L-gulonolactone_oxidase.txt:2","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 57 |
+
{"query_id":"biology:31","document_id":"neanderthals_vitamin_C_diet\/L-gulonolactone_oxidase.txt:1","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 58 |
+
{"query_id":"sustainable_living:95","document_id":"fresh_air_car\/useherbsasanallnaturalairfreshener5944860.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 59 |
+
{"query_id":"sustainable_living:56","document_id":"certificate\/2562pdf.txt:15","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 60 |
+
{"query_id":"economics:22","document_id":"bid_auction\/ci112pdf.txt:5","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 61 |
+
{"query_id":"economics:22","document_id":"bid_auction\/ci112pdf.txt:3","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 62 |
+
{"query_id":"economics:38","document_id":"matching_price\/matchingordersasp.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 63 |
+
{"query_id":"economics:38","document_id":"matching_price\/matchingordersasp.txt:1","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 64 |
+
{"query_id":"robotics:14","document_id":"odometry_trajectory\/PlotJuggler.txt:1","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 65 |
+
{"query_id":"robotics:14","document_id":"odometry_trajectory\/PlotJuggler.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 66 |
+
{"query_id":"sustainable_living:16","document_id":"spring_store_energy\/S187661021502576Xpdf.txt:6","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 67 |
+
{"query_id":"sustainable_living:45","document_id":"meal_kit\/comparisonlifecycleenvironmentalimpactsmealkitsand.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 68 |
+
{"query_id":"robotics:89","document_id":"moveit_config\/setupassistanttutori.txt:2","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 69 |
+
{"query_id":"robotics:89","document_id":"moveit_config\/setupassistanttutori.txt:4","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 70 |
+
{"query_id":"robotics:89","document_id":"moveit_config\/setupassistanttutori.txt:3","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 71 |
+
{"query_id":"robotics:89","document_id":"moveit_config\/setupassistanttutori.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 72 |
+
{"query_id":"robotics:89","document_id":"moveit_config\/setupassistanttutori.txt:1","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 73 |
+
{"query_id":"economics:15","document_id":"ceopay\/ExecutiveExcess1999pdf.txt:8","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 74 |
+
{"query_id":"sustainable_living:61","document_id":"meat_chicken\/Feedconversionrateforchickens.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 75 |
+
{"query_id":"psychology:34","document_id":"men_women_science\/19883140.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 76 |
+
{"query_id":"sustainable_living:81","document_id":"earth_warm\/geothermalenergymarketglobalindustryanalysissizesharegrowthtrendsandforecast20122018262290htm.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 77 |
+
{"query_id":"psychology:50","document_id":"fasting_workout\/5911317.txt:8","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 78 |
+
{"query_id":"psychology:50","document_id":"fasting_workout\/5911317.txt:2","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 79 |
+
{"query_id":"psychology:50","document_id":"fasting_workout\/5911317.txt:13","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 80 |
+
{"query_id":"psychology:50","document_id":"fasting_workout\/5911317.txt:1","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 81 |
+
{"query_id":"psychology:50","document_id":"fasting_workout\/5911317.txt:3","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 82 |
+
{"query_id":"psychology:50","document_id":"fasting_workout\/5911317.txt:16","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 83 |
+
{"query_id":"psychology:50","document_id":"fasting_workout\/5911317.txt:12","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 84 |
+
{"query_id":"psychology:50","document_id":"fasting_workout\/5911317.txt:14","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
|
| 85 |
+
{"query_id":"psychology:50","document_id":"fasting_workout\/5911317.txt:9","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"psychology:50","document_id":"fasting_workout\/5911317.txt:7","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"psychology:50","document_id":"fasting_workout\/5911317.txt:5","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"psychology:50","document_id":"fasting_workout\/5911317.txt:4","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"psychology:50","document_id":"fasting_workout\/5911317.txt:6","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"psychology:50","document_id":"fasting_workout\/5911317.txt:11","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"psychology:50","document_id":"fasting_workout\/5911317.txt:10","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"psychology:50","document_id":"fasting_workout\/5911317.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"psychology:50","document_id":"fasting_workout\/5911317.txt:15","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"sustainable_living:50","document_id":"shutdown_sleep\/indexhtm.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"sustainable_living:93","document_id":"aquaponics\/Gaslift.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"sustainable_living:93","document_id":"aquaponics\/Gaslift.txt:1","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"biology:16","document_id":"electrical_shock_freeze_up_muscles\/Tetanic_contraction.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"biology:102","document_id":"yeast_dissolve_in_sugar\/Osmosis.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"sustainable_living:47","document_id":"non_organic\/section205203.txt:1","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"economics:98","document_id":"treatment_difference\/180309015.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"sustainable_living:10","document_id":"wood_CO2\/stationaryemissions32016pdf.txt:32","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"sustainable_living:10","document_id":"wood_CO2\/stationaryemissions32016pdf.txt:31","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"biology:101","document_id":"eyes_tired\/Computer_vision_syndrome.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"sustainable_living:41","document_id":"foam\/Expandedpolyethylene.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"sustainable_living:41","document_id":"foam\/whatkindofpolyethylenematerialcanberecycledhtml.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"sustainable_living:31","document_id":"inefficient_driving\/rderealdrivingemissionstest.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"sustainable_living:66","document_id":"water_plant\/SolubleSalts.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"sustainable_living:66","document_id":"water_plant\/SolubleSalts.txt:1","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"sustainable_living:44","document_id":"data_center_heat\/wasteheatenergyreusehtml.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"psychology:20","document_id":"psycho_flow\/Flowpsychology.txt:6","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"psychology:20","document_id":"psycho_flow\/Flowpsychology.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"biology:52","document_id":"3D_vision\/Binocular_disparity.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"biology:52","document_id":"3D_vision\/Binocular_disparity.txt:1","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"biology:52","document_id":"3D_vision\/Binocular_disparity.txt:2","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"economics:8","document_id":"gdp_wellbeing\/wellbeingandgdphtm.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"robotics:99","document_id":"gz_sim\/edit.txt:6","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"psychology:98","document_id":"selection_bias\/Selectionbias.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"psychology:98","document_id":"selection_bias\/Selectionbias.txt:1","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"psychology:98","document_id":"selection_bias\/Selectionbias.txt:2","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"psychology:98","document_id":"selection_bias\/Selectionbias.txt:3","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"economics:70","document_id":"Irreversibility\/Irreversibleprocess.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"biology:85","document_id":"cancer_not_communicable\/Clonally_transmissible_cancer.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"psychology:29","document_id":"verbal_memory\/02687030701803788.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"psychology:29","document_id":"verbal_memory\/02687030701803788.txt:1","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"query_id":"psychology:29","document_id":"verbal_memory\/Memoryspan.txt:0","relevance_score":1.0,"binary_relevance":1,"task_split":"stack_exchange"}
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{"document_id":"230","document_content":"\\begin{definition}[Definition:Angular Momentum]\nThe '''angular momentum''' of a body about a point $P$ is its moment of inertia about $P$ multiplied by its angular velocity about $P$.\nAngular momentum is a vector quantity.\n{{expand|Separate out into orbital angular momentum and spin angular momentum.}}\n\\end{definition}","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"2380","document_content":"\\begin{definition}[Definition:Differential Equation\/Ordinary]\nAn '''ordinary differential equation''' (abbreviated '''O.D.E.''' or '''ODE''') is a '''differential equation''' which has exactly one independent variable.\nAll the derivatives occurring in it are therefore ordinary.\nThe general '''ODE''' of order $n$ is:\n:$\\map f {x, y, \\dfrac {\\d x} {\\d y}, \\dfrac {\\d^2 x} {\\d y^2}, \\ldots, \\dfrac {\\d^n x} {\\d y^n} } = 0$\nor, using the prime notation:\n:$\\map f {x, y, y', y'', \\ldots, y^{\\paren n} } = 0$\n\\end{definition}","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"2723","document_content":"\\begin{definition}[Definition:Eigenvector\/Linear Operator]\nLet $K$ be a field.\nLet $V$ be a vector space over $K$. \nLet $A : V \\to V$ be a linear operator.\nLet $\\lambda \\in K$ be an eigenvalue of $A$.\nA non-zero vector $v \\in V$ is an '''eigenvector corresponding to $\\lambda$''' {{iff}}:\n:$v \\in \\map \\ker {A - \\lambda I}$\nwhere: \n:$I : V \\to V$ is the identity mapping on $V$\n:$\\map \\ker {A - \\lambda I}$ denotes the kernel of $A - \\lambda I$.\nThat is, {{iff}}: \n:$A v = \\lambda v$\n\\end{definition}","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"2724","document_content":"\\begin{definition}[Definition:Eigenvector\/Real Square Matrix]\nLet $\\mathbf A$ be a square matrix of order $n$ over $\\R$. \nLet $\\lambda \\in \\R$ be an eigenvalue of $\\mathbf A$. \nA non-zero vector $\\mathbf v \\in \\R^n$ is an '''eigenvector corresponding to $\\lambda$''' {{iff}}: \n:$\\mathbf A \\mathbf v = \\lambda \\mathbf v$\n\\end{definition}","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"3778","document_content":"\\begin{definition}[Definition:Girth]\nLet $G$ be a graph.\nThe '''girth''' of $G$ is the smallest length of any cycle in $G$.\nAn acyclic graph is defined as having a girth of infinity.\nCategory:Definitions\/Graph Theory\n\\end{definition}","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"3830","document_content":"\\begin{definition}[Definition:Gravity\/Gravitational Force]\nThe '''gravitational force''' on a body $B$ is the force which is exerted on $B$ as a result of the gravitational field whose influence it is under.\n\\end{definition}","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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| 7 |
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{"document_id":"4138","document_content":"\\begin{definition}[Definition:Hypothesis Test]\nA '''hypothesis test''' is a rule that specifies, for a null hypothesis $H_0$ and alternative hypothesis $H_1$: \n* For which sample values the decision is made to accept $H_0$.\n* For which sample values $H_0$ is rejected and $H_1$ is accepted.\n\\end{definition}","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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| 8 |
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{"document_id":"5249","document_content":"\\begin{definition}[Definition:Local Gravitational Constant]\nThe '''local gravitational constant''' is the value of the acceleration $g$ caused by the gravitational field given rise to by whatever body or bodies are in a position to exert that gravitational force.\nIn the everyday context, $g$ is the acceleration due to the gravitational field of Earth at whatever point on or near its surface the observer happens to be.\nThus in this context it is approximately equal to $9 \\cdotp 8 \\ \\mathrm m \\ \\mathrm s^{-2}$.\n\\end{definition}","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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| 9 |
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{"document_id":"5461","document_content":"\\begin{definition}[Definition:Markov Chain]\nLet $\\sequence {X_n}_{n \\mathop \\ge 0}$ be a stochastic process over a countable set $S$.\nLet $\\map \\Pr X$ denote the probability of the random variable $X$.\nLet $\\sequence {X_n}_{n \\mathop \\ge 0}$ satisfy the Markov property:\n:$\\condprob {X_{n + 1} = i_{n + 1} } {X_0 = i_0, X_1 = i_1, \\ldots, X_n = i_n} = \\condprob {X_{n + 1} = i_{n + 1} } {X_n = i_n}$\nfor all $n \\ge 0$ and all $i_0, i_1, \\ldots, i_{n + 1} \\in S$.\nThat is, such that the conditional probability of $X_{i + 1}$ is dependent only upon $X_i$ and upon no earlier values of $\\sequence {X_n}$.\nThat is, the state of $\\sequence {X_n}$ in the future is unaffected by its history.\nThen $\\sequence {X_n}_{n \\mathop \\ge 0}$ is a '''Markov chain'''.\n\\end{definition}","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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| 10 |
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{"document_id":"5725","document_content":"\\begin{definition}[Definition:Minor of Determinant]\nLet $\\mathbf A = \\sqbrk a_n$ be a square matrix of order $n$.\nConsider the order $k$ square submatrix $\\mathbf B$ obtained by deleting $n - k$ rows and $n - k$ columns from $\\mathbf A$.\nLet $\\map \\det {\\mathbf B}$ denote the determinant of $\\mathbf B$.\nThen $\\map \\det {\\mathbf B}$ is an '''order-$k$ minor''' of $\\map \\det {\\mathbf A}$.\nThus a '''minor''' is a determinant formed from the elements (in the same relative order) of $k$ specified rows and columns.\n\\end{definition}","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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| 11 |
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{"document_id":"7627","document_content":"\\begin{definition}[Definition:Ramsey Number]\nRamsey's Theorem states that in any coloring of the edges of a sufficiently large complete graph, one will find monochromatic complete subgraphs.\nMore precisely, for any given number of colors $c$, and any given integers $n_1, \\ldots, n_c$, there is a number $\\map R {n_1, \\ldots, n_c}$ such that:\n:if the edges of a complete graph of order $\\map R {n_1, \\ldots, n_c}$ are colored with $c$ different colours, then for some $i$ between $1$ and $c$, it must contain a complete subgraph of order $n_i$ whose edges are all color $i$.\nThis number $\\map R {n_1, \\ldots, n_c}$ is called the '''Ramsey number''' for $n_1, \\ldots, n_c$.\n{{NamedforDef|Frank Plumpton Ramsey|cat = Ramsey}}\nCategory:Definitions\/Ramsey Theory\n\\end{definition}","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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| 12 |
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{"document_id":"8388","document_content":"\\begin{definition}[Definition:Series\/Complex]\nLet $\\sequence {a_n}$ be a sequence in $\\C$.\nA '''complex series''' $S_n$ is the limit to infinity of the sequence of partial sums of a complex sequence $\\sequence {a_n}$:\n{{begin-eqn}}\n{{eqn | l = S_n\n | r = \\lim_{N \\mathop \\to \\infty} \\sum_{n \\mathop = 1}^N a_n\n | c = \n}}\n{{eqn | r = \\sum_{n \\mathop = 1}^\\infty a_n\n | c = \n}}\n{{eqn | r = a_1 + a_2 + a_3 + \\cdots\n | c = \n}}\n{{end-eqn}}\n\\end{definition}","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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| 13 |
+
{"document_id":"8392","document_content":"\\begin{definition}[Definition:Series\/Real]\nA '''real series''' $S_n$ is the limit to infinity of the sequence of partial sums of a real sequence $\\sequence {a_n}$:\n{{begin-eqn}}\n{{eqn | l = S_n\n | r = \\lim_{N \\mathop \\to \\infty} \\sum_{n \\mathop = 1}^N a_n\n | c = \n}}\n{{eqn | r = \\sum_{n \\mathop = 1}^\\infty a_n\n | c = \n}}\n{{eqn | r = a_1 + a_2 + a_3 + \\cdots\n | c = \n}}\n{{end-eqn}}\n\\end{definition}","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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| 14 |
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{"document_id":"8547","document_content":"\\begin{definition}[Definition:Simple Harmonic Motion\/Frequency]\nConsider a physical system $S$ in a state of simple harmonic motion:\n:$x = A \\map \\sin {\\omega t + \\phi}$\nThe '''frequency''' $\\nu$ of the motion of $S$ is the number of complete cycles per unit time:\n:$\\nu = \\dfrac 1 T = \\dfrac \\omega {2 \\pi}$\n\\end{definition}","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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| 15 |
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{"document_id":"8569","document_content":"\\begin{definition}[Definition:Simultaneous Equations\/Solution Set]\nConsider the system of $m$ simultaneous equations in $n$ variables:\n:$\\mathbb S := \\forall i \\in \\set {1, 2, \\ldots, m} : \\map {f_i} {x_1, x_2, \\ldots x_n} = \\beta_i$\nLet $\\mathbb X$ be the set of ordered $n$-tuples:\n:$\\set {\\sequence {x_j}_{j \\mathop \\in \\set {1, 2, \\ldots, n} }: \\forall i \\in \\set {1, 2, \\ldots, m}: \\map {f_i} {\\sequence {x_j} } = \\beta_i}$\nwhich satisfies each of the equations in $\\mathbb S$.\nThen $\\mathbb X$ is called the '''solution set''' of $\\mathbb S$.\nThus to '''solve''' a system of simultaneous equations is to find all the elements of $\\mathbb X$\n\\end{definition}","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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| 16 |
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{"document_id":"8903","document_content":"\\begin{definition}[Definition:Stirling Numbers of the Second Kind\/Definition 1]\n'''Stirling numbers of the second kind''' are defined recursively by:\n:$\\ds {n \\brace k} := \\begin{cases}\n\\delta_{n k} & : k = 0 \\text{ or } n = 0 \\\\\n& \\\\\n\\ds {n - 1 \\brace k - 1} + k {n - 1 \\brace k} & : \\text{otherwise} \\\\\n\\end{cases}$\nwhere:\n: $\\delta_{n k}$ is the Kronecker delta\n: $n$ and $k$ are non-negative integers.\n\\end{definition}","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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| 17 |
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{"document_id":"9320","document_content":"\\begin{definition}[Definition:Test Statistic]\nLet $\\theta$ be a population parameter of some population $P$. \nLet $\\Omega$ be the parameter space of $\\theta$. \nLet $\\mathbf X$ be a random sample from $P$. \nLet $T = \\map f {\\mathbf X}$ be a sample statistic.\nLet $\\delta$ be a test procedure of the form: \n:reject $H_0$ if $T \\in C$\nfor some null hypothesis $H_0$ and some $C \\subset \\Omega$.\nWe refer to $T$ as the '''test statistic''' of $\\delta$.\n\\end{definition}","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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| 18 |
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{"document_id":"10462","document_content":"\\section{Multinomial Coefficient expressed as Product of Binomial Coefficients}\nTags: Multinomial Coefficients, Binomial Coefficients\n\n\\begin{theorem}\n:$\\dbinom {k_1 + k_2 + \\cdots + k_m} {k_1, k_2, \\ldots, k_m} = \\dbinom {k_1 + k_2} {k_1} \\dbinom {k_1 + k_2 + k_3} {k_1 + k_2} \\cdots \\dbinom {k_1 + k_2 + \\cdots + k_m} {k_1 + k_2 + \\cdots + k_{m - 1} }$\nwhere:\n:$\\dbinom {k_1 + k_2 + \\cdots + k_m} {k_1, k_2, \\ldots, k_m}$ denotes a multinomial coefficient\n:$\\dbinom {k_1 + k_2} {k_1}$ etc. denotes binomial coefficients.\n\\end{theorem}\n\n\\begin{proof}\nThe proof proceeds by induction.\nFor all $m \\in \\Z_{> 1}$, let $\\map P m$ be the proposition:\n:$\\dbinom {k_1 + k_2 + \\cdots + k_m} {k_1, k_2, \\ldots, k_m} = \\dbinom {k_1 + k_2} {k_1} \\dbinom {k_1 + k_2 + k_3} {k_1 + k_2} \\cdots \\dbinom {k_1 + k_2 + \\cdots + k_m} {k_1 + k_2 + \\cdots + k_{m - 1} }$\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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| 19 |
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{"document_id":"10463","document_content":"\\section{Multinomial Theorem}\nTags: Multinomial Coefficients, Binomial Coefficients, Discrete Mathematics, Proofs by Induction, Algebra\n\n\\begin{theorem}\nLet $x_1, x_2, \\ldots, x_k \\in F$, where $F$ is a field.\nThen:\n:$\\ds \\paren {x_1 + x_2 + \\cdots + x_m}^n = \\sum_{k_1 \\mathop + k_2 \\mathop + \\mathop \\cdots \\mathop + k_m \\mathop = n} \\binom n {k_1, k_2, \\ldots, k_m} {x_1}^{k_1} {x_2}^{k_2} \\cdots {x_m}^{k_m}$\nwhere:\n:$m \\in \\Z_{> 0}$ is a positive integer\n:$n \\in \\Z_{\\ge 0}$ is a non-negative integer\n:$\\dbinom n {k_1, k_2, \\ldots, k_m} = \\dfrac {n!} {k_1! \\, k_2! \\, \\cdots k_m!}$ denotes a multinomial coefficient.\nThe sum is taken for all non-negative integers $k_1, k_2, \\ldots, k_m$ such that $k_1 + k_2 + \\cdots + k_m = n$, and with the understanding that wherever $0^0$ may appear it shall be considered to have a value of $1$.\nThe '''multinomial theorem''' is a generalization of the Binomial Theorem.\n\\end{theorem}\n\n\\begin{proof}\nThe proof proceeds by induction on $m$.\nFor each $m \\in \\N_{\\ge 1}$, let $\\map P m$ be the proposition:\n:$\\ds \\forall n \\in \\N: \\paren {x_1 + x_2 + \\cdots + x_m}^n = \\sum_{k_1 \\mathop + k_2 \\mathop + \\mathop \\cdots \\mathop + k_m \\mathop = n} \\binom n {k_1, k_2, \\ldots, k_m} {x_1}^{k_1} {x_2}^{k_2} \\cdots {x_m}^{k_m}$\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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| 20 |
