task large_stringclasses 39
values | prompt large_stringlengths 37 14.9k | answer large_stringlengths 0 9.38k | metadata large_stringlengths 380 32.1k | cot large_stringlengths 0 9.42k | level int64 0 3 | mode large_stringclasses 4
values |
|---|---|---|---|---|---|---|
arithmetics | /trace Evaluate (-10) * -9 * (7).
The answer is a number. | <trace>
-10 * -9 = 90
90 * 7 = 630
</trace>
630 | {"expr": "(-10) * -9 * (7)", "height": 5, "cot": "-10 * -9 = 90\n90 * 7 = 630", "_time": 0.0015637874603271484, "_task": "arithmetics", "_level": 0, "_config": {"c": 1.0, "level": 0, "seed": null, "size": null, "min_depth": 3, "max_depth": 5, "float_prob": 0.25, "in_decimals": 1, "out_decimals": 3, "out_digits": 6, "n_... | -10 * -9 = 90
90 * 7 = 630 | 0 | cot |
arithmetics | Evaluate 6.9 / 1 % max(-1, -6.30).
The answer is a number.
Answer:
-0.1
Evaluate -11 * 9.1 + 10 / -8.0.
The answer is a number.
Answer:
| -101.35 | {"expr": "-11 * 9.1 + 10 / -8.0", "height": 5, "cot": "-11 * 9.1 = -100.1\n10 / -8 = -1.25\n-100.1 + -1.25 = -101.35", "_time": 0.0018534660339355469, "_task": "arithmetics", "_level": 0, "_config": {"c": 1.0, "level": 0, "seed": null, "size": null, "min_depth": 3, "max_depth": 5, "float_prob": 0.25, "in_decimals": 1, ... | -11 * 9.1 = -100.1
10 / -8 = -1.25
-100.1 + -1.25 = -101.35 | 0 | few_shot |
arithmetics | Evaluate 5.0 + -10.20.
The answer is a number. | -5.2 | {"expr": "5.0 + -10.20", "height": 3, "cot": "5 + -10.2 = -5.2", "_time": 0.0011348724365234375, "_task": "arithmetics", "_level": 0, "_config": {"c": 1.0, "level": 0, "seed": null, "size": null, "min_depth": 3, "max_depth": 5, "float_prob": 0.25, "in_decimals": 1, "out_decimals": 3, "out_digits": 6, "n_trials": 50000,... | 5 + -10.2 = -5.2 | 0 | instruct |
arithmetics | Evaluate (7.4 * -3)**2 % -9.
The answer is a number.
Answer:
-100.18
Correct? (Yes/No) | No | {"expr": "(7.4 * -3)**2 % -9", "height": 5, "cot": "7.4 * -3 = -22.2\n-22.2 ** 2 = 492.84\n492.84 % -9 = -2.16", "_time": 0.002615690231323242, "_task": "arithmetics", "_level": 0, "_config": {"c": 1.0, "level": 0, "seed": null, "size": null, "min_depth": 3, "max_depth": 5, "float_prob": 0.25, "in_decimals": 1, "out_de... | 7.4 * -3 = -22.2
-22.2 ** 2 = 492.84
492.84 % -9 = -2.16 | 0 | verification |
bayesian_association | /trace System:
P(X_0) = {'0': 0.6, '1': 0.4}
X_2 ~ Noisy-OR(leak=0.0, weights={'X_0': 0.3, 'X_1': 0.3})
P(X_1) = {'0': 0.3, '1': 0.7}
X_3 ~ Noisy-AND(leak=0.0, weights={'X_1': 0.6, 'X_2': 0.1})
Observed conditions:
Observing/Knowing that the state X_3 is equal to 1, and the state X_2 is equal to 0, and the state X_1... | <trace>
Goal: Compute Observational Probability: P(X_0 | X_3=1, X_2=0, X_1=0)
Result: P(X_0 | X_1=0, X_2=0) = {0: 0.7, 1: 0.3}
</trace>
{0: 0.7, 1: 0.3} | {"target_var_values": [0, 1], "bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: BinaryInfluenceModel\n// mode: OR\n// leak: None\n// activation_magnitude: [0.3,... | Goal: Compute Observational Probability: P(X_0 | X_3=1, X_2=0, X_1=0)
Result: P(X_0 | X_1=0, X_2=0) = {0: 0.7, 1: 0.3} | 0 | cot |
bayesian_association | System:
P(X_0) = {'0': 0.8, '1': 0.2}
P(X_1|X_0=0) = {'0': 0.9, '1': 0.1}
P(X_1|X_0=1) = {'0': 0.1, '1': 0.9}
P(X_2|X_0=0) = {'0': 0.4, '1': 0.6}
P(X_2|X_0=1) = {'0': 0.4, '1': 0.6}
P(X_3) = {'0': 0.4, '1': 0.6}
Observed conditions:
Without further Observation/Knowledge of other variable.
Task: Compute probability... | {0: 1.0, 1: 0.0} | {"target_var_values": [0, 1], "bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1... | Goal: Compute Observational Probability: P(X_2)
Elim order: ['X_1', 'X_0']
Sum out X_1 -> P(X_2 | X_0) = [Distribution over ['X_2', 'X_0']]
Sum out X_0 -> P(X_2) = {0: 1.0, 1: 0.0}
Normalize (sum=1.0) -> P(X_2) = {0: 1.0, 1: 0.0} | 0 | few_shot |
bayesian_association | System:
P(X_0) = {'0': 0.6, '1': 0.4}
P(X_1|X_0=0) = {'0': 0.4, '1': 0.6}
P(X_1|X_0=1) = {'0': 0.2, '1': 0.8}
P(X_2) = {'0': 0.5, '1': 0.5}
P(X_3) = {'0': 0.5, '1': 0.5}
Observed conditions:
Observing/Knowing that the state X_0 is equal to 0, and the state X_3 is equal to 1, and the state X_1 is equal to 0
Task: Co... | {0: 0.5, 1: 0.5} | {"target_var_values": [0, 1], "bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1]}\n// type: TabularCP... | Goal: Compute Observational Probability: P(X_2 | X_0=0, X_3=1, X_1=0)
Normalize (sum=1.0) -> P(X_2) = {0: 0.5, 1: 0.5} | 0 | instruct |
bayesian_association | System:
P(X_0) = {'0': 0.6, '1': 0.4}
P(X_1|X_0=0) = {'0': 0.6, '1': 0.4}
P(X_1|X_0=1) = {'0': 0.7, '1': 0.3}
X_3 ~ Noisy-OR(leak=0.0, weights={'X_0': 0.7, 'X_1': 0.9, 'X_2': 0.9})
P(X_2) = {'0': 0.8, '1': 0.2}
Observed conditions:
Observing/Knowing that the state X_3 is equal to 0, and the state X_1 is equal to 0,... | Yes | {"target_var_values": [0, 1], "bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_3\n// state_names: {'X_3': [0, 1], 'X_0': [0, 1], 'X_1... | Goal: Compute Observational Probability: P(X_0 | X_3=0, X_1=0, X_2=1)
Result: P(X_0 | X_1=0, X_2=1, X_3=0) = {0: 0.8, 1: 0.2} | 0 | verification |
bayesian_intervention | /trace System:
P(X_0) = {'0': 0.1, '1': 0.9}
X_2 ~ Noisy-AND(leak=0.0, weights={'X_0': 0.1, 'X_1': 0.4})
X_3 ~ Noisy-AND(leak=0.0, weights={'X_0': 0.4, 'X_1': 0.2})
P(X_1) = {'0': 0.4, '1': 0.6}
Observed conditions:
Doing/Imposing that the state X_2 is equal to 0
Task: Compute probability distribution for X_0 (possi... | <trace>
Goal: Compute Causal Effect: P(X_0 | do(X_2=0))
Surgery: Cut incoming edges to intervened node 'X_2': ['X_0', 'X_1'] -> X_2; P(X_2)= Point Mass at X_2=0.
Normalize (sum=1.0) -> P(X_0) = {0: 0.1, 1: 0.9}
</trace>
{0: 0.1, 1: 0.9} | {"target_var_values": [0, 1], "bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1], 'X_1': [0, 1]}\n// type: BinaryInfluenceModel\n// mode: AND\n// leak: None\n// activation_magnitude: [0.1... | Goal: Compute Causal Effect: P(X_0 | do(X_2=0))
Surgery: Cut incoming edges to intervened node 'X_2': ['X_0', 'X_1'] -> X_2; P(X_2)= Point Mass at X_2=0.
Normalize (sum=1.0) -> P(X_0) = {0: 0.1, 1: 0.9} | 0 | cot |
bayesian_intervention | System:
P(X_0) = {'0': 0.7, '1': 0.3}
X_3 ~ Noisy-AND(leak=0.0, weights={'X_0': 0.5, 'X_2': 0.4})
P(X_2) = {'0': 0.1, '1': 0.9}
P(X_1) = {'0': 0.9, '1': 0.1}
Observed conditions:
Doing/Imposing that the state X_3 is equal to 1
Task: Compute probability distribution for X_2 (possible values: [0, 1]).
The answer is a... | {0: 0.2, 1: 0.8} | {"target_var_values": [0, 1], "bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1]}\n// type: TabularCP... | Goal: Compute Causal Effect: P(X_0 | do(X_3=0), X_2=1)
Surgery: P(X_3)= Point Mass at X_3=0.
Normalize (sum=1.0) -> P(X_0) = {0: 0.2, 1: 0.8} | 0 | few_shot |
bayesian_intervention | System:
P(X_0) = {'0': 0.6, '1': 0.4}
P(X_2|X_0=0) = {'0': 0.2, '1': 0.8}
P(X_2|X_0=1) = {'0': 0.6, '1': 0.4}
P(X_3|X_2=0) = {'0': 1.0, '1': 0.0}
P(X_3|X_2=1) = {'0': 0.5, '1': 0.5}
P(X_1) = {'0': 0.6, '1': 0.4}
Observed conditions:
Doing/Imposing that the state X_3 is equal to 0. Observing/Knowing that the state ... | {0: 0.2, 1: 0.8} | {"target_var_values": [0, 1], "bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_2\n// state_names: {'X_2': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_3\n// state_names: {'X_3': [0, 1], 'X_2': [0, 1]}\n// ... | Goal: Compute Causal Effect: P(X_2 | do(X_3=0), X_0=0, X_1=1)
Surgery: Cut incoming edges to intervened node 'X_3': ['X_2'] -> X_3; P(X_3)= Point Mass at X_3=0.
Normalize (sum=1.0) -> P(X_2 | X_0=0) = {0: 0.2, 1: 0.8} | 0 | instruct |
bayesian_intervention | System:
P(X_0) = {'0': 0.7, '1': 0.3}
P(X_3|X_0=0) = {'0': 0.0, '1': 1.0}
P(X_3|X_0=1) = {'0': 0.9, '1': 0.1}
P(X_1) = {'0': 0.2, '1': 0.8}
P(X_2|X_1=0) = {'0': 0.4, '1': 0.6}
P(X_2|X_1=1) = {'0': 0.9, '1': 0.1}
Observed conditions:
Doing/Imposing that the state X_3 is equal to 0. Observing/Knowing that the state ... | No | {"target_var_values": [0, 1], "bif_description": "// CANONICAL\n// variable: X_0\n// state_names: {'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_3\n// state_names: {'X_3': [0, 1], 'X_0': [0, 1]}\n// type: TabularCPD\n// CANONICAL\n// variable: X_1\n// state_names: {'X_1': [0, 1]}\n// type: TabularCP... | Goal: Compute Causal Effect: P(X_1 | do(X_3=0), X_0=1)
Surgery: Cut incoming edges to intervened node 'X_3': ['X_0'] -> X_3; P(X_3)= Point Mass at X_3=0.
Normalize (sum=1.0) -> P(X_1) = {0: 0.2, 1: 0.8} | 0 | verification |
code_execution | Predict the printed output of the following Python code:
```python
r = 11
if r >= r:
print(r)
```
The answer is the exact printed output string.
Answer:
11
Predict the printed output of the following Python code:
```python
w = 11
b = 16 - 8
print([11, 0, 11][1])
```
The answer is the exact printed output string.
... | 0 | {"code": "w = 11\nb = 16 - 8\nprint([11, 0, 11][1])", "tinypy_level": "1.2", "_time": 0.02047276496887207, "_task": "code_execution", "_level": 1, "_config": {"c": 1.0, "level": 1, "seed": null, "size": null, "difficulty": 1.0, "min_depth": 4, "max_depth": 16, "max_attempts": 100}, "_prompt_tokens": 49, "_answer_tokens... | 1 | few_shot | |
code_execution | Predict the printed output of the following Python code:
```python
b = 1
i = 6
x = 14
print(x - i)
```
The answer is the exact printed output string. | 8 | {"code": "b = 1\ni = 6\nx = 14\nprint(x - i)", "tinypy_level": "1.1", "_time": 0.04253888130187988, "_task": "code_execution", "_level": 1, "_config": {"c": 1.0, "level": 1, "seed": null, "size": null, "difficulty": 1.0, "min_depth": 4, "max_depth": 16, "max_attempts": 100}, "_prompt_tokens": 44, "_answer_tokens": 1, "... | 1 | instruct | |
code_execution | Predict the printed output of the following Python code:
```python
d = 12
e = 15
if e >= d:
print(d)
elif e <= d:
print(d)
else:
print(d)
```
The answer is the exact printed output string.
