Add research_order5_hard subset (100 order-5 research problems, no ground truth)

README.md

@@ -40,6 +40,10 @@ configs:
   data_files:
   - split: train
     path: data/stage2_stress_test.jsonl
+- config_name: research_order5_hard
+  data_files:
+  - split: train
+    path: data/research_order5_hard.jsonl
 ---
 
 # Equational Theories Selected Problems
@@ -51,6 +55,8 @@ This dataset was updated on August 27, 2026.
 Main changes:
 - added the `stage2_stress_test` subset: 200 problems, 50 (25 TRUE / 25 FALSE) per category `order4_normal`, `order4_hard`, `order4_extra_hard`, `order5_normal`
 - added `metadata/stage2_stress_test.json`
+- added the `research_order5_hard` subset: 100 order-5 research problems **without ground truth** (`answer` is `null` on every record)
+- added `metadata/research_order5_hard.json`
 
 ## Update (April 27, 2026)
 
@@ -102,6 +108,7 @@ Because the full raw dataset is very large, the competition organizers selected
 - `evaluation_extra_hard`: 200 Stage 1 final evaluation problems, with 100 ground-truth `TRUE` labels and 100 ground-truth `FALSE` labels
 - `evaluation_order5`: 200 order-5 evaluation problems, with 100 ground-truth `TRUE` labels and 100 ground-truth `FALSE` labels
 - `stage2_stress_test`: 200 Stage 2 stress-test problems, 50 per category (`order4_normal`, `order4_hard`, `order4_extra_hard`, `order5_normal`; the `difficulty` field carries the category), with 100 ground-truth `TRUE` labels and 100 ground-truth `FALSE` labels
+- `research_order5_hard`: 100 order-5 research problems with **no ground truth** (`answer` is `null`); each problem's `equation2` is one of the 10 confirmed Austin laws of the [Order 5 Austin laws blueprint chapter](https://teorth.github.io/equational_theories/blueprint/order-5-austin-laws.html) and its `equation1` is one of the 120 blueprint laws with open model-status; every problem remained undecided by automated tooling (3 s Vampire+Mace4 race, finite-model checks, Vampire CASC 120 s)
 
 All subsets are exposed as the `train` split in this repository. The `evaluation_*` subsets are released Stage 1 evaluation subsets.
 
@@ -111,12 +118,12 @@ Each record has the following fields:
 
 - `id`: stable identifier such as `normal_0001`, `hard_0001`, `hard3_0001`, or `evaluation_normal_0001`
 - `index`: 1-based index within the subset
-- `difficulty`: subset difficulty label such as `normal`, `hard`, `extra_hard`, `order5_normal`, or (in `stage2_stress_test`) one of `order4_normal`, `order4_hard`, `order4_extra_hard`, `order5_normal`
+- `difficulty`: subset difficulty label such as `normal`, `hard`, `extra_hard`, `order5_normal`, `order5_hard` (in `research_order5_hard`), or (in `stage2_stress_test`) one of `order4_normal`, `order4_hard`, `order4_extra_hard`, `order5_normal`
 - `eq1_id`: 1-based equation identifier for `equation1`; for the order-4-and-below subsets, this refers to the full 4694-law equation list
 - `eq2_id`: 1-based equation identifier for `equation2`; for the order-4-and-below subsets, this refers to the full 4694-law equation list
 - `equation1`: Equation 1
 - `equation2`: Equation 2
-- `answer`: whether Equation 1 implies Equation 2 over all magmas
+- `answer`: whether Equation 1 implies Equation 2 over all magmas; in the `research_order5_hard` subset this is `null` for every record (no ground truth)
 
 ## Subset Metadata
 
@@ -139,6 +146,7 @@ Records in `hard1`, `hard2`, and `hard3` use subset-specific IDs and keep `diffi
 Records in `evaluation_order5` use order-5 equation identifiers.
 Records in `stage2_stress_test` with `difficulty: order5_normal` use order-5
 equation identifiers; its other records use the 4694-law list identifiers.
+Records in `research_order5_hard` use order-5 equation identifiers.