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{"document_id":"10521","document_content":"\\section{Modulus of Limit}\nTags: Modulus of Limit, Limits of Sequences\n\n\\begin{theorem}\nLet $X$ be one of the standard number fields $\\Q, \\R, \\C$.\nLet $\\sequence {x_n}$ be a sequence in $X$.\nLet $\\sequence {x_n}$ be convergent to the limit $l$.\nThat is, let $\\ds \\lim_{n \\mathop \\to \\infty} x_n = l$.\nThen\n:$\\ds \\lim_{n \\mathop \\to \\infty} \\cmod {x_n} = \\cmod l$\nwhere $\\cmod {x_n}$ is the modulus of $x_n$.\n\\end{theorem}\n\n\\begin{proof}\nBy the Triangle Inequality, we have:\n:$\\cmod {\\cmod {x_n} - \\cmod l} \\le \\cmod {x_n - l}$\nHence by the Squeeze Theorem and Convergent Sequence Minus Limit, $\\cmod {x_n} \\to \\cmod l$ as $n \\to \\infty$.\n{{Qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"10794","document_content":"\\section{Mean Value Theorem}\nTags: Differential Calculus, Named Theorems, Mean Value Theorem\n\n\\begin{theorem}\nLet $f$ be a real function which is continuous on the closed interval $\\closedint a b$ and differentiable on the open interval $\\openint a b$.\nThen:\n:$\\exists \\xi \\in \\openint a b: \\map {f'} \\xi = \\dfrac {\\map f b - \\map f a} {b - a}$\n\\end{theorem}\n\n\\begin{proof}\nFor any constant $h \\in \\R$ we may construct the real function defined on $\\closedint a b$ by:\n:$\\map F x = \\map f x + h x$\nWe have that $h x$ is continuous on $\\closedint a b$ from Linear Function is Continuous.\nFrom the Sum Rule for Continuous Functions, $F$ is continuous on $\\closedint a b$ and differentiable on $\\openint a b$.\nLet us calculate what the constant $h$ has to be such that $\\map F a = \\map F b$:\n{{begin-eqn}}\n{{eqn | l = \\map F a\n | r = \\map F b\n | c = \n}}\n{{eqn | ll= \\leadsto\n | l = \\map f a + h a\n | r = \\map f b + h b\n | c = \n}}\n{{eqn | ll= \\leadsto\n | l = \\map f a - \\map f b\n | r = h b - h a\n | c = rearranging\n}}\n{{eqn | ll= \\leadsto\n | l = \\map f a - \\map f b\n | r = h \\paren {b - a}\n | c = Real Multiplication Distributes over Real Addition\n}}\n{{eqn | ll= \\leadsto\n | l = h\n | r = -\\dfrac {\\map f b - \\map f a} {b - a}\n | c = rearranging\n}}\n{{end-eqn}}\nSince $F$ satisfies the conditions for the application of Rolle's Theorem:\n:$\\exists \\xi \\in \\openint a b: \\map {F'} \\xi = 0$\nBut then:\n:$\\map {F'} \\xi = \\map {f'} \\xi + h = 0$\nThe result follows.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"11018","document_content":"\\section{Liouville's Theorem (Complex Analysis)}\nTags: Complex Analysis, Named Theorems\n\n\\begin{theorem}\nLet $f: \\C \\to \\C$ be a bounded entire function.\nThen $f$ is constant.\n\\end{theorem}\n\n\\begin{proof}\nBy assumption, there is $M \\ge 0$ such that $\\cmod {\\map f z} \\le M$ for all $z \\in \\C$. \nFor any $R \\in \\R: R > 0$, consider the function:\n:$\\map {f_R} z := \\map f {R z}$\nUsing the Cauchy Integral Formula, we see that:\n:$\\ds \\cmod {\\map {f_R'} z} = \\frac 1 {2 \\pi} \\cmod {\\int_{\\map {C_1} z} \\frac {\\map f w} {\\paren {w - z}^2} \\rd w} \\le \\frac 1 {2 \\pi} \\int_{\\map {C_1} z} M \\rd w = M$\nwhere $\\map {C_1} z$ denotes the circle of radius $1$ around $z$.\nHence:\n:$\\ds \\cmod {\\map {f'} z} = \\cmod {\\map {f_R'} z} \/ R \\le M \/ R$\nSince $R$ was arbitrary, it follows that $\\cmod {\\map {f'} z} = 0$ for all $z \\in \\C$.\nThus $f$ is constant.\n{{qed}}\n{{MissingLinks}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"11239","document_content":"\\section{Linear Bound Lemma}\nTags: Named Theorems, Graph Theory\n\n\\begin{theorem}\nFor a simple connected planar graph $G_n$, where $n \\ge 3$ is a number of vertices:\n:$m \\le 3 n \u2212 6$, where $m$ is a number of edges.\n\\end{theorem}\n\n\\begin{proof}\nLet $f$ denote the number of faces of $G_n$. \nLet the sequence $\\sequence {s_i}_{i \\mathop = 1}^f$ be the regions of a planar embedding of $G_n$. \nConsider the sequence $\\sequence {r_i}_{i \\mathop = 1}^f$ where $r_i$ denotes the number of boundary edges for $s_i$. \nSince $G$ is simple, then (by the definition of planar embedding): \n* every region has at least $3$ boundary edges\n* every edge is a boundary edge of at most two regions in the planar embedding.\nUsing this two facts, we can find the boundary for $\\ds \\sum_{i \\mathop = 1}^f r_i$ as:\n:$3 f \\le \\ds \\sum_{i \\mathop = 1}^f r_i \\le 2m$\nNow calculating the Euler Polyhedron Formula with $f \\le 2 m \/3$, we will arrive to $m \\le 3 n \u2212 6$.\n{{qed}}\nCategory:Graph Theory\nCategory:Named Theorems\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"11276","document_content":"\\section{Limit Comparison Test}\nTags: Convergence Tests, Series\n\n\\begin{theorem}\nLet $\\sequence {a_n}$ and $\\sequence {b_n}$ be sequences in $\\R$.\nLet $\\ds \\frac {a_n} {b_n} \\to l$ as $n \\to \\infty$ where $l \\in \\R_{>0}$.\nThen the series $\\ds \\sum_{n \\mathop = 1}^\\infty a_n$ and $\\ds \\sum_{n \\mathop = 1}^\\infty b_n$ are either both convergent or both divergent.\n\\end{theorem}\n\n\\begin{proof}\nLet $\\ds \\sum_{n \\mathop = 1}^\\infty b_n$ be convergent.\nThen by Terms in Convergent Series Converge to Zero, $\\sequence {b_n}$ converges to zero.\nA Convergent Sequence is Bounded.\nSo it follows that:\n:$\\exists H: \\forall n \\in \\N_{>0}: a_n \\le H b_n$\nThus, by the corollary to the Comparison Test, $\\ds \\sum_{n \\mathop = 1}^\\infty a_n$ is convergent.\nSince $l > 0$, from Sequence Converges to Within Half Limit:\n:$\\exists N: \\forall n > N: a_n > \\dfrac 1 2 l b_n$\nHence the convergence of $\\ds \\sum_{n \\mathop = 1}^\\infty a_n$ implies the convergence of $\\ds \\sum_{n \\mathop = 1}^\\infty b_n$.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"11426","document_content":"\\section{Lebesgue Measure is Diffuse}\nTags: Measure Theory, Lebesgue Measure, Diffuse Measures\n\n\\begin{theorem}\nLet $\\lambda^n$ be Lebesgue measure on $\\R^n$.\nThen $\\lambda^n$ is a diffuse measure.\n\\end{theorem}\n\n\\begin{proof}\nA singleton $\\set {\\mathbf x} \\subseteq \\R^n$ is seen to be closed by combining:\n:Euclidean Space is Complete Metric Space\n:Metric Space is Hausdorff\n:Corollary to Compact Subspace of Hausdorff Space is Closed\nHence by Closed Set Measurable in Borel Sigma-Algebra:\n:$\\set {\\mathbf x} \\in \\map \\BB {\\R^n}$\nwhere $\\map \\BB {\\R^n}$ is the Borel $\\sigma$-algebra on $\\R^n$.\nWrite $\\mathbf x + \\epsilon = \\tuple {x_1 + \\epsilon, \\ldots, x_n + \\epsilon}$ for $\\epsilon > 0$.\nThen:\n:$\\ds \\set {\\mathbf x} = \\bigcap_{m \\mathop \\in \\N} \\horectr {\\mathbf x} {\\mathbf x + \\frac 1 m}$\nwhere $\\\\horectr {\\mathbf x} {\\mathbf x + \\dfrac 1 m}$ is a half-open $n$-rectangle.\n{{handwaving|justify equality}}\nBy definition of Lebesgue measure, we have (for all $m \\in \\N$):\n:$\\ds \\map {\\lambda^n} {\\horectr {\\mathbf x} {\\mathbf x + \\frac 1 m} } = \\prod_{i \\mathop = 1}^n \\frac 1 m = m^{-n}$\nFrom Characterization of Measures, it follows that:\n:$\\ds \\map {\\lambda^n} {\\set {\\mathbf x} } = \\lim_{m \\mathop \\to \\infty} m^{-n}$\nwhich equals $0$ from Sequence of Powers of Reciprocals is Null Sequence.\nTherefore, for each $\\mathbf x \\in \\R^n$:\n:$\\map {\\lambda^n} {\\set {\\mathbf x} } = 0$\nthat is, $\\lambda^n$ is a diffuse measure.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"11592","document_content":"\\section{L'H\u00f4pital's Rule}\nTags: Calculus, limits, derivatives, infinity, zero, Calculus, Limits, L'H\u00f4pital's Rule, Limits of Real Functions, Limits of Functions, Differential Calculus, Named Theorems, Calculus, Limits\n\n\\begin{theorem}\nLet $f$ and $g$ be real functions which are continuous on the closed interval $\\closedint a b$ and differentiable on the open interval $\\openint a b$.\nLet:\n:$\\forall x \\in \\openint a b: \\map {g'} x \\ne 0$\nwhere $g'$ denotes the derivative of $g$ {{WRT|Differentiation}} $x$.\nLet:\n:$\\map f a = \\map g a = 0$\nThen:\n:$\\ds \\lim_{x \\mathop \\to a^+} \\frac {\\map f x} {\\map g x} = \\lim_{x \\mathop \\to a^+} \\frac {\\map {f'} x} {\\map {g'} x}$\nprovided that the second limit exists.\n\\end{theorem}\n\n\\begin{proof}\nLet $l = \\displaystyle \\lim_{x \\to a^+} {f' \\left({x}\\right)} {g' \\left({x}\\right)}$.\nLet $\\epsilon > 0$.\nBy the definition of limit, we ought to find a $\\delta > 0$ such that:\n:$\\forall x: \\left\\vert{x - a}\\right\\vert < \\delta \\implies \\left\\vert{ \\dfrac {f \\left({x}\\right)} {g \\left({x}\\right)} - l }\\right\\vert < \\epsilon$\nFix $\\delta$ such that:\n:$\\forall x: \\left\\vert{x - a}\\right\\vert < \\delta \\implies \\left\\vert{ \\dfrac {f' \\left({x}\\right)} {g' \\left({x}\\right)} - l }\\right\\vert < \\epsilon$\nwhich is possible by the definition of limit.\nLet $x$ be such that $\\left\\vert{x - a}\\right\\vert < \\delta$.\nBy the Cauchy Mean Value Theorem with $b = x$:\n: $\\exists \\xi \\in \\left({a \\,.\\,.\\, x}\\right): \\dfrac {f' \\left({\\xi}\\right)} {g' \\left({\\xi}\\right)} = \\dfrac {f \\left({x}\\right) - f \\left({a}\\right)} {g \\left({x}\\right) - g \\left({a}\\right)}$\nSince $f \\left({a}\\right) = g \\left({a}\\right) = 0$, we have:\n: $\\exists \\xi \\in \\left({a \\,.\\,.\\, x}\\right): \\dfrac {f' \\left({\\xi}\\right)} {g' \\left({\\xi}\\right)} = \\dfrac {f \\left({x}\\right)} {g \\left({x}\\right)}$\nNow, as $a < \\xi < x$, it follows that $\\left\\vert{\\xi - a}\\right\\vert < \\delta$ as well.\nTherefore:\n:$\\left\\vert{ \\dfrac {f \\left({x}\\right)} {g \\left({x}\\right)} - l }\\right\\vert = \\left\\vert{ \\dfrac {f' \\left({\\xi}\\right)} {g' \\left({\\xi}\\right)} - l }\\right\\vert < \\epsilon$\nwhich leads us to the desired conclusion that:\n:$\\displaystyle \\lim_{x \\to a^+} \\frac {f \\left({x}\\right)} {g \\left({x}\\right)} = \\lim_{x \\to a^+} \\frac {f^{\\prime} \\left({x}\\right)} {g^{\\prime} \\left({x}\\right)}$\n{{qed}}\n{{namedfor|Guillaume de l'H\u00f4pital|cat=L'H\u00f4pital}}\nHowever, this result was in fact discovered by Johann Bernoulli.\nBecause of variants in the rendition of his name, this proof is often seen written as '''L'Hospital's Rule'''.\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"11617","document_content":"\\section{Jensen's Inequality (Measure Theory)\/Concave Functions}\nTags: Measure Theory\n\n\\begin{theorem}\nLet $\\struct {X, \\Sigma, \\mu}$ be a measure space.\nLet $f: X \\to \\R$ be a $\\mu$-integrable function such that $f \\ge 0$ pointwise.\nLet $\\Lambda: \\hointr 0 \\infty \\to \\hointr 0 \\infty$ be a concave function.\nThen for all positive measurable functions $g: X \\to \\R$, $g \\in \\map {\\MM^+} \\Sigma$:\n:$\\dfrac {\\int \\paren {\\Lambda \\circ g} \\cdot f \\rd \\mu} {\\int f \\rd \\mu} \\le \\map \\Lambda {\\dfrac {\\int g \\cdot f \\rd \\mu} {\\int f \\rd \\mu} }$\nwhere $\\circ$ denotes composition, and $\\cdot$ denotes pointwise multiplication.\n\\end{theorem}\n\n\\begin{proof}\n{{proof wanted}}\nCategory:Measure Theory\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"11618","document_content":"\\section{Jensen's Inequality (Measure Theory)\/Convex Functions}\nTags: Measure Theory\n\n\\begin{theorem}\nLet $\\struct {X, \\Sigma, \\mu}$ be a measure space.\nLet $f: X \\to \\R$ be a $\\mu$-integrable function such that $f \\ge 0$ pointwise.\nLet $V: \\hointr 0 \\infty \\to \\hointr 0 \\infty$ be a convex function.\nThen for all positive measurable functions $g: X \\to \\R$, $g \\in \\map {\\MM^+} \\Sigma$:\n:$\\map V {\\dfrac {\\int g \\cdot f \\rd \\mu} {\\int f \\rd \\mu} } \\le \\dfrac {\\int \\paren {V \\circ g} \\cdot f \\rd \\mu} {\\int f \\rd \\mu}$\nwhere $\\circ$ denotes composition, and $\\cdot$ denotes pointwise multiplication.\n\\end{theorem}\n\n\\begin{proof}\n{{MissingLinks}}\nLet $\\d \\map \\nu x := \\dfrac {\\map f x} {\\int \\map f s \\rd \\map \\mu s} \\rd \\map \\mu x$ be a probability measure.\n{{explain|This proof invokes a probability measure. Needs to be for a measure space. Does the proof work for both?}}\nLet $\\ds x_0 := \\int \\map g s \\rd \\map \\nu s$.\nThen by convexity there exists constants $a, b$ such that:\n{{begin-eqn}}\n{{eqn | l = \\map V {x_0}\n | r = a x_0 + b\n}}\n{{eqn | q = \\forall x \\in \\R_{\\ge 0}\n | l = \\map V x\n | o = \\ge\n | r = a x + b\n}}\n{{end-eqn}}\nIn other words, there is a tangent line at $\\tuple {x_0, V_0}$ that falls below the graph of $V$.\nTherefore:\n{{begin-eqn}}\n{{eqn | l = \\map V {\\map g s}\n | o = \\ge\n | r = a \\map g s + b\n | c = \n}}\n{{eqn | ll= \\leadsto\n | l = \\int \\map V {\\map g s} \\rd \\map \\nu s\n | o = \\ge\n | r = a \\int \\map g s \\rd \\map \\nu s + b\n | c = Integration {{WRT|Integration}} $\\map \\nu s$\n}}\n{{eqn | r = \\map V {x_0}\n | c = \n}}\n{{eqn | r = \\map V {\\int \\map g s \\rd \\map \\nu s}\n | c = \n}}\n{{end-eqn}}\n{{explain|why this does what it purports to}}\nCategory:Measure Theory\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"11619","document_content":"\\section{Jensen's Inequality (Real Analysis)}\nTags: Jensen's Inequality (Real Analysis), Inequalities, Real Analysis, Analysis\n\n\\begin{theorem}\nLet $I$ be a real interval.\nLet $\\phi: I \\to \\R$ be a convex function.\nLet $x_1, x_2, \\ldots, x_n \\in I$.\nLet $\\lambda_1, \\lambda_2, \\ldots, \\lambda_n \\ge 0$ be real numbers, at least one of which is non-zero.\nThen:\n:$\\ds \\map \\phi {\\frac {\\sum_{k \\mathop = 1}^n \\lambda_k x_k} {\\sum_{k \\mathop = 1}^n \\lambda_k} } \\le \\frac {\\sum_{k \\mathop = 1}^n \\lambda_k \\map \\phi {x_k} } {\\sum_{k \\mathop = 1}^n \\lambda_k}$\nFor $\\phi$ strictly convex, equality holds {{iff}} $x_1 = x_2 = \\cdots = x_n$.\n\\end{theorem}\n\n\\begin{proof}\nThe proof proceeds by mathematical induction on $n$.\nFor all $n \\in \\N_{> 0}$, let $\\map P n$ be the proposition:\n:$\\ds \\map \\phi {\\frac {\\sum_{k \\mathop = 1}^n \\lambda_k x_k} {\\sum_{k \\mathop = 1}^n \\lambda_k} } \\le \\frac {\\sum_{k \\mathop = 1}^n \\lambda_k \\map \\phi {x_k} } {\\sum_{k \\mathop = 1}^n \\lambda_k}$\n$\\map P 1$ is true, as this just says:\n:$\\ds \\map \\phi {\\frac {\\lambda_1 x_1} {\\lambda_1} } \\le \\frac {\\lambda_1 \\map \\phi {x_1} } {\\lambda_1}$\n{{begin-eqn}}\n{{eqn | l = \\map \\phi {\\frac {\\lambda_1 x_1} {\\lambda_1} }\n | r = \\map \\phi {x_1}\n | c = \n}}\n{{eqn | r = \\frac {\\lambda_1 \\map \\phi {x_1} } {\\lambda_1}\n | c = \n}}\n{{end-eqn}}\ntrivially.\nThis is our basis for the induction.\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"11654","document_content":"\\section{Kepler's Laws of Planetary Motion\/Third Law\/Examples}\nTags: Kepler's Laws of Planetary Motion\n\n\\begin{theorem}\nLet $P$ be a planet orbiting the sun $S$\nLet $P$ be:\n:$\\text{(a)}: \\quad$ Twice as far away from $S$ as the Earth;\n:$\\text{(b)}: \\quad$ $3$ times as far away from $S$ as the Earth;\n:$\\text{(c)}: \\quad$ $25$ times as far away from $S$ as the Earth.\nThen the orbital period of $P$ is:\n:$\\text{(a)}: \\quad$ approximately $2.8$ years;\n:$\\text{(b)}: \\quad$ approximately $5.2$ years;\n:$\\text{(c)}: \\quad$ $125$ years.\n\\end{theorem}\n\n\\begin{proof}\nLet the orbital period of Earth be $T'$ years.\nLet the mean distance of Earth from $S$ be $A$.\nLet the orbital period of $P$ be $T$ years.\nLet the mean distance of $P$ from $S$ be $a$.\nBy Kepler's Third Law of Planetary Motion:\n{{begin-eqn}}\n{{eqn | l = \\dfrac {T'^2} {A^3}\n | r = \\dfrac {T^2} {a^3}\n | c = \n}}\n{{eqn | ll= \\leadsto\n | l = T^2\n | r = \\dfrac {a^3} {A^3}\n | c = as $T'$ is $1$ year\n}}\n{{eqn | ll= \\leadsto\n | l = T\n | r = \\left({\\dfrac a A}\\right)^{3\/2}\n | c = \n}}\n{{end-eqn}}\nThus the required orbital periods are:\n:$\\text{(a)}: \\quad 2^{3\/2} = 2 \\sqrt 2 \\approx 2.8$ years\n:$\\text{(b)}: \\quad 3^{3\/2} = 3 \\sqrt 3 \\approx 5.2$ years\n:$\\text{(c)}: \\quad 25^{3\/2} = 125$ years.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"11986","document_content":"\\section{Integration by Substitution\/Definite Integral}\nTags: Integration by Substitution\n\n\\begin{theorem}\nLet $\\phi$ be a real function which has a derivative on the closed interval $\\closedint a b$.\nLet $I$ be an open interval which contains the image of $\\closedint a b$ under $\\phi$.\nLet $f$ be a real function which is continuous on $I$.\nThe definite integral of $f$ from $a$ to $b$ can be evaluated by:\n:$\\ds \\int_{\\map \\phi a}^{\\map \\phi b} \\map f t \\rd t = \\int_a^b \\map f {\\map \\phi u} \\dfrac \\d {\\d u} \\map \\phi u \\rd u$\nwhere $t = \\map \\phi u$.\nThe technique of solving an integral in this manner is called '''integration by substitution'''.\n\\end{theorem}\n\n\\begin{proof}\nLet $F$ be an antiderivative of $f$.\nWe have:\n{{begin-eqn}}\n{{eqn | l = \\map {\\frac \\d {\\d u} } {\\map F t}\n | r = \\map {\\frac \\d {\\d u} } {\\map F {\\map \\phi u} }\n | c = Definition of $\\map \\phi u$\n}}\n{{eqn | r = \\dfrac \\d {\\d t} \\map F {\\map \\phi u} \\dfrac \\d {\\d u} \\map \\phi u\n | c = Chain Rule for Derivatives\n}}\n{{eqn | r = \\map f {\\map \\phi u} \\dfrac \\d {\\d u} \\map \\phi u\n | c = as $\\map F t = \\ds \\int \\map f t \\rd t$\n}}\n{{end-eqn}}\nHence $\\map F {\\map \\phi u}$ is an antiderivative of $\\map f {\\map \\phi u} \\dfrac \\d {\\d u} \\map \\phi u$.\nThus:\n{{begin-eqn}}\n{{eqn | l = \\int_a^b \\map f {\\map \\phi u} \\map {\\phi'} u \\rd u\n | r = \\bigintlimits {\\map F {\\map \\phi u} } a b\n | c = Fundamental Theorem of Calculus: Second Part\n}}\n{{eqn | n = 1\n | r = \\map F {\\map \\phi b} - \\map F {\\map \\phi a}\n | c = \n}}\n{{end-eqn}}\nHowever, also:\n{{begin-eqn}}\n{{eqn | l = \\int_{\\map \\phi a}^{\\map \\phi b} \\map f t \\rd t\n | r = \\bigintlimits {\\map F t} {\\map \\phi a} {\\map \\phi b}\n | c = \n}}\n{{eqn | r = \\map F {\\map \\phi b} - \\map F {\\map \\phi a}\n | c = \n}}\n{{eqn | r = \\int_a^b \\map f {\\map \\phi u} \\map {\\phi'} u \\rd u\n | c = from $(1)$\n}}\n{{end-eqn}}\nwhich was to be proved. \n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"12010","document_content":"\\section{Intermediate Value Theorem}\nTags: Proofs, Named Theorems, Analysis\n\n\\begin{theorem}\nLet $f: S \\to \\R$ be a real function on some subset $S$ of $\\R$.\nLet $I \\subseteq S$ be a real interval.\nLet $f: I \\to \\R$ be continuous on $I$.\nThen $f$ is a Darboux function.\nThat is:\nLet $a, b \\in I$.\nLet $k \\in \\R$ lie between $\\map f a$ and $\\map f b$.\nThat is, either:\n:$\\map f a < k < \\map f b$\nor:\n:$\\map f b < k < \\map f a$\nThen $\\exists c \\in \\openint a b$ such that $\\map f c = k$.\n\\end{theorem}\n\n\\begin{proof}\nThis theorem is a restatement of Image of Interval by Continuous Function is Interval.\nFrom Image of Interval by Continuous Function is Interval, the image of $\\openint a b$ under $f$ is also a real interval (but not necessarily open).\nThus if $k$ lies between $\\map f a$ and $\\map f b$, it must be the case that:\n:$k \\in \\Img {\\openint a b}$\nThe result follows.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"12011","document_content":"\\section{Intermediate Value Theorem\/Corollary}\nTags: Named Theorems, Analysis\n\n\\begin{theorem}\nLet $I$ be a real interval.\nLet $a, b \\in I$ such that $\\openint a b$ is an open interval.\nLet $f: I \\to \\R$ be a real function which is continuous on $\\openint a b$.\nLet $0 \\in \\R$ lie between $\\map f a$ and $\\map f b$.\nThat is, either:\n:$\\map f a < 0 < \\map f b$\nor:\n:$\\map f b < 0 < \\map f a$\nThen $f$ has a root in $\\openint a b$.\n\\end{theorem}\n\n\\begin{proof}\nFollows directly from the Intermediate Value Theorem and from the definition of root.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"12012","document_content":"\\section{Intermediate Value Theorem (Topology)}\nTags: Connected Spaces, Order Topology, Connectedness, Continuous Mappings\n\n\\begin{theorem}\nLet $X$ be a connected topological space.\nLet $\\struct {Y, \\preceq, \\tau}$ be a totally ordered set equipped with the order topology.\nLet $f: X \\to Y$ be a continuous mapping.\nLet $a$ and $b$ are two points of $a, b \\in X$ such that:\n:$\\map f a \\prec \\map f b$\nLet:\n:$r \\in Y: \\map f a \\prec r \\prec \\map f b$\nThen there exists a point $c$ of $X$ such that:\n:$\\map f c = r$\n\\end{theorem}\n\n\\begin{proof}\nLet $a, b \\in X$, and let $r \\in Y$ lie between $\\map f a$ and $\\map f b$.\nDefine the sets:\n:$A = f \\sqbrk X \\cap r^\\prec$ and $B = f \\sqbrk X \\cap r^\\succ$\nwhere $r^\\prec$ and $r^\\succ$ denote the strict lower closure and strict upper closure respectively of $r$ in $Y$.\n$A$ and $B$ are disjoint by construction.\n$A$ and $B$ are also non-empty since one contains $\\map f a$ and the other contains $\\map f b$.\n$A$ and $B$ are also both open by definition as the intersection of open sets.\nSuppose there is no point $c$ such that $\\map f c = r$.\nThen:\n:$f \\sqbrk X = A \\cup B$\nso $A$ and $B$ constitute a separation of $X$.\nBut this contradicts the fact that Continuous Image of Connected Space is Connected.\nHence by Proof by Contradiction:\n:$\\exists c \\in X: \\map f c = r$\nwhich is what was to be proved.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"12693","document_content":"\\section{Homogeneous Linear Equations with More Unknowns than Equations}\nTags: Algebra, Linear Algebra, Definitions: Linear Algebra, Definitions: Algebra\n\n\\begin{theorem}\nLet $\\alpha_{ij}$ be elements of a field $F$, where $1 \\le i \\le m, 1 \\le j \\le n$.\nLet $n > m$.\nThen there exist $x_1, x_2, \\ldots, x_n \\in F$ not all zero, such that:\n:$\\ds \\forall i: 1 \\le i \\le m: \\sum_{j \\mathop = 1}^n \\alpha_{ij} x_j = 0$\nAlternatively, this can be expressed as:\nIf $n > m$, the following system of homogeneous linear equations:\n{{begin-eqn}}\n{{eqn | l = 0\n | r = \\alpha_{11} x_1 + \\alpha_{12} x_2 + \\cdots + \\alpha_{1n} x_n\n}}\n{{eqn | l = 0\n | r = \\alpha_{21} x_1 + \\alpha_{22} x_2 + \\cdots + \\alpha_{2n} x_n\n}}\n{{eqn | o = \\cdots\n}}\n{{eqn | l = 0\n | r = \\alpha_{m1} x_1 + \\alpha_{m2} x_2 + \\cdots + \\alpha_{mn} x_n\n}}\n{{end-eqn}}\nhas at least one solution such that not all of $x_1, \\ldots, x_n$ is zero.\n\\end{theorem}\n\n\\begin{proof}\nConsider these vectors for $1 \\le k \\le n$:\n:$\\mathbf a_k = \\tuple {\\alpha_{1k}, \\alpha_{2k}, \\dots, \\alpha_{mk}} \\in F^m$\nSince $n > m$, by Cardinality of Linearly Independent Set is No Greater than Dimension, $\\set {\\mathbf a_1, \\mathbf a_2, \\dots, \\mathbf a_n}$ is linearly dependent.\nBy definition of linearly dependent:\n:$\\ds \\exists \\set {\\lambda_k: 1 \\le k \\le n} \\subseteq F: \\sum_{k \\mathop = 1}^n \\lambda_k \\mathbf a_k = \\mathbf 0$\nwhere at least one of $\\lambda_k$ is not equal to $0$.\nThe system of homogeneous linear equations above can be written as:\n:$\\ds \\sum_{k \\mathop = 1}^n x_k \\mathbf a_k = \\mathbf 0$\nThe result follows from taking $x_k = \\lambda_k$.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"13011","document_content":"\\section{Generating Function for Binomial Coefficients}\nTags: Generating Functions\n\n\\begin{theorem}\nLet $\\sequence {a_n}$ be the sequence defined as:\n:$\\forall n \\in \\N: a_n = \\begin{cases}\n\\dbinom m n & : n = 0, 1, 2, \\ldots, m \\\\\n0 & : \\text{otherwise}\\end{cases}$\nwhere $\\dbinom m n$ denotes a binomial coefficient.\nThen the generating function for $\\sequence {a_n}$ is given as:\n:$\\ds \\map G z = \\sum_{n \\mathop = 0}^m \\dbinom m n z^n = \\paren {1 + z}^m$\n\\end{theorem}\n\n\\begin{proof}\n{{begin-eqn}}\n{{eqn | l = \\paren {1 + z}^m\n | r = \\sum_{n \\mathop = 0}^m \\binom m n z^n\n | c = Binomial Theorem\n}}\n{{end-eqn}}\nThe result follows from the definition of a generating function.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"13467","document_content":"\\section{Finite Semigroup Equal Elements for Different Powers}\nTags: Semigroups\n\n\\begin{theorem}\nLet $\\left({S, \\circ}\\right)$ be a finite semigroup.\nThen:\n: $\\forall x \\in S: \\exists m, n \\in \\N: m \\ne n: x^m = x^n$\n\\end{theorem}\n\n\\begin{proof}\nList the positive powers $x, x^2, x^3, \\ldots$ of any element $x$ of a finite semigroup $\\left({S, \\circ}\\right)$.\nSince all are elements of $S$, and the semigroup has a finite number of elements, it follows from the Pigeonhole Principle this list must contain repetitions.\nSo there must be at least one instance where $x^m = x^n$ for some $m, n \\in \\N$.\n{{Qed}}\nCategory:Semigroups\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"13468","document_content":"\\section{Finite Sequences in Set Form Acyclic Graph}\nTags: Graph Theory\n\n\\begin{theorem}\nLet $S$ be a set.\nLet $V$ be the set of finite sequences in $S$.\nLet $E$ be the set of unordered pairs $\\set {p, q}$ of elements of $V$ such that either:\n:$q$ is formed by extending $p$ by one element or\n:$p$ is formed by extending $q$ by one element.\nThat is:\n:$\\card {\\Dom p \\symdif \\Dom q} = 1$, where $\\symdif$ is symmetric difference\n:$p \\restriction D = q \\restriction D$, where $D = \\Dom p \\cap \\Dom q$\nThen $T = \\struct{V, E}$ is an acyclic graph.\n\\end{theorem}\n\n\\begin{proof}\n{{proof wanted}}\nCategory:Graph Theory\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"13939","document_content":"\\section{Existence of Positive Root of Positive Real Number\/Positive Exponent}\nTags: Real Numbers, Existence of Positive Root of Positive Real Number\n\n\\begin{theorem}\nLet $x \\in \\R$ be a real number such that $x > 0$.\nLet $n \\in \\Z$ be an integer such that $n > 0$.\nThen there exists a $y \\in \\R: y \\ge 0$ such that $y^n = x$.\n\\end{theorem}\n\n\\begin{proof}\nLet $f$ be the real function defined on the unbounded closed interval $\\hointr 0 \\to$ defined by $\\map f y = y^n$.\nConsider first the case of $n > 0$.\nBy Strictly Positive Integer Power Function is Unbounded Above:\n:$\\exists q \\in \\R_{>0}: \\map f q \\ge x$\nSince $x \\ge 0$:\n:$\\map f 0 \\le x$\nBy the Intermediate Value Theorem:\n:$\\exists y \\in \\R: 0 \\le y \\le q, \\map f y = x$\nHence the result has been shown to hold for $n > 0$.\n{{qed|lemma}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"14101","document_content":"\\section{Error Correction Capability of Linear Code}\nTags: Linear Codes\n\n\\begin{theorem}\nLet $C$ be a linear code.\nLet $C$ have a minimum distance $d$.\nThen $C$ corrects $e$ transmission errors for all $e$ such that $2 e + 1 \\le d$.\n\\end{theorem}\n\n\\begin{proof}\nLet $C$ be a linear code whose master code is $V$.\nLet $c \\in C$ be a transmitted codeword.\nLet $v$ be the received word from $c$.\nBy definition, $v$ is an element of $V$.\nLet $v$ have a distance $e$ from $c$, where $2 e + 1 \\le d$.\nThus there have been $e$ transmission errors.\n{{AimForCont}} $c_1$ is a codeword of $C$, distinct from $c$, such that $\\map d {v, c_1} \\le e$.\nThen:\n{{begin-eqn}}\n{{eqn | l = \\map d {c, c_1}\n | o = \\le\n | r = \\map d {c, v} + \\map d {v, c_1}\n | c = \n}}\n{{eqn | o = \\le\n | r = e + e\n | c = \n}}\n{{eqn | o = <\n | r = d\n | c = \n}}\n{{end-eqn}}\nSo $c_1$ has a distance from $c$ less than $d$.\nBut $C$ has a minimum distance $d$.\nThus $c_1$ cannot be a codeword of $C$.\nFrom this contradiction it follows that there is no codeword of $C$ closer to $v$ than $c$.\nHence there is a unique codeword of $C$ which has the smallest distance from $v$.\nHence it can be understood that $C$ has corrected the transmission errors of $v$.\n{{Qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"14139","document_content":"\\section{Euler's Theorem for Planar Graphs}\nTags: Graph Theory\n\n\\begin{theorem}\nLet $G = \\struct {V, E}$ be a connected planar graph with $V$ vertices and $E$ edges.\nLet $F$ be the number of faces of $G$.\nThen:\n:$V - E + F = 2$\n\\end{theorem}\n\n\\begin{proof}\nThe proof proceeds by complete induction.\nLet $G$ be a planar graph with $V$ vertices and $E$ edges.\nFor all $n \\in \\Z_{\\ge 0}$, let $\\map P n$ be the proposition:\n:For all planar graphs $G = \\struct {V, E}$ such that $V + E = n$, the equation $V - E + F = 2$ holds.\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"14371","document_content":"\\section{Equiangular Triangles are Similar}\nTags: Triangles\n\n\\begin{theorem}\nLet two triangles have the same corresponding angles.\nThen their corresponding sides are proportional.\nThus, by definition, such triangles are similar.\n{{:Euclid:Proposition\/VI\/4}}\n\\end{theorem}\n\n\\begin{proof}\nLet $\\triangle ABC, \\triangle DCE$ be equiangular triangles such that:\n:$\\angle ABC = \\angle DCE$\n:$\\angle BAC = \\angle CDE$\n:$\\angle ACB = \\angle CED$\n:300px\nLet $BC$ be placed in a straight line with $CE$.\nFrom Two Angles of Triangle Less than Two Right Angles $\\angle ABC + \\angle ACB$ is less than two right angles.\nAs $\\angle ACB = \\angle DEC$, it follows that $\\angle ABC + \\angle DEC$ is also less than two right angles.\nSo from the Parallel Postulate, $BA$ and $ED$, when produced, will meet.\nLet this happen at $F$.\nWe have that $\\angle ABC = \\angle DCE$.\nSo from Equal Corresponding Angles implies Parallel Lines:\n:$BF \\parallel CD$\nAgain, we have that $\\angle ACB = \\angle CED$.\nAgain from Equal Corresponding Angles implies Parallel Lines:\n:$AC \\parallel FE$\nTherefore by definition $\\Box FACD$ is a parallelogram.\nTherefore from Opposite Sides and Angles of Parallelogram are Equal $FA = DC$ and $AC = FD$.\nSince $AC \\parallel FE$, it follows from Parallel Transversal Theorem that:\n:$BA : AF = BC : CE$\nBut $AF = CD$ so:\n:$BA : AF = BC : CE$\nFrom Proportional Magnitudes are Proportional Alternately:\n:$AB : BC = DC : CE$\nSince $CD \\parallel BF$, from Parallel Transversal Theorem:\n:$BC : CE = FD : DE$\nBut $FD = AC$ so $BC : CE = AC : DE$.\nSo from Proportional Magnitudes are Proportional Alternately, $BC : CA = CE : ED$.\nIt then follows from Equality of Ratios Ex Aequali that $BA : AC = CD : DE$.\n{{qed}}\n{{Euclid Note|4|VI}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"14493","document_content":"\\section{Entire Function with Bounded Real Part is Constant}\nTags: Complex Analysis\n\n\\begin{theorem}\nLet $f : \\C \\to \\C$ be an entire function. \nLet the real part of $f$ be bounded.\nThat is, there exists a positive real number $M$ such that: \n:$\\cmod {\\map \\Re {\\map f z} } < M$\nfor all $z \\in \\C$, where $\\map \\Re {\\map f z}$ denotes the real part of $\\map f z$.\nThen $f$ is constant.