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[eval-basic] remove large results files, add gitignore, only leave summary

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rishabhranawat 2025-02-09 22:52:10 -08:00
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commit 0657222a8f
10 changed files with 42 additions and 1059 deletions
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eval/.gitignore vendored Normal file
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@ -0,0 +1,2 @@
results/*
!results/summary*

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eval/__init__.py
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eval/eval_basic.py → eval/eval.py
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2
eval/eval_basic.sh → eval/eval.sh
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@ -21,7 +21,7 @@ mkdir -p "$OUTPUT_DIR"
# Run evaluations
for model in "${MODELS[@]}"; do
echo "Evaluating $model..."
python eval_basic.py \
python eval.py \
--model "$model" \
--config "eval_basic.json" \
--output-dir "$OUTPUT_DIR"

647
eval/results/evaluation_google_gemini-2.0-flash-001_20250209_223527.json
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@ -1,647 +0,0 @@
[
{
"metrics": {
"dataset_name": "letter_counting",
"model": "google/gemini-2.0-flash-001",
"size": 10,
"average_score": 0.20600000000000002,
"total_examples": 10,
"timestamp": "2025-02-10T06:34:37.091554",
"config": {
"min_words": 5,
"max_words": 15,
"size": 10,
"seed": 42
}
},
"results": [
{
"question": "How many times does the letter \"a\" appear in the text: \"bed and enters his mechanical dresser Two minutes later the machine deposited him all dressed\"?",
"expected_answer": "6",
"model_answer": "The letter \"a\" appears 7 times in the text: \"bed and enters his mechanical dresser Two minutes later the machine deposited him all dressed\".\n",
"score": 0.01,
"metadata": {
"span_length": 15,
"target_letter": "a",
"span": [
"bed",
"and",
"enters",
"his",
"mechanical",
"dresser",
"Two",
"minutes",
"later",
"the",
"machine",
"deposited",
"him",
"all",
"dressed"
]
}
},
{
"question": "How many times does the letter \"w\" appear in the text: \"it into a watering place\"?",
"expected_answer": "1",
"model_answer": "The letter \"w\" appears 1 time in the text \"it into a watering place\".\n",
"score": 0.5,
"metadata": {
"span_length": 5,
"target_letter": "w",
"span": [
"it",
"into",
"a",
"watering",
"place"
]
}
},
{
"question": "How many times does the letter \"t\" appear in the text: \"readable form accessible by the widest array of equipment including outdated\"?",
"expected_answer": "5",
"model_answer": "Let's count the \"t\"s in the sentence \"readable form accessible by the widest array of equipment including outdated\":\n\n* readable: 0\n* form: 0\n* accessible: 0\n* by: 0\n* the: 1\n* widest: 1\n* array: 0\n* of: 0\n* equipment: 1\n* including: 0\n* outdated: 2\n\nTotal: 1 + 1 + 1 + 2 = 5\n\nTherefore, the letter \"t\" appears 5 times in the text.",
"score": 0.5,
"metadata": {
"span_length": 11,
"target_letter": "t",
"span": [
"readable",
"form",
"accessible",
"by",
"the",
"widest",
"array",
"of",
"equipment",
"including",
"outdated"
]
}
},
{
"question": "How many times does the letter \"n\" appear in the text: \"does not contain a notice indicating that it is\"?",
"expected_answer": "6",
"model_answer": "The letter \"n\" appears 7 times in the text \"does not contain a notice indicating that it is\".\n",
"score": 0.01,
"metadata": {
"span_length": 9,
"target_letter": "n",
"span": [
"does",
"not",
"contain",
"a",
"notice",
"indicating",
"that",
"it",
"is"
]
}
},
{
"question": "How many times does the letter \"a\" appear in the text: \"keeping this work in the same\"?",
"expected_answer": "1",
"model_answer": "The letter \"a\" appears **3** times in the text \"keeping this work in the same\".\n",
"score": 0.01,
"metadata": {
"span_length": 6,
"target_letter": "a",
"span": [
"keeping",
"this",
"work",
"in",
"the",
"same"
]
}
},
{
"question": "How many times does the letter \"r\" appear in the text: \"years ago its subscription list contained but a few hundred\"?",
"expected_answer": "3",
"model_answer": "The letter \"r\" appears 4 times in the text \"years ago its subscription list contained but a few hundred\".\n",
"score": 0.01,
"metadata": {
"span_length": 10,
"target_letter": "r",
"span": [
"years",
"ago",
"its",
"subscription",
"list",
"contained",
"but",
"a",
"few",
"hundred"
]
}
},
{
"question": "How many times does the letter \"e\" appear in the text: \"me As in the morning the table rose out of the floor Again\"?",
"expected_answer": "6",
"model_answer": "The letter \"e\" appears 6 times in the text \"me As in the morning the table rose out of the floor Again\".\n",
"score": 0.5,
"metadata": {
"span_length": 13,
"target_letter": "e",
"span": [
"me",
"As",
"in",
"the",
"morning",
"the",
"table",
"rose",
"out",
"of",
"the",
"floor",
"Again"
]
}
},
{
"question": "How many times does the letter \"t\" appear in the text: \"said Faithburn was dead quite certainly\"?",
"expected_answer": "3",
"model_answer": "The letter \"t\" appears 5 times in the text \"said Faithburn was dead quite certainly\".\n",
"score": 0.01,
"metadata": {
"span_length": 6,
"target_letter": "t",
"span": [
"said",
"Faithburn",
"was",
"dead",
"quite",
"certainly"
]
}
},
{
"question": "How many times does the letter \"n\" appear in the text: \"these eight had only impracticable schemes to propose In fact one of\"?",
"expected_answer": "3",
"model_answer": "Let's count the \"n\"s:\n\n* **n**\n* o**n**ly\n* i**n**\n* o**n**e\n\nThere are **4** \"n\"s in the text.",
"score": 0.01,
"metadata": {
"span_length": 12,
"target_letter": "n",
"span": [
"these",
"eight",
"had",
"only",
"impracticable",
"schemes",
"to",
"propose",
"In",
"fact",