 
 ## Usage
 
@@ -204,6 +212,12 @@ stage2_stress_test = load_dataset(
     "stage2_stress_test",
     split="train",
 )
+
+research_order5_hard = load_dataset(
+    "SAIRfoundation/equational-theories-selected-problems",
+    "research_order5_hard",
+    split="train",
+)
 ```
 
 ## Files
@@ -218,8 +232,10 @@ stage2_stress_test = load_dataset(
 - `data/evaluation_extra_hard.jsonl`
 - `data/evaluation_order5.jsonl`
 - `data/stage2_stress_test.jsonl`
+- `data/research_order5_hard.jsonl`
 - `metadata/normal.json`
 - `metadata/stage2_stress_test.json`
+- `metadata/research_order5_hard.json`
 - `metadata/hard.json`
 - `metadata/hard1.json`
 - `metadata/hard2.json`

data/research_order5_hard.jsonl

@@ -0,0 +1,100 @@
+{"id": "research_order5_hard_0001", "index": 1, "difficulty": "order5_hard", "eq1_id": 24200, "eq2_id": 22455, "equation1": "x = ((y * x) * x) * ((x * z) * z)", "equation2": "x = (y * (x * x)) * ((y * z) * y)", "answer": null}
+{"id": "research_order5_hard_0002", "index": 2, "difficulty": "order5_hard", "eq1_id": 39163, "eq2_id": 22818, "equation1": "x = (((y * x) * (y * z)) * y) * y", "equation2": "x = (y * (z * y)) * ((x * x) * y)", "answer": null}
+{"id": "research_order5_hard_0003", "index": 3, "difficulty": "order5_hard", "eq1_id": 11081, "eq2_id": 41082, "equation1": "x = y * ((x * (y * x)) * (z * y))", "equation2": "x = ((((y * y) * z) * x) * x) * z", "answer": null}
+{"id": "research_order5_hard_0004", "index": 4, "difficulty": "order5_hard", "eq1_id": 41253, "eq2_id": 4916, "equation1": "x = ((((y * z) * y) * y) * x) * z", "equation2": "x = y * (x * (x * (y * (z * z))))", "answer": null}
+{"id": "research_order5_hard_0005", "index": 5, "difficulty": "order5_hard", "eq1_id": 10222, "eq2_id": 20034, "equation1": "x = y * ((x * y) * ((z * y) * y))", "equation2": "x = (y * y) * ((z * (x * x)) * z)", "answer": null}
+{"id": "research_order5_hard_0006", "index": 6, "difficulty": "order5_hard", "eq1_id": 32281, "eq2_id": 41082, "equation1": "x = (y * ((y * (y * x)) * z)) * z", "equation2": "x = ((((y * y) * z) * x) * x) * z", "answer": null}
+{"id": "research_order5_hard_0007", "index": 7, "difficulty": "order5_hard", "eq1_id": 12073, "eq2_id": 28770, "equation1": "x = y * (((y * x) * x) * (z * z))", "equation2": "x = (((y * y) * y) * x) * (y * z)", "answer": null}
+{"id": "research_order5_hard_0008", "index": 8, "difficulty": "order5_hard", "eq1_id": 13764, "eq2_id": 22455, "equation1": "x = y * ((x * ((z * y) * y)) * y)", "equation2": "x = (y * (x * x)) * ((y * z) * y)", "answer": null}
+{"id": "research_order5_hard_0009", "index": 9, "difficulty": "order5_hard", "eq1_id": 11116, "eq2_id": 22455, "equation1": "x = y * ((x * (z * x)) * (y * y))", "equation2": "x = (y * (x * x)) * ((y * z) * y)", "answer": null}
+{"id": "research_order5_hard_0010", "index": 10, "difficulty": "order5_hard", "eq1_id": 34889, "eq2_id": 22818, "equation1": "x = ((y * y) * ((x * z) * x)) * z", "equation2": "x = (y * (z * y)) * ((x * x) * y)", "answer": null}
+{"id": "research_order5_hard_0011", "index": 11, "difficulty": "order5_hard", "eq1_id": 40057, "eq2_id": 28770, "equation1": "x = (((y * (x * z)) * x) * y) * y", "equation2": "x = (((y * y) * y) * x) * (y * z)", "answer": null}
+{"id": "research_order5_hard_0012", "index": 12, "difficulty": "order5_hard", "eq1_id": 33020, "eq2_id": 28770, "equation1": "x = (y * (((x * y) * z) * x)) * y", "equation2": "x = (((y * y) * y) * x) * (y * z)", "answer": null}