\n\\end{theorem}\n\n\\begin{proof}\nLet $g : \\C \\to \\C$ be a complex function with:\n:$\\ds \\map g z = e^{\\map f z}$\nBy Derivative of Complex Composite Function, $g$ is entire with derivative:\n:$\\ds \\map {g'} z = \\map {f'} z e^{\\map f z}$\nWe have:\n{{begin-eqn}}\n{{eqn\t| l = \\cmod {\\map g z}\n\t| r = e^{\\map \\Re {\\map f z} }\n\t| c = Modulus of Positive Real Number to Complex Power is Positive Real Number to Power of Real Part\n}}\n{{eqn\t| o = \\le\n\t| r = e^{\\cmod {\\map \\Re {\\map f z} } }\n\t| c = Exponential is Strictly Increasing\n}}\n{{eqn\t| o = <\n\t| r = e^M\n\t| c = Exponential is Strictly Increasing\n}}\n{{end-eqn}}\nSo $g$ is a bounded entire function.\nBy Liouville's Theorem, $g$ is therefore a constant function.\nWe therefore have, by Derivative of Constant: Complex:\n:$\\map {g'} z = 0$\nfor all $z \\in \\C$.\nThat is:\n:$\\map {f'} z e^{\\map f z} = 0$\nSince the exponential function is non-zero, we must have: \n:$\\map {f'} z = 0$\nfor all $z \\in \\C$.\nFrom Zero Derivative implies Constant Complex Function, we then have that $f$ is constant on $\\C$. \n{{qed}}\nCategory:Complex Analysis\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"15210","document_content":"\\section{Derivative of Composite Function}\nTags: Differential Calculus\n\n\\begin{theorem}\nLet $f, g, h$ be continuous real functions such that:\n:$\\forall x \\in \\R: \\map h x = \\map {f \\circ g} x = \\map f {\\map g x}$\nThen:\n:$\\map {h'} x = \\map {f'} {\\map g x} \\map {g'} x$\nwhere $h'$ denotes the derivative of $h$.\nUsing the $D_x$ notation:\n:$\\map {D_x} {\\map f {\\map g x} } = \\map {D_{\\map g x} } {\\map f {\\map g x} } \\map {D_x} {\\map g x}$\nThis is often informally referred to as the '''chain rule (for differentiation)'''.\n\\end{theorem}\n\n\\begin{proof}\nLet $\\map g x = y$, and let:\n{{begin-eqn}}\n{{eqn | l = \\map g {x + \\delta x}\n | r = y + \\delta y\n | c = \n}}\n{{eqn | ll= \\leadsto\n | l = \\delta y\n | r = \\map g {x + \\delta x} - \\map g x\n | c = \n}}\n{{end-eqn}}\nThus:\n:$\\delta y \\to 0$ as $\\delta x \\to 0$\nand:\n:$(1): \\quad \\dfrac {\\delta y} {\\delta x} \\to \\map {g'} x$\nThere are two cases to consider:\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"15648","document_content":"\\section{Convergence of P-Series\/Real}\nTags: Convergence Tests, P-Series, Convergence of P-Series\n\n\\begin{theorem}\nLet $p \\in \\R$ be a real number.\nThen the $p$-series:\n:$\\ds \\sum_{n \\mathop = 1}^\\infty n^{-p}$\nis convergent {{iff}} $p > 1$.\n\\end{theorem}\n\n\\begin{proof}\nBy the Integral Test:\n:$\\displaystyle \\sum_{n \\mathop = 1}^\\infty \\frac 1 {n^x}$ converges {{iff}} the improper integral $\\displaystyle \\int_1^\\infty \\frac {\\d t} {t^x}$ exists.\nThe result follows from Integral to Infinity of Reciprocal of Power of x.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"15865","document_content":"\\section{Conservation of Angular Momentum}\nTags: Classical Mechanics\n\n\\begin{theorem}\nNewton's Laws of Motion imply the conservation of angular momentum in systems of masses in which no external force is acting.\n\\end{theorem}\n\n\\begin{proof}\nWe start by stating Newton's Third Law of Motion in all its detail.\nWe consider a collection of massive bodies denoted by the subscripts $1$ to $N$.\nThese bodies interact with each other and exert forces on each other and these forces occur in equal and opposite pairs.\nThe force $F_{i j}$ exerted by body $i$ on body $j$ is related to the force exerted by body $j$ on body $i$ by:\n:$(1): \\quad \\vec {F_{i j}} = -\\vec {F_{j i}}$\nThe final part of Newton's Third Law of Motion is that these equal and opposite forces act through the line that connects the two bodies in question.\nThis can be stated thus:\n:$(2): \\quad \\vec {F_{i j}} = a_{i j} \\paren {\\vec {r_j} - \\vec {r_i} }$\nwhere:\n:$\\vec{r_i}$ is the position of body $i$\n:$a_{i j} $ is the magnitude of the force.\nAs a consequence of $(1)$:\n:$a_{j i} = a_{i j}$\nLet the total torque $\\vec {\\tau_{\\operatorname {total} } }$ on the system be measured about an origin located at $\\vec {r_0}$.\nThus:\n{{begin-eqn}}\n{{eqn | l = \\vec {\\tau_{\\operatorname {total} } }\n | r = \\sum_i \\vec{\\tau_i}\n | c = \n}}\n{{eqn | r = \\sum_i \\paren {\\paren {\\vec {r_i} - \\vec {r_0} } \\times \\sum_j \\vec {F_{j i} } }\n | c = \n}}\n{{eqn | r = \\sum_{i, j} \\paren {\\paren {\\paren {\\vec {r_j} - \\vec {r_0} } - \\paren {\\vec {r_j} - \\vec {r_i} } } \\times \\vec {F_{j i} } }\n | c = \n}}\n{{eqn | r = \\sum_{i, j} \\paren {\\paren {\\paren {\\vec {r_j} - \\vec {r_0} } - \\paren {\\vec {r_j} - \\vec {r_i} } } \\times a_{i j} \\paren {\\vec {r_j} - \\vec {r_i} } }\n | c = \n}}\n{{eqn | r = \\sum_{i, j} \\paren {\\vec {r_j} - \\vec {r_0} } \\times a_{i j} \\paren {\\vec {r_j} - \\vec {r_i} }\n | c = \n}}\n{{eqn | r = \\sum_{i, j} \\vec {r_j} \\times a_{i j} \\paren {\\vec {r_j} - \\vec {r_i} } - \\paren {\\vec {r_0} \\times \\sum_{i, j} \\vec {F_{i j} } }\n | c = \n}}\n{{end-eqn}}\nBy hypothesis there is no external force.\nThus the second term disappears, and:\n{{begin-eqn}}\n{{eqn | l = \\vec {\\tau_{\\operatorname {total} } }\n | r = \\sum_{i, j} \\vec {r_j} \\times a_{i j} \\paren {\\vec {r_j} - \\vec {r_i} }\n | c = \n}}\n{{eqn | r = \\sum_{i \\mathop > j} \\vec {r_j} \\times a_{i j} \\paren {\\vec {r_j} - \\vec {r_i} } + \\vec {r_i} \\times a_{j i} \\paren {\\vec {r_j} - \\vec {r_i} }\n | c = \n}}\n{{eqn | r = \\sum_{i \\mathop > j} \\vec {r_j} \\times \\vec {r_i} \\paren {a_{j i} - a_{i j} }\n | c = \n}}\n{{eqn | r = \\vec 0\n | c = \n}}\n{{end-eqn}}\nIn summary, in a system of masses in which there is no external force, the total torque on the system is equal to $0$.\nThis is because the pair of torque between two bodies must cancel out.\nSince the rate of change of angular momentum is proportional to the torque, the angular momentum of a system is conserved when no external force is applied.\n{{qed}}\nCategory:Classical Mechanics\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"16790","document_content":"\\section{Cayley's Formula}\nTags: Named Theorems, Graph Theory, Combinatorics\n\n\\begin{theorem}\nThe number of distinct labeled trees with $n$ nodes is $n^{n - 2}$.\n\\end{theorem}\n\n\\begin{proof}\nFollows directly from Bijection between Pr\u00fcfer Sequences and Labeled Trees.\nThis shows that there is a bijection between the set of labeled trees with $n$ nodes and the set of all Pr\u00fcfer sequences of the form:\n:$\\tuple {\\mathbf a_1, \\mathbf a_2, \\ldots, \\mathbf a_{n - 2} }$\nwhere each of the $\\mathbf a_i$'s is one of the integers $1, 2, \\ldots, n$, allowing for repetition.\nSince there are exactly $n$ possible values for each integer $\\mathbf a_i$, the total number of such sequences is $\\ds \\prod_{i \\mathop = 1}^{n - 2} n$.\nThe result follows from Equivalence of Mappings between Sets of Same Cardinality.\n{{qed}}\n{{Namedfor|Arthur Cayley|cat = Cayley}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"16899","document_content":"\\section{Cauchy-Goursat Theorem}\nTags: Complex Analysis\n\n\\begin{theorem}\nLet $D$ be a simply connected open subset of the complex plane $\\C$.\nLet $\\partial D$ denote the closed contour bounding $D$.\nLet $f: D \\to \\C$ be holomorphic everywhere in $D$.\nThen:\n:$\\ds \\oint_{\\partial D} \\map f z \\rd z = 0$\n\\end{theorem}\n\n\\begin{proof}\nBegin by rewriting the function $f$ and differential $\\rd z$ in terms of their real and complex parts:\n:$f = u + iv$\n:$\\d z = \\d x + i \\rd y$\nThen we have:\n:$\\ds \\oint_{\\partial D} \\map f z \\rd z = \\oint_{\\partial D} \\paren {u + iv} \\paren {\\d x + i \\rd y}$\nExpanding the result and again separating into real and complex parts yields two integrals of real variables:\n:$\\ds \\oint_{\\partial D} \\paren {u \\rd x - v \\rd y} + i \\oint_{\\partial D} \\paren {v \\rd x + u \\rd y}$\nWe next apply Green's Theorem to each integral term to convert the contour integrals to surface integrals over $D$:\n:$\\ds \\iint_D \\paren {-\\dfrac {\\partial v} {\\partial x} - \\dfrac {\\partial u} {\\partial y} } \\rd x \\rd y + \\iint_D \\paren {\\dfrac {\\partial u} {\\partial x} - \\dfrac {\\partial v} {\\partial y} } \\rd x \\rd y$\nBy the assumption that $f$ is holomorphic, it satisfies the Cauchy-Riemann Equations\n:$\\dfrac {\\partial v} {\\partial x} + \\dfrac {\\partial u} {\\partial y} = 0$\n:$\\dfrac {\\partial u} {\\partial x} - \\dfrac {\\partial v} {\\partial y} = 0$\nThe integrands are therefore zero and hence the integral is zero.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"16984","document_content":"\\section{Cantor Set has Zero Lebesgue Measure}\nTags: Cantor Set, Measure Theory, Lebesgue Measure, Cantor Space\n\n\\begin{theorem}\nLet $\\CC$ be the Cantor set.\nLet $\\lambda$ denote the Lebesgue measure on the Borel $\\sigma$-algebra $\\map \\BB \\R$ on $\\R$.\nThen $\\CC$ is $\\map \\BB \\R$-measurable, and $\\map \\lambda \\CC = 0$.\nThat is, $\\CC$ is a $\\lambda$-null set.\n\\end{theorem}\n\n\\begin{proof}\nConsider the definition of $\\CC$ as a limit of a decreasing sequence.\nIn the notation as introduced there, we see that each $S_n$ is a collection of disjoint closed intervals.\nFrom Closed Set Measurable in Borel Sigma-Algebra, these are measurable sets.\nFurthermore, each $S_n$ is finite.\nHence by Sigma-Algebra Closed under Union, it follows that $C_n := \\ds \\bigcup S_n$ is measurable as well.\nThen, as we have:\n:$\\CC = \\ds \\bigcap_{n \\mathop \\in \\N} C_n$\nit follows from Sigma-Algebra Closed under Countable Intersection that $\\CC$ is measurable.\nThe $C_n$ also form a decreasing sequence of sets with limit $\\CC$.\nThus, from Characterization of Measures: $(3')$, it follows that:\n:$\\map \\lambda \\CC = \\ds \\lim_{n \\mathop \\to \\infty} \\map \\lambda {C_n}$\nIt is not too hard to show that, for all $n \\in \\N$:\n:$\\map \\lambda {C_n} = \\paren {\\dfrac 2 3}^n$\n{{finish|yes, I know}}\nNow we have by Sequence of Powers of Number less than One that:\n:$\\ds \\lim_{n \\mathop \\to \\infty} \\paren {\\frac 2 3}^n = 0$\nand the result follows.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"17066","document_content":"\\section{Brouwer's Fixed Point Theorem\/One-Dimensional Version}\nTags: Continuity, Brouwer's Fixed Point Theorem, Analysis, Fixed Point Theorems, Continuous Real Functions, Named Theorems, Continuous Functions, Topology\n\n\\begin{theorem}\nLet $f: \\closedint a b \\to \\closedint a b$ be a real function which is continuous on the closed interval $\\closedint a b$.\nThen:\n:$\\exists \\xi \\in \\closedint a b: \\map f \\xi = \\xi$\nThat is, a continuous real function from a closed real interval to itself fixes some point of that interval.\n\\end{theorem}\n\n\\begin{proof}\nAs the codomain of $f$ is $\\closedint a b$, it follows that the image of $f$ is a subset of $\\closedint a b$.\nThus $\\map f a \\ge a$ and $\\map f b \\le b$.\nLet us define the real function $g: \\closedint a b \\to \\R$ by $g \\left({x}\\right) = \\map f x - x$.\nThen by the Combined Sum Rule for Continuous Functions, $\\map g x$ is continuous on $\\closedint a b$.\nBut $\\map g a \\ge 0$ and $\\map g b \\le 0$.\nBy the Intermediate Value Theorem, $\\exists \\xi: \\map g \\xi = 0$.\nThus $\\map f \\xi = \\xi$.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"17218","document_content":"\\section{Binomial Theorem\/Examples\/4th Power of Sum}\nTags: Fourth Powers, Algebra, Examples of Use of Binomial Theorem\n\n\\begin{theorem}\n:$\\paren {x + y}^4 = x^4 + 4 x^3 y + 6 x^2 y^2 + 4 x y^3 + y^4$\n\\end{theorem}\n\n\\begin{proof}\nFollows directly from the Binomial Theorem:\n:$\\ds \\forall n \\in \\Z_{\\ge 0}: \\paren {x + y}^n = \\sum_{k \\mathop = 0}^n \\binom n k x^{n - k} y^k$\nputting $n = 4$.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"17301","document_content":"\\section{Bijection between Pr\u00fcfer Sequences and Labeled Trees}\nTags: Tree Theory, Trees, Graph Theory, Combinatorics\n\n\\begin{theorem}\nThere is a one-to-one correspondence between Pr\u00fcfer sequences and labeled trees.\nThat is, every labeled tree has a unique Pr\u00fcfer sequence that defines it, and every Pr\u00fcfer sequence defines just one labeled tree.\n\\end{theorem}\n\n\\begin{proof}\nLet $T$ be the set of all labeled trees of order $n$.\nLet $P$ be the set of all Pr\u00fcfer sequence of length $n-2$.\nLet $\\phi: T \\to P$ be the mapping that maps each tree to its Pr\u00fcfer sequence.\n* From Pr\u00fcfer Sequence from Labeled Tree, $\\phi$ is clearly well-defined, as every element of $T$ maps uniquely to an element of $P$.\n* However, from Labeled Tree from Pr\u00fcfer Sequence, $\\phi^{-1}: P \\to T$ is also clearly well-defined, as every element of $P$ maps to a unique element of $T$.\nHence the result.\n{{questionable|How is it immediate that the two constructions are mutually inverse?}}\n{{qed}}\nCategory:Tree Theory\nCategory:Combinatorics\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"17471","document_content":"\\section{Area of Trapezoid}\nTags: Trapezoids, Areas of Quadrilaterals, Area Formulas, Quadrilaterals\n\n\\begin{theorem}\n:410px\nLet $ABCD$ be a trapezoid:\n:whose parallel sides are of lengths $a$ and $b$\nand\n:whose height is $h$.\nThen the area of $ABCD$ is given by:\n:$\\Box ABCD = \\dfrac {h \\paren {a + b} } 2$\n\\end{theorem}\n\n\\begin{proof}\n:600px\nExtend line $AB$ to $E$ by length $a$.\nExtend line $DC$ to $F$ by length $b$.\nThen $BECF$ is another trapezoid whose parallel sides are of lengths $a$ and $b$ and whose height is $h$.\nAlso, $AEFD$ is a parallelogram which comprises the two trapezoids $ABCD$ and $BECF$.\nSo $\\Box ABCD + \\Box BECF = \\Box AEFD$ and $\\Box ABCD = \\Box BECF$.\n$AEFD$ is of altitude $h$ with sides of length $a + b$.\nThus from Area of Parallelogram the area of $AEFD$ is given by:\n: $\\Box AEFD = h \\paren {a + b}$\nIt follows that $\\Box ABCD = \\dfrac {h \\paren {a + b} } 2$\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"17901","document_content":"\\section{Number of Compositions}\nTags: Combinatorics\n\n\\begin{theorem}\nA $k$-composition of a positive integer $n$ is an ordered $k$-tuple: $c = \\tuple {c_1, c_2, \\ldots, c_k}$ such that $c_1 + c_2 + \\cdots + c_k = n$ and $c_i $ are strictly positive integers.\nThe number of $k$-composition of $n$ is $\\dbinom {n - 1} {k - 1}$ and the total number of compositions of $n$ is $2^{n - 1}$ (that is for $k = 1, 2, 3, \\ldots, n$).\n\\end{theorem}\n\n\\begin{proof}\nConsider the following array consisting of $n$ ones and $n - 1$ blanks:\n:$\\begin{bmatrix} 1 \\ \\_ \\ 1 \\ \\_ \\ \\cdots \\ \\_ \\ 1 \\ \\_ \\ 1 \\end{bmatrix}$\nIn each blank we can either put a comma or a plus sign.\nEach way of choosing $,$ or $+$ will give a composition of $n$ with the commas separating the individual $c_i$'s.\nIt follows easily that there are $2^{n-1}$ ways of doing this, since there are two choices for each of $n-1$ blanks.\nThe result follows from the Product Rule for Counting.\nSimilarly if we want specifically $k$ different $c_i$'s then we are left with choosing $k - 1$ out of $n - 1$ blanks to place the $k - 1$ commas.\nThe number of ways of doing so is $\\dbinom {n - 1} {k - 1}$ from the Binomial Theorem.\n{{qed}}\nCategory:Combinatorics\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"17913","document_content":"\\section{Number of Distinct Parenthesizations on Word}\nTags: Parenthesization, Catalan Numbers\n\n\\begin{theorem}\nLet $w_n$ denote an arbitrary word of $n$ elements.\nThe number of distinct parenthesizations of $w_n$ is the Catalan number $C_{n - 1}$:\n:$C_{n - 1} = \\dfrac 1 n \\dbinom {2 \\paren {n - 1} } {n - 1}$\n\\end{theorem}\n\n\\begin{proof}\nLet $w_n$ denote an arbitrary word of $n$ elements.\nLet $a_n$ denote the number of ways $W_n$ elements may be parenthesized.\nFirst note that we have:\n{{begin-eqn}}\n{{eqn | l = a_1\n | r = 1\n | c = \n}}\n{{eqn | l = a_2\n | r = 1\n | c = \n}}\n{{eqn | l = a_3\n | r = 2\n | c = that is, $b_1 \\paren {b_2 b_3}$ and $\\paren {b_1 b_2} b_3$\n}}\n{{end-eqn}}\nand from Parenthesization of Word of $4$ Elements:\n:$a_4 = 5$\nConsider a word $w_{n + 1}$ of $n + 1$ elements.\nThen $w_{n + 1}$ can be formed as any one of:\n:$w_1$ concatenated with $w_n$\n:$w_2$ concatenated with $w_{n - 1}$\n:$\\dotsc$ and so on until:\n:$w_n$ concatenated with $w_1$\nThus the $i$th row in the above sequence is the number of parenthesizations of $w_{n + 1}$ in which the two outermost parenthesizations contain $i$ and $n - i + 1$ terms respectively.\nWe have that:\n:there are $a_i$ parenthesizations of $w_i$\n:there are $a_{n - i + 1}$ parenthesizations of $w_{n - i + 1}$\nHence the total number of parenthesizations of $w_{n + 1}$ is the sum of all these parenthesizations for $1 \\le i \\le n$.\nThat is:\n:$(1): \\quad a_{n + 1} = a_1 a_n + a_2 a_{n - 1} + \\dotsb + a_n a_1$\nLet us start with the generating function:\n:$\\ds \\map {G_A} z = \\sum_{n \\mathop = 1}^\\infty a_n z^n$\nThen:\n{{begin-eqn}}\n{{eqn | l = \\map {G_A} z\n | r = z + \\sum_{n \\mathop = 2}^\\infty \\paren {a_1 a_n + a_2 a_{n - 1} + \\dotsb + a_n a_1} z^n\n | c = from $(1)$\n}}\n{{eqn | r = z + \\sum_{n \\mathop = 1}^\\infty a_n z^n \\sum_{n \\mathop = 1}^\\infty a_n z^n\n | c = \n}}\n{{eqn | r = z + \\paren {\\map {G_A} z}^2\n | c = \n}}\n{{end-eqn}}\nThus $\\map {G_A} z$ satisfies the quadratic equation:\n:$\\paren {\\map {G_A} z}^2 - \\map {G_A} z + z = 0$\nBy the Quadratic Formula, this gives:\n:$\\map {G_A} z = \\dfrac {1 \\pm \\sqrt {1 - 4 z} } 2$\nSince $\\map {G_A} 0 = 0$, we can eliminate the positive square root and arrive at:\n:$(2): \\quad \\map {G_A} z = \\dfrac 1 2 - \\dfrac {\\sqrt {1 - 4 z} } 2$\nExpanding $\\sqrt {1 - 4 z}$ using the Binomial Theorem:\n:$\\ds \\map {G_A} z = \\dfrac 1 2 - \\dfrac 1 2 \\sum_{n \\mathop = 0}^\\infty \\paren {-1}^n \\dbinom {\\frac 1 2} n 4^n z^n$\nwhere:\n:$\\dbinom {\\frac 1 2} 0 = 1$\nand:\n:$\\dbinom {\\frac 1 2} n = \\dfrac {\\frac 1 2 \\paren {\\frac 1 2 - 1} \\dotsm \\paren {\\frac 1 2 - n + 1} } {n!}$\nAs a result:\n:$\\ds (3): \\quad \\map {G_A} z = -\\dfrac 1 2 \\sum_{n \\mathop = 1}^\\infty \\paren {-1}^n \\dbinom {\\frac 1 2} n 4^n z^n$\nWe can expand $(3)$ as a Taylor series about $0$.\nAs such a series, when it exists, is unique, the coefficients must be $a_n$.\nHence:\n{{begin-eqn}}\n{{eqn | l = a_n\n | r = -\\dfrac 1 2 \\paren {-1}^n \\dbinom {\\frac 1 2} n 4^n\n | c = \n}}\n{{eqn | r = \\paren {-1}^{n - 1} \\dfrac 1 2 \\dfrac {\\frac 1 2 \\paren {\\frac 1 2 - 1} \\dotsm \\paren {\\frac 1 2 - n + 1} } {n!} 4^n\n | c = \n}}\n{{eqn | r = \\paren {-1}^n \\dfrac 1 2 \\dfrac {\\paren {-1} \\paren {1 - 2} \\dotsm \\paren {1 - 2 \\paren {n - 1 } } 2^n} {n!}\n | c = \n}}\n{{eqn | r = \\dfrac 1 2 \\dfrac {1 \\times 3 \\times \\dotsb \\times \\paren {2 n - 3} 2^n} {n!}\n | c = \n}}\n{{eqn | r = \\dfrac 1 2 \\dfrac {1 \\times 3 \\times \\dotsb \\times \\paren {2 n - 3} n! 2^n} {n! n!}\n | c = multiplying top and bottom by $n!$\n}}\n{{eqn | r = \\dfrac 1 2 \\dfrac {1 \\times 2 \\times 3 \\times 4 \\times \\dotsb \\times \\paren {2 n - 4} \\paren {2 n - 3} \\paren {2 n - 2} \\paren {2 n} } {\\paren {n!}^2}\n | c = \n}}\n{{eqn | r = \\dfrac 1 2 \\dfrac {1 \\times 2 \\times 3 \\times 4 \\times \\dotsb \\times \\paren {2 n - 2} } {\\paren {\\paren {n - 1}!}^2}\n | c = \n}}\n{{eqn | r = \\frac 1 n \\binom {2 n - 2} {n - 1}\n | c = \n}}\n{{end-eqn}}\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"18400","document_content":"\\section{Orthogonal Projection onto Closed Linear Span}\nTags: Linear Transformations on Hilbert Spaces, Hilbert Spaces\n\n\\begin{theorem}\nLet $H$ be a Hilbert space with inner product $\\innerprod \\cdot \\cdot$ and inner product norm $\\norm \\cdot$. \nLet $E = \\set {e_1, \\ldots, e_n}$ be an orthonormal subset of $H$.\nLet $M = \\vee E$, where $\\vee E$ is the closed linear span of $E$. \nLet $P$ be the orthogonal projection onto $M$.\nThen:\n:$\\forall h \\in H: P h = \\ds \\sum_{k \\mathop = 1}^n \\innerprod h {e_k} e_k$\n\\end{theorem}\n\n\\begin{proof}\nLet $h \\in H$. \nLet: \n:$\\ds u = \\sum_{k \\mathop = 1}^n \\innerprod h {e_k} e_k$ \nWe have that:\n:$u \\in \\map \\span E$\nand from the definition of closed linear span:\n:$M = \\paren {\\map \\span E}^-$\nWe therefore have, by the definition of closure: \n:$u \\in M$ \nLet $v = h - u$ \nWe want to show that $v \\in M^\\bot$. \nFrom Intersection of Orthocomplements is Orthocomplement of Closed Linear Span, it suffices to show that: \n:$v \\in E^\\bot$\nNote that for each $l$ we have: \n:$\\innerprod v {e_l} = \\innerprod h {e_l} - \\innerprod u {e_l}$\nsince the inner product is linear in its first argument. \nWe have: \n{{begin-eqn}}\n{{eqn\t| l = \\innerprod u {e_l} \n\t| r = \\innerprod {\\sum_{k \\mathop = 1}^n \\innerprod h {e_k} e_k} {e_l}\n}}\n{{eqn\t| r = \\sum_{k \\mathop = 1}^n \\innerprod {\\innerprod h {e_k} e_k} {e_l}\n\t| c = linearity of inner product in first argument\n}}\n{{eqn\t| r = \\sum_{k \\mathop = 1}^n \\innerprod h {e_k} \\innerprod {e_k} {e_l}\n\t| c = linearity of inner product in first argument\n}}\n{{eqn\t| r = \\innerprod h {e_l} \\innerprod {e_l} {e_l}\n\t| c = {{Defof|Orthonormal Subset}}\n}}\n{{eqn\t| r = \\innerprod h {e_l} \\norm {e_l}^2\n\t| c = {{Defof|Inner Product Norm}}\n}}\n{{eqn\t| r = \\innerprod h {e_l}\n\t| c = since $\\norm {e_l} = 1$\n}}\n{{end-eqn}}\nso:\n:$\\innerprod v {e_l} = 0$ \nThat is: \n:$v \\in E^\\bot$\nso, by Intersection of Orthocomplements is Orthocomplement of Closed Linear Span, we have: \n:$v \\in M^\\bot$\nWe can therefore decompose each $h \\in H$ as: \n:$h = u + v$\nwith $u \\in M$ and $v \\in M^\\bot$. \nSo we have: \n{{begin-eqn}}\n{{eqn\t| l = P h \n\t| r = \\map P {u + v}\n}}\n{{eqn\t| r = \\map P u + \\map P v\n\t| c = Orthogonal Projection on Closed Linear Subspace of Hilbert Space is Linear Transformation\n}}\n{{eqn\t| r = v\n\t| c = Kernel of Orthogonal Projection on Closed Linear Subspace of Hilbert Space, Fixed Points of Orthogonal Projection on Closed Linear Subspace of Hilbert Space\n}}\n{{eqn\t| r = \\sum_{k \\mathop = 1}^n \\innerprod h {e_k} e_k\n}}\n{{end-eqn}}\nfor each $h \\in H$. \n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"18695","document_content":"\\section{Pigeonhole Principle}\nTags: Pigeonhole Principle, Named Theorems, Combinatorics\n\n\\begin{theorem}\nLet $S$ be a finite set whose cardinality is $n$.\nLet $S_1, S_2, \\ldots, S_k$ be a partition of $S$ into $k$ subsets.\nThen:\n:at least one subset $S_i$ of $S$ contains at least $\\ceiling {\\dfrac n k}$ elements\nwhere $\\ceiling {\\, \\cdot \\,}$ denotes the ceiling function.\n\\end{theorem}\n\n\\begin{proof}\n{{AimForCont}} no subset $S_i$ of $S$ has as many as $\\ceiling {\\dfrac n k}$ elements.\nThen the maximum number of elements of any $S_i$ would be $\\ceiling {\\dfrac n k} - 1$.\nSo the total number of elements of $S$ would be no more than $k \\paren {\\ceiling {\\dfrac n k} - 1} = k \\ceiling {\\dfrac n k} - k$.\nThere are two cases:\n:$n$ is divisible by $k$\n:$n$ is not divisible by $k$.\nSuppose $k \\divides n$.\nThen $\\ceiling {\\dfrac n k} = \\dfrac n k$ is an integer and:\n:$k \\ceiling {\\dfrac n k} - k = n - k$\nThus:\n:$\\ds \\card S = \\sum_{i \\mathop = 1}^k \\card {S_i} \\le n - k < n$\nThis contradicts the fact that $\\card S = n$.\nHence our assumption that no subset $S_i$ of $S$ has as many as $\\ceiling {\\dfrac n k}$ elements was false.\nNext, suppose that $k \\nmid n$.\nThen:\n:$\\card S = k \\ceiling {\\dfrac n k} - k < \\dfrac {k \\paren {n + k} } k - k = n$\nand again this contradicts the fact that $\\card S = n$.\nIn the same way, our assumption that no subset $S_i$ of $S$ has as many as $\\ceiling {\\dfrac n k}$ elements was false.\nHence, by Proof by Contradiction, there has to be at least $\\ceiling {\\dfrac n k}$ elements in at least one $S_i \\subseteq S$.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"18841","document_content":"\\section{Positive Real has Real Square Root}\nTags: Real Numbers\n\n\\begin{theorem}\nLet $x \\in \\R_{>0}$ be a (strictly) positive real number.\nThen:\n:$\\exists y \\in \\R: x = y^2$\n\\end{theorem}\n\n\\begin{proof}\nLet $f: \\R \\to \\R$ be defined as:\n:$\\forall x \\in \\R: \\map f x = x^2$\nWe have that $f$ is the pointwise product of the identity mapping with itself.\nBy Product Rule for Continuous Real Functions and Identity Mapping is Continuous, $f$ is continuous.\nBy Power Function is Unbounded Above:\n:$\\exists q \\in \\R: \\map f q > x$\nThen:\n:$0^2 = 0 \\le x$\nBy the Intermediate Value Theorem:\n:$\\exists y \\in \\R: 0 < y < q: y^2 = x$\n{{qed}}\nCategory:Real Numbers\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"19708","document_content":"\\section{Product Rule for Counting}\nTags: Product Rule for Counting, Counting Arguments, Combinatorics, combinatorics\n\n\\begin{theorem}\nLet it be possible to choose an element $\\alpha$ from a given set $S$ in $m$ different ways.\nLet it be possible to choose an element $\\beta$ from a given set $T$ in $n$ different ways.\nThen the ordered pair $\\tuple {\\alpha, \\beta}$ can be chosen from the cartesian product $S \\times T$ in $m n$ different ways.\n\\end{theorem}\n\n\\begin{proof}\n{{handwaving}}\nThe validity of this rule follows directly from the definition of multiplication of integers.\nThe product $a b$ (for $a, b \\in \\N_{>0}$) is the number of sequences $\\sequence {A, B}$, where $A$ can be any one of $a$ items and $B$ can be any one of $b$ items.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"20117","document_content":"\\section{Ramsey's Theorem}\nTags: Ramsey Theory, Named Theorems, Combinatorics\n\n\\begin{theorem}\nIn any coloring of the edges of a sufficiently large complete graph, one will find monochromatic complete subgraphs.\nFor 2 colors, Ramsey's theorem states that for any pair of positive integers $\\tuple {r, s}$, there exists a least positive integer $\\map R {r, s}$ such that for any complete graph on $\\map R {r, s}$ vertices, whose edges are colored red or blue, there exists either a complete subgraph on $r$ vertices which is entirely red, or a complete subgraph on $s$ vertices which is entirely blue.\nMore generally, for any given number of colors $c$, and any given integers $n_1, \\ldots, n_c$, there is a number $\\map R {n_1, \\ldots, n_c}$ such that:\n:if the edges of a complete graph of order $\\map R {n_1, \\ldots, n_c}$ are colored with $c$ different colours, then for some $i$ between $1$ and $c$, it must contain a complete subgraph of order $n_i$ whose edges are all color $i$.\nThis number $\\map R {n_1, \\ldots, n_c}$ is called the Ramsey number for $n_1, \\ldots, n_c$.