conversations listlengths 2 2 | question stringclasses 4
values | source stringclasses 1
value | id int64 11.7k 11.7k ⌀ | prompt listlengths 2 2 | answer stringclasses 4
values | prompt__example_annotation__metadata dict | task_source stringclasses 1
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values | reflection_prompt listlengths 2 2 | model_responses__mutated_prompts_reflection listlengths 1 1 | model_responses__mutated_prompts_reflection__finish_reason_length_flags listlengths 1 1 | model_responses__mutated_prompts_reflection__length_partial_responses listlengths 1 1 | reflection_prompt__mutated_prompts_reflection__metadata dict | model_responses__mutated_prompts_reflection__metadata dict |
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[
{
"from": "user",
"value": "$2 \\cdot 131$ The number of roots of the equation $\\sqrt{x^{2}+12 x+36}+x+6=0$ is\n(A) 0.\n(B) 2.\n(C) 4.\n(D) Infinitely many.\n(3rd \"Five Sheep Cup\" Junior High School Mathematics Competition, 1991)"
},
{
"from": "assistant",
"value": "<think>\nOkay, let me try ... | $2 \cdot 131$ The number of roots of the equation $\sqrt{x^{2}+12 x+36}+x+6=0$ is
(A) 0.
(B) 2.
(C) 4.
(D) Infinitely many.
(3rd "Five Sheep Cup" Junior High School Mathematics Competition, 1991) | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | D | {
"api_url": "http://10.32.36.231:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | openthoughts | openthoughts | [
"Rewritten Question: Find the number of real roots for the equation $\\sqrt{x^2 + 12x + 36} + x + 6 = 0$.\n\nStep 1: Simplify the expression under the square root. Notice that $x^2 + 12x + 36 = (x + 6)^2$. So, the equation becomes $\\sqrt{(x + 6)^2} + x + 6 = 0$.\n\nStep 2: Recognize that $\\sqrt{(x + 6)^2}$ simpli... | [
false
] | [
"(D)"
] | rephrase_rationalized | [
{
"content": "You think step by step and reflect on the given answer for the question reasoning about if the answer was correct or incorrect. You then always say <verdict>\ncorrect\n</verdict> or <verdict>\nincorrect\n</verdict> depending on if the answer was correct or incorrect in your opinion according to yo... | [
"Let us verify this answer. The model correctly identified that the equation simplifies to \\( |x + 6| + x + 6 = 0 \\) and then considered two cases. In Case 1, \\( x = -6 \\) is a valid solution. In Case 2, any \\( x < -6 \\) would theoretically satisfy the equation, but the model noted that these values are inval... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.225:10080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 512,
"n": 1,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[
{
"from": "user",
"value": "$2 \\cdot 131$ The number of roots of the equation $\\sqrt{x^{2}+12 x+36}+x+6=0$ is\n(A) 0.\n(B) 2.\n(C) 4.\n(D) Infinitely many.\n(3rd \"Five Sheep Cup\" Junior High School Mathematics Competition, 1991)"
},
{
"from": "assistant",
"value": "<think>\nOkay, let me try ... | $2 \cdot 131$ The number of roots of the equation $\sqrt{x^{2}+12 x+36}+x+6=0$ is
(A) 0.
(B) 2.
(C) 4.
(D) Infinitely many.
(3rd "Five Sheep Cup" Junior High School Mathematics Competition, 1991) | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | D | {
"api_url": "http://10.32.36.231:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | openthoughts | openthoughts | [
"Rewritten Question: Find the number of roots for the equation $\\sqrt{x^2 + 12x + 36} + x + 6 = 0$.\n\nStep 1: Simplify the expression under the square root.\nThe expression $x^2 + 12x + 36$ can be rewritten as $(x + 6)^2$. Thus, the equation becomes:\n\\[\n\\sqrt{(x + 6)^2} + x + 6 = 0\n\\]\n\nStep 2: Analyze the... | [
true
] | [
"D"
] | rephrase_rationalized | [
{
"content": "You think step by step and reflect on the given answer for the question reasoning about if the answer was correct or incorrect. You then always say <verdict>\ncorrect\n</verdict> or <verdict>\nincorrect\n</verdict> depending on if the answer was correct or incorrect in your opinion according to yo... | [
"Let us verify this answer. The model correctly identified that the equation simplifies to \\( |x + 6| + x + 6 = 0 \\). It then analyzed the two cases: \\( x + 6 \\geq 0 \\) and \\( x + 6 < 0 \\). In the first case, it found \\( x = -6 \\) as a valid solution. In the second case, it determined that any \\( x < -6 \... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.225:10080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 512,
"n": 1,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[
{
"from": "user",
"value": "$2 \\cdot 131$ The number of roots of the equation $\\sqrt{x^{2}+12 x+36}+x+6=0$ is\n(A) 0.\n(B) 2.\n(C) 4.\n(D) Infinitely many.\n(3rd \"Five Sheep Cup\" Junior High School Mathematics Competition, 1991)"
},
{
"from": "assistant",
"value": "<think>\nOkay, let me try ... | $2 \cdot 131$ The number of roots of the equation $\sqrt{x^{2}+12 x+36}+x+6=0$ is
(A) 0.