"one",
"of"
]
}
},
{
"question": "How many times does the letter \"g\" appear in the text: \"computers including obsolete old middle aged and new\"?",
"expected_answer": "2",
"model_answer": "The letter \"g\" appears 2 times in the text: \"computers including obsolete old middle aged and new\".\n",
"score": 0.5,
"metadata": {
"span_length": 8,
"target_letter": "g",
"span": [
"computers",
"including",
"obsolete",
"old",
"middle",
"aged",
"and",
"new"
]
}
}
]
},
{
"metrics": {
"dataset_name": "propositional_logic",
"model": "google/gemini-2.0-flash-001",
"size": 10,
"average_score": 0.059,
"total_examples": 10,
"timestamp": "2025-02-10T06:35:11.432275",
"config": {
"size": 10,
"seed": 42
}
},
"results": [
{
"question": "Given:\n1. R\n2. Q\nWhat can we conclude?",
"expected_answer": "(P \u2228 Q)",
"model_answer": "Given just \"R\" and \"Q\" as individual statements, we can't directly *conclude* anything meaningful in a logical or mathematical sense *unless* we know more context. Here's why and some possibilities:\n\n**Without Context:**\n\n* **Independent Statements:** They are simply two distinct statements that might be true or false depending on what \"R\" and \"Q\" represent. They exist independently.\n\n**With Possible Context (and Possible Conclusions):**\n\n* **Logic/Propositional Logic:** If \"R\" and \"Q\" represent propositions (statements that can be true or false), then we can form compound statements:\n * **R AND Q (R \u2227 Q):** The statement \"R is true AND Q is true.\" This is only true if *both* R and Q are true.\n * **R OR Q (R \u2228 Q):** The statement \"R is true OR Q is true (or both).\" This is true if *either* R or Q or both are true.\n * **IF R THEN Q (R \u2192 Q):** The statement \"If R is true, then Q is true.\" This is only false if R is true and Q is false.\n * **IF Q THEN R (Q \u2192 R):** The statement \"If Q is true, then R is true.\" This is only false if Q is true and R is false.\n * **R IFF Q (R \u2194 Q):** The statement \"R is true if and only if Q is true.\" This is true if R and Q have the same truth value (both true or both false).\n * **NOT R (\u00acR):** The statement \"R is false.\"\n * **NOT Q (\u00acQ):** The statement \"Q is false.\"\n\n *From the information given, we cannot deduce the individual truth values of `R` and `Q` (e.g., whether `R` is true or false, whether `Q` is true or false).*\n\n* **Set Theory:** If R and Q are sets, then we can discuss:\n * **Intersection (R \u2229 Q):** The set containing elements that are *both* in R and in Q. We can't *conclude* what's in this intersection without knowing the elements of R and Q.\n * **Union (R \u222a Q):** The set containing elements that are in R, in Q, or in both. We can't *conclude* what's in this union without knowing the elements of R and Q.\n\n* **Mathematics (Variables):** If R and Q are variables, then we can't conclude anything about their relationship or values *unless* we have an equation or further information linking them. We don't know if R = Q, R < Q, R > Q, R + Q = some value, etc.\n\n* **Premises in an Argument:** If R and Q are presented as premises (assumptions) in a larger argument, we can only draw conclusions if there are *other* premises or rules of inference involved.\n\n**Example Scenarios and Conclusions:**\n\n* **Scenario:** R: \"It is raining.\" Q: \"The ground is wet.\"\n * **Possible Conclusion with an additional premise:** If we know \"IF it is raining, THEN the ground is wet (R \u2192 Q)\", then we can say *if* it is raining (we know R), *then* the ground is wet (we can conclude Q). But *given only* R and Q, we cannot derive this conditional.\n\n* **Scenario:** R: x > 5 Q: x > 0 (where 'x' is a real number)\n * **Conclusion:** If both R and Q are true for the same value of x, then x > 5 implies x > 0. Therefore we can deduce that Q is true if R is. R -> Q.\n\n**In summary, the best answer is:**\n\nWithout any further context or relationship between R and Q, we can only acknowledge them as two independent statements, values or sets. We cannot draw any meaningful logical conclusions *solely* from the information given.\n",
"score": 0.01,
"metadata": {
"premises": [
"R",
"Q"
],
"variables": [
"P",
"Q",
"R",
"S"
],
"complexity": 3
}
},
{
"question": "Given:\n1. ((Q \u2192 P) \u2228 (Q \u2192 P))\n2. ((Q \u2194 Q) \u2192 (P \u2192 P))\n3. P\nWhat can we conclude?",
"expected_answer": "(P \u2192 P)",
"model_answer": "Let's analyze each statement and see what conclusions can be drawn from them and the given information.\n\n1. **((Q \u2192 P) \u2228 (Q \u2192 P))** simplifies to **(Q \u2192 P)**. This means \"if Q is true, then P is true.\" Since we know P is true (given in statement 3), then this statement is true whether Q is true or false. (Remember, a conditional is only false when the antecedent is true and the consequent is false).\n\n2. **((Q \u2194 Q) \u2192 (P \u2192 P))** simplifies significantly. `Q \u2194 Q` is always true (it's a tautology). `P \u2192 P` is also always true (it's another tautology). So, this becomes `(True \u2192 True)`, which is always true. This statement doesn't help us determine anything about the relationship between Q and P beyond what is already implied by P being true.\n\n3. **P** is given as true.\n\nTherefore, based on the given information and the simplification of the statements, the main conclusion is that **P is true**. The truth value of Q is indeterminate. Q can be either true or false, and all the given statements will still hold.\n**Therefore, we can conclude: P.**\n",
"score": 0.5,
"metadata": {
"premises": [
"((Q \u2192 P) \u2228 (Q \u2192 P))",
"((Q \u2194 Q) \u2192 (P \u2192 P))",
"P"
],
"variables": [
"P",
"Q"
],
"complexity": 3
}
},
{
"question": "Given:\n1. ((Q \u2228 P) \u2227 \u00acP)\n2. P\n3. ((P \u2227 R) \u2227 \u00acR)\n4. ((Q \u2194 R) \u2192 \u00acQ)\nWhat can we conclude?",