Answer:
[5, 5, 4]
Correct? (Yes/No) | No | {"code": "d = 12\ne = 15\nif e >= d:\n\tprint(d)\nelif e <= d:\n\tprint(d)\nelse:\n\tprint(d)", "tinypy_level": "2.1", "_time": 0.023468732833862305, "_task": "code_execution", "_level": 3, "_config": {"c": 1.0, "level": 3, "seed": null, "size": null, "difficulty": 3.0, "min_depth": 4, "max_depth": 18, "max_attempts": ... | 3 | verification | |
config_edition | Apply the requested edits to the JSON config.
Keep unrelated fields unchanged. Apply the instructions in order; if instructions conflict, later ones win.
Preserve JSON data types. Return the updated JSON only.
Original config:
{
"cache": {
"enabled": false,
"ttl": 300,
"backend": "mps"
},
"evaluation... | {
"runtime": {
"mode": "eval",
"timeout": 5,
"retries": 3,
"save_traces": true
},
"model": {
"id": "base",
"top_p": 0.9,
"backend": "cuda",
"precision": "int8"
},
"evaluation": {
"batch_size": 32,
"enabled": false,
"save_traces": false,
"description": "default"
... | {"src_text": "{\n \"runtime\": {\n \"mode\": \"eval\",\n \"timeout\": 5,\n \"retries\": 3\n },\n \"model\": {\n \"id\": \"base\",\n \"top_p\": 0.9,\n \"backend\": \"cuda\",\n \"precision\": \"int8\"\n },\n \"evaluation\": {\n \"batch_size\": 32,\n \"enabled\": false,\n \"save_traces\"... | 2 | few_shot | |
config_edition | Apply the requested edits to the JSON config.
Keep unrelated fields unchanged. Apply the instructions in order; if instructions conflict, later ones win.
Preserve JSON data types. Return the updated JSON only.
Original config:
{
"security": {
"private": false,
"owner": "evals",
"enabled": false
},
"r... | {
"security": {
"private": false,
"owner": "evals",
"enabled": true
},
"runtime": {
"mode": "debug",
"retries": 15,
"timeout": 10
},
"server": {
"timeout": 115,
"port": 9000,
"retries": 1,
"endpoint": "/v1/chat"
},
"evaluation": {
"enabled": true,
"save_trac... | {"src_text": "{\n \"security\": {\n \"private\": false,\n \"owner\": \"evals\",\n \"enabled\": false\n },\n \"runtime\": {\n \"mode\": \"debug\",\n \"retries\": 5,\n \"timeout\": 10\n },\n \"server\": {\n \"timeout\": 120,\n \"port\": 9000,\n \"retries\": 1,\n \"endpoint\": \"/v1/chat... | 0 | instruct | |
config_edition | Apply the requested edits to the JSON config.
Keep unrelated fields unchanged. Apply the instructions in order; if instructions conflict, later ones win.
Preserve JSON data types. Return the updated JSON only.
Original config:
{
"logging": {
"level": "error",
"save_traces": true,
"format": "json"
},
... | No | {"src_text": "{\n \"logging\": {\n \"level\": \"error\",\n \"save_traces\": true,\n \"format\": \"json\"\n },\n \"data\": {\n \"shuffle\": true,\n \"seed\": 1234,\n \"batch_size\": 64\n },\n \"runtime\": {\n \"features\": [\n \"cache\",\n \"streaming\"\n ],\n \"timeout\": 120,\... | 1 | verification | |
conjecture_entailment | Decide if the given premises entail the conjecture (i.e., the conjecture is provable) using Superposition/Resolution/Paramodulation.
Domain: Number Theory
Premises:
- (integer_of(recursion_equation_functions(X1))=ordinal_numbers|null_class!=ordinal_numbers)
- (domain_of(limit_ordinals)=limit_ordinals|limit_ordinals!=... | True | {"hypotheses": ["(member(omega,universal_class))", "(subclass(domain_of(X1),X2)|null_class!=X1)", "(operation(X3)|~homomorphism(X1,X2,X3))", "(~member(X1,complement(X2))|~member(X1,X2))", "(intersection(X1,X2)=null_class|X3!=X2|~subclass(X3,null_class))", "(null_class!=X1|~subclass(complement(X1),null_class))", "(membe... | 3 | few_shot | |
conjecture_entailment | Decide if the given premises entail the conjecture (i.e., the conjecture is provable) using Superposition/Resolution/Paramodulation.
Domain: Geometry
Premises:
- (between(X1,X2,extension(X1,X2,X3,X4)))
Conjecture: `(between(X1,X2,X3)|~between(X2,X3,extension(X3,X2,X4,X5)))`
The answer is `True` (provable) or `False... | False | {"hypotheses": ["(between(X1,X2,extension(X1,X2,X3,X4)))"], "conjecture": "(between(X1,X2,X3)|~between(X2,X3,extension(X3,X2,X4,X5)))", "correct_hypotheses": ["(between(X1,X2,X3)|~between(X3,X2,X4)|~between(X2,X3,X4))", "(between(X1,X2,extension(X1,X2,X3,X4)))"], "proof_depth": 1, "perturbation": 1, "useful_axioms": ["... | 0 | instruct | |
conjecture_entailment | Decide if the given premises entail the conjecture (i.e., the conjecture is provable) using Superposition/Resolution/Paramodulation.
Domain: Set Theory
Premises:
- (subset(X1,X2)|member(member_of_1_not_of_2(X1,X2),X3)|~intersection(X4,X3,X1))
- (subset(X1,X2)|~subset(X3,X2)|~member(member_of_1_not_of_2(X1,X2),X3))
- ... | No | {"hypotheses": ["(subset(X1,X2)|member(member_of_1_not_of_2(X1,X2),X3)|~intersection(X4,X3,X1))", "(subset(X1,X2)|~subset(X3,X2)|~member(member_of_1_not_of_2(X1,X2),X3))", "(subset(X1,X2)|member(member_of_1_not_of_2(X1,X2),X3)|~subset(X1,X3))", "(subset(X1,X2)|~member(member_of_1_not_of_2(X1,X2),X3)|~intersection(X2,X4... | 1 | verification | |
constrained_continuation | (GRAMMAR)
start -> seq
seq ->
seq -> expr seq
expr -> '(' seq ')'
expr -> '[' seq ']'
expr -> '<' seq '>'
(PREFIX)
[
(TEMPLATE)
___ ] ___
(SUFFIX)
> ] [ ]
Fill in the 2 blanks (___) so that PREFIX + filled-TEMPLATE + SUFFIX is a grammatical sentence. Fixed tokens of TEMPLATE must remain in place.
The answer is the... | > > > | {"g": "S -> B\nB -> 'law' '<' B '>'\nB -> 'product'", "k": 3, "prefix": ["law", "<", "law", "<", "law", "<", "product"], "suffix": [], "hints": {"0": ">"}, "template": "> ___ ___", "blanks": [1, 2], "n_blanks": 2, "n_hints": 1, "n_options": 1, "_time": 0.3186149597167969, "_task": "constrained_continuation", "_level": ... | 2 | few_shot | |
constrained_continuation | (GRAMMAR)
vp_lex_base -> v_intr_base opt_adv
start -> root
opt_adv ->
v_intr_base -> 'arrive'
np_pl_subj -> pro_pl_subj
pro_pl_subj -> 'we'
do -> 'do'
v_intr_base -> 'run'
question -> do np_pl_subj vp_lex_base
root -> question '?'
(PREFIX)
do
(TEMPLATE)
___ arrive ___
(SUFFIX)
<empty>
Fill in the 2 blanks (___) so... | we arrive ? | {"g": "vp_lex_base -> v_intr_base opt_adv\nstart -> root\nopt_adv -> \nv_intr_base -> 'arrive'\nnp_pl_subj -> pro_pl_subj\npro_pl_subj -> 'we'\ndo -> 'do'\nv_intr_base -> 'run'\nquestion -> do np_pl_subj vp_lex_base\nroot -> question '?'", "k": 3, "prefix": ["do"], "suffix": [], "hints": {"1": "arrive"}, "template": "_... | 0 | instruct | |
constrained_continuation | (GRAMMAR)
start -> seq
seq ->
seq -> expr seq
expr -> '(' seq ')'
expr -> '[' seq ']'
expr -> '<' seq '>'
(PREFIX)
< [ ] [ ]
(TEMPLATE)
> ___ ___
(SUFFIX)
] > ( ) < >
Fill in the 2 blanks (___) so that PREFIX + filled-TEMPLATE + SUFFIX is a grammatical sentence. Fixed tokens of TEMPLATE must remain in place.
The a... | No | {"g": "start -> seq\nseq -> \nseq -> expr seq\nexpr -> '(' seq ')'\nexpr -> '[' seq ']'\nexpr -> '<' seq '>'", "k": 3, "prefix": ["<", "[", "]", "[", "]"], "suffix": ["]", ">", "(", ")", "<", ">"], "hints": {"0": ">"}, "template": "> ___ ___", "blanks": [1, 2], "n_blanks": 2, "n_hints": 1, "n_options": 7, "_time": 5.39... | 2 | verification | |
constraint_satisfaction | Variables/domains:
- 0 <= x0 <= 1
- 0 <= x1 <= 3
- 0 <= x2 <= 2
Constraints:
1. (2*x0 + x1 + 2*x2) % 4 == 1
2. (x0 + 2*x1) % 2 == 1
3. 3*x0 + 4*x1 + 3*x2 == 10
4. (3*x0 + 3*x1) % 2 == 0
5. -4*x2 >= -9
6. x0 >= -3
7. x2 == 2
8. x2 == 1
Enumerate ALL satisfying assignments in variable order [x0, x1, x2].
The answer is ... | [[2, 0, 0, 0], [2, 0, 0, 1], [2, 0, 1, 0], [2, 0, 1, 1], [2, 0, 2, 0], [2, 0, 2, 1]] | {"domains": [2, 2, 2, 1], "constraints": [{"type": "lin", "idx": [0], "coeffs": [3], "op": ">=", "rhs": 5}, {"type": "lin", "idx": [1], "coeffs": [-2], "op": "==", "rhs": 0}, {"type": "lin", "idx": [2], "coeffs": [3], "op": ">=", "rhs": -2}, {"type": "lin", "idx": [0, 3], "coeffs": [1, 3], "op": "<=", "rhs": 6}, {"type... | 3 | few_shot | |
constraint_satisfaction | Variables/domains:
- 0 <= x0 <= 2
- 0 <= x1 <= 2
- 0 <= x2 <= 2
- 0 <= x3 <= 2
Constraints:
1. 4*x2 >= 3
2. AllDifferent(x0, x1, x2)
3. -4*x1 - 2*x2 + 3*x3 <= -4
4. (2*x3) % 4 == 2
5. 3*x1 - x2 + 2*x3 == 3
6. 3*x0 + 2*x1 != 3
7. 3*x0 + x1 >= 1
Enumerate ALL satisfying assignments in variable order [x0, x1, x2, x3].
T... | [[0, 1, 2, 1]] | {"domains": [2, 2, 2, 2], "constraints": [{"type": "lin", "idx": [2], "coeffs": [4], "op": ">=", "rhs": 3}, {"type": "alldiff", "idx": [0, 1, 2]}, {"type": "lin", "idx": [1, 2, 3], "coeffs": [-4, -2, 3], "op": "<=", "rhs": -4}, {"type": "mod", "idx": [3], "coeffs": [2], "mod": 4, "rem": 2}, {"type": "lin", "idx": [1, 2... | 3 | instruct | |
constraint_satisfaction | Variables/domains:
- 0 <= x0 <= 2
- 0 <= x1 <= 1
- 0 <= x2 <= 2
Constraints:
1. AllDifferent(x0, x1)
2. x2 <= 3
3. x0 + 2*x1 + 3*x2 != 4
4. 3*x0 + 2*x1 - 3*x2 == 3
Enumerate ALL satisfying assignments in variable order [x0, x1, x2].
The answer is a Python list of lists of ints, sorted lexicographically, or UNSAT if n... | No | {"domains": [2, 1, 2], "constraints": [{"type": "alldiff", "idx": [0, 1]}, {"type": "lin", "idx": [2], "coeffs": [1], "op": "<=", "rhs": 3}, {"type": "lin", "idx": [0, 1, 2], "coeffs": [1, 2, 3], "op": "!=", "rhs": 4}, {"type": "lin", "idx": [0, 1, 2], "coeffs": [3, 2, -3], "op": "==", "rhs": 3}], "solution": [[1, 0, 0... | 1 | verification | |
continuation | /trace List all valid next tokens for this prefix. The answer is the list of valid tokens sorted alphabetically and separated by |, with STOP at the end if the prefix forms a complete string.