\nThe special case above has $c = 2$ (and $n_1 = r$ and $n_2 = s$).\nHere $\\map R {r, s}$ signifies an integer that depends on both $r$ and $s$. It is understood to represent the smallest integer for which the theorem holds.\n\\end{theorem}\n\n\\begin{proof}\nFirst we prove the theorem for the 2-color case, by induction on $r + s$.\nIt is clear from the definition that\n:$\\forall n \\in \\N: \\map R {n, 1} = \\map R {1, n} = 1$\nbecause the complete graph on one node has no edges.\nThis is the base case.\nWe prove that $R \\left({r, s}\\right)$ exists by finding an explicit bound for it.\nBy the inductive hypothesis, $\\map R {r - 1, s}$ and $\\map R {r, s - 1}$ exist.\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"20341","document_content":"\\section{Real Symmetric Positive Definite Matrix has Positive Eigenvalues}\nTags: Symmetric Matrices, Positive Definite Matrices\n\n\\begin{theorem}\nLet $A$ be a symmetric positive definite matrix over $\\mathbb R$.\nLet $\\lambda$ be an eigenvalue of $A$. \nThen $\\lambda$ is real with $\\lambda > 0$.\n\\end{theorem}\n\n\\begin{proof}\nLet $\\lambda$ be an eigenvalue of $A$ and let $\\mathbf v$ be a corresponding eigenvector.\nFrom Real Symmetric Matrix has Real Eigenvalues, $\\lambda$ is real.\nFrom the definition of a positive definite matrix, we have: \n:$\\mathbf v^\\intercal A \\mathbf v > 0$\nThat is: \n{{begin-eqn}}\n{{eqn\t| l = 0\n\t| o = <\n\t| r = \\mathbf v^\\intercal A \\mathbf v\n}}\n{{eqn\t| r = \\mathbf v^\\intercal \\paren {\\lambda \\mathbf v}\n\t| c = {{Defof|Eigenvector of Real Square Matrix}}\n}}\n{{eqn\t| r = \\lambda \\paren {\\mathbf v^\\intercal \\mathbf v}\n}}\n{{eqn\t| r = \\lambda \\paren {\\mathbf v \\cdot \\mathbf v}\n\t| c = {{Defof|Dot Product}}\n}}\n{{eqn\t| r = \\lambda \\norm {\\mathbf v}^2\n\t| c = Dot Product of Vector with Itself\n}}\n{{end-eqn}}\nFrom Euclidean Space is Normed Space, we have: \n:$\\norm {\\mathbf v}^2 > 0$\nso:\n:$\\lambda > 0$\n{{qed}}\nCategory:Symmetric Matrices\nCategory:Positive Definite Matrices\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"20418","document_content":"\\section{Reduction of Explicit ODE to First Order System}\nTags: Ordinary Differential Equations\n\n\\begin{theorem}\nLet $\\map {x^{\\paren n} } t = \\map F {t, x, x', \\ldots, x^{\\paren {n - 1} } }$, $\\map x {t_0} = x_0$ be an explicit ODE with $x \\in \\R^m$.\nLet there exist $I \\subseteq \\R$ such that there exists a unique particular solution:\n:$x: I \\to \\R^m$\nto this ODE.\nThen there exists a system of first order ODEs:\n:$y' = \\map {\\tilde F} {t, y}$\nwith $y = \\tuple {y_1, \\ldots, y_{m n} }^T \\in \\R^{m n}$ such that:\n:$\\tuple {\\map {y_1} t, \\ldots, \\map {y_m} t} = \\map x t$\nfor all $t \\in I$ and $\\map y {t_0} = x_0$.\n\\end{theorem}\n\n\\begin{proof}\nDefine the mappings:\n:$z_1, \\ldots, z_n: I \\to \\R^m$\nby:\n:$z_j = x^{\\paren {j - 1} }$, $j = 1, \\ldots, n$\nThen:\n{{begin-eqn}}\n{{eqn | l = z_1'\n | r = z_2\n}}\n{{eqn | o = \\vdots\n}}\n{{eqn | l = z_{n - 1}'\n | r = z_n\n}}\n{{eqn | l = z_n'\n | r = \\map F {t, z_1, \\ldots, z_n}\n}}\n{{end-eqn}}\nThis is a system of $m n$ first order ODEs.\nBy construction:\n:$\\map {z_1} t = \\map x t$\nfor all $t \\in I$ and $\\map {z_1} {t_0} = x_0$.\nTherefore we can take:\n:$y = \\begin {pmatrix} z_1 \\\\ \\vdots \\\\ z_{n - 1} \\\\ z_n \\end {pmatrix}, \\quad \\tilde F: \\begin {pmatrix} z_1 \\\\ \\vdots \\\\ z_n \\end{pmatrix} \\mapsto \\begin {pmatrix} z_2 \\\\ \\vdots \\\\ z_n \\\\ \\map F {t, z_1, \\ldots, z_n} \\end {pmatrix}$\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"20530","document_content":"\\section{Removable Singularity at Infinity implies Constant Function}\nTags: Complex Analysis\n\n\\begin{theorem}\nLet $f : \\C \\to \\C$ be an entire function.\nLet $f$ have an removable singularity at $\\infty$. \nThen $f$ is constant.\n\\end{theorem}\n\n\\begin{proof}\nWe are given that $f$ has a removable singularity at $\\infty$.\nBy Riemann Removable Singularities Theorem, $f$ must be bounded in a neighborhood of $\\infty$.\nThat is, there exists a real number $M > 0$ such that:\n:$\\forall z \\in \\set {z : \\cmod z > r}: \\cmod {\\map f z} \\le M$\nfor some real $r \\ge 0$.\nHowever, by Continuous Function on Compact Space is Bounded, $f$ is also bounded on $\\set {z: \\cmod z \\le r}$. \nAs $\\set {z: \\cmod z > r} \\cup \\set {z: \\cmod z \\le r} = \\C$, $f$ is therefore bounded on $\\C$.\nTherefore by Liouville's Theorem, $f$ is constant.\n{{qed}}\nCategory:Complex Analysis\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"20759","document_content":"\\section{Rolle's Theorem}\nTags: Continuity, Differential Calculus, Continuous Real Functions, Rolle's Theorem, Named Theorems, Continuous Functions, Differentiable Real Functions, Differential Real Functions\n\n\\begin{theorem}\nLet $f$ be a real function which is:\n:continuous on the closed interval $\\closedint a b$\nand:\n:differentiable on the open interval $\\openint a b$.\nLet $\\map f a = \\map f b$.\nThen:\n:$\\exists \\xi \\in \\openint a b: \\map {f'} \\xi = 0$\n\\end{theorem}\n\n\\begin{proof}\nWe have that $f$ is continuous on $\\closedint a b$.\nIt follows from Continuous Image of Closed Interval is Closed Interval that $f$ attains:\n:a maximum $M$ at some $\\xi_1 \\in \\closedint a b$\nand:\n:a minimum $m$ at some $\\xi_2 \\in \\closedint a b$.\nSuppose $\\xi_1$ and $\\xi_2$ are both end points of $\\closedint a b$.\nBecause $\\map f a = \\map f b$ it follows that $m = M$ and so $f$ is constant on $\\closedint a b$.\nThen, by Derivative of Constant, $\\map {f'} \\xi = 0$ for all $\\xi \\in \\openint a b$.\nSuppose $\\xi_1$ is not an end point of $\\closedint a b$.\nThen $\\xi_1 \\in \\openint a b$ and $f$ has a local maximum at $\\xi_1$.\nHence the result follows from Derivative at Maximum or Minimum.\nSimilarly, suppose $\\xi_2$ is not an end point of $\\closedint a b$.\nThen $\\xi_2 \\in \\openint a b$ and $f$ has a local minimum at $\\xi_2$.\nHence the result follows from Derivative at Maximum or Minimum.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"20761","document_content":"\\section{Root of Equation e^x (x - 1) = e^-x (x + 1)}\nTags: Analysis\n\n\\begin{theorem}\nThe equation:\n:$e^x \\paren {x - 1} = e^{-x} \\paren {x + 1}$\nhas a root:\n:$x = 1 \\cdotp 19966 \\, 78640 \\, 25773 \\, 4 \\ldots$\n\\end{theorem}\n\n\\begin{proof}\nLet $\\map f x = e^x \\paren {x - 1} - e^{-x} \\paren {x + 1}$.\nThen if $\\map f c = 0$, $c$ is a root of $e^x \\paren {x - 1} = e^{-x} \\paren {x + 1}$.\nNotice that:\n:$\\map f 1 = e^1 \\paren {1 - 1} - e^{-1} \\paren {1 + 1} = -\\dfrac 2 e < 0$\n:$\\map f 2 = e^2 \\paren {2 - 1} - e^{-2} \\paren {2 + 1} = e^2 - \\dfrac 3 {e^2} > 0$\nBy Intermediate Value Theorem:\n:$\\exists c \\in \\openint 1 2: \\map f c = 0$.\nThis shows that our equation has a root between $1$ and $2$.\nThe exact value of this root can be found using any numerical method, e.g. Newton's Method.\n{{ProofWanted|Analysis needed of the Kepler Equation}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"20819","document_content":"\\section{Sample Matrix Independence Test}\nTags: Linear Second Order ODEs, Linear Algebra\n\n\\begin{theorem}\nLet $V$ be a vector space of real or complex-valued functions on a set $J$.\nLet $f_1, \\ldots, f_n$ be functions in $V$.\nLet '''samples''' $x_1, \\ldots, x_n$ from $J$ be given.\nDefine the '''sample matrix''' :\n:$S = \\begin{bmatrix}\n\\map {f_1} {x_1} & \\cdots & \\map {f_n} {x_1} \\\\\n\\vdots & \\ddots & \\vdots \\\\\n\\map {f_1} {x_n} & \\cdots & \\map {f_n} {x_n} \\\\\n\\end{bmatrix}$\nLet $S$ be invertible.\nThen $f_1, \\ldots, f_n$ are linearly independent in $V$.\n\\end{theorem}\n\n\\begin{proof}\nThe definition of linear independence is applied.\nAssume a linear combination of the functions $f_1, \\ldots, f_n$ is the zero function:\n{{begin-eqn}}\n{{eqn | n = 1\n | l = \\sum_{i \\mathop = 1}^n c_i \\map {f_i} x \n | r = 0\n | c = for all $x$\n}}\n{{end-eqn}}\nLet $\\vec c$ have components $c_1, \\ldots, c_n$.\nFor $i = 1, \\ldots, n$ replace $x = x_i$ in $(1)$.\nThere are $n$ linear homogeneous algebraic equations, written as:\n:$S \\vec c = \\vec 0$\nBecause $S$ is invertible:\n:$\\vec c = \\vec 0$\nThe functions are linearly independent.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"20859","document_content":"\\section{Schauder Basis is Linearly Independent}\nTags: Linear Independence, Schauder Bases\n\n\\begin{theorem}\nLet $\\Bbb F \\in \\set {\\R, \\C}$. \nLet $\\struct {X, \\norm \\cdot}$ be a normed vector space over $\\Bbb F$.\nLet $\\set {e_n : n \\in \\N}$ be a Schauder basis for $X$. \nThen $\\set {e_n : n \\in \\N}$ is linearly independent.\n\\end{theorem}\n\n\\begin{proof}\nSuppose that: \n:$\\ds \\sum_{k \\mathop = 1}^n \\alpha_{i_k} e_{i_k} = 0$\nfor some $n \\in \\N$, $i_1, \\ldots, i_n \\in \\N$ and $\\alpha_{i_1}, \\ldots, \\alpha_{i_n} \\in \\Bbb F$.\nDefine a sequence $\\sequence {\\alpha_j}_{j \\mathop \\in \\N}$ in $\\Bbb F$ by: \n:$\\ds \\alpha_j = \\begin{cases}\\alpha_{i_k} & \\text { if there exists } k \\text { such that } j = i_k \\\\ 0 & \\text { otherwise}\\end{cases}$\nThen, we have: \n:$\\ds \\sum_{j \\mathop = 1}^\\infty \\alpha_j e_j = \\sum_{k \\mathop = 1}^n \\alpha_{i_k} e_{i_k} = 0$\nFrom the definition of Schauder basis, we then have: \n:$\\alpha_j = 0$ for each $j \\in \\N$\nand in particular: \n:$\\alpha_{i_k} = 0$ for each $k$. \nSince the coefficients $\\alpha_{i_1}, \\ldots, \\alpha_{i_n}$ and $n \\in \\N$ were arbitrary, we have that:\n:$\\set {e_n : n \\in \\N}$ is linearly independent.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"21599","document_content":"\\section{Solution of Second Order Differential Equation with Missing Dependent Variable}\nTags: Second Order ODEs\n\n\\begin{theorem}\nLet $\\map f {x, y', y''} = 0$ be a second order ordinary differential equation in which the dependent variable $y$ is not explicitly present.\nThen $f$ can be reduced to a first order ordinary differential equation, whose solution can be determined.\n\\end{theorem}\n\n\\begin{proof}\nConsider the second order ordinary differential equation:\n:$(1): \\quad \\map f {x, y', y''} = 0$\nLet a new dependent variable $p$ be introduced:\n:$y' = p$\n:$y'' = \\dfrac {\\d p} {\\d x}$\nThen $(1)$ can be transformed into:\n:$(2): \\quad \\map f {x, p, \\dfrac {\\d p} {\\d x} } = 0$\nwhich is a first order ODE.\nIf $(2)$ has a solution which can readily be found, it will be expressible in the form:\n:$(3): \\quad \\map g {x, p}$\nwhich can then be expressed in the form:\n:$\\map g {x, \\dfrac {\\d y} {\\d x} } = 0$\nwhich is likewise subject to the techniques of solution of a first order ODE.\nHence such a second order ODE is reduced to the problem of solving two first order ODEs in succession.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"21600","document_content":"\\section{Solution of Second Order Differential Equation with Missing Independent Variable}\nTags: Second Order ODEs\n\n\\begin{theorem}\nLet $\\map g {y, \\dfrac {\\d y} {\\d x}, \\dfrac {\\d^2 y} {\\d x^2} } = 0$ be a second order ordinary differential equation in which the independent variable $x$ is not explicitly present.\nThen $g$ can be reduced to a first order ordinary differential equation, whose solution can be determined.\n\\end{theorem}\n\n\\begin{proof}\nConsider the second order ordinary differential equation:\n:$(1): \\quad \\map g {y, \\dfrac {\\d y} {\\d x}, \\dfrac {\\d^2 y} {\\d x^2} } = 0$\nLet a new dependent variable $p$ be introduced:\n:$y' = p$\nHence:\n:$y'' = \\dfrac {\\d p} {\\d x} = \\dfrac {\\d p} {\\d y} \\dfrac {\\d y} {\\d x} = p \\dfrac {\\d p} {\\d y}$\nThen $(1)$ can be transformed into:\n:$(2): \\quad \\map g {y, p, p \\dfrac {\\d p} {\\d y} = 0}$\nwhich is a first order ODE.\nIf $(2)$ has a solution which can readily be found, it will be expressible in the form:\n:$(3): \\quad \\map g {x, p}$\nwhich can then be expressed in the form:\n:$\\map g {x, \\dfrac {\\d y} {\\d x} }$\nwhich is likewise subject to the techniques of solution of a first order ODE.\nHence such a second order ODE is reduced to the problem of solving two first order ODEs in succession.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"21758","document_content":"\\section{Squeeze Theorem\/Functions}\nTags: Named Theorems, Limits of Real Functions, Limits of Functions, Squeeze Theorem\n\n\\begin{theorem}\nLet $a$ be a point on an open real interval $I$.\nLet $f$, $g$ and $h$ be real functions defined at all points of $I$ except for possibly at point $a$.\nSuppose that:\n:$\\forall x \\ne a \\in I: \\map g x \\le \\map f x \\le \\map h x$\n:$\\ds \\lim_{x \\mathop \\to a} \\map g x = \\lim_{x \\mathop \\to a} \\map h x = L$\nThen:\n:$\\ds \\lim_{x \\mathop \\to a} \\ \\map f x = L$\n\\end{theorem}\n\n\\begin{proof}\nWe start by proving the special case where $\\forall x: g \\left({x}\\right) = 0$ and $L=0$, in which case $\\displaystyle \\lim_{x \\to a} \\ h \\left({x}\\right) = 0$.\nLet $\\epsilon > 0$ be a positive real number.\nThen by the definition of the limit of a function:\n: $\\exists \\delta > 0: 0 < \\left|{x - a}\\right| < \\delta \\implies \\left|{h \\left({x}\\right)}\\right| < \\epsilon$\nNow:\n: $\\forall x \\ne a: 0 = g \\left({x}\\right) \\le f \\left({x}\\right) \\le h \\left({x}\\right)$\nso that:\n:$\\left|{f \\left({x}\\right)}\\right| \\le \\left|{h \\left({x}\\right)}\\right|$\nThus:\n: $0 < |x-a| < \\delta \\implies \\left|{f \\left({x}\\right)}\\right| \\le \\left|{h \\left({x}\\right)}\\right| < \\epsilon$\nBy the transitive property of $\\le$, this proves that:\n: $\\displaystyle \\lim_{x \\to a} \\ f \\left({x}\\right) = 0 = L$\nWe now move on to the general case, with $g \\left({x}\\right)$ and $L$ arbitrary.\nFor $x \\ne a$, we have:\n: $g \\left({x}\\right) \\le f \\left({x}\\right) \\le h \\left({x}\\right)$\nBy subtracting $g \\left({x}\\right)$ from all expressions, we have:\n: $0 \\le f \\left({x}\\right) - g \\left({x}\\right) \\le h \\left({x}\\right) - g \\left({x}\\right)$\nSince as $x \\to a, h \\left({x}\\right) \\to L$ and $g \\left({x}\\right) \\to L$, we have:\n: $h \\left({x}\\right) - g \\left({x}\\right) \\to L - L = 0$\nFrom the special case, we now have:\n: $f \\left({x}\\right) - g \\left({x}\\right) \\to 0$\nWe conclude that:\n: $f \\left({x}\\right) = \\left({f \\left({x}\\right) - g \\left({x}\\right)}\\right) + g \\left({x}\\right) \\to 0 + L = L$\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"21762","document_content":"\\section{Squeeze Theorem\/Sequences\/Real Numbers}\nTags: Named Theorems, Limits of Sequences, Squeeze Theorem, Real Analysis\n\n\\begin{theorem}\nLet $\\sequence {x_n}$, $\\sequence {y_n}$ and $\\sequence {z_n}$ be sequences in $\\R$.\nLet $\\sequence {y_n}$ and $\\sequence {z_n}$ both be convergent to the following limit:\n:$\\ds \\lim_{n \\mathop \\to \\infty} y_n = l, \\lim_{n \\mathop \\to \\infty} z_n = l$\nSuppose that:\n:$\\forall n \\in \\N: y_n \\le x_n \\le z_n$\nThen:\n:$x_n \\to l$ as $n \\to \\infty$\nthat is:\n:$\\ds \\lim_{n \\mathop \\to \\infty} x_n = l$\nThus, if $\\sequence {x_n}$ is always between two other sequences that both converge to the same limit, $\\sequence {x_n} $ is said to be '''sandwiched''' or '''squeezed''' between those two sequences and itself must therefore converge to that same limit.\n\\end{theorem}\n\n\\begin{proof}\nFrom Negative of Absolute Value: Corollary 1:\n:$\\size {x - l} < \\epsilon \\iff l - \\epsilon < x < l + \\epsilon$\nLet $\\epsilon > 0$.\nWe need to prove that:\n:$\\exists N: \\forall n > N: \\size {x_n - l} < \\epsilon$\nAs $\\ds \\lim_{n \\mathop \\to \\infty} y_n = l$ we know that:\n:$\\exists N_1: \\forall n > N_1: \\size {y_n - l} < \\epsilon$\nAs $\\ds \\lim_{n \\mathop \\to \\infty} z_n = l$ we know that:\n:$\\exists N_2: \\forall n > N_2: \\size {z_n - l} < \\epsilon$\nLet $N = \\max \\set {N_1, N_2}$.\nThen if $n > N$, it follows that $n > N_1$ and $n > N_2$.\nSo:\n:$\\forall n > N: l - \\epsilon < y_n < l + \\epsilon$\n:$\\forall n > N: l - \\epsilon < z_n < l + \\epsilon$\nBut:\n:$\\forall n \\in \\N: y_n \\le x_n \\le z_n$\nSo:\n:$\\forall n > N: l - \\epsilon < y_n \\le x_n \\le z_n < l + \\epsilon$\nand so:\n:$\\forall n > N: l - \\epsilon < x_n < l + \\epsilon$\nSo:\n:$\\forall n > N: \\size {x_n - l} < \\epsilon$\nHence the result.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"22806","document_content":"\\section{Triangles with Proportional Sides are Similar}\nTags: Triangles\n\n\\begin{theorem}\nLet two triangles have corresponding sides which are proportional.\nThen their corresponding angles are equal.\nThus, by definition, such triangles are similar.\n{{:Euclid:Proposition\/VI\/5}}\n\\end{theorem}\n\n\\begin{proof}\nLet $\\triangle ABC, \\triangle DEF$ be triangles whose sides are proportional, so that:\n:$ AB : BC = DE : EF$\n:$ BC : CA = EF : FD$\n:$ BA : AC = ED : DF$\nWe need to show that\n: $\\angle ABC = \\angle DEF$\n: $\\angle BCA = \\angle EFD$\n: $\\angle BAC = \\angle EDF$\n:400px\nOn the straight line $EF$, and at the points $E, F$ on it, construct $\\angle FEG = \\angle ABC$ and $\\angle EFG = \\angle ACB$.\nFrom Sum of Angles of Triangle Equals Two Right Angles, the remaining angle at $A$ equals the remaining angle at $G$.\nTherefore $\\triangle ABC$ is equiangular with $\\triangle GEF$.\nFrom Equiangular Triangles are Similar, the sides about the equal angles are proportional, and those are corresponding sides which subtend the equal angles.\nSo:\n: $AB : BD = GE : EF$\nBut by hypothesis:\n: $AB : BC = DE : EF$\nSo from Equality of Ratios is Transitive\n: $DE : EF = GE : EF$\nSo each of $DE, GE$ has the same ratio to $EF$.\nSo from Magnitudes with Same Ratios are Equal:\n: $DE = GE$\nFor the same reason:\n: $DF = GF$\nSo we have that $DE = EG$, $EF$ is common and $DF = FG$.\nSo from Triangle Side-Side-Side Equality:\n: $\\triangle DEF = \\triangle GEF$\nThat is:\n: $\\angle DEF = \\angle GEF, \\angle DFE = \\angle GFE, \\angle EDF = \\angle EGF$\nAs $\\angle GEF = \\angle ABC$ it follows that:\n: $\\angle ABC = \\angle DEF$\nFor the same reason $\\angle ACB = \\angle DFE$ and $\\angle BAC = \\angle EDF$.\nHence the result.\n{{Qed}}\n{{Euclid Note|5|VI}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"23033","document_content":"\\section{Union of Non-Disjoint Convex Sets is Convex Set}\nTags: Set Union, Convex Sets (Order Theory), Convex Sets, Union\n\n\\begin{theorem}\nLet $\\struct {S, \\preccurlyeq}$ be an ordered set.\nLet $\\CC$ be a set of convex sets of $S$ such that their intersection is non-empty:\n:$\\ds \\bigcap \\CC \\ne \\O$\nThen the union $\\ds \\bigcup \\CC$ is also convex.\n\\end{theorem}\n\n\\begin{proof}\nLet $x, y, z \\in S$ be arbitrary elements of $S$ such that $x \\prec y \\prec z$.\nLet $x, z \\in \\ds \\bigcup \\CC$.\nFirst let $x, z \\in C$ where $C \\in \\CC$.\nThen as $C$ is convex, $y \\in C$.\nHence, by definition of union, $y \\in \\ds \\bigcup \\CC$.\nNow let $x \\in C_1, z \\in C_2$ where $C_1, C_2 \\in \\CC$.\nWe have that $\\ds \\bigcap \\CC \\ne \\O$.\nThus $C_1 \\cap C_2 \\ne \\O$.\nThen $\\exists a \\in C_1 \\cap C_2: x < a < z$.\nHence one of the following cases holds:\n:$(1): \\quad x < y < a < z$, whence $y \\in C_1$, by convexity of $C_1$\n:$(2): \\quad x < a < y < z$, whence $y \\in C_2$, by convexity of $C_2$\n:$(3): \\quad y = a$, whence $y \\in C_1$ and $y \\in C_2$, by definition of $a$.\nThus in all cases $y \\in \\ds \\bigcup \\CC$.\nThus $\\ds \\bigcup \\CC$ is convex by definition.\n{{qed}}\n\\end{proof}\n\n","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"document_id":"23699","document_content":"\\begin{definition}[Definition:Acyclic Graph]\nAn '''acyclic graph''' is a graph or digraph with no cycles.\nAn acyclic connected undirected graph is a tree.\nAn acyclic disconnected undirected graph is a forest.\nCategory:Definitions\/Graph Theory\n\\end{definition}","parent_id":null,"metadata":null,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_panlu\/rigid-body3.json","document_id":"15865","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_panlu\/rigid-body3.json","document_id":"230","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_elainewan\/math_calculus_12.json","document_id":"15210","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_jianyu_xu\/Multinomial_4.json","document_id":"10463","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_jianyu_xu\/Multinomial_4.json","document_id":"10462","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_wenhuchen\/L'H\u00f4pital_rule1.json","document_id":"11592","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_wenhuchen\/Liouville\u2019s_theorem2.json","document_id":"14493","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_wenhuchen\/Liouville\u2019s_theorem2.json","document_id":"11018","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_wenhuchen\/Liouville\u2019s_theorem2.json","document_id":"20530","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_wenhuchen\/t_test3.json","document_id":"9320","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_wenhuchen\/t_test3.json","document_id":"4138","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_jianyu_xu\/Cayley_3.json","document_id":"16790","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_xueguangma\/intermediate_value_theorem.json","document_id":"12010","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_xueguangma\/intermediate_value_theorem.json","document_id":"12011","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_xueguangma\/intermediate_value_theorem.json","document_id":"12012","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_xueguangma\/intermediate_value_theorem.json","document_id":"13939","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_xueguangma\/intermediate_value_theorem.json","document_id":"17066","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_xueguangma\/intermediate_value_theorem.json","document_id":"18841","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_xueguangma\/intermediate_value_theorem.json","document_id":"20761","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_xinyi\/dag_1.json","document_id":"3778","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_xinyi\/dag_1.json","document_id":"13468","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_xinyi\/dag_1.json","document_id":"23699","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_maxku\/ipnetwork13-hammingdist.json","document_id":"14101","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_jianyu_xu\/Multinomial_6.json","document_id":"10462","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_panlu\/similarity2.json","document_id":"22806","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_panlu\/similarity2.json","document_id":"14371","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_mingyin\/Fundamental-Theorem-of-Calculus3.json","document_id":"11986","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_tonyxia\/maxplanar3.json","document_id":"11239","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_tonyxia\/maxplanar3.json","document_id":"14139","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_mingyin\/cauchy-integral-theorem1.json","document_id":"16899","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_jianyu_xu\/pigeonhole_4.json","document_id":"13467","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_jianyu_xu\/pigeonhole_4.json","document_id":"18695","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_jianyu_xu\/Stirling_number_second_kind_5.json","document_id":"8903","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_wenhuchen\/viterbi2.json","document_id":"5461","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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{"query_id":"TheoremQA_jianyu_xu\/Binomial_6.json","document_id":"10463","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
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| 36 |
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|
| 37 |
+
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|
| 38 |
+
{"query_id":"TheoremQA_jianyu_xu\/Binomial_6.json","document_id":"17901","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 39 |
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{"query_id":"TheoremQA_xinyi\/linear_projection.json","document_id":"18400","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 40 |
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{"query_id":"TheoremQA_jianyu_xu\/Multinomial_1.json","document_id":"10463","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 41 |
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|
| 42 |
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|
| 43 |
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{"query_id":"TheoremQA_tonyxia\/maxplanar1.json","document_id":"11239","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 44 |
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|
| 45 |
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| 46 |
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|
| 47 |
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{"query_id":"TheoremQA_wenhuchen\/Liouville\u2019s_theorem1.json","document_id":"14493","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 48 |
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|
| 49 |
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|
| 50 |
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|
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|
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|
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|
| 54 |
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|
| 55 |
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|
| 56 |
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|
| 57 |
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|
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{"query_id":"TheoremQA_elainewan\/math_algebra_3_2.json","document_id":"20819","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 59 |
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|
| 60 |
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|
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{"query_id":"TheoremQA_wenhuchen\/series_convergen2.json","document_id":"15648","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 62 |
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|
| 63 |
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|
| 64 |
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|
| 65 |
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|
| 66 |