(B) 2.
(C) 4.
(D) Infinitely many.
(3rd "Five Sheep Cup" Junior High School Mathematics Competition, 1991) | null | null | [
{
"content": "You answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | D | {
"api_url": "http://10.32.36.231:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | openthoughts | openthoughts | [
"Let's analyze the given equation step-by-step:\n\nThe equation is:\n\\[\n\\sqrt{x^2 + 12x + 36} + x + 6 = 0\n\\]\n\nFirst, we simplify the expression under the square root:\n\\[\nx^2 + 12x + 36 = (x + 6)^2\n\\]\nSo the equation becomes:\n\\[\n\\sqrt{(x + 6)^2} + x + 6 = 0\n\\]\n\nSince \\(\\sqrt{(x + 6)^2}\\) simp... | [
true
] | [
"D"
] | alternative_rationalized | [
{
"content": "You think step by step and reflect on the given answer for the question reasoning about if the answer was correct or incorrect. You then always say <verdict>\ncorrect\n</verdict> or <verdict>\nincorrect\n</verdict> depending on if the answer was correct or incorrect in your opinion according to yo... | [
"Let us verify this answer. The model correctly identified that the equation simplifies to \\(|x + 6| + x + 6 = 0\\), and analyzed it into two cases. In Case 1, it found \\(x = -6\\) as a valid solution. In Case 2, it concluded that any \\(x < -6\\) is also a solution, leading to infinitely many solutions. Given th... | [
false
] | [
""
] | {
"api_url": "http://10.32.36.225:10080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 512,
"n": 1,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which (...TRUNCATED) | "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following proposi(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | B | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: Determine which proposition about vectors is correct among the given options.\(...TRUNCATED) | [
true
] | [
"B"
] | rephrase_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer: The model response correctly identifies that Option B, \\( |\\overright(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.225:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which (...TRUNCATED) | "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following proposi(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | B | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: \nWhich of the following propositions about vectors is correct?\n\nA: If $|\\o(...TRUNCATED) | [
true
] | [
"B"
] | rephrase_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer: The model correctly identified that proposition A is incorrect due to t(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.225:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which (...TRUNCATED) | "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following proposi(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | B | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: \nWhich of the following propositions about vectors is correct?\n\nA: If $|\\o(...TRUNCATED) | [
true
] | [
"B"
] | rephrase_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer: The model response correctly identifies that proposition B, which state(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.225:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which (...TRUNCATED) | "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following proposi(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | B | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Rewritten Question: \nFor any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, determi(...TRUNCATED) | [
true
] | [
"B"
] | rephrase_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer: The model correctly identified that proposition B ($|\\overrightarrow{a(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.225:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which (...TRUNCATED) | "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following proposi(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | B | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Let's evaluate each proposition one by one.\n\n**Proposition A:** If \\( |\\overrightarrow{a}| > |(...TRUNCATED) | [
false
] | [
"(B)"
] | alternative_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer: The model correctly identified that Proposition B is the correct propos(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.225:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which (...TRUNCATED) | "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following proposi(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | B | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Let's examine each proposition one by one:\n\n**Proposition A:** If \\( |\\overrightarrow{a}| > |\(...TRUNCATED) | [
false
] | [
"(B)"
] | alternative_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer: \n\nThe model correctly identifies that Proposition B is the correct an(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.225:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
[{"from":"user","value":"For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which (...TRUNCATED) | "For any two vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$, which of the following proposi(...TRUNCATED) | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | B | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | openthoughts | openthoughts | ["Let's evaluate each proposition one by one:\n\n**Proposition A:** If \\(|\\overrightarrow{a}| > |\(...TRUNCATED) | [
true
] | [
"B"
] | alternative_rationalized | [{"content":"You think step by step and reflect on the given answer for the question reasoning about(...TRUNCATED) | ["Let us verify this answer: The model response correctly identifies Proposition B as the correct on(...TRUNCATED) | [
false
] | [
""
] | {"api_url":"http://10.32.36.225:10080/v1","backend":"litellm","chat_template_applied":true,"generati(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 1
} |
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