(GRAMMAR)
vp_sg -> v_intr_sg opt_adv
who -> 'who'
start -> root
v_intr_sg -> 'runs'
opt_adv ->
root -> question '?'
question ->... | <trace>
root→question • ?⇒?
</trace>
? | {"g": "vp_sg -> v_intr_sg opt_adv\nwho -> 'who'\nstart -> root\nv_intr_sg -> 'runs'\nopt_adv -> \nroot -> question '?'\nquestion -> who vp_sg", "prefix": ["who", "runs"], "depth": 2, "cot": "root\u2192question \u2022 ?\u21d2?", "_time": 0.0021886825561523438, "_task": "continuation", "_level": 0, "_config": {"c": 1.0, ... | root→question • ?⇒? | 0 | cot |
continuation | List all valid next tokens for this prefix. The answer is the list of valid tokens sorted alphabetically and separated by |, with STOP at the end if the prefix forms a complete string.
(GRAMMAR)
start -> seq
seq ->
seq -> expr seq
expr -> '(' seq ')'
expr -> '[' seq ']'
expr -> '<' seq '>'
(PREFIX)
( ) (
Answer:
(|)|<... | explain|STOP | {"g": "S -> E\nE -> 'explain'\nE -> E E", "prefix": ["explain", "explain", "explain"], "depth": 3, "cot": "S\u2192E \u2022\u21d2STOP\nE\u2192E \u2022 E\u21d2explain", "_time": 0.7771272659301758, "_task": "continuation", "_level": 1, "_config": {"c": 1.0, "level": 1, "seed": null, "size": null, "n_types": 5, "n_termina... | S→E •⇒STOP
E→E • E⇒explain | 1 | few_shot |
continuation | List all valid next tokens for this prefix. The answer is the list of valid tokens sorted alphabetically and separated by |, with STOP at the end if the prefix forms a complete string.
(GRAMMAR)
S -> B
B -> '<' B '>'
B -> 'analysis'
(PREFIX)
< < | <|analysis | {"g": "S -> B\nB -> '<' B '>'\nB -> 'analysis'", "prefix": ["<", "<"], "depth": 2, "cot": "B\u2192< \u2022 B >\u21d2<\nB\u2192< \u2022 B >\u21d2analysis", "_time": 0.635251522064209, "_task": "continuation", "_level": 3, "_config": {"c": 1.0, "level": 3, "seed": null, "size": null, "n_types": 7, "n_terminals": 8, "pert... | B→< • B >⇒<
B→< • B >⇒analysis | 3 | instruct |
continuation | List all valid next tokens for this prefix. The answer is the list of valid tokens sorted alphabetically and separated by |, with STOP at the end if the prefix forms a complete string.
(GRAMMAR)
decl -> decl_simple
n_sg_v -> 'artist'
det_sg_an -> 'an'
decl -> decl_simple ',' conj decl_simple
conj -> 'but'
root -> decl ... | No | {"g": "decl -> decl_simple\nn_sg_v -> 'artist'\ndet_sg_an -> 'an'\ndecl -> decl_simple ',' conj decl_simple\nconj -> 'but'\nroot -> decl '.'\nis -> 'is'\nthere -> 'there'\nstart -> root\ndecl_simple -> there is det_sg_an n_sg_v", "prefix": ["there", "is", "an", "artist", ","], "depth": 5, "cot": "decl\u2192decl_simple ... | decl→decl_simple , • conj decl_simple⇒but | 3 | verification |
coreference | /trace (1) A kind loud scientist named John questioned a short young engineer named Lily.
(2) He called her.
(3) He avoided the engineer.
(4) An old quiet farmer named Owen praised John.
(5) Owen met a quiet short teacher named Lena.
(6) Owen met a kind tall lawyer named Ben.
(7) The engineer called Lena.
In sentence ... | <trace>
s3 pron 'He' | s2: {John, Lily} | unique male → John
</trace>
John | {"sentences": "(1) A kind loud scientist named John questioned a short young engineer named Lily.\n(2) He called her.\n(3) He avoided the engineer.\n(4) An old quiet farmer named Owen praised John.\n(5) Owen met a quiet short teacher named Lena.\n(6) Owen met a kind tall lawyer named Ben.\n(7) The engineer called Lena.... | s3 pron 'He' | s2: {John, Lily} | unique male → John | 0 | cot |
coreference | (1) A loud tall farmer named Eric praised a quiet tall scientist named Rose.
(2) A kind short banker named Noah questioned the scientist.
(3) A quiet tall chef named Max avoided the farmer.
(4) The chef called a loud young teacher named Jack.
(5) Max questioned a kind loud teacher named Ben.
(6) A kind short writer nam... | Jack | {"sentences": "(1) A stern tall banker named Eve called a kind young doctor named Hugo.\n(2) She thanked him.\n(3) A kind quiet nurse named Max helped her.\n(4) Max avoided her.\n(5) He met a loud young baker named Adam.\n(6) Eve praised an old quiet lawyer named Jack.\n(7) He avoided a stern young lawyer named Eric.",... | s7 pron 'He' | s6: {Eve, Jack} | unique male → Jack | 0 | few_shot |
coreference | (1) An old quiet engineer named Luke thanked a loud tall farmer named Eve.
(2) Eve greeted a loud young doctor named Sam.
(3) An old quiet baker named Nora praised Eve.
(4) Luke praised the loud farmer.
(5) She met a quiet stern banker named Mark.
(6) Mark questioned the doctor.
(7) A quiet short farmer named Kate prai... | Kate | {"sentences": "(1) An old quiet engineer named Luke thanked a loud tall farmer named Eve.\n(2) Eve greeted a loud young doctor named Sam.\n(3) An old quiet baker named Nora praised Eve.\n(4) Luke praised the loud farmer.\n(5) She met a quiet stern banker named Mark.\n(6) Mark questioned the doctor.\n(7) A quiet short f... | s8 desc 'the quiet farmer' | role=farmer, attrs=['quiet'] | {Kate} → Kate | 2 | instruct |
coreference | (1) A kind loud writer named Leo watched an old short pilot named Iris.
(2) A short stern doctor named Adam called the old pilot.
(3) Adam watched Leo.
(4) A kind short lawyer named Lily questioned Leo.
(5) Iris met Adam.
(6) A kind short pilot named Lena greeted the writer.
(7) Adam met a short stern doctor named Ben.... | No | {"sentences": "(1) A kind loud writer named Leo watched an old short pilot named Iris.\n(2) A short stern doctor named Adam called the old pilot.\n(3) Adam watched Leo.\n(4) A kind short lawyer named Lily questioned Leo.\n(5) Iris met Adam.\n(6) A kind short pilot named Lena greeted the writer.\n(7) Adam met a short st... | s2 desc 'the old pilot' | role=pilot, attrs=['old'] | {Iris} → Iris | 0 | verification |
count_elements | List: ['seven', 'sixteen', 'seven', 'ten', 'two', 'eighteen', 'eighteen', 'two', 'two', 'fifteen', 'sixteen', 'two']
How many times does 'two' appear? The answer is a number.
Answer:
4
Correct? (Yes/No)
Answer:
Yes
List: ['six', 'five', 'eight', 'sixteen', 'six', 'seventeen', 'twelve', 'twenty', 'fifteen', 'eighteen',... | 1 | {"elements": ["six", "five", "eight", "sixteen", "six", "seventeen", "twelve", "twenty", "fifteen", "eighteen", "fifteen", "two"], "target": "twenty", "_time": 0.0003840923309326172, "_task": "count_elements", "_level": 2, "_config": {"c": 1.0, "level": 2, "seed": null, "size": null, "max_count": 5, "list_size": 12, "d... | 2 | few_shot | |
count_elements | List: ['January 11, 2020', 'January 02, 2020', 'January 07, 2020', 'January 09, 2020', 'January 20, 2020', 'January 19, 2020', 'January 02, 2020', 'January 10, 2020', 'January 17, 2020', 'January 13, 2020']
How many times does 'January 13, 2020' appear? The answer is a number. | 1 | {"elements": ["January 11, 2020", "January 02, 2020", "January 07, 2020", "January 09, 2020", "January 20, 2020", "January 19, 2020", "January 02, 2020", "January 10, 2020", "January 17, 2020", "January 13, 2020"], "target": "January 13, 2020", "_time": 0.0004222393035888672, "_task": "count_elements", "_level": 0, "_c... | 0 | instruct | |
count_elements | List: ['three', 'eight', 'sixteen', 'fourteen', 'sixteen', 'five', 'seventeen', 'sixteen', 'eighteen', 'ten', 'sixteen', 'sixteen', 'sixteen']
How many times does 'sixteen' appear? The answer is a number.
Answer:
3
Correct? (Yes/No) | No | {"elements": ["three", "eight", "sixteen", "fourteen", "sixteen", "five", "seventeen", "sixteen", "eighteen", "ten", "sixteen", "sixteen", "sixteen"], "target": "sixteen", "_time": 0.0004870891571044922, "_task": "count_elements", "_level": 3, "_config": {"c": 1.0, "level": 3, "seed": null, "size": null, "max_count": 6... | 3 | verification | |
diff_prediction | Below is the version history of a file.
Version 0e79dc2:
1 | Any mouth tough financial listen
2 | Agent face west teacher gun little actually certainly
3 | Meeting community man easy painting
4 | Goal national eight candidate
5 | City magazine let watch less read
6 | Condition learn ago good arm toge... | @@ -2,5 +2,4 @@
Girl certain important lay short short environment
Seek truth exactly animal
Evidence focus how we already maybe
-at treat great nor determine
Bank green themselves design media officer power serve | {"history": "Version e881d33:\n1 | Sound important safe officer direction close\n2 | Girl certain important lay short short environment\n3 | Seek truth exactly animal\n4 | Evidence focus how we already maybe\n5 | Bank green themselves design media officer power serve\n\nVersion d7b39da:\n1 | Sound imp... | 0 | few_shot | |
diff_prediction | Below is the version history of a file.
Version 63fee1b:
1 | Impact walk with necessary
2 | Officer customer economic sing live
3 | Hospital peace employee white national west open
4 | Position evidence financial rest door measure
5 | Into more protect trouble purpose community
Version 299e935:
1 | ... | @@ -1,4 +1,5 @@
Impact walk with necessary
Officer customer economic sing live
Hospital peace employee white national west open
+Position evidence financial rest door measure
Into more protect trouble purpose community | {"history": "Version 63fee1b:\n1 | Impact walk with necessary\n2 | Officer customer economic sing live\n3 | Hospital peace employee white national west open\n4 | Position evidence financial rest door measure\n5 | Into more protect trouble purpose community\n\nVersion 299e935:\n1 | Impact walk with nec... | 0 | instruct | |
diff_prediction | Below is the version history of a file.
Version 39e0f18:
1 | School main military everything base thus organization
2 | Suggest fill image whose gun study
3 | Bring speak them middle act more collection
4 | Thought or many performance
5 | Industry build source behavior seat year wonder
Version e8e354e:... | Yes | {"history": "Version 39e0f18:\n1 | School main military everything base thus organization\n2 | Suggest fill image whose gun study\n3 | Bring speak them middle act more collection\n4 | Thought or many performance\n5 | Industry build source behavior seat year wonder\n\nVersion e8e354e:\n1 | School main ... | 0 | verification | |
equation_system | /trace Solve the following system of equations for the variable 'X1'.
System:
3*X1 + X2 + 103 = 0
2*X1 + X2 + 74 = 0
The answer is the numerical value for X1, or 'No solution' / 'Multiple solutions' if a unique numerical solution does not exist. | <trace>
1. Forward:
R2 -= 2/3*R1
2. Backward:
X2 = -16
X1 = -29
</trace>
-29 | {"equations": ["3*X1 + X2 + 103 = 0", "2*X1 + X2 + 74 = 0"], "query_variable": "X1", "full_solution_map": {"X1": -29, "X2": -16}, "case": "unique", "cot": "1. Forward:\nR2 -= 2/3*R1\n\n2. Backward:\nX2 = -16\nX1 = -29", "_time": 0.024497270584106445, "_task": "equation_system", "_level": 0, "_config": {"c": 1.0, "level... | 1. Forward:
R2 -= 2/3*R1
2. Backward:
X2 = -16
X1 = -29 | 0 | cot |
equation_system | /trace Solve the following system of equations for the variable 'X3'.
System:
X1 - X3 + 40 = 0
X2 - X3 + 33 = 0
-X1 + 2*X3 - 56 = 0
The answer is the numerical value for X3, or 'No solution' / 'Multiple solutions' if a unique numerical solution does not exist.