"expected_answer": "(Q \u2227 Q)",
"model_answer": "Let's analyze the given statements and see what conclusions we can draw using logical deduction:\n\n1. **((Q \u2228 P) \u2227 \u00acP)**: This says that either Q or P is true, AND P is false. Since P is false, Q must be true for the entire statement to be true. Thus, we can conclude: **Q is true.**\n\n2. **P**: This says that P is true.\n\n3. **((P \u2227 R) \u2227 \u00acR)**: This says that both P and R are true, AND R is false. This entire statement is a contradiction, as R cannot be both true and false. This statement implies: **False (Contradiction)**.\n\n4. **((Q \u2194 R) \u2192 \u00acQ)**: This says that IF Q is equivalent to R (i.e., Q and R have the same truth value), THEN Q is false.\n\nNow, let's combine our findings:\n\n* From (1), we deduced **Q**. However from (2) and (3), we found that statement (3) resulted in a contradiction. This contradiction stems from assuming both Q and R are false, despite Q already being false as a logical conclusion from (1). Therefore something must be wrong with the premises given.\n\nHere's a more methodical analysis, considering the contradiction:\n\nSince statement (3) leads to a contradiction, we must question our assumptions and how they interact. Here's where things get interesting:\n\n* We initially deduced Q from statement (1). Thus since P is false and P is true (2), this creates another contradiction. Thus we are concluding contradictory truths when all assumptions are in effect.\n\nSince we arrive at a contradiction, the set of premises is inconsistent. Therefore, anything can be formally derived. In essence, we can conclude anything we want via *ex falso quod libet*.\n\n**Therefore, due to the contradictory statements provided, we can conclude anything.** However, within a standard logic system, we would first need to address which statement must be removed to allow the system to converge.\n",
"score": 0.01,
"metadata": {
"premises": [
"((Q \u2228 P) \u2227 \u00acP)",
"P",
"((P \u2227 R) \u2227 \u00acR)",
"((Q \u2194 R) \u2192 \u00acQ)"
],
"variables": [
"P",
"Q",
"R"
],
"complexity": 3
}
},
{
"question": "Given:\n1. \u00acP\n2. \u00acP\n3. Q\nWhat can we conclude?",
"expected_answer": "(Q \u2228 R)",
"model_answer": "From the given premises:\n\n* \u00acP (P is false)\n* \u00acP (P is false)\n* Q (Q is true)\n\nWe can conclude the following:\n\n* **P is false.** (This is directly from \u00acP)\n* **Q is true.** (This is directly from Q)\n* **\u00acQ is false.** (Since Q is true)\n\nNow we can also conclude the following with propositional logic principles:\n\n* **P \u2228 Q** is true. (Since Q is true, the disjunction is true regardless of the truth value of P).\n* **P \u2192 Q** is true. (Since P is false, the conditional is true).\n* **\u00acP \u2228 Q** is true. (Since both \u00acP and Q are true, the disjunction is true).\n* **\u00acP \u2192 Q** is true. (Since \u00acP is true, the conditional is true).\n\nIn summary, we can validly conclude many things, the most straightforward being the truth values of P and Q:\n\n* **P is false.**\n* **Q is true.**\n\nAnd other valid conclusions such as those related to ORs and implication.\n",
"score": 0.01,
"metadata": {
"premises": [
"\u00acP",
"\u00acP",
"Q"
],
"variables": [
"P",
"Q",
"R"
],
"complexity": 3
}
},
{
"question": "Given:\n1. P\n2. ((P \u2228 P) \u2194 (Q \u2227 P))\n3. P\nWhat can we conclude?",
"expected_answer": "(Q \u2194 Q)",
"model_answer": "Let's analyze the given statements:\n\n1. P: This statement is true.\n2. ((P \u2228 P) \u2194 (Q \u2227 P)): This is a biconditional. Let's break it down:\n * (P \u2228 P) is logically equivalent to P (by the idempotent law).\n * So the statement simplifies to (P \u2194 (Q \u2227 P)).\n * Since we know P is true (from statement 1 and 3), the statement becomes (True \u2194 (Q \u2227 True)).\n * (Q \u2227 True) is logically equivalent to Q.\n * Therefore, the statement simplifies further to (True \u2194 Q).\n * For the biconditional (True \u2194 Q) to be true, Q must be true.\n\nTherefore, we can conclude:\n\n* **Q** is true.\n",
"score": 0.01,
"metadata": {
"premises": [
"P",
"((P \u2228 P) \u2194 (Q \u2227 P))",
"P"
],
"variables": [
"P",
"Q"
],
"complexity": 3
}
},
{
"question": "Given:\n1. (Q \u2194 R)\n2. \u00acR\nWhat can we conclude?",
"expected_answer": "(Q \u2192 R)",
"model_answer": "From the given premises:\n\n1. Q \u2194 R (Q is logically equivalent to R, meaning Q is true if and only if R is true)\n2. \u00acR (R is false)\n\nSince Q \u2194 R, Q and R have the same truth value. Because \u00acR, we know R is false. Therefore, Q must also be false.\n\nConclusion: **\u00acQ**\n",
"score": 0.01,
"metadata": {
"premises": [
"(Q \u2194 R)",
"\u00acR"
],
"variables": [
"P",
"Q",
"R"
],
"complexity": 3
}
},
{
"question": "Given:\n1. R\n2. ((Q \u2192 Q) \u2228 (S \u2227 Q))\n3. Q\nWhat can we conclude?",
"expected_answer": "(S \u2228 Q)",
"model_answer": "Let's analyze the given statements:\n\n1. **R:** This statement simply asserts that R is true.\n\n2. **(Q \u2192 Q) \u2228 (S \u2227 Q):** This is a disjunction (OR). Let's break it down:\n * **Q \u2192 Q:** This is a tautology. A statement implies itself is always true. Therefore, the entire disjunction is true regardless of the value of (S \u2227 Q).\n\n3. **Q:** This statement says Q is true.\n\nSince Q is true:\n\n* **(Q -> Q)** is true (since Q is true implies Q is true).\n\n* **(S ^ Q)** is true if and only if *both* S and Q are true. We know Q is true, so if S is also true then this is true. If S is false this is false.\n\n* **((Q -> Q) v (S ^ Q))** is true, since **(Q -> Q)** which is part of the disjunction is true. We already knew that from line 2.\n\nTherefore, from these premises, we can definitively conclude:\n\n* **R** is true (given).\n* **Q** is true (given).\n* **(Q \u2192 Q) \u2228 (S \u2227 Q)** is true (given, and verifiable).\n* **(Q -> Q)** is true (implied from Q being true, since this is a tautology).\n* The truth value of S is undetermined. If S is true, then (S ^ Q) is true. If S is false, then (S ^ Q) is false.\n\nFinal Answer: The conclusions are **R**, **Q**, and **(Q \u2192 Q) \u2228 (S \u2227 Q)** are all true. Additionally, we know **(Q \u2192 Q)** is true. We cannot determine the truth value of S.\n",