+{"id": "research_order5_hard_0013", "index": 13, "difficulty": "order5_hard", "eq1_id": 5066, "eq2_id": 41082, "equation1": "x = y * (y * (x * (y * (z * y))))", "equation2": "x = ((((y * y) * z) * x) * x) * z", "answer": null}
+{"id": "research_order5_hard_0014", "index": 14, "difficulty": "order5_hard", "eq1_id": 40909, "eq2_id": 28770, "equation1": "x = ((((y * x) * y) * y) * z) * y", "equation2": "x = (((y * y) * y) * x) * (y * z)", "answer": null}
+{"id": "research_order5_hard_0015", "index": 15, "difficulty": "order5_hard", "eq1_id": 5012, "eq2_id": 15535, "equation1": "x = y * (x * (z * (z * (y * z))))", "equation2": "x = y * (((x * (z * z)) * y) * y)", "answer": null}
+{"id": "research_order5_hard_0016", "index": 16, "difficulty": "order5_hard", "eq1_id": 40914, "eq2_id": 4916, "equation1": "x = ((((y * x) * y) * z) * x) * z", "equation2": "x = y * (x * (x * (y * (z * z))))", "answer": null}
+{"id": "research_order5_hard_0017", "index": 17, "difficulty": "order5_hard", "eq1_id": 22591, "eq2_id": 20034, "equation1": "x = (y * (y * x)) * ((x * x) * z)", "equation2": "x = (y * y) * ((z * (x * x)) * z)", "answer": null}
+{"id": "research_order5_hard_0018", "index": 18, "difficulty": "order5_hard", "eq1_id": 9663, "eq2_id": 22818, "equation1": "x = y * ((z * y) * (x * (x * y)))", "equation2": "x = (y * (z * y)) * ((x * x) * y)", "answer": null}
+{"id": "research_order5_hard_0019", "index": 19, "difficulty": "order5_hard", "eq1_id": 5012, "eq2_id": 20034, "equation1": "x = y * (x * (z * (z * (y * z))))", "equation2": "x = (y * y) * ((z * (x * x)) * z)", "answer": null}
+{"id": "research_order5_hard_0020", "index": 20, "difficulty": "order5_hard", "eq1_id": 21866, "eq2_id": 20034, "equation1": "x = (y * (z * x)) * (x * (x * w))", "equation2": "x = (y * y) * ((z * (x * x)) * z)", "answer": null}
+{"id": "research_order5_hard_0021", "index": 21, "difficulty": "order5_hard", "eq1_id": 5837, "eq2_id": 22818, "equation1": "x = y * (x * (y * ((z * y) * y)))", "equation2": "x = (y * (z * y)) * ((x * x) * y)", "answer": null}
+{"id": "research_order5_hard_0022", "index": 22, "difficulty": "order5_hard", "eq1_id": 12073, "eq2_id": 41082, "equation1": "x = y * (((y * x) * x) * (z * z))", "equation2": "x = ((((y * y) * z) * x) * x) * z", "answer": null}
+{"id": "research_order5_hard_0023", "index": 23, "difficulty": "order5_hard", "eq1_id": 40914, "eq2_id": 28770, "equation1": "x = ((((y * x) * y) * z) * x) * z", "equation2": "x = (((y * y) * y) * x) * (y * z)", "answer": null}
+{"id": "research_order5_hard_0024", "index": 24, "difficulty": "order5_hard", "eq1_id": 12087, "eq2_id": 28770, "equation1": "x = y * (((y * x) * z) * (x * z))", "equation2": "x = (((y * y) * y) * x) * (y * z)", "answer": null}
+{"id": "research_order5_hard_0025", "index": 25, "difficulty": "order5_hard", "eq1_id": 17286, "eq2_id": 20034, "equation1": "x = (y * x) * (z * (z * (x * z)))", "equation2": "x = (y * y) * ((z * (x * x)) * z)", "answer": null}
+{"id": "research_order5_hard_0026", "index": 26, "difficulty": "order5_hard", "eq1_id": 39214, "eq2_id": 41082, "equation1": "x = (((y * x) * (z * z)) * y) * y", "equation2": "x = ((((y * y) * z) * x) * x) * z", "answer": null}
+{"id": "research_order5_hard_0027", "index": 27, "difficulty": "order5_hard", "eq1_id": 23354, "eq2_id": 17522, "equation1": "x = ((y * x) * y) * (x * (x * z))", "equation2": "x = (y * z) * (x * (z * (z * z)))", "answer": null}