Answer:
<trace>
1. Forward:
R3 -= -1*R1
2. Backwar... | 5 | {"equations": ["X1 + X2 + 45 = 0", "6*X1 + X2 + 2*X3 + 120 = 0", "3*X1 + X3 + 46 = 0"], "query_variable": "X3", "full_solution_map": {"X1": -17, "X2": -28, "X3": 5}, "case": "unique", "cot": "1. Forward:\nR2 -= 6*R1\nR3 -= 3*R1\nR3 -= 3/5*R2\n\n2. Backward:\nX3 = 5\nX2 = -28\nX1 = -17", "_time": 0.04075026512145996, "_... | 1. Forward:
R2 -= 6*R1
R3 -= 3*R1
R3 -= 3/5*R2
2. Backward:
X3 = 5
X2 = -28
X1 = -17 | 1 | few_shot |
equation_system | Solve the following system of equations for the variable 'X1'.
System:
X1 - 2*X2 + 4*X3 - 99 = 0
X2 + 2*X3 + 7 = 0
X3 - 9 = 0
The answer is the numerical value for X1, or 'No solution' / 'Multiple solutions' if a unique numerical solution does not exist. | 13 | {"equations": ["X1 - 2*X2 + 4*X3 - 99 = 0", "X2 + 2*X3 + 7 = 0", "X3 - 9 = 0"], "query_variable": "X1", "full_solution_map": {"X1": 13, "X2": -25, "X3": 9}, "case": "unique", "cot": "1. Forward:\n\n2. Backward:\nX3 = 9\nX2 = -25\nX1 = 13", "_time": 0.04874825477600098, "_task": "equation_system", "_level": 1, "_config"... | 1. Forward:
2. Backward:
X3 = 9
X2 = -25
X1 = 13 | 1 | instruct |
equation_system | Solve the following system of equations for the variable 'X2'.
System:
5*X1 + 4*X2 - 4*X3 - 2*X4 + 21 = 0
-4*X1 - 3*X2 + 2*X3 + 2*X4 - 30 = 0
6*X1 + 6*X2 + X3 - 3*X4 + 101 = 0
-2*X1 - 2*X2 + X4 - 31 = 0
The answer is the numerical value for X2, or 'No solution' / 'Multiple solutions' if a unique numerical sol... | No | {"equations": ["5*X1 + 4*X2 - 4*X3 - 2*X4 + 21 = 0", "-4*X1 - 3*X2 + 2*X3 + 2*X4 - 30 = 0", "6*X1 + 6*X2 + X3 - 3*X4 + 101 = 0", "-2*X1 - 2*X2 + X4 - 31 = 0"], "query_variable": "X2", "full_solution_map": {"X1": 9, "X2": -16, "X3": -8, "X4": 17}, "case": "unique", "cot": "1. Forward:\nR2 -= -4/5*R1\nR3 -= 6/5*R1\nR4 -=... | 1. Forward:
R2 -= -4/5*R1
R3 -= 6/5*R1
R4 -= -2/5*R1
R3 -= 6*R2
R4 -= -2*R2
R4 -= -4/13*R3
2. Backward:
X4 = 17
X3 = -8
X2 = -16
X1 = 9 | 2 | verification |
evidence_retrieval | /trace Premise:
[0] there is a room.
[1] everyone in the room who is not uniform tagged is a quiet person
[2] Brenda is not a quiet person
[3] Heidi is kilo tagged
[4] everyone in the room is not quiet if and only if she is not quiet
[5] everyone anywhere who is not old is oscar tagged
[6] Brenda is whiskey tagged
[7] ... | <trace>
0. [input 2] ~(quiet(brenda) & person(brenda))
1. [pure ] quiet(brenda) & person(brenda)
2. [ennf 1] ~quiet(brenda) | ~person(brenda)
3. [cnf 2] person(brenda)
4. [cnf 2] quiet(brenda)
5. [forward 3, 5] ~person(brenda)
6. [forward 6, 4] $false
</trace>
[2] | {"verbalize_seed": 428484, "proof": {"proof": "% Running in auto input_syntax mode. Trying TPTP\n% Refutation found. Thanks to Tanya!\n% SZS status Unsatisfiable for tmpzjswtt_6\n% SZS output start Proof for tmpzjswtt_6\n4. ~(quiet(brenda) & person(brenda)) [input(axiom) 2]\n25. old(brenda) & quiet(brenda) & person(bre... | 0. [input 2] ~(quiet(brenda) & person(brenda))
1. [pure ] quiet(brenda) & person(brenda)
2. [ennf 1] ~quiet(brenda) | ~person(brenda)
3. [cnf 2] person(brenda)
4. [cnf 2] quiet(brenda)
5. [forward 3, 5] ~person(brenda)
6. [forward 6, 4] $false | 2 | cot |
evidence_retrieval | /trace Premise:
[0] Thomas is the only person in the room.
[1] everyone in the room who is zulu tagged is quiet
[2] everyone in the room either is not india tagged or is a quiet person or both
[3] not everyone in the room who is zulu tagged is a quiet person
[4] Lee and Thomas are respectively quiet and old
[5] all old... | [1] | {"verbalize_seed": 11204, "proof": {"proof": "% Running in auto input_syntax mode. Trying TPTP\n% Refutation found. Thanks to Tanya!\n% SZS status Unsatisfiable for tmplxcfjunk\n% SZS output start Proof for tmplxcfjunk\n3. prede(kimberly) => (propositiona & ~propositiona & ~propositionc) [input(axiom) 1]\n14. prede(kim... | 0. [input 1] juliet_tagged(kimberly) => (Gravity_inverts_in_Oakhaven_on_Tuesdays. & Gravity_does_not_invert_in_Oakhaven_on_Tuesdays. & John_Smith's_car_does_not_run_on_ethanol.)
1. [pure 1] juliet_tagged(kimberly) => (Gravity_inverts_in_Oakhaven_on_Tuesdays. & Gravity_does_not_invert_in_Oakhaven_on_Tuesdays.)
2. [ennf ... | 1 | few_shot |
evidence_retrieval | Premise:
[0] there is a room.
[1] Amber is an old person
[2] everyone in the room is bravo tagged or is romeo tagged or both if she is yankee tagged
[3] everyone in the room is yankee tagged if she is xray tagged
[4] Nancy is quebec tagged
[5] everyone in the room who is bravo tagged is yankee tagged or is old or both
... | [1] | {"verbalize_seed": 455225, "proof": {"proof": "% Running in auto input_syntax mode. Trying TPTP\n% Refutation found. Thanks to Tanya!\n% SZS status Unsatisfiable for tmpnue7bjrr\n% SZS output start Proof for tmpnue7bjrr\n3. old(amber) & person(amber) [input(axiom) 1]\n8. ~old(amber) [input(axiom) hyp]\n13. old(amber) [... | 0. [input 1] old(amber) & person(amber)
1. [pure 1] old(amber)
2. [cnf ] ~old(amber)
3. [forward 2, 3] $false | 0 | instruct |
evidence_retrieval | Premise:
[0] Michael is the only person in the room.
[1] everyone in the room either is not old and not quiet or is not bravo tagged or both
[2] Charles is not old
[3] no old person anywhere is old
[4] if someone is a quiet person then he is not a quiet old person and vice versa
[5] Michael is not not quiet
Hypothesis:... | Yes | {"verbalize_seed": 639972, "proof": {"proof": "% Running in auto input_syntax mode. Trying TPTP\n% Refutation found. Thanks to Tanya!\n% SZS status Unsatisfiable for tmphb_c32bq\n% SZS output start Proof for tmphb_c32bq\n6. ! [X0] : ((quiet(X0) & person(X0)) <=> ~(quiet(X0) & old(X0) & person(X0))) [input(axiom) 4]\n8.... | 0. [input 4] ! [X0] : ((quiet(X0) & person(X0)) <=> ~(quiet(X0) & old(X0) & person(X0)))
1. [ennf 1] ! [X0] : ((quiet(X0) & person(X0)) <=> (~quiet(X0) | ~old(X0) | ~person(X0)))
2. [nnf 2] ! [X0] : (((quiet(X0) & person(X0)) | (quiet(X0) & old(X0) & person(X0))) & ((~quiet(X0) | ~old(X0) | ~person(X0)) | (~quiet(X0) |... | 0 | verification |
graph_dependencies | Consider the directed graph:
0:; 1: 1->0; 2: 2->3; 3:; 4: 4->1 4->6; 5:; 6:
In this scenario, a directed edge from U to V means V depends on U (so U is a prerequisite of V).
List all prerequisites of node 0 (recursively), making sure to order base prerequisites first.
Do not include the query node itself.
If A is a p... | [0, 1] | {"graph_description": "0: 0->2 0->7; 1: 1->2; 2: 2->3; 3: 3->4; 4:; 5: 5->6; 6:; 7:", "query": 2, "nodes": [0, 1, 2, 3, 4, 5, 6, 7], "edges": [[0, 7], [0, 2], [1, 2], [2, 3], [3, 4], [5, 6]], "_time": 0.0014045238494873047, "_task": "graph_dependencies", "_level": 2, "_config": {"c": 1.0, "level": 2, "seed": null, "siz... | 2 | few_shot | |
graph_dependencies | Consider the directed graph:
Node 0 has directed edges to: 3.
Node 1 has directed edges to: 2, 4.
Node 2 has no outgoing edges.
Node 3 has no outgoing edges.
Node 4 has directed edges to: 3.
Node 5 has directed edges to: 4, 8.
Node 6 has directed edges to: 3.
Node 7 has directed edges to: 4, 8.
Node 8 has no outgoing ... | [0, 1, 5, 6, 7, 4] | {"graph_description": "Node 0 has directed edges to: 3.\nNode 1 has directed edges to: 2, 4.\nNode 2 has no outgoing edges.\nNode 3 has no outgoing edges.\nNode 4 has directed edges to: 3.\nNode 5 has directed edges to: 4, 8.\nNode 6 has directed edges to: 3.\nNode 7 has directed edges to: 4, 8.\nNode 8 has no outgoing... | 3 | instruct | |
graph_dependencies | Consider the directed graph:
digraph { 0->1; 0->2; 0->3; 2->4; 4->3 }
In this scenario, a directed edge from U to V means V depends on U (so U is a prerequisite of V).
List all prerequisites of node 3 (recursively), making sure to order base prerequisites first.
Do not include the query node itself.
If A is a prerequ... | Yes | {"graph_description": "digraph { 0->1; 0->2; 0->3; 2->4; 4->3 }", "query": 3, "nodes": [0, 1, 2, 3, 4, 5], "edges": [[0, 1], [0, 2], [0, 3], [2, 4], [4, 3]], "_time": 0.0010938644409179688, "_task": "graph_dependencies", "_level": 0, "_config": {"c": 1.0, "level": 0, "seed": null, "size": null, "num_nodes": 6, "max_pre... | 0 | verification | |
graph_isomorphism | Consider two directed graphs described below.
Graph A:
Directed Edges: 0->1, 0->2, 0->4, 1->5, 2->0, 2->1, 2->4, 3->0, 3->1, 3->5, 4->2, 4->3, 4->5, 5->1, 5->2, 5->3
Graph B:
Directed Edges: 0->3, 0->4, 0->5, 1->0, 1->2, 1->5, 2->1, 2->3, 2->4, 3->5, 4->1, 4->2, 4->3, 5->0, 5->2, 5->3
Do Graph A and Graph B have the... | True | {"graph1_description": "0: 0->2 0->3 0->6 0->7 0->8 0->10 0->11; 1: 1->13; 2: 2->1 2->3 2->9 2->14 2->17; 3: 3->2 3->4 3->7 3->13 3->15 3->17 3->20 3->23; 4: 4->0 4->22 4->23; 5: 5->0 5->2 5->9; 6: 6->0 6->4 6->10 6->18; 7: 7->3; 8: 8->0 8->2 8->14; 9: 9->2 9->5 9->16; 10: 10->6 10->11 10->12 10->19; 11:; 12: 12->3; 13... | 2 | few_shot | |
graph_isomorphism | Consider two directed graphs described below.
Graph A:
Nodes [0, 1, 2, 3, 4, 5] and directed edges: (0, 3), (0, 5), (1, 2), (1, 4), (1, 5), (2, 3), (3, 5), (4, 0), (4, 1), (4, 2), (5, 3).
Graph B:
Nodes [0, 1, 2, 3, 4, 5] and directed edges: (0, 2), (0, 5), (1, 3), (1, 4), (1, 5), (2, 3), (3, 5), (4, 0), (4, 1), (4, ... | False | {"graph1_description": "Nodes [0, 1, 2, 3, 4, 5] and directed edges: (0, 3), (0, 5), (1, 2), (1, 4), (1, 5), (2, 3), (3, 5), (4, 0), (4, 1), (4, 2), (5, 3).", "graph2_description": "Nodes [0, 1, 2, 3, 4, 5] and directed edges: (0, 2), (0, 5), (1, 3), (1, 4), (1, 5), (2, 3), (3, 5), (4, 0), (4, 1), (4, 2), (5, 3).", "_t... | 0 | instruct | |
graph_isomorphism | Consider two directed graphs described below.