"score": 0.01,
"metadata": {
"premises": [
"R",
"((Q \u2192 Q) \u2228 (S \u2227 Q))",
"Q"
],
"variables": [
"P",
"Q",
"R",
"S"
],
"complexity": 3
}
},
{
"question": "Given:\n1. (Q \u2227 P)\n2. (\u00acP \u2227 (P \u2192 P))\n3. \u00ac(Q \u2194 Q)\nWhat can we conclude?",
"expected_answer": "(P \u2227 P)",
"model_answer": "Let's analyze each statement to see what we can derive:\n\n* **1. (Q \u2227 P)** This statement tells us that both Q and P are true.\n * Q is True\n * P is True\n\n* **2. (\u00acP \u2227 (P \u2192 P))** Let's break this down:\n * `\u00acP`: This means \"Not P\".\n * `P \u2192 P`: This is a tautology (always true). If P is true, then P implies P is true. If P is false then P implies P is true.\n\n So the statement is essentially `(\u00acP) \u2227 (True)`. This simplifies to just `\u00acP`. Therefore, the statement tells us that P is false.\n\n* **3. \u00ac(Q \u2194 Q)** The biconditional `Q \u2194 Q` means \"Q if and only if Q\". This is always true, regardless of Q's value (Q is true, so \"true if and only if true\" is true; Q is false, so \"false if and only if false\" is true). Therefore \u00ac(Q \u2194 Q) always resolves to `\u00ac(True)`, meaning that `False`.\n\nNow we consider these conclusions together:\n\n* From statement 1: `Q` is True and `P` is True.\n* From statement 2: `P` is False.\n* From statment 3: the statement is `False`.\n\nWe have a **Contradiction**.\n\nStatement 1 tells us that P is true, while Statement 2 tells us that P is false. This means the entire set of statements is inconsistent. Therefore, we can conclude the system is flawed.\nFinal Answer: The final answer is $\\boxed{Contradiction}$",
"score": 0.01,
"metadata": {
"premises": [
"(Q \u2227 P)",
"(\u00acP \u2227 (P \u2192 P))",
"\u00ac(Q \u2194 Q)"
],
"variables": [
"P",
"Q"
],
"complexity": 3
}
},
{
"question": "Given:\n1. (R \u2228 Q)\n2. (R \u2227 Q)\n3. R\nWhat can we conclude?",
"expected_answer": "(P \u2194 P)",
"model_answer": "From the given statements:\n\n1. (R \u2228 Q): R or Q (or both) is true.\n2. (R \u2227 Q): R and Q are both true.\n3. R: R is true.\n\nWe can conclude the following:\n\n* **Q is true.** Statement (R \u2227 Q) tells us that R and Q are both true. Since statement 3 tells us that R is true, Q must also be true.\n\nTherefore, the main conclusion is **Q**.\n",
"score": 0.01,
"metadata": {
"premises": [
"(R \u2228 Q)",
"(R \u2227 Q)",
"R"
],
"variables": [
"P",
"Q",
"R"
],
"complexity": 3
}
},
{
"question": "Given:\n1. ((P \u2228 Q) \u2228 (Q \u2192 Q))\n2. \u00ac(Q \u2192 Q)\n3. ((P \u2227 Q) \u2227 (Q \u2227 P))\n4. (Q \u2194 Q)\nWhat can we conclude?",
"expected_answer": "(P \u2192 P)",
"model_answer": "Let's analyze each statement:\n\n* **1. ((P \u2228 Q) \u2228 (Q \u2192 Q))**: `Q \u2192 Q` is always true (tautology). Therefore, `(P \u2228 Q) \u2228 True` is always true, regardless of the values of P and Q. So, this statement provides no specific information about P or Q.\n\n* **2. \u00ac(Q \u2192 Q)**: `Q \u2192 Q` is always true. Therefore `\u00ac(Q \u2192 Q)` means \u00acTrue which is False. So, the statement asserts a contradiction.\n\n* **3. ((P \u2227 Q) \u2227 (Q \u2227 P))**: This statement is equivalent to (P \u2227 Q). Both (P \u2227 Q) and (Q \u2227 P) are true only when both P and Q are true.\n\n* **4. (Q \u2194 Q)**: This statement is a tautology (always true). It provides no specific information.\n\nNow let's consider the implications of having all four statements:\n\nStatements 1 and 4 are always true, so they do not provide any useful information. Statement 2 says that a tautology is false, which is a contradiction. Statement 3 indicates that both P and Q are true. However, statement 2 means the entire set of statements is contradictory.\n\nTherefore, we can conclude that the given set of premises is **inconsistent (or contradictory).** You cannot simultaneously assert these four statements without creating a logical absurdity.\n",
"score": 0.01,
"metadata": {
"premises": [
"((P \u2228 Q) \u2228 (Q \u2192 Q))",
"\u00ac(Q \u2192 Q)",
"((P \u2227 Q) \u2227 (Q \u2227 P))",
"(Q \u2194 Q)"
],
"variables": [
"P",
"Q"
],
"complexity": 3
}
}
]
},
{
"metrics": {
"dataset_name": "leg_counting",
"model": "google/gemini-2.0-flash-001",
"size": 10,
"average_score": 0.40199999999999997,
"total_examples": 10,
"timestamp": "2025-02-10T06:35:27.087469",
"config": {
"min_animals": 3,
"max_animals": 8,
"size": 10,
"seed": 42
}
},
"results": [
{
"question": "How many legs are there in total if you have 3 humans, 3 sea slugs, 3 deers, 1 giraffe, 3 elephants, 2 ducks, 1 beetle, 1 flatworm?",
"expected_answer": "44",
"model_answer": "Okay, let's break it down:\n\n* **Humans:** 3 humans * 2 legs/human = 6 legs\n* **Sea Slugs:** 3 sea slugs * 0 legs/sea slug = 0 legs\n* **Deer:** 3 deer * 4 legs/deer = 12 legs\n* **Giraffe:** 1 giraffe * 4 legs/giraffe = 4 legs\n* **Elephants:** 3 elephants * 4 legs/elephant = 12 legs\n* **Ducks:** 2 ducks * 2 legs/duck = 4 legs\n* **Beetle:** 1 beetle * 6 legs/beetle = 6 legs\n* **Flatworm:** 1 flatworm * 0 legs/flatworm = 0 legs\n\nNow, let's add them all up:\n\n6 + 0 + 12 + 4 + 12 + 4 + 6 + 0 = 44 legs\n\nSo, there are a total of 44 legs.",
"score": 0.5,
"metadata": {
"difficulty": {