+{"id": "research_order5_hard_0028", "index": 28, "difficulty": "order5_hard", "eq1_id": 21866, "eq2_id": 22818, "equation1": "x = (y * (z * x)) * (x * (x * w))", "equation2": "x = (y * (z * y)) * ((x * x) * y)", "answer": null}
+{"id": "research_order5_hard_0029", "index": 29, "difficulty": "order5_hard", "eq1_id": 32280, "eq2_id": 22818, "equation1": "x = (y * ((y * (y * x)) * z)) * y", "equation2": "x = (y * (z * y)) * ((x * x) * y)", "answer": null}
+{"id": "research_order5_hard_0030", "index": 30, "difficulty": "order5_hard", "eq1_id": 11081, "eq2_id": 22818, "equation1": "x = y * ((x * (y * x)) * (z * y))", "equation2": "x = (y * (z * y)) * ((x * x) * y)", "answer": null}
+{"id": "research_order5_hard_0031", "index": 31, "difficulty": "order5_hard", "eq1_id": 12883, "eq2_id": 30591, "equation1": "x = y * ((x * (z * (y * x))) * y)", "equation2": "x = (y * (y * ((z * z) * x))) * y", "answer": null}
+{"id": "research_order5_hard_0032", "index": 32, "difficulty": "order5_hard", "eq1_id": 32281, "eq2_id": 15535, "equation1": "x = (y * ((y * (y * x)) * z)) * z", "equation2": "x = y * (((x * (z * z)) * y) * y)", "answer": null}
+{"id": "research_order5_hard_0033", "index": 33, "difficulty": "order5_hard", "eq1_id": 21864, "eq2_id": 20034, "equation1": "x = (y * (z * x)) * (x * (x * y))", "equation2": "x = (y * y) * ((z * (x * x)) * z)", "answer": null}
+{"id": "research_order5_hard_0034", "index": 34, "difficulty": "order5_hard", "eq1_id": 6878, "eq2_id": 28770, "equation1": "x = y * (y * ((z * x) * (x * y)))", "equation2": "x = (((y * y) * y) * x) * (y * z)", "answer": null}
+{"id": "research_order5_hard_0035", "index": 35, "difficulty": "order5_hard", "eq1_id": 36713, "eq2_id": 25964, "equation1": "x = (((y * y) * z) * (y * x)) * y", "equation2": "x = (y * ((x * x) * y)) * (z * z)", "answer": null}
+{"id": "research_order5_hard_0036", "index": 36, "difficulty": "order5_hard", "eq1_id": 34889, "eq2_id": 17522, "equation1": "x = ((y * y) * ((x * z) * x)) * z", "equation2": "x = (y * z) * (x * (z * (z * z)))", "answer": null}
+{"id": "research_order5_hard_0037", "index": 37, "difficulty": "order5_hard", "eq1_id": 28626, "eq2_id": 15535, "equation1": "x = (((y * x) * y) * y) * (x * z)", "equation2": "x = y * (((x * (z * z)) * y) * y)", "answer": null}
+{"id": "research_order5_hard_0038", "index": 38, "difficulty": "order5_hard", "eq1_id": 28626, "eq2_id": 22818, "equation1": "x = (((y * x) * y) * y) * (x * z)", "equation2": "x = (y * (z * y)) * ((x * x) * y)", "answer": null}
+{"id": "research_order5_hard_0039", "index": 39, "difficulty": "order5_hard", "eq1_id": 21865, "eq2_id": 28770, "equation1": "x = (y * (z * x)) * (x * (x * z))", "equation2": "x = (((y * y) * y) * x) * (y * z)", "answer": null}
+{"id": "research_order5_hard_0040", "index": 40, "difficulty": "order5_hard", "eq1_id": 17286, "eq2_id": 28770, "equation1": "x = (y * x) * (z * (z * (x * z)))", "equation2": "x = (((y * y) * y) * x) * (y * z)", "answer": null}
+{"id": "research_order5_hard_0041", "index": 41, "difficulty": "order5_hard", "eq1_id": 9345, "eq2_id": 22818, "equation1": "x = y * ((x * y) * (z * (y * y)))", "equation2": "x = (y * (z * y)) * ((x * x) * y)", "answer": null}
+{"id": "research_order5_hard_0042", "index": 42, "difficulty": "order5_hard", "eq1_id": 18137, "eq2_id": 25964, "equation1": "x = (y * x) * (z * ((x * z) * z))", "equation2": "x = (y * ((x * x) * y)) * (z * z)", "answer": null}
+{"id": "research_order5_hard_0043", "index": 43, "difficulty": "order5_hard", "eq1_id": 20911, "eq2_id": 20034, "equation1": "x = (y * y) * (((z * x) * x) * z)", "equation2": "x = (y * y) * ((z * (x * x)) * z)", "answer": null}