Graph A:
0: 0->1 0->2; 1: 1->0 1->2; 2: 2->0; 3: 3->4; 4:; 5: 5->0 5->4
Graph B:
0: 0->1 0->2; 1: 1->0 1->2; 2: 2->0; 3: 3->0 3->5; 4: 4->5; 5:
Do Graph A and Graph B have the exact same structure, just with different node labels? (In other words, are they isomorphic?)
T... | No | {"graph1_description": "0: 0->1 0->2; 1: 1->0 1->2; 2: 2->0; 3: 3->4; 4:; 5: 5->0 5->4", "graph2_description": "0: 0->1 0->2; 1: 1->0 1->2; 2: 2->0; 3: 3->0 3->5; 4: 4->5; 5:", "_time": 0.0013010501861572266, "_task": "graph_isomorphism", "_level": 0, "_config": {"c": 1.0, "level": 0, "seed": null, "size": null, "num_n... | 0 | verification | |
graph_pathfinding | /trace Consider the directed graph:
Node 0 has directed edges to: 1, 2, 4, 8, 10, 12, 14, 17, 20, 21, 22.
Node 1 has directed edges to: 0, 2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14, 16, 17, 18, 20, 21, 22.
Node 2 has directed edges to: 0, 1, 3, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23.
Node 3 has direc... | <trace>
BFS path from 11 to 9.
Queue: [11]
Pop 11. Current Path: [11]
-> Found new outgoing neighbors: [2, 5, 6, 7, 9, 13, 16, 18, 19, 23]
-> Queue is now: [2, 5, 6, 7, 9, 13, 16, 18, 19, 23]
Pop 2. Current Path: [11, 2]
-> Found new outgoing neighbors: [0, 1, 3, 8, 10, 12, 14, 15, 17, 20, 21]
-> Queue is now... | {"graph_description": "Node 0 has directed edges to: 1, 2, 4, 8, 10, 12, 14, 17, 20, 21, 22.\nNode 1 has directed edges to: 0, 2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14, 16, 17, 18, 20, 21, 22.\nNode 2 has directed edges to: 0, 1, 3, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23.\nNode 3 has directed edges t... | BFS path from 11 to 9.
Queue: [11]
Pop 11. Current Path: [11]
-> Found new outgoing neighbors: [2, 5, 6, 7, 9, 13, 16, 18, 19, 23]
-> Queue is now: [2, 5, 6, 7, 9, 13, 16, 18, 19, 23]
Pop 2. Current Path: [11, 2]
-> Found new outgoing neighbors: [0, 1, 3, 8, 10, 12, 14, 15, 17, 20, 21]
-> Queue is now: [5, 6,... | 2 | cot |
graph_pathfinding | Consider the directed graph:
Nodes [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11] and directed edges: (0, 1), (0, 3), (0, 4), (1, 8), (2, 0), (2, 1), (2, 3), (2, 5), (2, 9), (3, 0), (3, 2), (3, 7), (3, 11), (4, 0), (4, 1), (4, 2), (4, 7), (4, 8), (4, 9), (5, 1), (5, 2), (5, 4), (5, 8), (5, 9), (6, 8), (6, 10), (7, 0), (7, 2),... | [5, 6] | {"graph_description": "Adjacency Dictionary (source to targets): {0: [1, 3, 11], 1: [0], 2: [1], 3: [], 4: [1], 5: [6], 6: [5, 7], 7: [6, 8], 8: [7, 9], 9: [10], 10: [2, 11], 11: [0, 10]}", "start_node": 5, "end_node": 6, "nodes": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], "edges": [[0, 1], [0, 11], [0, 3], [1, 0], [2, 1]... | BFS path from 5 to 6.
Queue: [5]
Pop 5. Current Path: [5]
-> Found new outgoing neighbors: [6]
-> Queue is now: [6]
Pop 6. Current Path: [5, 6]
Target found. | 1 | few_shot |
graph_pathfinding | Consider the directed graph:
Nodes [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11] and directed edges: (0, 4), (0, 6), (0, 7), (1, 3), (1, 8), (1, 11), (2, 10), (3, 4), (3, 6), (4, 9), (4, 10), (5, 2), (5, 6), (6, 9), (6, 11), (7, 0), (7, 9), (7, 11), (8, 0), (8, 5), (8, 6), (8, 9), (9, 2), (9, 4), (9, 6), (9, 7), (10, 0), (10... | [3, 6, 11, 5] | {"graph_description": "Nodes [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11] and directed edges: (0, 4), (0, 6), (0, 7), (1, 3), (1, 8), (1, 11), (2, 10), (3, 4), (3, 6), (4, 9), (4, 10), (5, 2), (5, 6), (6, 9), (6, 11), (7, 0), (7, 9), (7, 11), (8, 0), (8, 5), (8, 6), (8, 9), (9, 2), (9, 4), (9, 6), (9, 7), (10, 0), (10, 6), (... | BFS path from 3 to 5.
Queue: [3]
Pop 3. Current Path: [3]
-> Found new outgoing neighbors: [4, 6]
-> Queue is now: [4, 6]
Pop 4. Current Path: [3, 4]
-> Found new outgoing neighbors: [9, 10]
-> Queue is now: [6, 9, 10]
Pop 6. Current Path: [3, 6]
-> Found new outgoing neighbors: [11]
-> Queue is now: [9,... | 1 | instruct |
graph_pathfinding | Consider the directed graph:
Adjacency Dictionary (source to targets): {0: [10, 17], 1: [15], 2: [6, 7, 20, 23], 3: [17, 18, 19], 4: [0, 6, 13, 16], 5: [10, 15, 17], 6: [4, 21, 22], 7: [1, 11], 8: [1, 17, 18], 9: [19, 21], 10: [1, 5, 20], 11: [3, 12], 12: [8, 11, 18], 13: [0, 11, 19], 14: [12, 18, 21], 15: [1, 20], 16... | Yes | {"graph_description": "Adjacency Dictionary (source to targets): {0: [10, 17], 1: [15], 2: [6, 7, 20, 23], 3: [17, 18, 19], 4: [0, 6, 13, 16], 5: [10, 15, 17], 6: [4, 21, 22], 7: [1, 11], 8: [1, 17, 18], 9: [19, 21], 10: [1, 5, 20], 11: [3, 12], 12: [8, 11, 18], 13: [0, 11, 19], 14: [12, 18, 21], 15: [1, 20], 16: [9, 2... | BFS path from 15 to 11.
Queue: [15]
Pop 15. Current Path: [15]
-> Found new outgoing neighbors: [1, 20]
-> Queue is now: [1, 20]
Pop 1. Current Path: [15, 1]
-> All outgoing neighbors visited or empty. Backtrack.
-> Queue is now: [20]
Pop 20. Current Path: [15, 20]
-> Found new outgoing neighbors: [5]
->... | 2 | verification |
graph_successors | Consider the directed graph:
Nodes: [0, 1, 2, 3, 4, 5, 6]
Adjacency Matrix (row indicates source, column indicates target):
[0, 0, 0, 0, 0, 1, 0]
[1, 0, 0, 0, 0, 0, 0]
[0, 0, 1, 0, 0, 0, 0]
[0, 1, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 0, 0]
[0, 0, 0, 1, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 1]
Queries: [(3, 3)]
Each pair (x, k) asks ... | [5] | {"graph_description": "Node 0 points to 5. Node 1 points to 3. Node 2 points to 2. Node 3 points to 0. Node 4 points to 1. Node 5 points to 4.", "queries": [[0, 1]], "nodes": [0, 1, 2, 3, 4, 5], "edges": [[0, 5], [1, 3], [2, 2], [3, 0], [4, 1], [5, 4]], "_time": 0.0005960464477539062, "_task": "graph_successors", "_lev... | 0 | few_shot | |
graph_successors | Consider the directed graph:
Nodes: [0, 1, 2, 3, 4, 5]
Adjacency Matrix (row indicates source, column indicates target):
[0, 0, 0, 1, 0, 0]
[0, 0, 0, 0, 0, 1]
[0, 1, 0, 0, 0, 0]
[0, 0, 1, 0, 0, 0]
[0, 0, 0, 0, 1, 0]
[1, 0, 0, 0, 0, 0]
Queries: [(4, 2)]
Each pair (x, k) asks for the k-th successor of x (following exac... | [4] | {"graph_description": "Nodes: [0, 1, 2, 3, 4, 5]\nAdjacency Matrix (row indicates source, column indicates target):\n[0, 0, 0, 1, 0, 0]\n[0, 0, 0, 0, 0, 1]\n[0, 1, 0, 0, 0, 0]\n[0, 0, 1, 0, 0, 0]\n[0, 0, 0, 0, 1, 0]\n[1, 0, 0, 0, 0, 0]", "queries": [[4, 2]], "nodes": [0, 1, 2, 3, 4, 5], "edges": [[0, 3], [1, 5], [2, 1]... | 0 | instruct | |
graph_successors | Consider the directed graph:
Node 0 has directed edges to: 1.
Node 1 has directed edges to: 2.
Node 2 has directed edges to: 4.
Node 3 has directed edges to: 3.
Node 4 has directed edges to: 5.
Node 5 has directed edges to: 0.
Queries: [(5, 1)]
Each pair (x, k) asks for the k-th successor of x (following exact direct... | Yes | {"graph_description": "Node 0 has directed edges to: 1.\nNode 1 has directed edges to: 2.\nNode 2 has directed edges to: 4.\nNode 3 has directed edges to: 3.\nNode 4 has directed edges to: 5.\nNode 5 has directed edges to: 0.", "queries": [[5, 1]], "nodes": [0, 1, 2, 3, 4, 5], "edges": [[0, 1], [1, 2], [2, 4], [3, 3], ... | 0 | verification | |
lambda_reduction | Reduce the following untyped λ-term to β-normal form.
Syntax: `\x.body` denotes λx.body; application is left-associative juxtaposition; free identifiers are treated as constants.
Term: (((\_0.d) (b d)) (\v0.v0))
The answer is the β-normal form (compared up to α-equivalence).
Answer:
(d (\v0.v0))
Reduce the following... | (\v0.((a v0) (\v1.(\v2.c)))) | {"term": "(\\v0.(((\\_1.(((\\_2.a) (d (\\v0.v0))) (((\\_3.(\\_0._3)) _1) b))) v0) (\\v1.(\\v2.c))))", "normal_form": "(\\v0.((a v0) (\\v1.(\\v2.c))))", "_time": 0.0010976791381835938, "_task": "lambda_reduction", "_level": 3, "_config": {"c": 1.0, "level": 3, "seed": null, "size": null, "nf_depth": 5, "n_insertions": 4... | 3 | few_shot | |
lambda_reduction | Reduce the following untyped λ-term to β-normal form.
Syntax: `\x.body` denotes λx.body; application is left-associative juxtaposition; free identifiers are treated as constants.
Term: (\v0.(v0 (d ((((\_0.b) ((\_2.b) (b a))) v0) ((\_1.v0) d)))))
The answer is the β-normal form (compared up to α-equivalence). | (\v0.(v0 (d ((b v0) v0)))) | {"term": "(\\v0.(v0 (d ((((\\_0.b) ((\\_2.b) (b a))) v0) ((\\_1.v0) d)))))", "normal_form": "(\\v0.(v0 (d ((b v0) v0))))", "_time": 0.0007872581481933594, "_task": "lambda_reduction", "_level": 2, "_config": {"c": 1.0, "level": 2, "seed": null, "size": null, "nf_depth": 4, "n_insertions": 3}, "_prompt_tokens": 95, "_an... | 2 | instruct | |
lambda_reduction | Reduce the following untyped λ-term to β-normal form.
Syntax: `\x.body` denotes λx.body; application is left-associative juxtaposition; free identifiers are treated as constants.
Term: (\v0.((\_0.(\v1.v0)) (a d)))
The answer is the β-normal form (compared up to α-equivalence).
Answer:
(\v0.(\v1.v0))
Correct? (Yes/No) | Yes | {"term": "(\\v0.((\\_0.(\\v1.v0)) (a d)))", "normal_form": "(\\v0.(\\v1.v0))", "_time": 0.0003535747528076172, "_task": "lambda_reduction", "_level": 0, "_config": {"c": 1.0, "level": 0, "seed": null, "size": null, "nf_depth": 2, "n_insertions": 1}, "_prompt_tokens": 77, "_answer_tokens": 10, "_generator_name": "reason... | 0 | verification | |
lexical_knowledge | Context: WordNet (relation holds for any valid noun sense).
Select all cohyponyms(luggage)
From: [briefcase, barn, wallet, armament, analyzer, staircase, windshield]
The answer is a JSON list.
Answer:
["briefcase", "wallet"]
Context: WordNet (relation holds for any valid noun sense).
Select hypernym(hypernym(predicti... | thinking | {"expr": "hypernym(hypernym(prediction))", "answer_type": "word", "candidates": ["thinking", "layout", "faculty", "remembrance", "superstition", "syndrome"], "gold_synsets": ["thinking.n.01"], "_time": 0.001409769058227539, "_task": "lexical_knowledge", "_level": 1, "_config": {"c": 1.0, "level": 1, "seed": null, "size... | 1 | few_shot | |
lexical_knowledge | Context: WordNet (relation holds for any valid noun sense).