"num_animals": 8
},
"animals": {
"human": 3,
"sea slug": 3,
"deer": 3,
"giraffe": 1,
"elephant": 3,
"duck": 2,
"beetle": 1,
"flatworm": 1
},
"total_legs": 44
}
},
{
"question": "How many legs are there in total if you have 2 sheeps, 3 dogs, 3 praying mantiss?",
"expected_answer": "38",
"model_answer": "Here's how to calculate the total number of legs:\n\n* **Sheep:** 2 sheep * 4 legs/sheep = 8 legs\n* **Dogs:** 3 dogs * 4 legs/dog = 12 legs\n* **Praying Mantises:** 3 mantises * 6 legs/mantis = 18 legs\n\n**Total:** 8 + 12 + 18 = 38 legs\n",
"score": 0.5,
"metadata": {
"difficulty": {
"num_animals": 3
},
"animals": {
"sheep": 2,
"dog": 3,
"praying mantis": 3
},
"total_legs": 38
}
},
{
"question": "How many legs are there in total if you have 2 crabs, 1 lobster, 1 human, 1 cow, 3 bees, 1 elephant?",
"expected_answer": "58",
"model_answer": "Here's the breakdown:\n\n* **Crabs:** 2 crabs * 10 legs/crab = 20 legs\n* **Lobster:** 1 lobster * 10 legs/lobster = 10 legs\n* **Human:** 1 human * 2 legs/human = 2 legs\n* **Cow:** 1 cow * 4 legs/cow = 4 legs\n* **Bees:** 3 bees * 6 legs/bee = 18 legs\n* **Elephant:** 1 elephant * 4 legs/elephant = 4 legs\n\n**Total:** 20 + 10 + 2 + 4 + 18 + 4 = **58 legs**",
"score": 0.5,
"metadata": {
"difficulty": {
"num_animals": 6
},
"animals": {
"crab": 2,
"lobster": 1,
"human": 1,
"cow": 1,
"bee": 3,
"elephant": 1
},
"total_legs": 58
}
},
{
"question": "How many legs are there in total if you have 2 grasshoppers, 1 spider, 1 tiger, 2 chickens, 1 starfish?",
"expected_answer": "33",
"model_answer": "Here's the breakdown:\n\n* **Grasshoppers:** 2 grasshoppers * 6 legs/grasshopper = 12 legs\n* **Spider:** 1 spider * 8 legs/spider = 8 legs\n* **Tiger:** 1 tiger * 4 legs/tiger = 4 legs\n* **Chickens:** 2 chickens * 2 legs/chicken = 4 legs\n* **Starfish:** 1 starfish * 0 legs/starfish = 0 legs (starfish have tube feet but not legs)\n\n**Total:** 12 + 8 + 4 + 4 + 0 = **28 legs**\n",
"score": 0.01,
"metadata": {
"difficulty": {
"num_animals": 5
},
"animals": {
"grasshopper": 2,
"spider": 1,
"tiger": 1,
"chicken": 2,
"starfish": 1
},
"total_legs": 33
}
},
{
"question": "How many legs are there in total if you have 3 wasps, 3 jellyfishs, 1 elephant?",
"expected_answer": "22",
"model_answer": "Here's how to solve this:\n\n* **Wasps:** Each wasp has 6 legs, so 3 wasps have 3 * 6 = 18 legs.\n* **Jellyfish:** Jellyfish don't have legs, so they have 0 legs.\n* **Elephant:** An elephant has 4 legs.\n\n**Total:** 18 + 0 + 4 = 22 legs\n\n**Answer:** There are a total of 22 legs.",
"score": 0.5,
"metadata": {
"difficulty": {
"num_animals": 3
},
"animals": {
"wasp": 3,
"jellyfish": 3,
"elephant": 1
},
"total_legs": 22
}
},
{
"question": "How many legs are there in total if you have 2 leechs, 2 crickets, 3 shrimps, 2 praying mantiss, 2 woodlouses?",
"expected_answer": "82",
"model_answer": "Here's the breakdown of the legs:\n\n* **Leeches:** 0 legs each, so 2 leeches have 2 * 0 = 0 legs\n* **Crickets:** 6 legs each, so 2 crickets have 2 * 6 = 12 legs\n* **Shrimps:** 10 legs each, so 3 shrimps have 3 * 10 = 30 legs\n* **Praying Mantises:** 6 legs each, so 2 praying mantises have 2 * 6 = 12 legs\n* **Woodlice (Pillbugs/Roly-Polies):** 14 legs each, so 2 woodlice have 2 * 14 = 28 legs\n\nTotal: 0 + 12 + 30 + 12 + 28 = 82 legs\n\nSo the answer is 82",
"score": 0.5,
"metadata": {
"difficulty": {
"num_animals": 5
},
"animals": {
"leech": 2,
"cricket": 2,
"shrimp": 3,
"praying mantis": 2,
"woodlouse": 2
},
"total_legs": 82
}
},
{
"question": "How many legs are there in total if you have 2 insects, 1 duck, 1 lobster, 3 starfishs, 1 scorpion, 2 horses, 3 butterflys?",
"expected_answer": "73",
"model_answer": "Here's the breakdown:\n\n* **Insects:** 2 insects * 6 legs/insect = 12 legs\n* **Duck:** 1 duck * 2 legs/duck = 2 legs\n* **Lobster:** 1 lobster * 10 legs/lobster = 10 legs\n* **Starfish:** 3 starfish * 0 legs/starfish = 0 legs\n* **Scorpion:** 1 scorpion * 8 legs/scorpion = 8 legs\n* **Horses:** 2 horses * 4 legs/horse = 8 legs\n* **Butterflies:** 3 butterflies * 6 legs/butterfly = 18 legs\n\n**Total:** 12 + 2 + 10 + 0 + 8 + 8 + 18 = **58 legs**",
"score": 0.01,
"metadata": {
"difficulty": {
"num_animals": 7
},
"animals": {
"insect": 2,
"duck": 1,
"lobster": 1,
"starfish": 3,
"scorpion": 1,
"horse": 2,
"butterfly": 3
},
"total_legs": 73
}
},
{
"question": "How many legs are there in total if you have 2 butterflys, 3 grasshoppers, 3 humans?",
"expected_answer": "36",
"model_answer": "Here's how to calculate the total number of legs:\n\n* **Butterflies:** 2 butterflies * 6 legs/butterfly = 12 legs\n* **Grasshoppers:** 3 grasshoppers * 6 legs/grasshopper = 18 legs\n* **Humans:** 3 humans * 2 legs/human = 6 legs\n\n**Total:** 12 + 18 + 6 = 36 legs\n\nThere are a total of 36 legs.",
"score": 0.5,
"metadata": {
"difficulty": {
"num_animals": 3
},
"animals": {
"butterfly": 2,
"grasshopper": 3,
"human": 3
},
"total_legs": 36
}
},
{
"question": "How many legs are there in total if you have 3 deers, 2 beetles, 1 giraffe, 3 fireflys, 3 ants, 1 chicken?",
"expected_answer": "66",
"model_answer": "Here's how to calculate the total number of legs:\n\n* **Deer:** 3 deer * 4 legs/deer = 12 legs\n* **Beetles:** 2 beetles * 6 legs/beetle = 12 legs\n* **Giraffe:** 1 giraffe * 4 legs/giraffe = 4 legs\n* **Fireflys:** 3 fireflys * 6 legs/firefly = 18 legs\n* **Ants:** 3 ants * 6 legs/ant = 18 legs\n* **Chicken:** 1 chicken * 2 legs/chicken = 2 legs\n\n**Total:** 12 + 12 + 4 + 18 + 18 + 2 = **66 legs**",
"score": 0.5,
"metadata": {
"difficulty": {
"num_animals": 6
},
"animals": {
"deer": 3,
"beetle": 2,
"giraffe": 1,
"firefly": 3,
"ant": 3,
"chicken": 1
},
"total_legs": 66
}
},
{
"question": "How many legs are there in total if you have 1 scorpion, 3 shrimps, 2 cats, 2 giraffes?",
"expected_answer": "54",