+{"id": "research_order5_hard_0044", "index": 44, "difficulty": "order5_hard", "eq1_id": 39126, "eq2_id": 22455, "equation1": "x = (((y * x) * (x * z)) * y) * y", "equation2": "x = (y * (x * x)) * ((y * z) * y)", "answer": null}
+{"id": "research_order5_hard_0045", "index": 45, "difficulty": "order5_hard", "eq1_id": 5837, "eq2_id": 25964, "equation1": "x = y * (x * (y * ((z * y) * y)))", "equation2": "x = (y * ((x * x) * y)) * (z * z)", "answer": null}
+{"id": "research_order5_hard_0046", "index": 46, "difficulty": "order5_hard", "eq1_id": 34888, "eq2_id": 22818, "equation1": "x = ((y * y) * ((x * z) * x)) * y", "equation2": "x = (y * (z * y)) * ((x * x) * y)", "answer": null}
+{"id": "research_order5_hard_0047", "index": 47, "difficulty": "order5_hard", "eq1_id": 11116, "eq2_id": 28770, "equation1": "x = y * ((x * (z * x)) * (y * y))", "equation2": "x = (((y * y) * y) * x) * (y * z)", "answer": null}
+{"id": "research_order5_hard_0048", "index": 48, "difficulty": "order5_hard", "eq1_id": 23357, "eq2_id": 22455, "equation1": "x = ((y * x) * y) * (x * (y * z))", "equation2": "x = (y * (x * x)) * ((y * z) * y)", "answer": null}
+{"id": "research_order5_hard_0049", "index": 49, "difficulty": "order5_hard", "eq1_id": 6912, "eq2_id": 28770, "equation1": "x = y * (y * ((z * z) * (x * y)))", "equation2": "x = (((y * y) * y) * x) * (y * z)", "answer": null}
+{"id": "research_order5_hard_0050", "index": 50, "difficulty": "order5_hard", "eq1_id": 27859, "eq2_id": 4916, "equation1": "x = ((y * (y * x)) * x) * (z * z)", "equation2": "x = y * (x * (x * (y * (z * z))))", "answer": null}
+{"id": "research_order5_hard_0051", "index": 51, "difficulty": "order5_hard", "eq1_id": 36487, "eq2_id": 17522, "equation1": "x = (((y * x) * x) * (y * z)) * y", "equation2": "x = (y * z) * (x * (z * (z * z)))", "answer": null}
+{"id": "research_order5_hard_0052", "index": 52, "difficulty": "order5_hard", "eq1_id": 22591, "eq2_id": 28770, "equation1": "x = (y * (y * x)) * ((x * x) * z)", "equation2": "x = (((y * y) * y) * x) * (y * z)", "answer": null}
+{"id": "research_order5_hard_0053", "index": 53, "difficulty": "order5_hard", "eq1_id": 27863, "eq2_id": 30591, "equation1": "x = ((y * (y * x)) * y) * (x * z)", "equation2": "x = (y * (y * ((z * z) * x))) * y", "answer": null}
+{"id": "research_order5_hard_0054", "index": 54, "difficulty": "order5_hard", "eq1_id": 33020, "eq2_id": 20034, "equation1": "x = (y * (((x * y) * z) * x)) * y", "equation2": "x = (y * y) * ((z * (x * x)) * z)", "answer": null}
+{"id": "research_order5_hard_0055", "index": 55, "difficulty": "order5_hard", "eq1_id": 38316, "eq2_id": 22455, "equation1": "x = ((y * ((x * z) * y)) * x) * y", "equation2": "x = (y * (x * x)) * ((y * z) * y)", "answer": null}
+{"id": "research_order5_hard_0056", "index": 56, "difficulty": "order5_hard", "eq1_id": 11116, "eq2_id": 22818, "equation1": "x = y * ((x * (z * x)) * (y * y))", "equation2": "x = (y * (z * y)) * ((x * x) * y)", "answer": null}
+{"id": "research_order5_hard_0057", "index": 57, "difficulty": "order5_hard", "eq1_id": 21865, "eq2_id": 41082, "equation1": "x = (y * (z * x)) * (x * (x * z))", "equation2": "x = ((((y * y) * z) * x) * x) * z", "answer": null}
+{"id": "research_order5_hard_0058", "index": 58, "difficulty": "order5_hard", "eq1_id": 5833, "eq2_id": 22818, "equation1": "x = y * (x * (y * ((z * x) * y)))", "equation2": "x = (y * (z * y)) * ((x * x) * y)", "answer": null}