Select hypernym(sword)
From: [weapon, brick, axle, monochrome, guitar, bucket]
The answer is one word. | weapon | {"expr": "hypernym(sword)", "answer_type": "word", "candidates": ["weapon", "brick", "axle", "monochrome", "guitar", "bucket"], "gold_synsets": ["weapon.n.01"], "_time": 0.0042269229888916016, "_task": "lexical_knowledge", "_level": 0, "_config": {"c": 1.0, "level": 0, "seed": null, "size": null, "n_words": 600, "max_r... | 0 | instruct | |
lexical_knowledge | Context: WordNet (relation holds for any valid noun sense).
Select hypernym(hypernym(cricket))
From: [feather, algae, snail, caterpillar, mane, insect]
The answer is one word.
Answer:
["beating", "skirmish"]
Correct? (Yes/No) | No | {"expr": "hypernym(hypernym(cricket))", "answer_type": "word", "candidates": ["feather", "algae", "snail", "caterpillar", "mane", "insect"], "gold_synsets": ["insect.n.01"], "_time": 0.0038094520568847656, "_task": "lexical_knowledge", "_level": 0, "_config": {"c": 1.0, "level": 0, "seed": null, "size": null, "n_words"... | 0 | verification | |
locate_error | /trace (GRAMMAR)
start -> seq
seq ->
seq -> expr seq
expr -> '(' seq ')'
expr -> '[' seq ']'
expr -> '<' seq '>'
expr -> '⟨' seq '⟩'
expr -> '⟦' seq '⟧'
expr -> '⟪' seq '⟫'
(STRING)
[ ⟩ ⟩ ⟪ ⟫ ] < > < > ⟪ ⟫
The answer is the shortest contiguous span from STRING that ends at the first invalid token and occurs only onc... | <trace>
[ ✓
⟩ ∉ {(,<,[,],⟦,⟨,⟪}
Answer: [ >>⟩<<
</trace>
[ >>⟩<< | {"g": "start -> seq\nseq -> \nseq -> expr seq\nexpr -> '(' seq ')'\nexpr -> '[' seq ']'\nexpr -> '<' seq '>'\nexpr -> '\u27e8' seq '\u27e9'\nexpr -> '\u27e6' seq '\u27e7'\nexpr -> '\u27ea' seq '\u27eb'", "tokens": ["[", "\u27e9", "\u27e9", "\u27ea", "\u27eb", "]", "<", ">", "<", ">", "\u27ea", "\u27eb"], "error_index":... | [ ✓
⟩ ∉ {(,<,[,],⟦,⟨,⟪}
Answer: [ >>⟩<< | 0 | cot |
locate_error | (GRAMMAR)
is -> 'is'
decl -> decl_simple
there -> 'there'
start -> root
discourse -> decl
root -> discourse '.'
decl_simple -> there is det_sg_an n_sg_v
n_sg_v -> 'artist'
det_sg_an -> 'an'
(STRING)
there is artist artist .
The answer is the shortest contiguous span from STRING that ends at the first invalid token an... | student >>a<< | {"g": "decl_simple -> there is det_sg_a n_sg_c\nthere -> 'there'\ndecl -> decl_simple ',' conj decl_simple\nstart -> root\nconj -> 'but'\nn_sg_c -> 'student'\nroot -> decl '.'\ndet_sg_a -> 'a'\nis -> 'is'", "tokens": ["there", "is", "a", "student", ",", "but", "there", "is", "a", "student", "a"], "error_index": 10, "co... | there ✓
is ✓
a ✓
student ✓
, ✓
but ✓
there ✓
is ✓
a ✓
student ✓
a ∉ {.}
Answer: student >>a<< | 3 | few_shot |
locate_error | (GRAMMAR)
start -> seq
seq ->
seq -> expr seq
expr -> '(' seq ')'
expr -> '[' seq ']'
expr -> '<' seq '>'
(STRING)
[ ( ) < > ]
The answer is the shortest contiguous span from STRING that ends at the first invalid token and occurs only once in STRING.
Mark the invalid token as >>token<<.
If the token alone is enough,... | OK | {"g": "start -> seq\nseq -> \nseq -> expr seq\nexpr -> '(' seq ')'\nexpr -> '[' seq ']'\nexpr -> '<' seq '>'", "tokens": ["[", "(", ")", "<", ">", "]"], "error_index": -1, "cot": "[ \u2713\n( \u2713\n) \u2713\n< \u2713\n> \u2713\n] \u2713", "_time": 0.009994268417358398, "_task": "locate_error", "_level": 2, "_config":... | [ ✓
( ✓
) ✓
< ✓
> ✓
] ✓ | 2 | instruct |
locate_error | (GRAMMAR)
start -> root
det_pl_indef -> 'some'
discourse -> decl
conj -> 'yet'
n_thing_pl -> 'gifts'
are -> 'are'
decl_simple -> there are det_pl_indef n_thing_pl
root -> discourse '.'
decl -> decl_simple ',' conj decl_simple
there -> 'there'
(STRING)
there are some gifts , yet gifts are some gifts .
The answer is th... | Yes | {"g": "start -> root\ndet_pl_indef -> 'some'\ndiscourse -> decl\nconj -> 'yet'\nn_thing_pl -> 'gifts'\nare -> 'are'\ndecl_simple -> there are det_pl_indef n_thing_pl\nroot -> discourse '.'\ndecl -> decl_simple ',' conj decl_simple\nthere -> 'there'", "tokens": ["there", "are", "some", "gifts", ",", "yet", "gifts", "are... | there ✓
are ✓
some ✓
gifts ✓
, ✓
yet ✓
gifts ∉ {there}
Answer: yet >>gifts<< | 0 | verification |
logic_formalization | Premise:
Aaron is echo tagged
A singing flower blooms in the Amazon.
Glossary (English phrase -> TPTP symbol):
'echo tagged' -> predd
'A singing flower blooms in the Amazon.' -> propositiond
Translate the premise into a single TPTP first-order-logic formula, joining the lines with '&'.
Connectives: '&', '|', '~',... | ((![X]:((~quiet(X))<=>(old(X)))))&
(?[X,Y]:((((predg(X))|(predc(X))))&(((predf(Y))<~>(old(Y))))&(hate(X,Y))))&
(prede(kim))&
(![X]:(in_the_room(X)=>(old(X)=>old(X))))&
(![X]:(~in_the_room(X)=>(old(X)=>old(X))))&
(![X]:(anywhere(X)=>(((~~old(X))=>(predd(X))))))&
(predg(jeanne))&
(![X]:(in_the_room(X)=>(((old(X)&person(X... | {"prem": {"tptp": "((![X]:((~quiet(X))<=>(old(X)))))&\n(?[X,Y]:((((predg(X))|(predc(X))))&(((predf(Y))<~>(old(Y))))&(hate(X,Y))))&\n(prede(kim))&\n(![X]:(room(X)=>(old(X)=>old(X))))&\n(![X]:(~room(X)=>(old(X)=>old(X))))&\n(![X]:(anywhere(X)=>(((~~old(X))=>(predd(X))))))&\n(predg(jeanne))&\n(![X]:(room(X)=>(((old(X)&per... | 2 | few_shot | |
logic_formalization | Premise:
Kyle is juliet tagged
Kyle is hotel tagged
Glossary (English phrase -> TPTP symbol):
'juliet tagged' -> predb
'hotel tagged' -> predi
Translate the premise into a single TPTP first-order-logic formula, joining the lines with '&'.
Connectives: '&', '|', '~', '=>', '<=>'. Quantifiers: '![X]:...' (forall) a... | (predb(kyle))&
(predi(kyle)) | {"prem": {"tptp": "(predb(kyle))&\n(predi(kyle))", "eng": "Kyle is predb\nKyle is predi"}, "verbalize_seed": 305207, "_time": 0.03844141960144043, "_task": "logic_formalization", "_level": 0, "_config": {"c": 1.0, "level": 0, "seed": null, "size": null, "n_formulas": 3, "generation_algorithm": "sequential", "n_names": ... | 0 | instruct | |
logic_formalization | Premise:
Nicole is echo tagged
all old people in the room are quiet
everyone in the room who is zulu tagged is not old
someone who is echo tagged likes someone who is old
Nicole is papa tagged
Glossary (English phrase -> TPTP symbol):
'zulu tagged' -> preda
'echo tagged' -> predb
'papa tagged' -> predd
Translat... | No | {"prem": {"tptp": "(predb(nicole))&\n(![X]:(room(X)=>(old(X)=>quiet(X))))&\n(![X]:(room(X)=>(((preda(X))=>(~old(X))))))&\n(?[X,Y]:((predb(X))&(old(Y))&(like(X,Y))))&\n(predd(nicole))", "eng": "Nicole is predb\nall old people in the room are quiet\neveryone in the room who is preda is not old\nsomeone who is predb likes... | 1 | verification | |
logic_nli | /trace Premise:
Joseph is the only person in the room.
everyone in the room is charlie tagged if he is charlie tagged, india tagged or india tagged
all old people in the room are old
everyone outside the room who is delta tagged is kilo tagged
Kenneth is not a quiet old person or is delta tagged or both
Michael is kilo... | <trace>
</trace>
neutral | {"verbalize_seed": 233173, "proof": null, "cot": "", "prem": {"tptp": "room(joseph)&(![X]:(room(X)=>(X='joseph')))&\n(![X]:(room(X)=>(((((predf(X))|(prede(X))|(prede(X))))=>(predf(X))))))&\n(![X]:(room(X)=>(old(X)=>old(X))))&\n(![X]:(~room(X)=>(((preda(X))=>(predb(X))))))&\n(((~(quiet(kenneth)&old(kenneth)&person(kenne... | 2 | cot | |
logic_nli | Premise:
Catherine is the only person in the room.
everyone in the room who is romeo tagged is lima tagged or is lima tagged or both
at least one person in the room is not lima tagged
someone in the room is delta tagged
if someone neither is alpha tagged nor is papa tagged then she is not not quiet and vice versa
someo... | entailment | {"verbalize_seed": 108337, "proof": {"proof": "% Running in auto input_syntax mode. Trying TPTP\n% Refutation found. Thanks to Tanya!\n% SZS status Unsatisfiable for tmp5zqrl0pr\n% SZS output start Proof for tmp5zqrl0pr\n15. predf(edward) & ~old(edward) [input(axiom) 13]\n24. old(edward) [input(axiom) hyp]\n29. ~old(ed... | 0. [input 13] yankee_tagged(edward) & ~old(edward)
1. [pure 1] ~old(edward)
2. [cnf ] old(edward)
3. [forward 2, 3] $false | 2 | few_shot |
logic_nli | Premise:
there is a room.
Patricia and Stacy are not quiet old people
Stacy is india tagged
everyone in the room who is quiet is lima tagged
everyone in the room is echo tagged if she is kilo tagged and not xray tagged
it is not the case that “Patricia is xray tagged”
Patricia is not an old person and is sierra tagged
... | entailment | {"verbalize_seed": 68405, "proof": {"proof": "% Running in auto input_syntax mode. Trying TPTP\n% Refutation found. Thanks to Tanya!\n% SZS status Unsatisfiable for tmpgq3u94w5\n% SZS output start Proof for tmpgq3u94w5\n9. old(alicia) & quiet(stacy) [input(axiom) 7]\n14. ~old(alicia) [input(axiom) hyp]\n25. old(alicia)... | 0. [input 7] old(alicia) & quiet(stacy)
1. [pure 1] old(alicia)
2. [cnf ] ~old(alicia)
3. [forward 2, 3] $false | 1 | instruct |
logic_nli | Premise:
there is a room.
someone who is quiet likes someone who is papa tagged
no old person in the room is quiet
everyone outside the room either is not echo tagged or is papa tagged or both
someone outside the room is lima tagged
everyone in the room is lima tagged if she is oscar tagged
no quiet person in the room ... | No | {"verbalize_seed": 18043, "proof": null, "cot": "", "prem": {"tptp": "(there_is_a_room)&\n(?[X,Y]:((quiet(X))&(predb(Y))&(like(X,Y))))&\n(![X]:(room(X)=>(old(X)=>~quiet(X))))&\n(![X]:(~room(X)=>(((predb(X))|(~predd(X))))))&\n(?[X]:(~room(X)&(predf(X))))&\n(![X]:(room(X)=>(((prede(X))=>(predf(X))))))&\n(![X]:(room(X)=>(... | 1 | verification | |
navigation | Objects occupy distinct points on the integer grid [0, 5] x [0, 5].
North is +y and East is +x. Any object not mentioned in a step stays fixed.
Initial facts:
- D starts at (5, 2).
- D is right of C.
- B is above C.
- C is above D.
- B is in the same row as A.
- C is left of B.
- C is left of A.
- B is left of D.