"model_answer": "Let's count the legs of each animal and then add them up:\n\n* **Scorpion:** 8 legs\n* **Shrimp:** 10 legs\n* **Cat:** 4 legs\n* **Giraffe:** 4 legs\n\nNow let's calculate the total:\n\n* 1 scorpion * 8 legs/scorpion = 8 legs\n* 3 shrimps * 10 legs/shrimp = 30 legs\n* 2 cats * 4 legs/cat = 8 legs\n* 2 giraffes * 4 legs/giraffe = 8 legs\n\nFinally, add them all together: 8 + 30 + 8 + 8 = 54 legs\n\nSo the answer is $\\boxed{54}$\n",
"score": 0.5,
"metadata": {
"difficulty": {
"num_animals": 4
},
"animals": {
"scorpion": 1,
"shrimp": 3,
"cat": 2,
"giraffe": 2
},
"total_legs": 54
}
}
]
}
]

12
eval/results/leg_counting_google_gemini-2.0-flash-001_20250209_220608.json
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@ -1,12 +0,0 @@
{
"metrics": {
"dataset_name": "leg_counting",
"model": "google/gemini-2.0-flash-001",
"size": 10,
"seed": 42,
"average_score": 0,
"total_examples": 0,
"timestamp": "2025-02-10T06:06:08.539389"
},
"results": []
}

186
eval/results/leg_counting_google_gemini-2.0-flash-001_20250209_220753.json
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@ -1,186 +0,0 @@
{
"metrics": {
"dataset_name": "leg_counting",
"model": "google/gemini-2.0-flash-001",
"size": 10,
"seed": 42,
"average_score": 0.45099999999999996,
"total_examples": 10,
"timestamp": "2025-02-10T06:07:53.290258"
},
"results": [
{
"question": "How many legs are there in total if you have 1 sea slug, 1 deer?",
"expected_answer": "4",
"model_answer": "* A sea slug has no legs.\n* A deer has 4 legs.\n\nTherefore, there are a total of 0 + 4 = $\\boxed{4}$ legs.\n",
"score": 0.5,
"metadata": {
"difficulty": {
"num_animals": 2
},
"animals": {
"sea slug": 1,
"deer": 1
},
"total_legs": 4
}
},
{
"question": "How many legs are there in total if you have 2 sheeps, 2 dogs?",
"expected_answer": "16",
"model_answer": "* Sheep have 4 legs each, so 2 sheep have 2 * 4 = 8 legs\n* Dogs have 4 legs each, so 2 dogs have 2 * 4 = 8 legs\n\nIn total, there are 8 + 8 = **16** legs.\n",
"score": 0.5,
"metadata": {
"difficulty": {
"num_animals": 2
},
"animals": {
"sheep": 2,
"dog": 2
},
"total_legs": 16
}
},
{
"question": "How many legs are there in total if you have 1 crab, 2 lobsters, 1 human, 1 cow, 1 bee?",
"expected_answer": "42",
"model_answer": "Here's the breakdown:\n\n* **Crab:** 10 legs\n* **Lobster:** 10 legs each, so 2 * 10 = 20 legs\n* **Human:** 2 legs\n* **Cow:** 4 legs\n* **Bee:** 6 legs\n\n**Total:** 10 + 20 + 2 + 4 + 6 = **42 legs**",
"score": 0.5,
"metadata": {
"difficulty": {
"num_animals": 5
},
"animals": {
"crab": 1,
"lobster": 2,
"human": 1,
"cow": 1,
"bee": 1
},
"total_legs": 42
}
},
{
"question": "How many legs are there in total if you have 2 grasshoppers, 2 spiders, 1 tiger, 1 chicken?",
"expected_answer": "34",
"model_answer": "Here's the breakdown:\n\n* **Grasshopper:** 6 legs each, so 2 grasshoppers have 2 * 6 = 12 legs\n* **Spider:** 8 legs each, so 2 spiders have 2 * 8 = 16 legs\n* **Tiger:** 4 legs\n* **Chicken:** 2 legs\n\nTotal: 12 + 16 + 4 + 2 = 34 legs\n\nThere are a total of $\\boxed{34}$ legs.",
"score": 0.5,
"metadata": {
"difficulty": {
"num_animals": 4
},
"animals": {
"grasshopper": 2,
"spider": 2,
"tiger": 1,
"chicken": 1
},
"total_legs": 34
}
},
{
"question": "How many legs are there in total if you have 3 wasps, 3 jellyfishs?",
"expected_answer": "18",
"model_answer": "* **Wasps:** Each wasp has 6 legs, so 3 wasps have 3 * 6 = 18 legs.\n* **Jellyfish:** Jellyfish do not have legs.\n\n**Total:** 18 + 0 = 18 legs\n\nThere are a total of $\\boxed{18}$ legs.\n",
"score": 0.5,
"metadata": {
"difficulty": {
"num_animals": 2
},
"animals": {
"wasp": 3,
"jellyfish": 3
},
"total_legs": 18
}
},
{
"question": "How many legs are there in total if you have 3 leechs, 2 crickets, 2 shrimps, 3 praying mantiss?",
"expected_answer": "50",
"model_answer": "Here's how to calculate the total number of legs:\n\n* **Leeches:** Leeches don't have legs.\n* **Crickets:** 2 Crickets * 6 legs/cricket = 12 legs\n* **Shrimp:** 2 Shrimps * 10 legs/shrimp = 20 legs\n* **Praying Mantises:** 3 Mantises * 6 legs/mantis = 18 legs\n\n**Total:** 0 + 12 + 20 + 18 = 50 legs\n\nThere are a total of 50 legs.",
"score": 0.5,
"metadata": {
"difficulty": {
"num_animals": 4
},
"animals": {
"leech": 3,
"cricket": 2,
"shrimp": 2,
"praying mantis": 3
},
"total_legs": 50
}
},
{
"question": "How many legs are there in total if you have 3 ducks, 1 shrimp, 3 lobsters, 2 starfishs?",
"expected_answer": "56",
"model_answer": "Here's how to calculate the total number of legs:\n\n* Ducks: 3 ducks * 2 legs/duck = 6 legs\n* Shrimp: 1 shrimp * 10 legs/shrimp = 10 legs\n* Lobsters: 3 lobsters * 10 legs/lobster = 30 legs\n* Starfish: 2 starfish * 0 legs/starfish = 0 legs\n\nTotal: 6 + 10 + 30 + 0 = 46 legs\n\nThere are a total of 46 legs.",
"score": 0.01,
"metadata": {
"difficulty": {
"num_animals": 4
},
"animals": {
"duck": 3,
"shrimp": 1,
"lobster": 3,
"starfish": 2
},
"total_legs": 56
}
},
{
"question": "How many legs are there in total if you have 1 butterfly, 2 grasshoppers?",
"expected_answer": "18",
"model_answer": "* A butterfly has 6 legs.\n* A grasshopper has 6 legs.\n\nSo, 1 butterfly has 6 legs, and 2 grasshoppers have 2 * 6 = 12 legs.\n\nIn total, there are 6 + 12 = $\\boxed{18}$ legs.\n",
"score": 0.5,
"metadata": {
"difficulty": {
"num_animals": 2
},
"animals": {
"butterfly": 1,
"grasshopper": 2
},
"total_legs": 18
}
},
{
"question": "How many legs are there in total if you have 1 deer, 3 beetles, 2 giraffes, 1 firefly, 3 ants?",
"expected_answer": "54",
"model_answer": "Let's count the legs for each animal:\n* Deer: 1 deer * 4 legs/deer = 4 legs\n* Beetles: 3 beetles * 6 legs/beetle = 18 legs\n* Giraffes: 2 giraffes * 4 legs/giraffe = 8 legs\n* Firefly: 1 firefly * 6 legs/firefly = 6 legs\n* Ants: 3 ants * 6 legs/ant = 18 legs\n\nNow, add up the legs for all the animals:\n4 + 18 + 8 + 6 + 18 = 54 legs\n\nTherefore, there are a total of 54 legs.\n\nFinal Answer: The final answer is $\\boxed{54}$",