+{"id": "research_order5_hard_0059", "index": 59, "difficulty": "order5_hard", "eq1_id": 5295, "eq2_id": 30591, "equation1": "x = y * (z * (y * (y * (x * y))))", "equation2": "x = (y * (y * ((z * z) * x))) * y", "answer": null}
+{"id": "research_order5_hard_0060", "index": 60, "difficulty": "order5_hard", "eq1_id": 36638, "eq2_id": 28770, "equation1": "x = (((y * y) * x) * (y * z)) * y", "equation2": "x = (((y * y) * y) * x) * (y * z)", "answer": null}
+{"id": "research_order5_hard_0061", "index": 61, "difficulty": "order5_hard", "eq1_id": 12234, "eq2_id": 22818, "equation1": "x = y * (((z * x) * y) * (x * y))", "equation2": "x = (y * (z * y)) * ((x * x) * y)", "answer": null}
+{"id": "research_order5_hard_0062", "index": 62, "difficulty": "order5_hard", "eq1_id": 4952, "eq2_id": 4916, "equation1": "x = y * (x * (y * (y * (z * y))))", "equation2": "x = y * (x * (x * (y * (z * z))))", "answer": null}
+{"id": "research_order5_hard_0063", "index": 63, "difficulty": "order5_hard", "eq1_id": 36524, "eq2_id": 41082, "equation1": "x = (((y * x) * y) * (y * z)) * y", "equation2": "x = ((((y * y) * z) * x) * x) * z", "answer": null}
+{"id": "research_order5_hard_0064", "index": 64, "difficulty": "order5_hard", "eq1_id": 32294, "eq2_id": 22818, "equation1": "x = (y * ((y * (y * z)) * x)) * y", "equation2": "x = (y * (z * y)) * ((x * x) * y)", "answer": null}
+{"id": "research_order5_hard_0065", "index": 65, "difficulty": "order5_hard", "eq1_id": 38316, "eq2_id": 20034, "equation1": "x = ((y * ((x * z) * y)) * x) * y", "equation2": "x = (y * y) * ((z * (x * x)) * z)", "answer": null}
+{"id": "research_order5_hard_0066", "index": 66, "difficulty": "order5_hard", "eq1_id": 5141, "eq2_id": 4916, "equation1": "x = y * (y * (z * (y * (x * y))))", "equation2": "x = y * (x * (x * (y * (z * z))))", "answer": null}
+{"id": "research_order5_hard_0067", "index": 67, "difficulty": "order5_hard", "eq1_id": 40951, "eq2_id": 4916, "equation1": "x = ((((y * x) * z) * y) * y) * y", "equation2": "x = y * (x * (x * (y * (z * z))))", "answer": null}
+{"id": "research_order5_hard_0068", "index": 68, "difficulty": "order5_hard", "eq1_id": 32281, "eq2_id": 17522, "equation1": "x = (y * ((y * (y * x)) * z)) * z", "equation2": "x = (y * z) * (x * (z * (z * z)))", "answer": null}
+{"id": "research_order5_hard_0069", "index": 69, "difficulty": "order5_hard", "eq1_id": 22591, "eq2_id": 41082, "equation1": "x = (y * (y * x)) * ((x * x) * z)", "equation2": "x = ((((y * y) * z) * x) * x) * z", "answer": null}
+{"id": "research_order5_hard_0070", "index": 70, "difficulty": "order5_hard", "eq1_id": 34889, "eq2_id": 30591, "equation1": "x = ((y * y) * ((x * z) * x)) * z", "equation2": "x = (y * (y * ((z * z) * x))) * y", "answer": null}
+{"id": "research_order5_hard_0071", "index": 71, "difficulty": "order5_hard", "eq1_id": 9667, "eq2_id": 25964, "equation1": "x = y * ((z * y) * (x * (y * y)))", "equation2": "x = (y * ((x * x) * y)) * (z * z)", "answer": null}
+{"id": "research_order5_hard_0072", "index": 72, "difficulty": "order5_hard", "eq1_id": 38249, "eq2_id": 22818, "equation1": "x = ((y * ((x * x) * z)) * y) * y", "equation2": "x = (y * (z * y)) * ((x * x) * y)", "answer": null}
+{"id": "research_order5_hard_0073", "index": 73, "difficulty": "order5_hard", "eq1_id": 35036, "eq2_id": 17522, "equation1": "x = ((y * z) * ((x * y) * x)) * y", "equation2": "x = (y * z) * (x * (z * (z * z)))", "answer": null}