Ste... | 2 | {"answer_type": "distance", "query_a": "B", "query_b": "D", "grid": 5, "objects": ["A", "B", "C", "D"], "facts": [{"k": "v", "a": "A", "b": "B", "r": "below"}, {"k": "coord", "a": "A", "p": [0, 1]}, {"k": "v", "a": "B", "b": "C", "r": "below"}, {"k": "h", "a": "B", "b": "D", "r": "right"}, {"k": "v", "a": "B", "b": "D"... | 1 | few_shot | |
navigation | Objects occupy distinct points on the integer grid [0, 6] x [0, 6].
North is +y and East is +x. Any object not mentioned in a step stays fixed.
Initial facts:
- A is above B.
- D is above B.
- E is right of B.
- A is right of C.
- D is in the same row as E.
- C is below B.
- E starts at (6, 4).
- E is above C.
- D is ... | (6, 4) | {"answer_type": "coord", "query_a": "A", "query_b": null, "grid": 6, "objects": ["A", "B", "C", "D", "E"], "facts": [{"k": "v", "a": "A", "b": "B", "r": "above"}, {"k": "v", "a": "D", "b": "B", "r": "above"}, {"k": "h", "a": "E", "b": "B", "r": "right"}, {"k": "h", "a": "A", "b": "C", "r": "right"}, {"k": "v", "a": "D"... | 2 | instruct | |
navigation | Objects occupy distinct points on the integer grid [0, 4] x [0, 4].
North is +y and East is +x. Any object not mentioned in a step stays fixed.
Initial facts:
- B is above A.
- C is right of B.
- A is right of B.
- C is above A.
- B is below C.
- A is in the same column as C.
Steps:
1. C and A swap positions.
What i... | Yes | {"answer_type": "relation", "query_a": "A", "query_b": "B", "grid": 4, "objects": ["A", "B", "C"], "facts": [{"k": "v", "a": "B", "b": "A", "r": "above"}, {"k": "h", "a": "C", "b": "B", "r": "right"}, {"k": "h", "a": "A", "b": "B", "r": "right"}, {"k": "v", "a": "C", "b": "A", "r": "above"}, {"k": "v", "a": "B", "b": "... | 0 | verification | |
parsability | /trace (GRAMMAR)
start -> seq
seq ->
seq -> expr seq
expr -> '(' seq ')'
expr -> '[' seq ']'
expr -> '<' seq '>'
expr -> '⟨' seq '⟩'
expr -> '⟦' seq '⟧'
expr -> '⟪' seq '⟫'
(STRING)
⟦ < > ⟧ ⟪ < > ⟫ [ ] < >
(QUESTION)
What is the parsability of this string?
The answer is exactly one word: unambiguous, ambiguous, or u... | <trace>
Parse 1:
'⟦': start > seq > expr (Depth: 3)
'<': start > seq > expr > seq > expr (Depth: 5)
'>': start > seq > expr > seq > expr (Depth: 5)
'⟧': start > seq > expr (Depth: 3)
'⟪': start > seq > seq > expr (Depth: 4)
'<': start > seq > seq > expr > seq > expr (Depth: 6)
'>': start > seq > seq > expr > seq > expr... | {"cot": "Parse 1:\n'\u27e6': start > seq > expr (Depth: 3)\n'<': start > seq > expr > seq > expr (Depth: 5)\n'>': start > seq > expr > seq > expr (Depth: 5)\n'\u27e7': start > seq > expr (Depth: 3)\n'\u27ea': start > seq > seq > expr (Depth: 4)\n'<': start > seq > seq > expr > seq > expr (Depth: 6)\n'>': start > seq > ... | Parse 1:
'⟦': start > seq > expr (Depth: 3)
'<': start > seq > expr > seq > expr (Depth: 5)
'>': start > seq > expr > seq > expr (Depth: 5)
'⟧': start > seq > expr (Depth: 3)
'⟪': start > seq > seq > expr (Depth: 4)
'<': start > seq > seq > expr > seq > expr (Depth: 6)
'>': start > seq > seq > expr > seq > expr (Depth:... | 1 | cot |
parsability | (GRAMMAR)
S -> D
A -> '<' B '>' D
A -> F
D -> '<' D '>'
D -> E
E -> 'push'
E -> D
(STRING)
< < push > >
(QUESTION)
What is the parsability of this string?
The answer is exactly one word: unambiguous, ambiguous, or unparsable.
Answer:
ambiguous
(GRAMMAR)
name -> 'Bob'
question -> wh_reason is np_sg_subj adj
wh_reason... | unparsable | {"cot": "", "label": "unparsable", "tokens": ["why", "is", "Charlie", "happy"], "g": "name -> 'Bob'\nquestion -> wh_reason is np_sg_subj adj\nwh_reason -> 'why'\nroot -> question '?'\nname -> 'Charlie'\nnp_sg_subj -> name\nstart -> root\nis -> 'is'\nadj -> 'happy'", "_time": 0.0037310123443603516, "_task": "parsability... | 0 | few_shot | |
parsability | (GRAMMAR)
start -> seq
seq ->
seq -> expr seq
expr -> '(' seq ')'
expr -> '[' seq ']'
expr -> '<' seq '>'
(STRING)
( < > ( ) )
(QUESTION)
What is the parsability of this string?
The answer is exactly one word: unambiguous, ambiguous, or unparsable. | unambiguous | {"cot": "Parse 1:\n'(': start > seq > expr (Depth: 3)\n'<': start > seq > expr > seq > expr (Depth: 5)\n'>': start > seq > expr > seq > expr (Depth: 5)\n'(': start > seq > expr > seq > seq > expr (Depth: 6)\n')': start > seq > expr > seq > seq > expr (Depth: 6)\n')': start > seq > expr (Depth: 3)", "label": "unambiguou... | Parse 1:
'(': start > seq > expr (Depth: 3)
'<': start > seq > expr > seq > expr (Depth: 5)
'>': start > seq > expr > seq > expr (Depth: 5)
'(': start > seq > expr > seq > seq > expr (Depth: 6)
')': start > seq > expr > seq > seq > expr (Depth: 6)
')': start > seq > expr (Depth: 3) | 1 | instruct |
parsability | (GRAMMAR)
S -> C
B -> 'town'
C -> B C C
E -> 'moment'
C -> B
(STRING)
town town town town town town town
(QUESTION)
What is the parsability of this string?
The answer is exactly one word: unambiguous, ambiguous, or unparsable.
Answer:
unparsable
Correct? (Yes/No) | No | {"cot": "Parse 1:\n'town': S > C > B (Depth: 3)\n'town': S > C > C > B (Depth: 4)\n'town': S > C > C > C > B (Depth: 5)\n'town': S > C > C > C > C > B (Depth: 6)\n'town': S > C > C > C > C > B (Depth: 6)\n'town': S > C > C > C > B (Depth: 5)\n'town': S > C > C > B (Depth: 4)\nParse 2:\n'town': S > C > B (Depth: 3)\n'to... | Parse 1:
'town': S > C > B (Depth: 3)
'town': S > C > C > B (Depth: 4)
'town': S > C > C > C > B (Depth: 5)
'town': S > C > C > C > C > B (Depth: 6)
'town': S > C > C > C > C > B (Depth: 6)
'town': S > C > C > C > B (Depth: 5)
'town': S > C > C > B (Depth: 4)
Parse 2:
'town': S > C > B (Depth: 3)
'town': S > C > C > B ... | 1 | verification |
parsing | /trace (GRAMMAR)
start -> seq
seq ->
seq -> expr seq
expr -> '(' seq ')'
expr -> '[' seq ']'
expr -> '<' seq '>'
expr -> '⟨' seq '⟩'
expr -> '⟦' seq '⟧'
expr -> '⟪' seq '⟫'
(STRING)
⟦ ⟧ ⟦ ⟧ ⟪ ⟫
(QUESTION)
Identify the Part-of-Speech (immediate parent) and tree depth for each token.
format per token: token<POS:depth>... | <trace>
'⟦': start > seq > expr (Depth: 3)
'⟧': start > seq > expr (Depth: 3)
'⟦': start > seq > seq > expr (Depth: 4)
'⟧': start > seq > seq > expr (Depth: 4)
'⟪': start > seq > seq > seq > expr (Depth: 5)
'⟫': start > seq > seq > seq > expr (Depth: 5)
</trace>
⟦<expr:3> ⟧<expr:3> ⟦<expr:4> ⟧<expr:4> ⟪<expr:5> ⟫<expr:... | {"cot": "'\u27e6': start > seq > expr (Depth: 3)\n'\u27e7': start > seq > expr (Depth: 3)\n'\u27e6': start > seq > seq > expr (Depth: 4)\n'\u27e7': start > seq > seq > expr (Depth: 4)\n'\u27ea': start > seq > seq > seq > expr (Depth: 5)\n'\u27eb': start > seq > seq > seq > expr (Depth: 5)", "parses": [[[["\u27e6", [], ... | '⟦': start > seq > expr (Depth: 3)
'⟧': start > seq > expr (Depth: 3)
'⟦': start > seq > seq > expr (Depth: 4)
'⟧': start > seq > seq > expr (Depth: 4)
'⟪': start > seq > seq > seq > expr (Depth: 5)
'⟫': start > seq > seq > seq > expr (Depth: 5) | 1 | cot |
parsing | (GRAMMAR)
S -> C
C -> 'nature' '<' 'picture' '>'
B -> '[' E ']' 'such'
C -> '[' C ']'
(STRING)
[ [ [ [ [ nature < picture > ] ] ] ] ]
(QUESTION)
The answer is the fully parenthesized parse tree of STRING in Lisp style.
Given G_ex: S -> NP VP, NP -> 'd' N, N -> 'n', VP -> 'v' and "d n v", correct is (S (NP d (N n)) (V... | I<A:2> I<A:3> I<A:4> I<A:5> I<A:6> house<A:7> | {"cot": "'I': S > A (Depth: 2)\n'I': S > A > A (Depth: 3)\n'I': S > A > A > A (Depth: 4)\n'I': S > A > A > A > A (Depth: 5)\n'I': S > A > A > A > A > A (Depth: 6)\n'house': S > A > A > A > A > A > A (Depth: 7)", "parses": [[["I", ["I", ["I", ["I", ["I", ["house"]]]]]]]], "label": "unambiguous", "tokens": ["I", "I", "I"... | 'I': S > A (Depth: 2)
'I': S > A > A (Depth: 3)
'I': S > A > A > A (Depth: 4)
'I': S > A > A > A > A (Depth: 5)
'I': S > A > A > A > A > A (Depth: 6)
'house': S > A > A > A > A > A > A (Depth: 7) | 2 | few_shot |
parsing | (GRAMMAR)
S -> B
B -> '[' '[' B ']' ']'
B -> '[' 'professional' ']'
B -> F E E 'join'
D -> C A 'professional'
B -> 'first'
(STRING)
[ [ [ [ [ [ [ professional ] ] ] ] ] ] ]
(QUESTION)
Identify the Part-of-Speech (immediate parent) and tree depth for each token.
format per token: token<POS:depth>
Example: the<Det:3> c... | [<B:2> [<B:2> [<B:3> [<B:3> [<B:4> [<B:4> [<B:5> professional<B:5> ]<B:5> ]<B:4> ]<B:4> ]<B:3> ]<B:3> ]<B:2> ]<B:2> | {"cot": "'[': S > B (Depth: 2)\n'[': S > B (Depth: 2)\n'[': S > B > B (Depth: 3)\n'[': S > B > B (Depth: 3)\n'[': S > B > B > B (Depth: 4)\n'[': S > B > B > B (Depth: 4)\n'[': S > B > B > B > B (Depth: 5)\n'professional': S > B > B > B > B (Depth: 5)\n']': S > B > B > B > B (Depth: 5)\n']': S > B > B > B (Depth: 4)\n']... | '[': S > B (Depth: 2)
'[': S > B (Depth: 2)
'[': S > B > B (Depth: 3)
'[': S > B > B (Depth: 3)
'[': S > B > B > B (Depth: 4)
'[': S > B > B > B (Depth: 4)
'[': S > B > B > B > B (Depth: 5)
'professional': S > B > B > B > B (Depth: 5)
']': S > B > B > B > B (Depth: 5)
']': S > B > B > B (Depth: 4)
']': S > B > B > B (D... | 3 | instruct |
parsing | (GRAMMAR)
start -> seq
seq ->
seq -> expr seq
expr -> '(' seq ')'
expr -> '[' seq ']'
expr -> '<' seq '>'
expr -> '⟨' seq '⟩'
expr -> '⟦' seq '⟧'
expr -> '⟪' seq '⟫'
(STRING)
[ < > ⟨ ⟩ ] ⟪ ⟫
(QUESTION)
The answer is the fully parenthesized parse tree of STRING in Lisp style.