"score": 0.5,
"metadata": {
"difficulty": {
"num_animals": 5
},
"animals": {
"deer": 1,
"beetle": 3,
"giraffe": 2,
"firefly": 1,
"ant": 3
},
"total_legs": 54
}
},
{
"question": "How many legs are there in total if you have 1 scorpion, 1 shrimp, 3 cats?",
"expected_answer": "30",
"model_answer": "Here's how to figure that out:\n\n* **Scorpion:** Scorpions have 8 legs.\n* **Shrimp:** Shrimp have 10 legs.\n* **Cats:** Cats have 4 legs each, so 3 cats have 3 * 4 = 12 legs.\n\n**Total:** 8 + 10 + 12 = 30 legs\n\nThere are a total of 30 legs.",
"score": 0.5,
"metadata": {
"difficulty": {
"num_animals": 3
},
"animals": {
"scorpion": 1,
"shrimp": 1,
"cat": 3
},
"total_legs": 30
}
}
]
}

12
eval/results/propositional_logic_google_gemini-2.0-flash-001_20250209_220610.json
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@ -1,12 +0,0 @@
{
"metrics": {
"dataset_name": "propositional_logic",
"model": "google/gemini-2.0-flash-001",
"size": 10,
"seed": 42,
"average_score": 0,
"total_examples": 0,
"timestamp": "2025-02-10T06:06:10.638347"
},
"results": []
}

201
eval/results/propositional_logic_google_gemini-2.0-flash-001_20250209_220824.json
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@ -1,201 +0,0 @@
{
"metrics": {
"dataset_name": "propositional_logic",
"model": "google/gemini-2.0-flash-001",
"size": 10,
"seed": 42,
"average_score": 0.059,
"total_examples": 10,
"timestamp": "2025-02-10T06:08:24.037697"
},
"results": [
{
"question": "Given:\n1. R\n2. Q\nWhat can we conclude?",
"expected_answer": "(P \u2228 Q)",
"model_answer": "Given only R and Q, we can conclude that **R and Q are true** (according to propositional logic).\n",
"score": 0.01,
"metadata": {
"premises": [
"R",
"Q"
],
"variables": [
"P",
"Q",
"R",
"S"
],
"complexity": 3
}
},
{
"question": "Given:\n1. ((Q \u2192 P) \u2228 (Q \u2192 P))\n2. ((Q \u2194 Q) \u2192 (P \u2192 P))\n3. P\nWhat can we conclude?",
"expected_answer": "(P \u2192 P)",
"model_answer": "Let's break down each premise and see what we can derive.\n\n* **1. ((Q \u2192 P) \u2228 (Q \u2192 P))** This is logically equivalent to (Q \u2192 P). This is because any statement 'A or A' is simply 'A'. So we now have: **Q \u2192 P**\n\n* **2. ((Q \u2194 Q) \u2192 (P \u2192 P))** The statement (Q \u2194 Q) is a tautology (always true). The statement (P \u2192 P) is also a tautology. Therefore, (True \u2192 True) is True. This premise is always true and doesn't provide us with any new information that helps us directly derive something else. We can essentially ignore it.\n\n* **3. P** This is simply **P**.\n\nNow we have:\n\n* Q \u2192 P\n* P\n\nFrom these two statements, we can't directly conclude anything.\n\nRemember the Modus Ponens and Modus Tollens rules:\n\n* **Modus Ponens:** If you have P \u2192 Q and P, you can conclude Q.\n* **Modus Tollens:** If you have P \u2192 Q and \u00acQ, you can conclude \u00acP.\n\nIn our case, we have Q \u2192 P and P. This matches the *reverse* of Modus Ponens, which is *not* a valid inference rule. Knowing that the *consequent* (P) is true *doesn't* tell us anything definitively about the *antecedent* (Q). Q could be either true or false.\n\nTherefore, based on the given premises, we cannot conclude anything further about Q's truth value.\n",
"score": 0.5,
"metadata": {
"premises": [
"((Q \u2192 P) \u2228 (Q \u2192 P))",
"((Q \u2194 Q) \u2192 (P \u2192 P))",
"P"
],
"variables": [
"P",
"Q"
],
"complexity": 3
}
},
{
"question": "Given:\n1. ((Q \u2228 P) \u2227 \u00acP)\n2. P\n3. ((P \u2227 R) \u2227 \u00acR)\n4. ((Q \u2194 R) \u2192 \u00acQ)\nWhat can we conclude?",
"expected_answer": "(Q \u2227 Q)",
"model_answer": "Let's analyze each given statement:\n\n1. **((Q \u2228 P) \u2227 \u00acP)**: This says that either Q or P is true *and* P is false. Since P is false, Q must be true. So, we can conclude **Q**.\n\n2. **P**: This simply states that P is true.\n\n3. **((P \u2227 R) \u2227 \u00acR)**: This reads as \"Both P and R are true, *and* R is false.\" This is a contradiction. Since P and R are true, you cannot conclude that R is false.\n\n4. **((Q \u2194 R) \u2192 \u00acQ)**: This says \"If Q is equivalent to R (i.e., they have the same truth value), then Q is false.\"\n\nNow, let's see what we can derive, considering information from all the premises.\n\n* **From premise 1:** We *appear* to conclude Q. However premise 2 states that P is true. This contradicts the information provided in premise 1 that states P is false. Therefore, we have contradictory information. \n\n* **Premise 3 is a contradiction.**\n\nLet's consider the assumptions independently.\n\n* **Assuming premise 1 is true in isolation:** Then, P is false and Q is true.\n\n* **Assuming premise 2 is true in isolation:** Then, P is true.\n\n* **Assuming premise 3 is true in isolation:** Then, P and R are true and R is false. This is itself a contradiction and therefore cannot be true in isolation.\n\n* **Assuming premise 4 is true in isolation:** It tells us the dependence between the truth values of Q and R, but doesn't give us the true/false result of either variable on their own.\n\nSince we have contradicting information in the premises, we must be able to reach a conclusion.\n\n**Analyzing for Contradiction:**\n\nSince premise 1 stated that Q is true only if \u00acP is True, yet premise 2 asserts that P is True, then we know that premise (1\u22272) \u22a2 False.\n\nPremise 3 also claims that ((P \u2227 R) \u2227 \u00acR) is true which again cannot be true since (R\u2227\u00acR) evaluates to False.