Datasets:

reasoning-core
/

procedural-pretraining-pile

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. (2x0 + x1 + 2x2) % 4 == 1 2. (x0 + 2x1) % 2 == 1 3. 3x0 + 4x1 + 3x2 == 10 4. (3x0 + 3x1) % 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. 4x2 >= 3 2. AllDifferent(x0, x1, x2) 3. -4x1 - 2x2 + 3x3 <= -4 4. (2x3) % 4 == 2 5. 3x1 - x2 + 2x3 == 3 6. 3x0 + 2x1 != 3 7. 3x0 + 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 + 2x1 + 3x2 != 4 4. 3x0 + 2x1 - 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: 3X1 + X2 + 103 = 0 2X1 + 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": ["3X1 + X2 + 103 = 0", "2X1 + 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 + 2X3 - 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 -= -1R1 2. Backwar...	5	{"equations": ["X1 + X2 + 45 = 0", "6X1 + X2 + 2X3 + 120 = 0", "3X1 + X3 + 46 = 0"], "query_variable": "X3", "full_solution_map": {"X1": -17, "X2": -28, "X3": 5}, "case": "unique", "cot": "1. Forward:\nR2 -= 6R1\nR3 -= 3R1\nR3 -= 3/5R2\n\n2. Backward:\nX3 = 5\nX2 = -28\nX1 = -17", "_time": 0.04075026512145996, "_...	1. Forward: R2 -= 6R1 R3 -= 3R1 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 - 2X2 + 4X3 - 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 - 2X2 + 4X3 - 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: 5X1 + 4X2 - 4X3 - 2X4 + 21 = 0 -4X1 - 3X2 + 2X3 + 2X4 - 30 = 0 6X1 + 6X2 + X3 - 3X4 + 101 = 0 -2X1 - 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": ["5X1 + 4X2 - 4X3 - 2X4 + 21 = 0", "-4X1 - 3X2 + 2X3 + 2X4 - 30 = 0", "6X1 + 6X2 + X3 - 3X4 + 101 = 0", "-2X1 - 2X2 + X4 - 31 = 0"], "query_variable": "X2", "full_solution_map": {"X1": 9, "X2": -16, "X3": -8, "X4": 17}, "case": "unique", "cot": "1. Forward:\nR2 -= -4/5R1\nR3 -= 6/5*R1\nR4 -=...	1. Forward: R2 -= -4/5R1 R3 -= 6/5R1 R4 -= -2/5R1 R3 -= 6R2 R4 -= -2R2 R4 -= -4/13R3 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

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Reasoning-Core : Procedural Pre-Training Pile (PPTP) ◉

PPTP is designed for formal/symbolic pre-training, mid-training and SFT.
The data is procedurally generated on cpu and can be scaled to trillion tokens, and the difficulty is also adjustable with a single knob.
Unlike LLM-generated synthetic data, the answers are correct by design.

Task Categories

📐 Formal Reasoning: planning • conjecture_entailment • proof_reconstruction
📜 Formal Semantics, Logic: logic_nli • evidence_retrieval
🔢 Mathematical computation: equation_system • arithmetics • symbolic_arithmetics • sequential_induction
💻 Code & Execution: code_execution • diff_prediction • diff_patching
🕸️ Graph Theory: graph_pathfinding • graph_node_centrality • graph_cycle_detection • graph_isomorphism
🎲 Probabilistic: bayesian_association • bayesian_intervention
📝 Language Parsing, Syntax: regex_following • regex_induction • parsability • parsing • continuation
📋 Table Processing: table_qa • table_conversion
🔎 Set Operations, Retrieval: set_intersection • set_missing_element • set_equality

Task Modes

We provide three modes for most tasks, all in SFT/pretraining suitable format:
➡️ Instruct mode: Direct prompt/answer format
🧠 Trace mode: Most tasks include reasoning traces to bake-in chain-of-thought reasoning patterns
✅ Verification mode: Tasks framed as prompt/candidate: valid (yes/no)? 10% of the time, to strengthen reasoning self-verification capabilities

🧪 Paper: Reasoning Core: A Scalable RL Environment for LLM Symbolic Reasoning
📦 Code: GitHub Repository (An updated paper for pre-training results is coming.)

RLVR version

See rc1 for the post-training/RLVR version

Abstract

We introduce Reasoning Core, a new scalable environment for Reinforcement Learning with Verifiable Rewards (RLVR), designed to advance foundational symbolic reasoning in Large Language Models (LLMs). Unlike existing benchmarks that focus on games or isolated puzzles, Reasoning Core procedurally generates problems across core formal domains, including PDDL planning, first-order logic, context-free grammar parsing, causal reasoning, and system equation solving. The environment is built on key design principles of high-generality problem distributions, verification via external tools, and continuous difficulty control, which together provide a virtually infinite supply of novel training instances. Initial zero-shot evaluations with frontier LLMs confirm the difficulty of Reasoning Core's tasks, positioning it as a promising resource to improve the reasoning capabilities of future models.

Usage

ds = load_dataset("reasoning-core/symbolic-pretraining-pile")

Citation

@article{reasoningcore2026,
  title={Reasoning Core: A Scalable Procedural Data Generation Suite for Symbolic Pre-training and Post-Training},
  author={Lacombe, Valentin and Quesnel, Valentin and Sileo, Damien},
  journal={arXiv preprint arXiv:2603.02208},
  year={2026},
  url={https://arxiv.org/abs/2603.02208}
}

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Collection including reasoning-core/procedural-pretraining-pile

datasets

Collection

Reasoning Core ◉ Pre-generated symbolic reasoning data, from pre-training pile to post-training environments • 5 items • Updated Mar 3 • 3

Papers for reasoning-core/procedural-pretraining-pile

Reasoning Core: A Scalable Procedural Data Generation Suite for Symbolic Pre-training and Post-Training

Paper • 2603.02208 • Published Mar 2 • 4

Reasoning Core: A Scalable RL Environment for LLM Symbolic Reasoning

Paper • 2509.18083 • Published Sep 22, 2025 • 5