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| 67 |
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| 68 |
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| 69 |
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{"query_id":"TheoremQA_mingyin\/Lebesgue-measure1.json","document_id":"11426","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 70 |
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{"query_id":"TheoremQA_mingyin\/Lebesgue-measure1.json","document_id":"16984","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 71 |
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|
| 72 |
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|
| 73 |
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|
| 74 |
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|
| 75 |
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{"query_id":"TheoremQA_jianyu_xu\/Graph_2.json","document_id":"16790","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 76 |
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{"query_id":"TheoremQA_jianyu_xu\/Graph_2.json","document_id":"17301","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 77 |
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{"query_id":"TheoremQA_wenhuchen\/definite_matrix1.json","document_id":"20341","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 78 |
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{"query_id":"TheoremQA_wenhuchen\/definite_matrix1.json","document_id":"5725","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 79 |
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|
| 80 |
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|
| 81 |
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|
| 82 |
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|
| 83 |
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|
| 84 |
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|
| 85 |
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{"query_id":"TheoremQA_wenhuchen\/eigen_value1.json","document_id":"2723","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 86 |
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|
| 87 |
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{"query_id":"TheoremQA_wenhuchen\/kepler's_law1.json","document_id":"11654","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 88 |
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{"query_id":"TheoremQA_mingyin\/convexity1.json","document_id":"23033","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 89 |
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{"query_id":"TheoremQA_jianyu_xu\/Multinomial_2.json","document_id":"10463","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 90 |
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{"query_id":"TheoremQA_jianyu_xu\/Multinomial_2.json","document_id":"10462","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 91 |
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{"query_id":"TheoremQA_wenhuchen\/jensen1.json","document_id":"11619","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 92 |
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|
| 93 |
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|
| 94 |
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{"query_id":"TheoremQA_jianyu_xu\/Ramsey_4.json","document_id":"20117","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 95 |
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{"query_id":"TheoremQA_jianyu_xu\/Ramsey_4.json","document_id":"7627","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 96 |
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|
| 97 |
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|
| 98 |
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{"query_id":"TheoremQA_elainewan\/math_calculus_2_11.json","document_id":"12010","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 99 |
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{"query_id":"TheoremQA_elainewan\/math_calculus_2_11.json","document_id":"12011","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 100 |
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{"query_id":"TheoremQA_elainewan\/math_calculus_2_11.json","document_id":"12012","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 101 |
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|
| 102 |
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{"query_id":"TheoremQA_wenhuchen\/Rolle's_theorem.json","document_id":"20759","relevance_score":1.0,"binary_relevance":1,"task_split":"theorem_retrieval"}
|
| 103 |
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|
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| 1 |
+
{"query_id":"980","document_id":"6722354:0","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
|
| 2 |
+
{"query_id":"980","document_id":"6722354:1","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
|
| 3 |
+
{"query_id":"980","document_id":"6722354:2","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
|
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{"query_id":"650","document_id":"12417140:2","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"650","document_id":"12417140:3","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"650","document_id":"12417140:4","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"650","document_id":"12417140:5","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"650","document_id":"12417140:6","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"650","document_id":"12417140:7","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"537","document_id":"1031292:0","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"537","document_id":"1031292:1","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"537","document_id":"1031292:2","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"537","document_id":"1031292:3","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"537","document_id":"1031292:4","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"537","document_id":"1031292:5","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"537","document_id":"1031292:6","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"537","document_id":"1031292:7","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"537","document_id":"1031292:8","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"945","document_id":"304725:0","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"945","document_id":"304725:1","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"945","document_id":"304725:2","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"945","document_id":"304725:3","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"945","document_id":"304725:4","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"945","document_id":"304725:5","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"945","document_id":"304725:6","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"945","document_id":"304725:7","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"945","document_id":"304725:8","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"108","document_id":"13607881:0","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"108","document_id":"13607881:1","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"108","document_id":"13607881:2","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"108","document_id":"13607881:3","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"108","document_id":"13607881:4","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"673","document_id":"28953349:0","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"673","document_id":"28953349:1","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"673","document_id":"28953349:2","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"632","document_id":"3261733:0","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"632","document_id":"3261733:1","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"632","document_id":"3261733:2","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"632","document_id":"3261733:3","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"632","document_id":"3261733:4","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"632","document_id":"3261733:5","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"632","document_id":"3261733:6","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"632","document_id":"3261733:7","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"632","document_id":"3261733:8","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"632","document_id":"3261733:9","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"632","document_id":"3261733:10","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"632","document_id":"3261733:11","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"632","document_id":"3261733:12","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"632","document_id":"3261733:13","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"632","document_id":"3261733:15","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"632","document_id":"3261733:16","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"632","document_id":"3261733:17","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"632","document_id":"3261733:18","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"632","document_id":"3261733:19","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"545","document_id":"448181:0","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"545","document_id":"448181:1","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"545","document_id":"448181:2","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"545","document_id":"448181:3","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
|
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{"query_id":"1031","document_id":"591309:0","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"1031","document_id":"591309:1","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"1031","document_id":"591309:2","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"1031","document_id":"591309:3","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"1031","document_id":"591309:4","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"1031","document_id":"591309:5","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"1031","document_id":"591309:6","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"1031","document_id":"591309:7","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"245","document_id":"1809458:0","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"245","document_id":"1809458:1","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"245","document_id":"1809458:2","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"245","document_id":"1809458:3","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
|
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{"query_id":"245","document_id":"1809458:4","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
|
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{"query_id":"245","document_id":"1809458:5","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
|
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{"query_id":"245","document_id":"1809458:6","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
|
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+
{"query_id":"245","document_id":"1809458:7","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"580","document_id":"5651517:0","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"580","document_id":"5651517:1","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
|
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{"query_id":"580","document_id":"5651517:2","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"580","document_id":"5651517:3","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"580","document_id":"5651517:4","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"580","document_id":"5651517:5","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"120","document_id":"1475272:0","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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{"query_id":"120","document_id":"1475272:1","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
|
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{"query_id":"120","document_id":"1475272:2","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
|
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{"query_id":"120","document_id":"1475272:3","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
|
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{"query_id":"120","document_id":"1475272:4","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
|
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{"query_id":"120","document_id":"1475272:5","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
|
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{"query_id":"120","document_id":"1475272:6","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
|
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+
{"query_id":"120","document_id":"1475272:7","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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+
{"query_id":"201","document_id":"22340794:0","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
|
| 362 |
+
{"query_id":"201","document_id":"22340794:1","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
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+
{"query_id":"201","document_id":"22340794:2","relevance_score":1.0,"binary_relevance":1,"task_split":"tip_of_the_tongue"}
|
tip_of_the_tongue/queries.jsonl
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{"query_id":"980","query_content":"Giant Spiders in 1960\u2019s comedy movie .\n This has driven me nuts for the last 25 years. Seen a couple of times on British TV in the 70\u2019s in the afternoon, in color (I think), an anthology comedy consisting of three stories (I think), made in the 1960\u2019s (I think). No idea of stars, no memory of the content of the other two stories, just a strong memory that the first story was about a woman in an English country house with pet tarantulas whose offspring were giant spiders (large dog sized). The climax involved the British police raiding the house and comically fighting the spiders, hitting them with bed pans, etc, simple effects that I remember being accomplished by shooting real spiders in a miniature house. I have tried to find any information on what this film might have been over the years, but with no luck. Any ideas?","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"6722354:0","label":1.0},{"id":"6722354:1","label":1.0},{"id":"6722354:2","label":1.0},{"id":"6722354:3","label":1.0},{"id":"6722354:4","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"6722354","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nGiant Spiders in 1960\\u2019s comedy movie .\\n This has driven me nuts for the last 25 years. Seen a couple of times on British TV in the 70\\u2019s in the afternoon, in color (I think), an anthology comedy consisting of three stories (I think), made in the 1960\\u2019s (I think). No idea of stars, no memory of the content of the other two stories, just a strong memory that the first story was about a woman in an English country house with pet tarantulas whose offspring were giant spiders (large dog sized). The climax involved the British police raiding the house and comically fighting the spiders, hitting them with bed pans, etc, simple effects that I remember being accomplished by shooting real spiders in a miniature house. I have tried to find any information on what this film might have been over the years, but with no luck. Any ideas?\"}","task_split":"tip_of_the_tongue"}
|
| 2 |
+
{"query_id":"852","query_content":"Cheque .\n I saw it probably after 2005, probably came out a bit before that. The first scene I remember is a man giving the boy who the\u00a0 films centred around a cheque for however much he wants I think. He later goes home and sets it up to get the money on the computer. He enters his name as what the computer is called. Later in the film it shows him with like a castle and all this stuff he bought with the money.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"1039329:0","label":1.0},{"id":"1039329:1","label":1.0},{"id":"1039329:2","label":1.0},{"id":"1039329:3","label":1.0},{"id":"1039329:4","label":1.0},{"id":"1039329:5","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"1039329","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nCheque .\\n I saw it probably after 2005, probably came out a bit before that. The first scene I remember is a man giving the boy who the\\u00a0 films centred around a cheque for however much he wants I think. He later goes home and sets it up to get the money on the computer. He enters his name as what the computer is called. Later in the film it shows him with like a castle and all this stuff he bought with the money.\"}","task_split":"tip_of_the_tongue"}
|
| 3 |
+
{"query_id":"750","query_content":"Gnome movie .\n I remember watching a animated movie as a kid in the 90\u2019s about gnomes and trolls ect. that lived in the forest. The gnomes are good, and the trolls are evil and always trying to I guess kill the gnomes? I don\u2019t know, but they\u2019re the bad guys. There\u2019s this one gnome, I think he might be like the main character, who helps sick and injured animals and stuff.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"357233:0","label":1.0},{"id":"357233:1","label":1.0},{"id":"357233:2","label":1.0},{"id":"357233:3","label":1.0},{"id":"357233:4","label":1.0},{"id":"357233:5","label":1.0},{"id":"357233:6","label":1.0},{"id":"357233:7","label":1.0},{"id":"357233:8","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"357233","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nGnome movie .\\n I remember watching a animated movie as a kid in the 90\\u2019s about gnomes and trolls ect. that lived in the forest. The gnomes are good, and the trolls are evil and always trying to I guess kill the gnomes? I don\\u2019t know, but they\\u2019re the bad guys. There\\u2019s this one gnome, I think he might be like the main character, who helps sick and injured animals and stuff.\"}","task_split":"tip_of_the_tongue"}
|
| 4 |
+
{"query_id":"466","query_content":"60\u2019s flick, evil scientist freezes murdered female models in capsule for future\u2026 .\n Ok, so I think this was a mid to late 60\u2019s detective caper. I\u2019m picturing a rumpled B movie gumshoe ala Peter Falk or Alan Arkin (but not them), solving this case of disappearing models\/actresses. It\u2019s sketchy, but I remember one of the girls was strangled with a snake that was hidden in a fur coat. I remember the final scene in this space age looking lab with giant cryogenic capsules that were holding the starlets for the evil scientist\u2019s future \u201cuse\u201d The movie had a strong technicolor aspect- that\u2019s pretty much all I got.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"1131593:0","label":1.0},{"id":"1131593:1","label":1.0},{"id":"1131593:2","label":1.0},{"id":"1131593:3","label":1.0},{"id":"1131593:4","label":1.0},{"id":"1131593:5","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"1131593","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\n60\\u2019s flick, evil scientist freezes murdered female models in capsule for future\\u2026 .\\n Ok, so I think this was a mid to late 60\\u2019s detective caper. I\\u2019m picturing a rumpled B movie gumshoe ala Peter Falk or Alan Arkin (but not them), solving this case of disappearing models\/actresses. It\\u2019s sketchy, but I remember one of the girls was strangled with a snake that was hidden in a fur coat. I remember the final scene in this space age looking lab with giant cryogenic capsules that were holding the starlets for the evil scientist\\u2019s future \\u201cuse\\u201d The movie had a strong technicolor aspect- that\\u2019s pretty much all I got.\"}","task_split":"tip_of_the_tongue"}
|
| 5 |
+
{"query_id":"126","query_content":"monster movie before the 2000s (i think) .\n so the movie I saw had monsters. It had color, and was I\u2019m English, I distinctly remember a flying monster kidnap a male teen and kill him then at them end the teens eyes are poked out and the monster is looking threw them. The monster could fly, and green (I think) I think I saw it on TV but I\u2019m not 100% I was fairly young I\u2019m 18 right now so if that gives an indication other than that I think some teens die from a variety of other monsters (but that last part could be a different movie). Thanks in advance","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"1690432:0","label":1.0},{"id":"1690432:1","label":1.0},{"id":"1690432:2","label":1.0},{"id":"1690432:3","label":1.0},{"id":"1690432:4","label":1.0},{"id":"1690432:5","label":1.0},{"id":"1690432:6","label":1.0},{"id":"1690432:7","label":1.0},{"id":"1690432:8","label":1.0},{"id":"1690432:9","label":1.0},{"id":"1690432:10","label":1.0},{"id":"1690432:11","label":1.0},{"id":"1690432:12","label":1.0},{"id":"1690432:13","label":1.0},{"id":"1690432:14","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"1690432","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nmonster movie before the 2000s (i think) .\\n so the movie I saw had monsters. It had color, and was I\\u2019m English, I distinctly remember a flying monster kidnap a male teen and kill him then at them end the teens eyes are poked out and the monster is looking threw them. The monster could fly, and green (I think) I think I saw it on TV but I\\u2019m not 100% I was fairly young I\\u2019m 18 right now so if that gives an indication other than that I think some teens die from a variety of other monsters (but that last part could be a different movie). Thanks in advance\"}","task_split":"tip_of_the_tongue"}
|
| 6 |
+
{"query_id":"118","query_content":"late 80\u2019s or 90\u2019s black comedy, guy locked out of his appartment .\n It\u2019s a comedy of situations with a lot of hints of black humour. The movie begins showing a man getting off from his word on a Friday evening. He somehow get\u2019s locked out of his appartment and then his comic adventure starts. We follow him through the night where he meets all different kinds of people in shaggy places who make his life miserable while the only thing he craves for is to return to the safety of his home. You kind of feel sorry for this guy but in the end I think that he reevaluates his life and\/or way of living. The movie is in english (I thing american but may as well be british), in colour and I had watched it in the cinema circa 2003","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"613037:0","label":1.0},{"id":"613037:1","label":1.0},{"id":"613037:2","label":1.0},{"id":"613037:3","label":1.0},{"id":"613037:4","label":1.0},{"id":"613037:5","label":1.0},{"id":"613037:6","label":1.0},{"id":"613037:7","label":1.0},{"id":"613037:8","label":1.0},{"id":"613037:9","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"613037","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nlate 80\\u2019s or 90\\u2019s black comedy, guy locked out of his appartment .\\n It\\u2019s a comedy of situations with a lot of hints of black humour. The movie begins showing a man getting off from his word on a Friday evening. He somehow get\\u2019s locked out of his appartment and then his comic adventure starts. We follow him through the night where he meets all different kinds of people in shaggy places who make his life miserable while the only thing he craves for is to return to the safety of his home. You kind of feel sorry for this guy but in the end I think that he reevaluates his life and\/or way of living. The movie is in english (I thing american but may as well be british), in colour and I had watched it in the cinema circa 2003\"}","task_split":"tip_of_the_tongue"}
|
| 7 |
+
{"query_id":"873","query_content":"What is this hostage movie title??? .\n I don\u2019t remember the title of this movie but I know I have seen it when I was about 7-8 years old. I\u2019m 16 now. Basically, I remember there were 2 siblings involved in the movie. One was a teenage girl with dark hair, and she had a little brother. I believe their home was invaded by a few boys but I don\u2019t remember why. One boy had long black hair for sure! In one scene, I remember the teenage girl being tied to a bed as If one of the boys were about to do something bad to her! In another scene, her little brother has a secret passage in his closet that leads to his own panic room. He gets in it before any of the intruders find him. I really don\u2019t remember much but I do know that in the end, the boy with the long hair ends up letting the siblings go and he burns the house down. Sorry for being vague but this is all I can remember and i haven\u2019t found it after several attempts. ?","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"1266043:0","label":1.0},{"id":"1266043:1","label":1.0},{"id":"1266043:2","label":1.0},{"id":"1266043:3","label":1.0},{"id":"1266043:4","label":1.0},{"id":"1266043:5","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"1266043","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nWhat is this hostage movie title??? .\\n I don\\u2019t remember the title of this movie but I know I have seen it when I was about 7-8 years old. I\\u2019m 16 now. Basically, I remember there were 2 siblings involved in the movie. One was a teenage girl with dark hair, and she had a little brother. I believe their home was invaded by a few boys but I don\\u2019t remember why. One boy had long black hair for sure! In one scene, I remember the teenage girl being tied to a bed as If one of the boys were about to do something bad to her! In another scene, her little brother has a secret passage in his closet that leads to his own panic room. He gets in it before any of the intruders find him. I really don\\u2019t remember much but I do know that in the end, the boy with the long hair ends up letting the siblings go and he burns the house down. Sorry for being vague but this is all I can remember and i haven\\u2019t found it after several attempts. ?\"}","task_split":"tip_of_the_tongue"}
|
| 8 |
+