+{"id": "research_order5_hard_0074", "index": 74, "difficulty": "order5_hard", "eq1_id": 35036, "eq2_id": 41082, "equation1": "x = ((y * z) * ((x * y) * x)) * y", "equation2": "x = ((((y * y) * z) * x) * x) * z", "answer": null}
+{"id": "research_order5_hard_0075", "index": 75, "difficulty": "order5_hard", "eq1_id": 39126, "eq2_id": 30591, "equation1": "x = (((y * x) * (x * z)) * y) * y", "equation2": "x = (y * (y * ((z * z) * x))) * y", "answer": null}
+{"id": "research_order5_hard_0076", "index": 76, "difficulty": "order5_hard", "eq1_id": 13992, "eq2_id": 30591, "equation1": "x = y * ((z * ((x * y) * y)) * y)", "equation2": "x = (y * (y * ((z * z) * x))) * y", "answer": null}
+{"id": "research_order5_hard_0077", "index": 77, "difficulty": "order5_hard", "eq1_id": 38565, "eq2_id": 41082, "equation1": "x = ((y * ((z * x) * z)) * y) * y", "equation2": "x = ((((y * y) * z) * x) * x) * z", "answer": null}
+{"id": "research_order5_hard_0078", "index": 78, "difficulty": "order5_hard", "eq1_id": 40037, "eq2_id": 25964, "equation1": "x = (((y * (x * y)) * z) * x) * z", "equation2": "x = (y * ((x * x) * y)) * (z * z)", "answer": null}
+{"id": "research_order5_hard_0079", "index": 79, "difficulty": "order5_hard", "eq1_id": 10218, "eq2_id": 30591, "equation1": "x = y * ((x * y) * ((z * x) * y))", "equation2": "x = (y * (y * ((z * z) * x))) * y", "answer": null}
+{"id": "research_order5_hard_0080", "index": 80, "difficulty": "order5_hard", "eq1_id": 23653, "eq2_id": 22818, "equation1": "x = ((y * z) * x) * (z * (x * z))", "equation2": "x = (y * (z * y)) * ((x * x) * y)", "answer": null}
+{"id": "research_order5_hard_0081", "index": 81, "difficulty": "order5_hard", "eq1_id": 13764, "eq2_id": 20034, "equation1": "x = y * ((x * ((z * y) * y)) * y)", "equation2": "x = (y * y) * ((z * (x * x)) * z)", "answer": null}
+{"id": "research_order5_hard_0082", "index": 82, "difficulty": "order5_hard", "eq1_id": 5107, "eq2_id": 22818, "equation1": "x = y * (y * (y * (z * (x * y))))", "equation2": "x = (y * (z * y)) * ((x * x) * y)", "answer": null}
+{"id": "research_order5_hard_0083", "index": 83, "difficulty": "order5_hard", "eq1_id": 36713, "eq2_id": 22818, "equation1": "x = (((y * y) * z) * (y * x)) * y", "equation2": "x = (y * (z * y)) * ((x * x) * y)", "answer": null}
+{"id": "research_order5_hard_0084", "index": 84, "difficulty": "order5_hard", "eq1_id": 40070, "eq2_id": 17522, "equation1": "x = (((y * (x * z)) * y) * x) * y", "equation2": "x = (y * z) * (x * (z * (z * z)))", "answer": null}
+{"id": "research_order5_hard_0085", "index": 85, "difficulty": "order5_hard", "eq1_id": 13992, "eq2_id": 22455, "equation1": "x = y * ((z * ((x * y) * y)) * y)", "equation2": "x = (y * (x * x)) * ((y * z) * y)", "answer": null}
+{"id": "research_order5_hard_0086", "index": 86, "difficulty": "order5_hard", "eq1_id": 24199, "eq2_id": 22455, "equation1": "x = ((y * x) * x) * ((x * z) * y)", "equation2": "x = (y * (x * x)) * ((y * z) * y)", "answer": null}
+{"id": "research_order5_hard_0087", "index": 87, "difficulty": "order5_hard", "eq1_id": 24200, "eq2_id": 30591, "equation1": "x = ((y * x) * x) * ((x * z) * z)", "equation2": "x = (y * (y * ((z * z) * x))) * y", "answer": null}
+{"id": "research_order5_hard_0088", "index": 88, "difficulty": "order5_hard", "eq1_id": 41252, "eq2_id": 20034, "equation1": "x = ((((y * z) * y) * y) * x) * y", "equation2": "x = (y * y) * ((z * (x * x)) * z)", "answer": null}
+{"id": "research_order5_hard_0089", "index": 89, "difficulty": "order5_hard", "eq1_id": 36713, "eq2_id": 15535, "equation1": "x = (((y * y) * z) * (y * x)) * y", "equation2": "x = y * (((x * (z * z)) * y) * y)", "answer": null}