Given G_ex: S -> NP VP, NP -> 'd' N, N ->... | Yes | {"cot": "'[': start > seq > expr (Depth: 3)\n'<': start > seq > expr > seq > expr (Depth: 5)\n'>': start > seq > expr > seq > expr (Depth: 5)\n'\u27e8': start > seq > expr > seq > seq > expr (Depth: 6)\n'\u27e9': start > seq > expr > seq > seq > expr (Depth: 6)\n']': start > seq > expr (Depth: 3)\n'\u27ea': start > seq... | '[': start > seq > expr (Depth: 3)
'<': start > seq > expr > seq > expr (Depth: 5)
'>': start > seq > expr > seq > expr (Depth: 5)
'⟨': start > seq > expr > seq > seq > expr (Depth: 6)
'⟩': start > seq > expr > seq > seq > expr (Depth: 6)
']': start > seq > expr (Depth: 3)
'⟪': start > seq > seq > expr (Depth: 4)
'⟫': ... | 2 | verification |
planning | /trace [OBJECTS]
object_1, object_2, object_3
[ACTIONS]
action_0(x0)
Requires: fluent_0(x0)
Effect: not fluent_0(x0)
action_1(x0)
Requires: fluent_2(x0)
Effect: not fluent_2(x0), not fluent_1(x0)
action_2(x0)
Requires: (not fluent_1(x0))
Effect: fluent_1(x0)
action_3(x0, x1)
Requires: fluent_1(x0), fluen... | <trace>
Target Goals: fluent_2 object_3
Selected Action: (action_2 object_1)
- Added effects: fluent_1 object_1
- Remaining goals: 1
Selected Action: (action_3 object_1 object_3)
- Added effects: fluent_0 object_3, fluent_2 object_3
- Removed effects: fluent_1 object_1, fluent_2 object_1
- Goal condition sati... | {"domain_seed": "4-252", "fluent_arity": 1, "na": 2, "problem_english": "[OBJECTS]\nobject_1, object_2, object_3\n\n[ACTIONS]\naction_0(x0)\n Requires: fluent_0(x0)\n Effect: not fluent_0(x0)\naction_1(x0)\n Requires: fluent_2(x0)\n Effect: not fluent_2(x0), not fluent_1(x0)\naction_2(x0)\n Requires: (not fluent_1... | Target Goals: fluent_2 object_3
Selected Action: (action_2 object_1)
- Added effects: fluent_1 object_1
- Remaining goals: 1
Selected Action: (action_3 object_1 object_3)
- Added effects: fluent_0 object_3, fluent_2 object_3
- Removed effects: fluent_1 object_1, fluent_2 object_1
- Goal condition satisfied. | 0 | cot |
planning | /trace [OBJECTS]
type_0: object_1_type_0, object_2_type_0, object_3_type_0, object_4_type_0
type_1: object_5_type_1, object_6_type_1, object_7_type_1, object_8_type_1, object_9_type_1
[ACTIONS]
action_0(x0:type_0, x1:type_0)
Requires: fluent_0(x1), (not fluent_0(x0))
Effect: not fluent_0(x1), not fluent_0(x0)
acti... | action_0(object_2, object_1)
action_2(object_2) | {"domain_seed": "4-128", "fluent_arity": 2, "na": 2, "problem_english": "[OBJECTS]\nobject_1, object_2\n\n[ACTIONS]\naction_0(x0, x1)\n Requires: (not fluent_2(x1))\n Effect: fluent_2(x1)\naction_1(x0)\n Requires: (not fluent_0), fluent_2(x0), fluent_3(x0)\n Effect: fluent_0, not fluent_2(x0), not fluent_3(x0)\nact... | Target Goals: fluent_2 object_1, fluent_1
Selected Action: (action_0 object_2 object_1)
- Added effects: fluent_2 object_1
- Remaining goals: 1
Selected Action: (action_2 object_2)
- Added effects: fluent_1
- Removed effects: fluent_0, fluent_2 object_2
- Goal condition satisfied. | 1 | few_shot |
planning | [OBJECTS]
object_1, object_2, object_3
[ACTIONS]
action_0(x0)
Requires: fluent_0
Effect: not fluent_0
action_1(x0)
Requires: (not fluent_0)
Effect: fluent_0
[STATE]
Default: False
Initial true values: None
[GOAL]
fluent_0
The answer is the plan.
Answer format: Multiple lines, one action per line: action(obj... | action_1(object_1) | {"domain_seed": "4-105", "fluent_arity": 2, "na": 1, "problem_english": "[OBJECTS]\nobject_1, object_2, object_3\n\n[ACTIONS]\naction_0(x0)\n Requires: fluent_0\n Effect: not fluent_0\naction_1(x0)\n Requires: (not fluent_0)\n Effect: fluent_0\n\n[STATE]\nDefault: False\nInitial true values: None\n\n[GOAL]\n\nfluen... | Target Goals: fluent_0
Selected Action: (action_1 object_1)
- Added effects: fluent_0
- Goal condition satisfied. | 0 | instruct |
planning | [OBJECTS]
object_1
[ACTIONS]
action_0(x0, x1)
Requires: (not fluent_0(x1)), fluent_0(x0)
Effect: fluent_0(x1), not fluent_0(x0)
action_1(x0)
Requires: (not fluent_0(x0))
Effect: fluent_0(x0)
action_2(x0)
Requires: fluent_0(x0)
Effect: not fluent_0(x0)
action_3(x0)
Effect: fluent_0(x0)
action_4(x0, x1)
... | Yes | {"domain_seed": "5-247", "fluent_arity": 1, "na": 1, "problem_english": "[OBJECTS]\nobject_1\n\n[ACTIONS]\naction_0(x0, x1)\n Requires: (not fluent_0(x1)), fluent_0(x0)\n Effect: fluent_0(x1), not fluent_0(x0)\naction_1(x0)\n Requires: (not fluent_0(x0))\n Effect: fluent_0(x0)\naction_2(x0)\n Requires: fluent_0(x0... | Target Goals: fluent_0 object_1
Selected Action: (action_1 object_1)
- Added effects: fluent_0 object_1
- Goal condition satisfied. | 0 | verification |
proof_reconstruction | /trace You are given the clauses from one generated proof trace, in shuffled order.
Domain: Geometry
Theorem: (~between(lower_dimension_point_1,lower_dimension_point_2,X1)|~between(lower_dimension_point_3,lower_dimension_point_1,X2)|~between(lower_dimension_point_1,X1,X2))
Each clause is either an axiom of this trace,... | <trace>
step_0 pm(premise_3, premise_4): [ '(~between(lower_dimension_point_1,lower_dimension_point_2,X1)|~between(lower_dimension_point_3,lower_dimension_point_1,X1))' ]
THEOREM pm(premise_3, step_0): [ '(~between(lower_dimension_point_1,lower_dimension_point_2,X1)|~between(lower_dimension_point_3,lower_dimension_poin... | {"numbered_clauses": ["(~between(lower_dimension_point_1,lower_dimension_point_2,X1)|~between(lower_dimension_point_3,lower_dimension_point_1,X1))", "(~between(lower_dimension_point_1,lower_dimension_point_2,X1)|~between(lower_dimension_point_3,lower_dimension_point_1,X2)|~between(lower_dimension_point_1,X1,X2))", "(be... | step_0 pm(premise_3, premise_4): [ '(~between(lower_dimension_point_1,lower_dimension_point_2,X1)|~between(lower_dimension_point_3,lower_dimension_point_1,X1))' ]
THEOREM pm(premise_3, step_0): [ '(~between(lower_dimension_point_1,lower_dimension_point_2,X1)|~between(lower_dimension_point_3,lower_dimension_point_1,X2)|... | 0 | cot |
proof_reconstruction | You are given the clauses from one generated proof trace, in shuffled order.
Domain: Geometry
Theorem: (inner_point(X1,X2)|end_point(X1,X2)|~inner_point(X1,X3)|~part_of(X3,X2))
Each clause is either an axiom of this trace, or a derived clause with exactly two recorded parent clauses.
Numbered clauses:
1. (incident_c(... | 4: axiom
2: axiom
5: axiom
3: parents 2 5
1: parents 3 4 | {"numbered_clauses": ["(equalish(X1,X2)|~less_or_equal(X2,X1)|~less_or_equal(X3,X2)|~equalish(X1,X3))", "(equalish(X1,X2)|~equalish(X2,X1))", "(less_or_equal(X1,X2)|~less_or_equal(X3,X2)|~equalish(X1,X3))", "(equalish(X1,X2)|~less_or_equal(X1,X2)|~less_or_equal(X2,X1))", "(less_or_equal(X1,X2)|~less_or_equal(X3,X2)|~eq... | step_0 pm(premise_2, premise_5): [ '(less_or_equal(X1,X2)|~less_or_equal(X3,X2)|~equalish(X1,X3))' ]
THEOREM pm(premise_4, step_0): [ '(equalish(X1,X2)|~less_or_equal(X2,X1)|~less_or_equal(X3,X2)|~equalish(X1,X3))' ] | 0 | few_shot |
proof_reconstruction | You are given the clauses from one generated proof trace, in shuffled order.
Domain: Set Theory
Theorem: (~subset(X1,X2)|~subset(X3,X1)|~member(X4,X5)|~member(X4,X3)|~difference(X6,X5,X2))
Each clause is either an axiom of this trace, or a derived clause with exactly two recorded parent clauses.
Numbered clauses:
1. ... | 3: axiom
1: axiom
4: parents 1 3
2: parents 1 4 | {"numbered_clauses": ["(member(X1,X3)|~member(X1,X2)|~subset(X2,X3))", "(~subset(X1,X2)|~subset(X3,X1)|~member(X4,X5)|~member(X4,X3)|~difference(X6,X5,X2))", "(~member(X1,X2)|~member(X1,X3)|~difference(X4,X2,X3))", "(~subset(X1,X2)|~member(X3,X4)|~member(X3,X1)|~difference(X5,X4,X2))"], "conjecture": "(~subset(X1,X2)|~... | step_0 pm(premise_3, premise_1): [ '(~subset(X1,X2)|~member(X3,X4)|~member(X3,X1)|~difference(X5,X4,X2))' ]
THEOREM pm(premise_1, step_0): [ '(~subset(X1,X2)|~subset(X3,X1)|~member(X4,X5)|~member(X4,X3)|~difference(X6,X5,X2))' ] | 0 | instruct |
proof_reconstruction | You are given the clauses from one generated proof trace, in shuffled order.
Domain: Geometry
Theorem: (X1=X2|~between(X1,X2,X3)|~between(X2,X1,X3))
Each clause is either an axiom of this trace, or a derived clause with exactly two recorded parent clauses.
Numbered clauses:
1. (X1=X2|~between(X1,X2,X3)|~between(X2,X1... | No | {"numbered_clauses": ["(X1=X2|~between(X1,X2,X3)|~between(X2,X1,X3))", "(X1=X2|~between(X1,X2,X1))", "(between(X5,inner_pasch(X1,X2,X3,X5,X4),X1)|~between(X1,X2,X3)|~between(X4,X5,X3))", "(between(X2,inner_pasch(X1,X2,X3,X5,X4),X4)|~between(X1,X2,X3)|~between(X4,X5,X3))", "(between(X1,X2,X3)|~between(X3,X2,X4)|~between... | step_0 pm(premise_2, premise_4): [ '(inner_pasch(X1,X2,X3,X1,X4)=X1|~between(X4,X1,X3)|~between(X1,X2,X3))' ]
step_1 pm(premise_4, step_0): [ '(between(X1,X2,X3)|~between(X3,X2,X4)|~between(X2,X1,X4))' ]
THEOREM pm(premise_2, step_1): [ '(X1=X2|~between(X1,X2,X3)|~between(X2,X1,X3))' ] | 0 | verification |
qualitative_reasoning | There are 5 entities labeled 0 through 4.
You are given the following facts (read 'i rel j' as 'entity i is rel to entity j'):
3 met-by 1
0 started-by 1
4 before 3
2 overlaps 4
1 contains 4
1 started-by 2
What is the relation of the vertical extent of box 2 to that of box 0?
The answer is exactly one of: a... | meets | {"calculus": "allen_time", "topic": "time intervals", "phrasing": "the temporal relation of interval {i} to interval {j}", "n_entities": 5, "hops": 3, "n_revealed": 4, "entities": [[-2, 0], [-3, -2], [-2, 4], [-2, -1], [-3, 4]], "revealed": [[3, 1, "met-by"], [0, 3, "started-by"], [4, 3, "contains"], [2, 0, "started-by... | 0 | few_shot | |
qualitative_reasoning | There are 5 entities labeled 0 through 4.
You are given the following facts (read 'i rel j' as 'entity i is rel to entity j'):
3 equals 1
0 meets 1
2 before 1
4 before 1
What is the temporal relation of interval 3 to interval 0?
The answer is exactly one of: after, before, contains, during, equals, finished-by... | met-by | {"calculus": "allen_time", "topic": "time intervals", "phrasing": "the temporal relation of interval {i} to interval {j}", "n_entities": 5, "hops": 2, "n_revealed": 4, "entities": [[-3, 3], [3, 4], [-3, 0], [3, 4], [-1, 2]], "revealed": [[3, 1, "equals"], [0, 1, "meets"], [2, 1, "before"], [4, 1, "before"]], "query": [... | 0 | instruct |
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