{"query_id":"820","query_content":"Japanese Crime\/Horror Movie .\n A few years ago I happened upon a Japanese movie \u2013 quite recent, in color and very well done. It involved a Japanese police homicide detective who went to work every day on a ferry, and as he travelled he began to see a face in the window of an abandoned warehouse. The face became more and more clear every day, and it to be a woman screaming for help. Of course, he investigated the warehouse, but found nothing on the first trip. He returned, and the woman materialized out of a puddle of water on the floor, and then disappeared again. After this, she would appear everytime he spilled water or tea on the floor of his apartment, or walked by a rain puddle in the street. Very weird, and unfortunately I had someplace to go and never saw the end of it. Dying to know if anyone recognizes it. Thanks!","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"8359558:0","label":1.0},{"id":"8359558:1","label":1.0},{"id":"8359558:2","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"8359558","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nJapanese Crime\/Horror Movie .\\n A few years ago I happened upon a Japanese movie \\u2013 quite recent, in color and very well done. It involved a Japanese police homicide detective who went to work every day on a ferry, and as he travelled he began to see a face in the window of an abandoned warehouse. The face became more and more clear every day, and it to be a woman screaming for help. Of course, he investigated the warehouse, but found nothing on the first trip. He returned, and the woman materialized out of a puddle of water on the floor, and then disappeared again. After this, she would appear everytime he spilled water or tea on the floor of his apartment, or walked by a rain puddle in the street. Very weird, and unfortunately I had someplace to go and never saw the end of it. Dying to know if anyone recognizes it. Thanks!\"}","task_split":"tip_of_the_tongue"}
|
| 9 |
+
{"query_id":"911","query_content":"Test scene in a diner .\n I\u2019m looking for a movie and I can only remember a scene in a diner. There are two people there and one of them has the prospect of a job (agent, spy, killer idk). He spots many things in the diner that are out of place, but the only one I am able to remember is that the waitress wears uncomfortable shoes, and as his aunt, mom, worked in a diner he knows she would never were those kind of shoes if she really worked there. I know it was a rather big movie, so I\u2019m going to be kicking myself. Thanks!","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"415156:0","label":1.0},{"id":"415156:1","label":1.0},{"id":"415156:2","label":1.0},{"id":"415156:3","label":1.0},{"id":"415156:4","label":1.0},{"id":"415156:5","label":1.0},{"id":"415156:6","label":1.0},{"id":"415156:7","label":1.0},{"id":"415156:8","label":1.0},{"id":"415156:9","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"415156","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nTest scene in a diner .\\n I\\u2019m looking for a movie and I can only remember a scene in a diner. There are two people there and one of them has the prospect of a job (agent, spy, killer idk). He spots many things in the diner that are out of place, but the only one I am able to remember is that the waitress wears uncomfortable shoes, and as his aunt, mom, worked in a diner he knows she would never were those kind of shoes if she really worked there. I know it was a rather big movie, so I\\u2019m going to be kicking myself. Thanks!\"}","task_split":"tip_of_the_tongue"}
|
| 10 |
+
{"query_id":"200","query_content":"Hope you guys can identifiy that movie .\n I know for sure that movie was filmed before 2013, because i have watched it earlier that year on a dvd, i would say it was probably filmed between 2008 and 2012 It was about the human race in the space that, were programmed to all at the same and they all were wearing white clothes all the time. Except there was one guy who was not like the others and was questioning everthing what was happening. the people in control always picked a lucky \u201cwinner\u201d that have just won a trip to a beautiful island and were brought out Well the one guy was curious and wondered what really happened and saw they were killed He was close to a blonde girl, he was talking to a lot and tried to \u201cwake her up\u201d, one day she got choosen as a winner and he wanted to prevent it hope the description was clear and detailed enough to have the answer thank you guys","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"1068520:0","label":1.0},{"id":"1068520:1","label":1.0},{"id":"1068520:2","label":1.0},{"id":"1068520:3","label":1.0},{"id":"1068520:4","label":1.0},{"id":"1068520:5","label":1.0},{"id":"1068520:6","label":1.0},{"id":"1068520:7","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"1068520","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nHope you guys can identifiy that movie .\\n I know for sure that movie was filmed before 2013, because i have watched it earlier that year on a dvd, i would say it was probably filmed between 2008 and 2012 It was about the human race in the space that, were programmed to all at the same and they all were wearing white clothes all the time. Except there was one guy who was not like the others and was questioning everthing what was happening. the people in control always picked a lucky \\u201cwinner\\u201d that have just won a trip to a beautiful island and were brought out Well the one guy was curious and wondered what really happened and saw they were killed He was close to a blonde girl, he was talking to a lot and tried to \\u201cwake her up\\u201d, one day she got choosen as a winner and he wanted to prevent it hope the description was clear and detailed enough to have the answer thank you guys\"}","task_split":"tip_of_the_tongue"}
|
| 11 |
+
{"query_id":"610","query_content":"Cop\u2019s son needs blood transfusion from an inmate .\n A cop\u2019s son is very sick and needs a certain type of blood transfusion. He finds out an inmate has the same type and once agreed the inmate takes advantage of the situation in the hospital and escapes. Then a long chasing odyssey till the end when the kid finally gets cured","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"2093587:0","label":1.0},{"id":"2093587:1","label":1.0},{"id":"2093587:2","label":1.0},{"id":"2093587:3","label":1.0},{"id":"2093587:4","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"2093587","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nCop\\u2019s son needs blood transfusion from an inmate .\\n A cop\\u2019s son is very sick and needs a certain type of blood transfusion. He finds out an inmate has the same type and once agreed the inmate takes advantage of the situation in the hospital and escapes. Then a long chasing odyssey till the end when the kid finally gets cured\"}","task_split":"tip_of_the_tongue"}
|
| 12 |
+
{"query_id":"662","query_content":"80\u2019s Movie\/Show with Mean Girls .\n I watched this when I was under 10 yrs old and it was in the 80\u2019s and in English. All I can remember is one scene. This group of 5 or 6 girls (high school or college age) convince this overweight girl to change into a bikini or skimpy outfit. They tell her to wait in a room. Next thing that happens is a guy that I think the girl likes, walks into the room and she\u2019s mortified and he\u2019s mad and feels bad for her. All the girls start laughing and the girl runs out of the room. Also, this scene was in the daytime. I remember it being very bright in the room from sunlight. I know it\u2019s not much to go on, but I hope someone knows what this is from. It\u2019s been driving me crazy trying to figure it out. Thanks","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"32467228:0","label":1.0},{"id":"32467228:1","label":1.0},{"id":"32467228:2","label":1.0},{"id":"32467228:3","label":1.0},{"id":"32467228:4","label":1.0},{"id":"32467228:5","label":1.0},{"id":"32467228:6","label":1.0},{"id":"32467228:7","label":1.0},{"id":"32467228:8","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"32467228","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\n80\\u2019s Movie\/Show with Mean Girls .\\n I watched this when I was under 10 yrs old and it was in the 80\\u2019s and in English. All I can remember is one scene. This group of 5 or 6 girls (high school or college age) convince this overweight girl to change into a bikini or skimpy outfit. They tell her to wait in a room. Next thing that happens is a guy that I think the girl likes, walks into the room and she\\u2019s mortified and he\\u2019s mad and feels bad for her. All the girls start laughing and the girl runs out of the room. Also, this scene was in the daytime. I remember it being very bright in the room from sunlight. I know it\\u2019s not much to go on, but I hope someone knows what this is from. It\\u2019s been driving me crazy trying to figure it out. Thanks\"}","task_split":"tip_of_the_tongue"}
|
| 13 |
+
{"query_id":"869","query_content":"Amovie where everything is controlled by a guy in a pod. .\n So its from the 90s or early 2000s. its like a cross between Chopping mall and Steel trap. the main badguy is a little robot and (spoilers) the secret badguy is a guy in a pod and the little i swear ive seen this movie described a hundred different times but i cant figure it out. (spoiler) the ending of the movie is the secret badguy gets found out and summons a big bosslike bad guy at the end thru the manipulation of these black spheres the size of a small rubber ball, he\u2019s defeated and the blow back surges to the badguy thru the umbilical and burns him but he\u2019s fine and calls someone to start another mach or something? andy help is appreciated.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"37702401:0","label":1.0},{"id":"37702401:1","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"37702401","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nAmovie where everything is controlled by a guy in a pod. .\\n So its from the 90s or early 2000s. its like a cross between Chopping mall and Steel trap. the main badguy is a little robot and (spoilers) the secret badguy is a guy in a pod and the little i swear ive seen this movie described a hundred different times but i cant figure it out. (spoiler) the ending of the movie is the secret badguy gets found out and summons a big bosslike bad guy at the end thru the manipulation of these black spheres the size of a small rubber ball, he\\u2019s defeated and the blow back surges to the badguy thru the umbilical and burns him but he\\u2019s fine and calls someone to start another mach or something? andy help is appreciated.\"}","task_split":"tip_of_the_tongue"}
|
| 14 |
+
{"query_id":"349","query_content":"70\u2019s Horror film (Not Poltergeist) .\n All I can recall is a large weird gnarled tree\/plant that was inside a living room and not much else unfortunately (it may have been an anthology but . \u00a0It was on British TV during the 80\u2019s and I have not seen it since\u2026\u2026","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"21003194:0","label":1.0},{"id":"21003194:1","label":1.0},{"id":"21003194:2","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"21003194","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\n70\\u2019s Horror film (Not Poltergeist) .\\n All I can recall is a large weird gnarled tree\/plant that was inside a living room and not much else unfortunately (it may have been an anthology but . \\u00a0It was on British TV during the 80\\u2019s and I have not seen it since\\u2026\\u2026\"}","task_split":"tip_of_the_tongue"}
|
| 15 |
+
{"query_id":"1067","query_content":"Netflix horror movie, house that is evil and controls you .\n Horror movie on netflix where a boy and girl I believe is a couple, stay at a house that is evil, and controls your actions by playing mind ticks of some sort, I remember they had to set an alarm to remember to hydrate themselves because the time perception was different in the house\u2026there was \u00a0murder scene at the end of the movie where the boy accidently kills his girlfriend in a wooden trap that was set for the evil house, before she died she actually called 911, they showed up right after he killed her and was arrested, the end scene was him being carried away in the cop car staring at the house","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"39469456:0","label":1.0},{"id":"39469456:1","label":1.0},{"id":"39469456:2","label":1.0},{"id":"39469456:3","label":1.0},{"id":"39469456:4","label":1.0},{"id":"39469456:5","label":1.0},{"id":"39469456:6","label":1.0},{"id":"39469456:7","label":1.0},{"id":"39469456:8","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"39469456","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nNetflix horror movie, house that is evil and controls you .\\n Horror movie on netflix where a boy and girl I believe is a couple, stay at a house that is evil, and controls your actions by playing mind ticks of some sort, I remember they had to set an alarm to remember to hydrate themselves because the time perception was different in the house\\u2026there was \\u00a0murder scene at the end of the movie where the boy accidently kills his girlfriend in a wooden trap that was set for the evil house, before she died she actually called 911, they showed up right after he killed her and was arrested, the end scene was him being carried away in the cop car staring at the house\"}","task_split":"tip_of_the_tongue"}
|
| 16 |
+
{"query_id":"558","query_content":"18th century period piece .\n At some point the the 90\u2019s I saw a film on tv (probably HBO) that was set in the 1700\u2019s. I don\u2019t remember much, but I was just thinking about it and it\u2019s bothering me not knowing now. I remember there was a decent amount of sex\/sexual references. It\u2019s not your typical pride and prejudiced, sense and sensibility type period piece. I\u2019m pretty sure there were quite a few well known actors in it as well, I just can\u2019t seem to remember any of them. There was a point in the film where there was some sort of scheme for this one man to sleep with a young girl and take her virginity. That\u2019s all I really remember. Any ideas?","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"75933:0","label":1.0},{"id":"75933:1","label":1.0},{"id":"75933:2","label":1.0},{"id":"75933:3","label":1.0},{"id":"75933:4","label":1.0},{"id":"75933:5","label":1.0},{"id":"75933:6","label":1.0},{"id":"75933:7","label":1.0},{"id":"75933:8","label":1.0},{"id":"75933:9","label":1.0},{"id":"75933:10","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"75933","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\n18th century period piece .\\n At some point the the 90\\u2019s I saw a film on tv (probably HBO) that was set in the 1700\\u2019s. I don\\u2019t remember much, but I was just thinking about it and it\\u2019s bothering me not knowing now. I remember there was a decent amount of sex\/sexual references. It\\u2019s not your typical pride and prejudiced, sense and sensibility type period piece. I\\u2019m pretty sure there were quite a few well known actors in it as well, I just can\\u2019t seem to remember any of them. There was a point in the film where there was some sort of scheme for this one man to sleep with a young girl and take her virginity. That\\u2019s all I really remember. Any ideas?\"}","task_split":"tip_of_the_tongue"}
|
| 17 |
+
{"query_id":"859","query_content":"Girl calling rape\u2026 .\n Ok, so a few years ago I saw a film on tv (I think it may have been on TCM) I didn\u2019t watch the whole thing, but I remember this one scene where a girl goes running through the street crying \u201cRape!\u201d I\u2019m pretty sure she even knocks on someone\u2019s door. No one seems to take her seriously though\u2026people look out their windows, but no one tries to help her from what I remember. I don\u2019t actually remember a rape scene, and she may have been lying. It was black and white, and probably set in the 50\u2019s","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"4429858:0","label":1.0},{"id":"4429858:1","label":1.0},{"id":"4429858:2","label":1.0},{"id":"4429858:3","label":1.0},{"id":"4429858:4","label":1.0},{"id":"4429858:5","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"4429858","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nGirl calling rape\\u2026 .\\n Ok, so a few years ago I saw a film on tv (I think it may have been on TCM) I didn\\u2019t watch the whole thing, but I remember this one scene where a girl goes running through the street crying \\u201cRape!\\u201d I\\u2019m pretty sure she even knocks on someone\\u2019s door. No one seems to take her seriously though\\u2026people look out their windows, but no one tries to help her from what I remember. I don\\u2019t actually remember a rape scene, and she may have been lying. It was black and white, and probably set in the 50\\u2019s\"}","task_split":"tip_of_the_tongue"}
|
| 18 |
+
{"query_id":"148","query_content":"Fish nose down on ocean floor .\n I remember this movie\u2026 There was a scene where there were a bunch of fish (tuna?) nose down on the sea floor. This same movie may also include a giant octopus attacking a bridge, but I couldn\u2019t swear to it. Fairly certain that it was in color, but it was a LONG time ago. I saw it years ago (25+?) on one of those Saturday Afternoon Monster Movie Matinees. I think. Maybe. My sis and mom both remember the same thing, but have no idea where it came from. Honestly, it\u2019s been driving us nuts for years. Hope someone can help.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"876592:0","label":1.0},{"id":"876592:1","label":1.0},{"id":"876592:2","label":1.0},{"id":"876592:3","label":1.0},{"id":"876592:4","label":1.0},{"id":"876592:5","label":1.0},{"id":"876592:6","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"876592","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nFish nose down on ocean floor .\\n I remember this movie\\u2026 There was a scene where there were a bunch of fish (tuna?) nose down on the sea floor. This same movie may also include a giant octopus attacking a bridge, but I couldn\\u2019t swear to it. Fairly certain that it was in color, but it was a LONG time ago. I saw it years ago (25+?) on one of those Saturday Afternoon Monster Movie Matinees. I think. Maybe. My sis and mom both remember the same thing, but have no idea where it came from. Honestly, it\\u2019s been driving us nuts for years. Hope someone can help.\"}","task_split":"tip_of_the_tongue"}
|
| 19 |
+
{"query_id":"105","query_content":"Romantic Comedy with a scene about cost vs worth .\n I am trying to remember the title of a film about a woman who meets a handsome guy in the city when she was in a line and wanted to buy some food or drink and she didnt have enough cash on her but a credit card or something, then a guy behind her pays for her because he says although the item costs less if he waited and paid just for him self it wasnt worth it because its worth the money to get the item sooner by paying for her\u2019s too. I want to teach my Chinese friends in China about why white people are not as cheap as they are (because they are more trifty). The scene from teh movie would help illustrate the pont.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"17112291:0","label":1.0},{"id":"17112291:1","label":1.0},{"id":"17112291:2","label":1.0},{"id":"17112291:3","label":1.0},{"id":"17112291:4","label":1.0},{"id":"17112291:5","label":1.0},{"id":"17112291:6","label":1.0},{"id":"17112291:7","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"17112291","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nRomantic Comedy with a scene about cost vs worth .\\n I am trying to remember the title of a film about a woman who meets a handsome guy in the city when she was in a line and wanted to buy some food or drink and she didnt have enough cash on her but a credit card or something, then a guy behind her pays for her because he says although the item costs less if he waited and paid just for him self it wasnt worth it because its worth the money to get the item sooner by paying for her\\u2019s too. I want to teach my Chinese friends in China about why white people are not as cheap as they are (because they are more trifty). The scene from teh movie would help illustrate the pont.\"}","task_split":"tip_of_the_tongue"}
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| 20 |
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{"query_id":"407","query_content":"Horror movie where the monsters lived in van\u2026 .\n I think I saw it back in the 80\u2019s, this horror movie that gave me nightmares for weeks. It had these bad ass looking monsters that came out of a van and well\u2026killed people. I remember there was one with a sword who, at some point, beheaded a guy who was with his girlfriend at a bench in a park. I also remember, towards the end there was this costume party, where the monsters blended right in\u2026 And in the end, they all gathered up inside an old van\u2026 What\u2019s the movie name???","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"13166007:0","label":1.0},{"id":"13166007:1","label":1.0},{"id":"13166007:2","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"13166007","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nHorror movie where the monsters lived in van\\u2026 .\\n I think I saw it back in the 80\\u2019s, this horror movie that gave me nightmares for weeks. It had these bad ass looking monsters that came out of a van and well\\u2026killed people. I remember there was one with a sword who, at some point, beheaded a guy who was with his girlfriend at a bench in a park. I also remember, towards the end there was this costume party, where the monsters blended right in\\u2026 And in the end, they all gathered up inside an old van\\u2026 What\\u2019s the movie name???\"}","task_split":"tip_of_the_tongue"}
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| 21 |
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{"query_id":"582","query_content":"Strange movie from 80\u2019s-early 90\u2019s .\n Strange movie\/tv show from a long time ago. I probably saw this in the late 90\u2019s, so I was super young. All I remember was a white male with blond hair sitting on the floor in the corner of a room. There were a bunch of bobble heads or figurines of some sort surrounding him. He looks terrified, tries to get up, grabs an American flag and the bobbleheads attack. You hear him scream and see a bead of blood on one of the bobble heads. Another scene ( maybe episode?) showed the same male going up against some alley wall , kind of fusing with the wall(I know, sounds crazy) while some force caused a bunch of needles to go shooting to the wall,kind of like stabbing him, but he\u2019s fused with the wall It\u2019s been driving me crazy for years","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"2883615:0","label":1.0},{"id":"2883615:1","label":1.0},{"id":"2883615:2","label":1.0},{"id":"2883615:3","label":1.0},{"id":"2883615:4","label":1.0},{"id":"2883615:5","label":1.0},{"id":"2883615:6","label":1.0},{"id":"2883615:7","label":1.0},{"id":"2883615:8","label":1.0},{"id":"2883615:9","label":1.0},{"id":"2883615:10","label":1.0},{"id":"2883615:11","label":1.0},{"id":"2883615:12","label":1.0},{"id":"2883615:13","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"2883615","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nStrange movie from 80\\u2019s-early 90\\u2019s .\\n Strange movie\/tv show from a long time ago. I probably saw this in the late 90\\u2019s, so I was super young. All I remember was a white male with blond hair sitting on the floor in the corner of a room. There were a bunch of bobble heads or figurines of some sort surrounding him. He looks terrified, tries to get up, grabs an American flag and the bobbleheads attack. You hear him scream and see a bead of blood on one of the bobble heads. Another scene ( maybe episode?) showed the same male going up against some alley wall , kind of fusing with the wall(I know, sounds crazy) while some force caused a bunch of needles to go shooting to the wall,kind of like stabbing him, but he\\u2019s fused with the wall It\\u2019s been driving me crazy for years\"}","task_split":"tip_of_the_tongue"}
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| 22 |
+
{"query_id":"661","query_content":"British film (1970s?), where clues are found in old newsreel footage .\n In this film someone searches for something via secret clues that are left in black and white newsreels from the 1930s (such as, I think, \u201cHop Picking in Kent\u201d). Each of the newsreels ends with the name of the next newsreel to find. I am not sure whether the protagonist ever finds what they want. It gets hectic and confusing\u2026 I remember one scene: the archive where they look for the film is an old underground government bunker situated in the middle of London, near Hyde Park.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"2706186:0","label":1.0},{"id":"2706186:1","label":1.0},{"id":"2706186:2","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"2706186","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nBritish film (1970s?), where clues are found in old newsreel footage .\\n In this film someone searches for something via secret clues that are left in black and white newsreels from the 1930s (such as, I think, \\u201cHop Picking in Kent\\u201d). Each of the newsreels ends with the name of the next newsreel to find. I am not sure whether the protagonist ever finds what they want. It gets hectic and confusing\\u2026 I remember one scene: the archive where they look for the film is an old underground government bunker situated in the middle of London, near Hyde Park.\"}","task_split":"tip_of_the_tongue"}
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| 23 |
+
{"query_id":"877","query_content":"unknown .\n I recall a scene or two from a black and white movie in which an insane mother tortures her young daughter by giving her laxatives and enemas and ties her to a chandalier. I believe it was from the 1980\u2019s.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"983692:0","label":1.0},{"id":"983692:1","label":1.0},{"id":"983692:2","label":1.0},{"id":"983692:3","label":1.0},{"id":"983692:4","label":1.0},{"id":"983692:5","label":1.0},{"id":"983692:6","label":1.0},{"id":"983692:7","label":1.0},{"id":"983692:8","label":1.0},{"id":"983692:9","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"983692","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nunknown .\\n I recall a scene or two from a black and white movie in which an insane mother tortures her young daughter by giving her laxatives and enemas and ties her to a chandalier. I believe it was from the 1980\\u2019s.\"}","task_split":"tip_of_the_tongue"}