+{"id": "research_order5_hard_0090", "index": 90, "difficulty": "order5_hard", "eq1_id": 5066, "eq2_id": 30591, "equation1": "x = y * (y * (x * (y * (z * y))))", "equation2": "x = (y * (y * ((z * z) * x))) * y", "answer": null}
+{"id": "research_order5_hard_0091", "index": 91, "difficulty": "order5_hard", "eq1_id": 6912, "eq2_id": 15535, "equation1": "x = y * (y * ((z * z) * (x * y)))", "equation2": "x = y * (((x * (z * z)) * y) * y)", "answer": null}
+{"id": "research_order5_hard_0092", "index": 92, "difficulty": "order5_hard", "eq1_id": 11280, "eq2_id": 25964, "equation1": "x = y * ((y * (z * y)) * (x * y))", "equation2": "x = (y * ((x * x) * y)) * (z * z)", "answer": null}
+{"id": "research_order5_hard_0093", "index": 93, "difficulty": "order5_hard", "eq1_id": 12294, "eq2_id": 41082, "equation1": "x = y * (((z * y) * x) * (x * y))", "equation2": "x = ((((y * y) * z) * x) * x) * z", "answer": null}
+{"id": "research_order5_hard_0094", "index": 94, "difficulty": "order5_hard", "eq1_id": 7701, "eq2_id": 15535, "equation1": "x = y * (y * ((x * (z * x)) * y))", "equation2": "x = y * (((x * (z * z)) * y) * y)", "answer": null}
+{"id": "research_order5_hard_0095", "index": 95, "difficulty": "order5_hard", "eq1_id": 35836, "eq2_id": 25964, "equation1": "x = ((y * (y * z)) * (y * x)) * y", "equation2": "x = (y * ((x * x) * y)) * (z * z)", "answer": null}
+{"id": "research_order5_hard_0096", "index": 96, "difficulty": "order5_hard", "eq1_id": 8485, "eq2_id": 4916, "equation1": "x = y * (x * (((z * x) * y) * y))", "equation2": "x = y * (x * (x * (y * (z * z))))", "answer": null}
+{"id": "research_order5_hard_0097", "index": 97, "difficulty": "order5_hard", "eq1_id": 12087, "eq2_id": 22818, "equation1": "x = y * (((y * x) * z) * (x * z))", "equation2": "x = (y * (z * y)) * ((x * x) * y)", "answer": null}
+{"id": "research_order5_hard_0098", "index": 98, "difficulty": "order5_hard", "eq1_id": 36487, "eq2_id": 22818, "equation1": "x = (((y * x) * x) * (y * z)) * y", "equation2": "x = (y * (z * y)) * ((x * x) * y)", "answer": null}
+{"id": "research_order5_hard_0099", "index": 99, "difficulty": "order5_hard", "eq1_id": 27859, "eq2_id": 25964, "equation1": "x = ((y * (y * x)) * x) * (z * z)", "equation2": "x = (y * ((x * x) * y)) * (z * z)", "answer": null}
+{"id": "research_order5_hard_0100", "index": 100, "difficulty": "order5_hard", "eq1_id": 25087, "eq2_id": 4916, "equation1": "x = (y * (x * (x * y))) * (z * z)", "equation2": "x = y * (x * (x * (y * (z * z))))", "answer": null}

metadata/research_order5_hard.json

@@ -0,0 +1,13 @@
+{
+  "subset_name": "research_order5_hard",
+  "source": "official",
+  "curators": [],
+  "difficulty": "order5_hard",
+  "problem_count": 100,
+  "true_count": 0,
+  "false_count": 0,
+  "unknown_count": 100,
+  "selection_method": "programmatic",
+  "derived_from": "order5_austin_blueprint_frontier",
+  "notes": "Research subset with NO ground truth: answer is null on every record. 100 order-5 implication problems whose conclusion (equation2) is one of the 10 confirmed Austin laws from the Equational Theories Project blueprint chapter 'Order 5 Austin laws', and whose hypothesis (equation1) is one of the 120 blueprint laws with open model-status. Every problem remained undecided after a 3 s Vampire+Mace4 race, finite-model checks where applicable, and Vampire CASC-mode 120 s in both directions."
+}