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| 24 |
+
{"query_id":"190","query_content":"An artist\u2019s cat is hiding in the wall and he accidentally kills it .\n A sculpter is trying to free his cat from the wall and kills it\u2026then he decides to make a sculpture out of it\u2026I think he sculpted human bodies too\u2026..older movie\u2026.that is all I really remember.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"5590094:0","label":1.0},{"id":"5590094:1","label":1.0},{"id":"5590094:2","label":1.0},{"id":"5590094:3","label":1.0},{"id":"5590094:4","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"5590094","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nAn artist\\u2019s cat is hiding in the wall and he accidentally kills it .\\n A sculpter is trying to free his cat from the wall and kills it\\u2026then he decides to make a sculpture out of it\\u2026I think he sculpted human bodies too\\u2026..older movie\\u2026.that is all I really remember.\"}","task_split":"tip_of_the_tongue"}
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| 25 |
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{"query_id":"1049","query_content":"australian school children .\n I saw this movie in the early 90\u2019s on tv. I think the setting was in Australia. The movie started in a single room school house in the outback when some thugs came and took them and led them to find something. It goes through their adventure of the school children of varying ages and their female teacher taking care of each other, surviving, aluding their captors and overcoming them. I remember the final scene back in the school house with a body part in a glass container. I loved the survival aspect of it and how they worked together. I wish I could see it again.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"11534107:0","label":1.0},{"id":"11534107:1","label":1.0},{"id":"11534107:2","label":1.0},{"id":"11534107:3","label":1.0},{"id":"11534107:4","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"11534107","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\naustralian school children .\\n I saw this movie in the early 90\\u2019s on tv. I think the setting was in Australia. The movie started in a single room school house in the outback when some thugs came and took them and led them to find something. It goes through their adventure of the school children of varying ages and their female teacher taking care of each other, surviving, aluding their captors and overcoming them. I remember the final scene back in the school house with a body part in a glass container. I loved the survival aspect of it and how they worked together. I wish I could see it again.\"}","task_split":"tip_of_the_tongue"}
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| 26 |
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{"query_id":"565","query_content":"70s film .\n Judging by the quality, I\u2019d say this film was made in the 70s. It\u2019s about a large American family who all come back home to attend the funeral of the youngest member, a guy who killed himself. After the funeral, which happens early in the film, they all go home, and from there it\u2019s basically one of those films where everyone\u2019s thinking about their life choices, etc. There\u2019s a bit of tension because they\u2019ve all got their own lives and live in different states so they don\u2019t see each other a lot.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"545795:0","label":1.0},{"id":"545795:1","label":1.0},{"id":"545795:2","label":1.0},{"id":"545795:3","label":1.0},{"id":"545795:4","label":1.0},{"id":"545795:5","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"545795","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\n70s film .\\n Judging by the quality, I\\u2019d say this film was made in the 70s. It\\u2019s about a large American family who all come back home to attend the funeral of the youngest member, a guy who killed himself. After the funeral, which happens early in the film, they all go home, and from there it\\u2019s basically one of those films where everyone\\u2019s thinking about their life choices, etc. There\\u2019s a bit of tension because they\\u2019ve all got their own lives and live in different states so they don\\u2019t see each other a lot.\"}","task_split":"tip_of_the_tongue"}
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| 27 |
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{"query_id":"356","query_content":"Old sci fi horror .\n Hi Im looking for this old I think from \u201990 sci fi horror movie and cant find it anywhere. From what I remember there was a group of some soldiers who try to stop an evil machine robot I think it was on a space station or some factory. Robot killed almost all of them and one of the main characters build a tank looking thing with a big gatling gun I think and was fighting that evil machine. I have no clue what is the title and its not, Virus, Hardware, saturn 3, space truckers, evil machine robot jox for sure. If anybody can help I whould be super gratefull cause Im looking for this movie for a very long time.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"8237560:0","label":1.0},{"id":"8237560:1","label":1.0},{"id":"8237560:2","label":1.0},{"id":"8237560:3","label":1.0},{"id":"8237560:4","label":1.0},{"id":"8237560:5","label":1.0},{"id":"8237560:6","label":1.0},{"id":"8237560:7","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"8237560","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nOld sci fi horror .\\n Hi Im looking for this old I think from \\u201990 sci fi horror movie and cant find it anywhere. From what I remember there was a group of some soldiers who try to stop an evil machine robot I think it was on a space station or some factory. Robot killed almost all of them and one of the main characters build a tank looking thing with a big gatling gun I think and was fighting that evil machine. I have no clue what is the title and its not, Virus, Hardware, saturn 3, space truckers, evil machine robot jox for sure. If anybody can help I whould be super gratefull cause Im looking for this movie for a very long time.\"}","task_split":"tip_of_the_tongue"}
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| 28 |
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{"query_id":"973","query_content":"Guy shoots other guy with tiny gun hidden in underwear .\n Ok, so all i remember from this movie is this one scene. A guy (possibly Brendan Gleeson, but since I\u2019ve tried looking up his movies, I\u2019m starting to doubt it\u2019s him) wants to kill another guy. Since he knows he\u2019s gonna get searched for weapons, he gets a very small gun and hides it in his underwear. He goes to see this guy then, and while they are sitting down and talking, he puts his hand down his pants. This guy looks at him funny (or asks him what he\u2019s doing, i don\u2019t remember exactly) and he just tells him he got an STD from a hooker or something like that. When he manages to adjust the gun properly he shoots the guy (don\u2019t remember if he actually kills him). Well that\u2019s all i remember. I will be very grateful if someone can figure out which movie this is, it\u2019s been killing me for weeks! Thanks in advance!","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"25102073:0","label":1.0},{"id":"25102073:1","label":1.0},{"id":"25102073:2","label":1.0},{"id":"25102073:3","label":1.0},{"id":"25102073:4","label":1.0},{"id":"25102073:5","label":1.0},{"id":"25102073:6","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"25102073","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nGuy shoots other guy with tiny gun hidden in underwear .\\n Ok, so all i remember from this movie is this one scene. A guy (possibly Brendan Gleeson, but since I\\u2019ve tried looking up his movies, I\\u2019m starting to doubt it\\u2019s him) wants to kill another guy. Since he knows he\\u2019s gonna get searched for weapons, he gets a very small gun and hides it in his underwear. He goes to see this guy then, and while they are sitting down and talking, he puts his hand down his pants. This guy looks at him funny (or asks him what he\\u2019s doing, i don\\u2019t remember exactly) and he just tells him he got an STD from a hooker or something like that. When he manages to adjust the gun properly he shoots the guy (don\\u2019t remember if he actually kills him). Well that\\u2019s all i remember. I will be very grateful if someone can figure out which movie this is, it\\u2019s been killing me for weeks! Thanks in advance!\"}","task_split":"tip_of_the_tongue"}
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| 29 |
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{"query_id":"964","query_content":"woman giving birth .\n I saw a movie some years ago, the film itself was older, probably early 70\u2019s. It was in color, and english, I think it was set in New York , or a city. I don\u2019t remember the plot very much, just mainly that it was about a woman. I mostly recall the beginning because it really caught me off guard. A woman (I believe the one the movie is about) was giving birth, and they actually showed the baby coming out. It wasn\u2019t fake at all, I\u2019m pretty sure it was an actual birth. They cut it together with the actresses face and it looked like she was really giving birth. Maybe that\u2019s too progressive for the 70\u2019s? I\u2019m not sure\u2026I saw the film in the early 2000\u2019s at some point, so maybe it was never an just looked old? I\u2019m not sure\u2026hoping someone knows what I\u2019m talking about.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"3138227:0","label":1.0},{"id":"3138227:1","label":1.0},{"id":"3138227:2","label":1.0},{"id":"3138227:3","label":1.0},{"id":"3138227:4","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"3138227","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nwoman giving birth .\\n I saw a movie some years ago, the film itself was older, probably early 70\\u2019s. It was in color, and english, I think it was set in New York , or a city. I don\\u2019t remember the plot very much, just mainly that it was about a woman. I mostly recall the beginning because it really caught me off guard. A woman (I believe the one the movie is about) was giving birth, and they actually showed the baby coming out. It wasn\\u2019t fake at all, I\\u2019m pretty sure it was an actual birth. They cut it together with the actresses face and it looked like she was really giving birth. Maybe that\\u2019s too progressive for the 70\\u2019s? I\\u2019m not sure\\u2026I saw the film in the early 2000\\u2019s at some point, so maybe it was never an just looked old? I\\u2019m not sure\\u2026hoping someone knows what I\\u2019m talking about.\"}","task_split":"tip_of_the_tongue"}
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| 30 |
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{"query_id":"621","query_content":"Boy uses machine becomes adult falls in love becomes boy again \u2013 not BIG .\n The movie has 2 best friends who go to school together, one invents a machine to make fruit\/vegetables really big (trying to solve world hunger I think) and the other friend then uses it on himself to become an adult. He then goes to the school and is mistaken for a teacher\/head teacher? He falls in love with the teacher he had a crush on and she falls in love with him. Eventually he gets turned back into a teenage boy \u2013 but it all ends happily when she gets turned into a teenage school girl\u2026 and I think the genius best friend turns himself into an adult. I watched this in the early 90\u2019s so my guess is that it was made sometime from the mid 80\u2019s on.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"18902861:0","label":1.0},{"id":"18902861:1","label":1.0},{"id":"18902861:2","label":1.0},{"id":"18902861:3","label":1.0},{"id":"18902861:4","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"18902861","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nBoy uses machine becomes adult falls in love becomes boy again \\u2013 not BIG .\\n The movie has 2 best friends who go to school together, one invents a machine to make fruit\/vegetables really big (trying to solve world hunger I think) and the other friend then uses it on himself to become an adult. He then goes to the school and is mistaken for a teacher\/head teacher? He falls in love with the teacher he had a crush on and she falls in love with him. Eventually he gets turned back into a teenage boy \\u2013 but it all ends happily when she gets turned into a teenage school girl\\u2026 and I think the genius best friend turns himself into an adult. I watched this in the early 90\\u2019s so my guess is that it was made sometime from the mid 80\\u2019s on.\"}","task_split":"tip_of_the_tongue"}
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| 31 |
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{"query_id":"1006","query_content":"Girl in a red dress enters a bizarre shop, where she gets chloroformed by the weird owner .\n This was a short movie I saw either on YT or Vimeo, not sure. Cannot find it now for the love of\u2026 A girl in a red dress enters a bizarre shop, to buy a present for her boyfriend (she says so), goes downstairs and inspects a shelf full of strange artifacts, when the shop owner chloroforms her and chains her. She wakes up and finds a way to cut herself loose, but she doesn\u2019t fight the owner, who chains her again and makes her get dressed in a pink ball dress. Thats pretty much it ? Thanks.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"17905510:0","label":1.0},{"id":"17905510:1","label":1.0},{"id":"17905510:2","label":1.0},{"id":"17905510:3","label":1.0},{"id":"17905510:4","label":1.0},{"id":"17905510:5","label":1.0},{"id":"17905510:6","label":1.0},{"id":"17905510:7","label":1.0},{"id":"17905510:8","label":1.0},{"id":"17905510:9","label":1.0},{"id":"17905510:10","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"17905510","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nGirl in a red dress enters a bizarre shop, where she gets chloroformed by the weird owner .\\n This was a short movie I saw either on YT or Vimeo, not sure. Cannot find it now for the love of\\u2026 A girl in a red dress enters a bizarre shop, to buy a present for her boyfriend (she says so), goes downstairs and inspects a shelf full of strange artifacts, when the shop owner chloroforms her and chains her. She wakes up and finds a way to cut herself loose, but she doesn\\u2019t fight the owner, who chains her again and makes her get dressed in a pink ball dress. Thats pretty much it ? Thanks.\"}","task_split":"tip_of_the_tongue"}
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| 32 |
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{"query_id":"533","query_content":"Aliens in Mexico .\n So I tried searching for this movie in google with the information that I remember and it actually brought me to this site. My dad rented this movie when I was a kid, it was probably around late 90\u2019s early 2000\u2019s I think. This is what I remember: it\u2019s about a guy who\u2019s either being hunted by aliens or tracking them (probably the later). At one point he\u2019s running through a crowd of people at night in Mexico City during Day of the Dead. I think maybe at the end he finds their spaceship. I could be making that up but I\u2019m pretty sure that happens, though.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"4260551:0","label":1.0},{"id":"4260551:1","label":1.0},{"id":"4260551:2","label":1.0},{"id":"4260551:3","label":1.0},{"id":"4260551:4","label":1.0},{"id":"4260551:5","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"4260551","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nAliens in Mexico .\\n So I tried searching for this movie in google with the information that I remember and it actually brought me to this site. My dad rented this movie when I was a kid, it was probably around late 90\\u2019s early 2000\\u2019s I think. This is what I remember: it\\u2019s about a guy who\\u2019s either being hunted by aliens or tracking them (probably the later). At one point he\\u2019s running through a crowd of people at night in Mexico City during Day of the Dead. I think maybe at the end he finds their spaceship. I could be making that up but I\\u2019m pretty sure that happens, though.\"}","task_split":"tip_of_the_tongue"}
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| 33 |
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{"query_id":"884","query_content":"90s horror movie????? .\n I think I saw this movie in the late 90s maybe early 2000s. Maybe made in the 90s or even 80s? It was kinda lower budget I think. I really don\u2019t remember too much of the movie, but I seem to remember it being 3 siblings-2 brothers and their sister. Their parents went out of town or something, leaving them alone. The eldest kid was driving with his brother and sister in the car, fell asleep at the wheel for a minute, and they ended up in some weird town. I think the sister noticed the people who lived in the town were doing the same thing over and over again, like the man would walk by and tip his hat, then do it again a few minutes later. By the end of the movie they find out that their parents fell asleep too and ended up in the town and were trapped in these pod type things. They get them out by stabbing the pod with a rattlesnake fang. I think that\u2019s all I can remember, I know there isn\u2019t too much to go off of, but hopefully someone out there recognizes this movie!","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"43983853:0","label":1.0},{"id":"43983853:1","label":1.0},{"id":"43983853:2","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"43983853","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\n90s horror movie????? .\\n I think I saw this movie in the late 90s maybe early 2000s. Maybe made in the 90s or even 80s? It was kinda lower budget I think. I really don\\u2019t remember too much of the movie, but I seem to remember it being 3 siblings-2 brothers and their sister. Their parents went out of town or something, leaving them alone. The eldest kid was driving with his brother and sister in the car, fell asleep at the wheel for a minute, and they ended up in some weird town. I think the sister noticed the people who lived in the town were doing the same thing over and over again, like the man would walk by and tip his hat, then do it again a few minutes later. By the end of the movie they find out that their parents fell asleep too and ended up in the town and were trapped in these pod type things. They get them out by stabbing the pod with a rattlesnake fang. I think that\\u2019s all I can remember, I know there isn\\u2019t too much to go off of, but hopefully someone out there recognizes this movie!\"}","task_split":"tip_of_the_tongue"}
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| 34 |
+
{"query_id":"266","query_content":"Botched sex operation lesbian horror movie .\n This memory isn\u2019t even mine this is for my wife. anyway, theres apparently this lesbian couple and one of them talks jokingly about how she misses having a penis so the other lesbian takes it seriously and gets a sex operation but it\u2019s really bad and botched and she goes to see her girlfriend and she freaks out and is talking about how it was a joke and she didn\u2019t mean it and she loved her the way she was. Please help?:(","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"1328188:0","label":1.0},{"id":"1328188:1","label":1.0},{"id":"1328188:2","label":1.0},{"id":"1328188:3","label":1.0},{"id":"1328188:4","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"1328188","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nBotched sex operation lesbian horror movie .\\n This memory isn\\u2019t even mine this is for my wife. anyway, theres apparently this lesbian couple and one of them talks jokingly about how she misses having a penis so the other lesbian takes it seriously and gets a sex operation but it\\u2019s really bad and botched and she goes to see her girlfriend and she freaks out and is talking about how it was a joke and she didn\\u2019t mean it and she loved her the way she was. Please help?:(\"}","task_split":"tip_of_the_tongue"}
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| 35 |
+
{"query_id":"833","query_content":"record played backwards to release a ghost.Please help. .\n I hope you can help. I remember seeing this film in late 80\u2019s early 90\u2019s. I remember a lad playing a heavy metal record( I think) forward and then playing it backwards to play a message and release the singers ghost. I remember a girl in the back seat of the car with her eyes closed thinking she was having sex with someone but when she opens her eyes it is the ghost. I also remember a radio station but not sure if this is in the same film. I cant remember anything else.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"7212423:0","label":1.0},{"id":"7212423:1","label":1.0},{"id":"7212423:2","label":1.0},{"id":"7212423:3","label":1.0},{"id":"7212423:4","label":1.0},{"id":"7212423:5","label":1.0},{"id":"7212423:6","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"7212423","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nrecord played backwards to release a ghost.Please help. .\\n I hope you can help. I remember seeing this film in late 80\\u2019s early 90\\u2019s. I remember a lad playing a heavy metal record( I think) forward and then playing it backwards to play a message and release the singers ghost. I remember a girl in the back seat of the car with her eyes closed thinking she was having sex with someone but when she opens her eyes it is the ghost. I also remember a radio station but not sure if this is in the same film. I cant remember anything else.\"}","task_split":"tip_of_the_tongue"}
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| 36 |
+
{"query_id":"745","query_content":"Help Emergency! .\n It was this movie I rented from Blockbuster long ago. It was about these blue ferret things who tried to save a forest of talking trees. I know it sounds really retarded. But there\u2019s more! It had these flies as side characters or something and wild cats too. One of the cats accidentally eat the flies. And then there\u2019s this evil old lady that tries to cut down the trees and kill the forest. The cats, trees, ferrets, and the old lady\u2019s \u00a0cat team up to try to stop her. They succeed in the end! I remember everything about the movie except the STUPID NAME! Please help!!! I don\u2019t think it went in theatres. It was a cheap straight to DVD release kind of film.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"17776753:0","label":1.0},{"id":"17776753:1","label":1.0},{"id":"17776753:2","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"17776753","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nHelp Emergency! .\\n It was this movie I rented from Blockbuster long ago. It was about these blue ferret things who tried to save a forest of talking trees. I know it sounds really retarded. But there\\u2019s more! It had these flies as side characters or something and wild cats too. One of the cats accidentally eat the flies. And then there\\u2019s this evil old lady that tries to cut down the trees and kill the forest. The cats, trees, ferrets, and the old lady\\u2019s \\u00a0cat team up to try to stop her. They succeed in the end! I remember everything about the movie except the STUPID NAME! Please help!!! I don\\u2019t think it went in theatres. It was a cheap straight to DVD release kind of film.\"}","task_split":"tip_of_the_tongue"}
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| 37 |
+
{"query_id":"557","query_content":"Foreign Movie about Young vs. Old Revolutionaries .\n I can\u2019t for the life of me remember this film. I remember seeing it in the mid 2000s. It was a foreign film, I think either French or German, but I could be wrong. It centers around a young couple who break into the home of an aging revolutionary man, or couple, and analyzes why the old man left that life and idealism behind. I believe there was also a pool in the house. It was definitely in color and was made recently (around 2000-2009). Thanks for the help!","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"1554502:0","label":1.0},{"id":"1554502:1","label":1.0},{"id":"1554502:2","label":1.0},{"id":"1554502:3","label":1.0},{"id":"1554502:4","label":1.0},{"id":"1554502:5","label":1.0},{"id":"1554502:6","label":1.0},{"id":"1554502:7","label":1.0},{"id":"1554502:8","label":1.0},{"id":"1554502:9","label":1.0},{"id":"1554502:10","label":1.0},{"id":"1554502:11","label":1.0},{"id":"1554502:12","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"1554502","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nForeign Movie about Young vs. Old Revolutionaries .\\n I can\\u2019t for the life of me remember this film. I remember seeing it in the mid 2000s. It was a foreign film, I think either French or German, but I could be wrong. It centers around a young couple who break into the home of an aging revolutionary man, or couple, and analyzes why the old man left that life and idealism behind. I believe there was also a pool in the house. It was definitely in color and was made recently (around 2000-2009). Thanks for the help!\"}","task_split":"tip_of_the_tongue"}
|
| 38 |
+
{"query_id":"253","query_content":"Old Scary movie .\n I remember this old B movie I watched about 35-40 years ago. All I remember is one scene when a woman is in a hallway and some scary woman zombie\/ghost is chasing her slowly. The scary woman\u2019s hands are outstretched as she is walking. Every time the woman gets to a different hallway you see the outstretched hands of the scary woman coming around the corner. I think it was in black and white but I\u2019m not positive. I\u2019m dying to know the name of it. I watched it when I was babysitting so it was on regular TV. There was no cable at the time. I have spent hours on you tube fast forwarding old movies but I have not seen it yet. Please help me!","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"1004972:0","label":1.0},{"id":"1004972:1","label":1.0},{"id":"1004972:2","label":1.0},{"id":"1004972:3","label":1.0},{"id":"1004972:4","label":1.0},{"id":"1004972:5","label":1.0},{"id":"1004972:6","label":1.0},{"id":"1004972:7","label":1.0},{"id":"1004972:8","label":1.0},{"id":"1004972:9","label":1.0},{"id":"1004972:10","label":1.0},{"id":"1004972:11","label":1.0},{"id":"1004972:12","label":1.0},{"id":"1004972:13","label":1.0},{"id":"1004972:14","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"1004972","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nOld Scary movie .\\n I remember this old B movie I watched about 35-40 years ago. All I remember is one scene when a woman is in a hallway and some scary woman zombie\/ghost is chasing her slowly. The scary woman\\u2019s hands are outstretched as she is walking. Every time the woman gets to a different hallway you see the outstretched hands of the scary woman coming around the corner. I think it was in black and white but I\\u2019m not positive. I\\u2019m dying to know the name of it. I watched it when I was babysitting so it was on regular TV. There was no cable at the time. I have spent hours on you tube fast forwarding old movies but I have not seen it yet. Please help me!\"}","task_split":"tip_of_the_tongue"}
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| 39 |
+
{"query_id":"650","query_content":"Creatures .\n What is the name of the old movie that has winged creatures swooping down and attacking people in a cave? I think the cave or cavern was under a house or some kind of building. I believe it was in color and I saw it at a movie theater in the fifties. It was in the English language.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"12417140:0","label":1.0},{"id":"12417140:1","label":1.0},{"id":"12417140:2","label":1.0},{"id":"12417140:3","label":1.0},{"id":"12417140:4","label":1.0},{"id":"12417140:5","label":1.0},{"id":"12417140:6","label":1.0},{"id":"12417140:7","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"12417140","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nCreatures .\\n What is the name of the old movie that has winged creatures swooping down and attacking people in a cave? I think the cave or cavern was under a house or some kind of building. I believe it was in color and I saw it at a movie theater in the fifties. It was in the English language.\"}","task_split":"tip_of_the_tongue"}
|
| 40 |
+
{"query_id":"537","query_content":"What is this movie???? .\n I don\u2019t remember much about this movie, I watched it a long time ago on the TV. It was in English, in colour and I think it was some kind of period fantasy film. So, there was this blonde guy, who could sketch really well, and he was travelling with a friend of his (I think his friend was exotic, but I\u2019m not really sure about that) and they were looking for a beast. I can remember a scene where this blonde guy was in a brothel and he drew this woman, who predicted something about his future (she had a black knife and I think she might have been a witch or something?).. Later he met with some aristocrats and fell in love with a girl there\u2026. so they were kind of constantly flirting and going back and forth throughout the movie. Eventually this guy was part of a hunting party with the girl and other aristocrats\u2026and I think his friend died. That\u2019s pretty much all I can remember and I really hope this movie actually exists.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"1031292:0","label":1.0},{"id":"1031292:1","label":1.0},{"id":"1031292:2","label":1.0},{"id":"1031292:3","label":1.0},{"id":"1031292:4","label":1.0},{"id":"1031292:5","label":1.0},{"id":"1031292:6","label":1.0},{"id":"1031292:7","label":1.0},{"id":"1031292:8","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"1031292","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nWhat is this movie???? .\\n I don\\u2019t remember much about this movie, I watched it a long time ago on the TV. It was in English, in colour and I think it was some kind of period fantasy film. So, there was this blonde guy, who could sketch really well, and he was travelling with a friend of his (I think his friend was exotic, but I\\u2019m not really sure about that) and they were looking for a beast. I can remember a scene where this blonde guy was in a brothel and he drew this woman, who predicted something about his future (she had a black knife and I think she might have been a witch or something?).. Later he met with some aristocrats and fell in love with a girl there\\u2026. so they were kind of constantly flirting and going back and forth throughout the movie. Eventually this guy was part of a hunting party with the girl and other aristocrats\\u2026and I think his friend died. That\\u2019s pretty much all I can remember and I really hope this movie actually exists.\"}","task_split":"tip_of_the_tongue"}
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| 41 |
+
{"query_id":"945","query_content":"Comedy movie .\n I think the movie is from the 80s or early 90s.It\u2019s about a polite calm man who is abducted by an escaped convict.They go to the mans house where they spend some time and afterwards the man\u2019s wife fall\u2019s in love with the convict and escapes with him.The man seemed happy by the fact as far as i remember.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"304725:0","label":1.0},{"id":"304725:1","label":1.0},{"id":"304725:2","label":1.0},{"id":"304725:3","label":1.0},{"id":"304725:4","label":1.0},{"id":"304725:5","label":1.0},{"id":"304725:6","label":1.0},{"id":"304725:7","label":1.0},{"id":"304725:8","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"304725","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nComedy movie .\\n I think the movie is from the 80s or early 90s.It\\u2019s about a polite calm man who is abducted by an escaped convict.They go to the mans house where they spend some time and afterwards the man\\u2019s wife fall\\u2019s in love with the convict and escapes with him.The man seemed happy by the fact as far as i remember.\"}","task_split":"tip_of_the_tongue"}
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| 42 |
+
{"query_id":"108","query_content":"Barbarian fantasy movie where a queen is escaped and saved by barbarians .\n I saw this movie in the 90s, it might be created between 1980 and 1995. It was on VHS tape Colored US movie Plot: At the first half maybe at the beginning of the movie there was a princess\/queen\/sorceresses who dressed in long skirt in the colors of rainbow, she wasn\u2019t a fighter, but she held something important according the plot Plot: At the second half of the movie a barbarian horde helped the princess to escape from the army of an evil emperor. Due the size of the army the barbarians (6-12 barbarian) remained one by one (sometimes two of them) to uphold the army in order to save time to the refugees. At the end of the movie I think only one or two man remained with the princess but they also scarified their lives in order to save the girl My memories could be a little bit blurred, but I am quite sure about the characters (barbarians and the princess). Please help!","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"13607881:0","label":1.0},{"id":"13607881:1","label":1.0},{"id":"13607881:2","label":1.0},{"id":"13607881:3","label":1.0},{"id":"13607881:4","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"13607881","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nBarbarian fantasy movie where a queen is escaped and saved by barbarians .\\n I saw this movie in the 90s, it might be created between 1980 and 1995. It was on VHS tape Colored US movie Plot: At the first half maybe at the beginning of the movie there was a princess\/queen\/sorceresses who dressed in long skirt in the colors of rainbow, she wasn\\u2019t a fighter, but she held something important according the plot Plot: At the second half of the movie a barbarian horde helped the princess to escape from the army of an evil emperor. Due the size of the army the barbarians (6-12 barbarian) remained one by one (sometimes two of them) to uphold the army in order to save time to the refugees. At the end of the movie I think only one or two man remained with the princess but they also scarified their lives in order to save the girl My memories could be a little bit blurred, but I am quite sure about the characters (barbarians and the princess). Please help!\"}","task_split":"tip_of_the_tongue"}
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| 43 |
+
{"query_id":"673","query_content":"I remember this from the movie and want to know the name of the movie. .\n What I remember about the movie is there a group of teens who were put in a contest \u00a0where they each were to create a music video and they soon later were put against each other but also later learn something which brought them together and created a one of kind music video and became best friends.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"28953349:0","label":1.0},{"id":"28953349:1","label":1.0},{"id":"28953349:2","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"28953349","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nI remember this from the movie and want to know the name of the movie. .\\n What I remember about the movie is there a group of teens who were put in a contest \\u00a0where they each were to create a music video and they soon later were put against each other but also later learn something which brought them together and created a one of kind music video and became best friends.\"}","task_split":"tip_of_the_tongue"}
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| 44 |
+
{"query_id":"632","query_content":"Little girl killed at the end .\n I saw this movie in 2014 (I think) on a cable channel \u2013 I have no idea how old it is, but it seemed old. It may have been foreign, but I don\u2019t recall subtitles. It was a dark and tragic film. I remember a little girl (perhaps 12 or 13) had a very sad life until she placed some sort of plant under a bed (hers, her parents, I can\u2019t remember) then things were better. The plant involved blood of some sort, and had to remain there, lest her situation revert to the dismal existence. This \u201cidea\u201d was given to her by some sort of spirit or fairy that she befriended in the woods who gave her hope\/vision of a beautiful fantasy land where she belonged (as queen???) I think the plant was discovered and destroyed (by the mother??) and, of course, things turned bad for the little girl\/family. Somewhere near the end, I recall the little girl running away for her life, but she was caught, by a male (her [step]father??) and I believe was fatally wounded with a knife. At the end, she laid dying on a stone fence or table when her fairy friend appeared and (I think) took her to the enchanted after-life she had dreamed of. Something like that. It was a bittersweet film that I caught midway through. I\u2019d love to see it again, but cannot remember the name. Help please.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"3261733:0","label":1.0},{"id":"3261733:1","label":1.0},{"id":"3261733:2","label":1.0},{"id":"3261733:3","label":1.0},{"id":"3261733:4","label":1.0},{"id":"3261733:5","label":1.0},{"id":"3261733:6","label":1.0},{"id":"3261733:7","label":1.0},{"id":"3261733:8","label":1.0},{"id":"3261733:9","label":1.0},{"id":"3261733:10","label":1.0},{"id":"3261733:11","label":1.0},{"id":"3261733:12","label":1.0},{"id":"3261733:13","label":1.0},{"id":"3261733:14","label":1.0},{"id":"3261733:15","label":1.0},{"id":"3261733:16","label":1.0},{"id":"3261733:17","label":1.0},{"id":"3261733:18","label":1.0},{"id":"3261733:19","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"3261733","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nLittle girl killed at the end .\\n I saw this movie in 2014 (I think) on a cable channel \\u2013 I have no idea how old it is, but it seemed old. It may have been foreign, but I don\\u2019t recall subtitles. It was a dark and tragic film. I remember a little girl (perhaps 12 or 13) had a very sad life until she placed some sort of plant under a bed (hers, her parents, I can\\u2019t remember) then things were better. The plant involved blood of some sort, and had to remain there, lest her situation revert to the dismal existence. This \\u201cidea\\u201d was given to her by some sort of spirit or fairy that she befriended in the woods who gave her hope\/vision of a beautiful fantasy land where she belonged (as queen???) I think the plant was discovered and destroyed (by the mother??) and, of course, things turned bad for the little girl\/family. Somewhere near the end, I recall the little girl running away for her life, but she was caught, by a male (her [step]father??) and I believe was fatally wounded with a knife. At the end, she laid dying on a stone fence or table when her fairy friend appeared and (I think) took her to the enchanted after-life she had dreamed of. Something like that. It was a bittersweet film that I caught midway through. I\\u2019d love to see it again, but cannot remember the name. Help please.\"}","task_split":"tip_of_the_tongue"}
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| 45 |
+
{"query_id":"545","query_content":"Alien Invasion + English + Adult .\n I watched this movie and remember parts of this \u2013 It is probably after 2000. Alien Invasion . Turns into girls. Tries to have sex with male characters in movie (Not Species). When kissed by aliens (Mouth to Mouth) the partner gets freezed. Lead girl is extremely hot (Now you know the reason) and wears specs. Thats all I remember. Help Appreciated and will remember you while jerking off . [ Just kiddin\u2019 ? ]","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"448181:0","label":1.0},{"id":"448181:1","label":1.0},{"id":"448181:2","label":1.0},{"id":"448181:3","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"448181","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nAlien Invasion + English + Adult .\\n I watched this movie and remember parts of this \\u2013 It is probably after 2000. Alien Invasion . Turns into girls. Tries to have sex with male characters in movie (Not Species). When kissed by aliens (Mouth to Mouth) the partner gets freezed. Lead girl is extremely hot (Now you know the reason) and wears specs. Thats all I remember. Help Appreciated and will remember you while jerking off . [ Just kiddin\\u2019 ? ]\"}","task_split":"tip_of_the_tongue"}
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| 46 |
+
{"query_id":"1031","query_content":"Italian gangster film? .\n I remember a movie with a Miles Davis song in the soundtrack. All I remember is a section from the perspective of a child in the back of a car (the narrator was an adult) and he appeared to be from a \u2018made\u2019 family of Italian-American gangsters. They had just passed a church; the boy sees his father cross himself and he follows suit. That\u2019s all I remember.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"591309:0","label":1.0},{"id":"591309:1","label":1.0},{"id":"591309:2","label":1.0},{"id":"591309:3","label":1.0},{"id":"591309:4","label":1.0},{"id":"591309:5","label":1.0},{"id":"591309:6","label":1.0},{"id":"591309:7","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"591309","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nItalian gangster film? .\\n I remember a movie with a Miles Davis song in the soundtrack. All I remember is a section from the perspective of a child in the back of a car (the narrator was an adult) and he appeared to be from a \\u2018made\\u2019 family of Italian-American gangsters. They had just passed a church; the boy sees his father cross himself and he follows suit. That\\u2019s all I remember.\"}","task_split":"tip_of_the_tongue"}
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| 47 |
+
{"query_id":"245","query_content":"Weird Cinemax Vanguard Film .\n In college (early to mid 90s) \u00a0I remember seeing a film on Cinemax under their Vanguard Cinema umbrella about a young boy in a small\u00a0farming community\u00a0whose father is accused of being a killer\/serial killer.\u00a0 The kid then\u00a0sets out to prove his father\u2019s innocence.\u00a0 There\u2019s one scene that stands out where he passes two nuns in the road who stare at him and make strange animal noises (clucking maybe?).\u00a0 In the end the boy finds out his dad is the killer and he raises his hands in the air and screams \u201cnoooo!\u201d\u00a0 It wasn\u2019t in English and I thought the name of the film was \u201cDark Dreams\u201d or \u201cDark Visions\u201d but I can find no trace of it.","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"1809458:0","label":1.0},{"id":"1809458:1","label":1.0},{"id":"1809458:2","label":1.0},{"id":"1809458:3","label":1.0},{"id":"1809458:4","label":1.0},{"id":"1809458:5","label":1.0},{"id":"1809458:6","label":1.0},{"id":"1809458:7","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"1809458","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nWeird Cinemax Vanguard Film .\\n In college (early to mid 90s) \\u00a0I remember seeing a film on Cinemax under their Vanguard Cinema umbrella about a young boy in a small\\u00a0farming community\\u00a0whose father is accused of being a killer\/serial killer.\\u00a0 The kid then\\u00a0sets out to prove his father\\u2019s innocence.\\u00a0 There\\u2019s one scene that stands out where he passes two nuns in the road who stare at him and make strange animal noises (clucking maybe?).\\u00a0 In the end the boy finds out his dad is the killer and he raises his hands in the air and screams \\u201cnoooo!\\u201d\\u00a0 It wasn\\u2019t in English and I thought the name of the film was \\u201cDark Dreams\\u201d or \\u201cDark Visions\\u201d but I can find no trace of it.\"}","task_split":"tip_of_the_tongue"}
|
| 48 |
+
{"query_id":"580","query_content":"Zombie or Monster Horror Movie .\n I remember this monster or zombie movie where a monster or zombie is going around biting and killing people and I remember the thing saw a group of cheerleaders training and it bit one of them on her bottom and she was running and screaming as well as the others but thats all i remember. I think its a popular movie","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"5651517:0","label":1.0},{"id":"5651517:1","label":1.0},{"id":"5651517:2","label":1.0},{"id":"5651517:3","label":1.0},{"id":"5651517:4","label":1.0},{"id":"5651517:5","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"5651517","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nZombie or Monster Horror Movie .\\n I remember this monster or zombie movie where a monster or zombie is going around biting and killing people and I remember the thing saw a group of cheerleaders training and it bit one of them on her bottom and she was running and screaming as well as the others but thats all i remember. I think its a popular movie\"}","task_split":"tip_of_the_tongue"}
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| 49 |
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{"query_id":"120","query_content":"Mental handicaped man, lonely, finds talent playing Jazz music .\n \u00a0 I would very much appreciate if someone could tell me how this film is called. Since 20 years I want to see it again but cant find out its name \u00a0 The movie (in colour) must be older then 1980 A low budget movie. I had the German version since I\u2019m in Switzerland A lonely man with mental handicap is the main actor He gives odd noises from himself He was walking around in the city, at night, empty streets\u2026. A black cat shows up that catches his attention He notices a bar that is still open, bright light from the windows, he hears the jazz music playing inside He enters the bar and stands still all at the entrance He observes the people having fun and listening to a live jazz concert He catches the rhythm and starts to move around and giving out sounds that match the beat oft the music The jazz band notices his participation and invites him on stage He gets the micro and gives out the monotone noise that is linked to his mental illness The audience loves it and he receives loads of applause From that moment I can\u2019t recall the rest oft he movie but he seem to have found sense in life playing jazz and entertaining the audience I think the film ended in that town, he has his own house, a wife and a kid playing in the garden","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"1475272:0","label":1.0},{"id":"1475272:1","label":1.0},{"id":"1475272:2","label":1.0},{"id":"1475272:3","label":1.0},{"id":"1475272:4","label":1.0},{"id":"1475272:5","label":1.0},{"id":"1475272:6","label":1.0},{"id":"1475272:7","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"1475272","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nMental handicaped man, lonely, finds talent playing Jazz music .\\n \\u00a0 I would very much appreciate if someone could tell me how this film is called. Since 20 years I want to see it again but cant find out its name \\u00a0 The movie (in colour) must be older then 1980 A low budget movie. I had the German version since I\\u2019m in Switzerland A lonely man with mental handicap is the main actor He gives odd noises from himself He was walking around in the city, at night, empty streets\\u2026. A black cat shows up that catches his attention He notices a bar that is still open, bright light from the windows, he hears the jazz music playing inside He enters the bar and stands still all at the entrance He observes the people having fun and listening to a live jazz concert He catches the rhythm and starts to move around and giving out sounds that match the beat oft the music The jazz band notices his participation and invites him on stage He gets the micro and gives out the monotone noise that is linked to his mental illness The audience loves it and he receives loads of applause From that moment I can\\u2019t recall the rest oft he movie but he seem to have found sense in life playing jazz and entertaining the audience I think the film ended in that town, he has his own house, a wife and a kid playing in the garden\"}","task_split":"tip_of_the_tongue"}
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| 50 |
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{"query_id":"201","query_content":"Movie with evil white ball devours this guy\u2019s arm, out comes two women wearing cobwebs as robes .\n So this movie has been really difficult to figure out for me, I THINK I found it once like five years ago, but I\u2019ve been through several laptops and never backed it up (I don\u2019t think I even bookmarked the page anyway)! I never saw the entire movie, I actually walked in on my mom watching it in the middle of the night when I was a kid. Think it might have been around 2002 if I\u2019m remembering correctly, since we lived in a lot of different apartments and I think both this movie and seeing the MJ Blanket incident on the news happened in the same apartment. Rough estimate. Anyway I saw presumably the beginning of the movie. It took place in a pretty old time iirc, maybe in Italy just going off of the architecture and clothing the man was wearing and I think he might have been in some kind of really old-looking art studio. He opened this old box and pulled out this big ball, kind of like a crystal ball but completely opaque white (or maybe kind of marbled). Something happened with the ball and it kind of\u2026swallowed his arm? And started changing shape a bit when it did. I don\u2019t remember what happened before that moment or what happened immediately after, but he died (or maybe his friend, I think he had a friend) and these two women emerged from the ball or were awakened BY the ball, and they were covered in these really thin, see-through cloaks that looked like they were made of cobwebs. I think one of them was blonde, and then they left the \u201dstudio\u201d and started walking down the street, still only wearing the robes. Anyway I think it was turned off and I was put back to bed. I think it might have been on the Sci Fi channel and they have SO MANY original movies that I can\u2019t find this specific one, if it even was a Sci Fi original. Any help is appreciated!","instruction":"Given a description of an entity, retrieve the entity that is described","passage_qrels":[{"id":"22340794:0","label":1.0},{"id":"22340794:1","label":1.0},{"id":"22340794:2","label":1.0}],"passage_binary_qrels":null,"full_document_qrels":[{"id":"22340794","label":1.0}],"use_max_p":true,"metadata":"{\"query_with_instruction\": \"Given a description of an entity, retrieve the entity that is described\\nMovie with evil white ball devours this guy\\u2019s arm, out comes two women wearing cobwebs as robes .\\n So this movie has been really difficult to figure out for me, I THINK I found it once like five years ago, but I\\u2019ve been through several laptops and never backed it up (I don\\u2019t think I even bookmarked the page anyway)! I never saw the entire movie, I actually walked in on my mom watching it in the middle of the night when I was a kid. Think it might have been around 2002 if I\\u2019m remembering correctly, since we lived in a lot of different apartments and I think both this movie and seeing the MJ Blanket incident on the news happened in the same apartment. Rough estimate. Anyway I saw presumably the beginning of the movie. It took place in a pretty old time iirc, maybe in Italy just going off of the architecture and clothing the man was wearing and I think he might have been in some kind of really old-looking art studio. He opened this old box and pulled out this big ball, kind of like a crystal ball but completely opaque white (or maybe kind of marbled). Something happened with the ball and it kind of\\u2026swallowed his arm? And started changing shape a bit when it did. I don\\u2019t remember what happened before that moment or what happened immediately after, but he died (or maybe his friend, I think he had a friend) and these two women emerged from the ball or were awakened BY the ball, and they were covered in these really thin, see-through cloaks that looked like they were made of cobwebs. I think one of them was blonde, and then they left the \\u201dstudio\\u201d and started walking down the street, still only wearing the robes. Anyway I think it was turned off and I was put back to bed. I think it might have been on the Sci Fi channel and they have SO MANY original movies that I can\\u2019t find this specific one, if it even was a Sci Fi original. Any help is appreciated!\"}","task_split":"tip_of_the_tongue"}
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