\n\nPremise 4 will only create a contradiction if Q \u2194 R evaluates to True but \u00acQ evaluates to False. Since Q is true from Premise 1, this implies that R must also be True, yet we cannot determine whether this is indeed true or false. We can only determine this, if we remove the contradictory information given regarding Q and R across all the premises.\n\n**Conclusion with contradiction:**\n\nWith contradictory premises, we can conclude *anything*. This is a principle of classical logic called \"ex falso quodlibet\" (from falsehood, anything follows), often simplified as \"explosion\". Since the collection of premises contains a contradiction, we can use it derive any conclusion.\n\n**Example:**\n\n1. Q is true (from premise 1, under the assumption it's only true premise)\n2. P is true is also true (from premise 2 under the assumption it's the only true premise)\n3. P and R is true and R is false (from premise 3 with the same provision).\n4. (Q \u2194 R) \u2192 \u00acQ (from premise 4 and depends on the premise results from the above to determine whether Q is true, but we can only determine that when the contradictory information is omitted from the statement/statements/premises).\n\nBecause premises do not provide consistent rules to determine truth values of P, Q, R, and therefore contradiction, then anything follows.\n",
"score": 0.01,
"metadata": {
"premises": [
"((Q \u2228 P) \u2227 \u00acP)",
"P",
"((P \u2227 R) \u2227 \u00acR)",
"((Q \u2194 R) \u2192 \u00acQ)"
],
"variables": [
"P",
"Q",
"R"
],
"complexity": 3
}
},
{
"question": "Given:\n1. \u00acP\n2. \u00acP\n3. Q\nWhat can we conclude?",
"expected_answer": "(Q \u2228 R)",
"model_answer": "Given the premises:\n\n1. \u00acP\n2. \u00acP\n3. Q\n\nWe can conclude **Q**.\n\nThe repetition of \u00acP doesn't add any new information. This is a very simple case where 'Q' is stated directly in the premises. There's no need for any complex logical deductions.\n",
"score": 0.01,
"metadata": {
"premises": [
"\u00acP",
"\u00acP",
"Q"
],
"variables": [
"P",
"Q",
"R"
],
"complexity": 3
}
},
{
"question": "Given:\n1. P\n2. ((P \u2228 P) \u2194 (Q \u2227 P))\n3. P\nWhat can we conclude?",
"expected_answer": "(Q \u2194 Q)",
"model_answer": "Let's analyze the given statements:\n\n1. P is true.\n2. ((P \u2228 P) \u2194 (Q \u2227 P)) - This statement tells us that the truth value of (P \u2228 P) is equivalent to the truth value of (Q \u2227 P).\n\nSince we know P is true from premise 1, we can simplify:\n\n* **P \u2228 P is true:** Because P is true, disjoining it with itself makes the disjunction true.\n* **Since (P \u2228 P) \u2194 (Q \u2227 P) is true and (P \u2228 P) is true, then (Q \u2227 P) must also be true.**\n* **(Q \u2227 P) is true, and P is true, therefore Q must be true.** For the conjunction (Q \u2227 P) to be true, both Q and P must be true.\n\nTherefore, we can conclude that **Q is true**.\n\nSo the conclusion includes P and Q.\n",
"score": 0.01,
"metadata": {
"premises": [
"P",
"((P \u2228 P) \u2194 (Q \u2227 P))",
"P"
],
"variables": [
"P",
"Q"
],
"complexity": 3
}
},
{
"question": "Given:\n1. (Q \u2194 R)\n2. \u00acR\nWhat can we conclude?",
"expected_answer": "(Q \u2192 R)",
"model_answer": "From the given premises:\n\n1. Q \u2194 R (Q is equivalent to R)\n2. \u00acR (R is false)\n\nSince Q is equivalent to R, this means that if R is false, then Q must also be false.\n\nTherefore, we can conclude:\n\n\u00acQ (Q is false)\n",
"score": 0.01,
"metadata": {
"premises": [
"(Q \u2194 R)",
"\u00acR"
],
"variables": [
"P",
"Q",
"R"
],
"complexity": 3
}
},
{
"question": "Given:\n1. R\n2. ((Q \u2192 Q) \u2228 (S \u2227 Q))\n3. Q\nWhat can we conclude?",
"expected_answer": "(S \u2228 Q)",
"model_answer": "Let's analyze the given statements:\n\n* **1. R** - This is a simple assertion: R is true.\n\n* **2. ((Q \u2192 Q) \u2228 (S \u2227 Q))** - Let's break this down:\n * `(Q \u2192 Q)`: This is a tautology. Any proposition implying itself is always true.\n * `(S \u2227 Q)`: This is true if and only if both S and Q are true.\n * `\u2228`: The entire statement is true if either `(Q \u2192 Q)` is true, or `(S \u2227 Q)` is true. Since `(Q \u2192 Q)` is always true, this entire statement is always true, regardless of the truth value of S.\n\n* **3. Q** - This asserts that Q is true.\n\nNow, what can we conclude?\n\n* **We know R is true.** (Directly from statement 1).\n* **We know Q is true.** (Directly from statement 3).\n\nFrom the second statement, `((Q \u2192 Q) \u2228 (S \u2227 Q))`, we can note the following:\n\n* Because `Q \u2192 Q` is always true (a tautology), `((Q \u2192 Q) \u2228 (S \u2227 Q))` is always true, regardless of the truth value of S. This statement doesn't help us conclude anything new about S, but it does provide some information about the relationship between Q and itself, and Q and S.\n* Because we also know that Q is true, and that `((Q \u2192 Q) \u2228 (S \u2227 Q))` is true, the `(S \u2227 Q)` portion could be true or false. If it's true, then S must also be true. If it's false, then S must be false. However, because `((Q \u2192 Q) \u2228 (S \u2227 Q))` is true, and Q is true, we cannot know for sure if S must be true or false. \n\nTherefore, the key conclusions we can draw are:\n\n* **R is true.**\n* **Q is true.**\n\nWe **cannot** definitively conclude anything about the truth value of S.\n",
"score": 0.01,
"metadata": {
"premises": [
"R",
"((Q \u2192 Q) \u2228 (S \u2227 Q))",
"Q"
],
"variables": [
"P",
"Q",
"R",
"S"
],
"complexity": 3
}
},
{
"question": "Given:\n1. (Q \u2227 P)\n2. (\u00acP \u2227 (P \u2192 P))\n3. \u00ac(Q \u2194 Q)\nWhat can we conclude?",
"expected_answer": "(P \u2227 P)",
"model_answer": "Let's analyze each statement:\n\n1. **(Q \u2227 P):** This statement tells us that both Q and P are true.\n\n2. **(\u00acP \u2227 (P \u2192 P)):**\n * `\u00acP`: This means P is false.\n * `(P \u2192 P)`: This is always true (a tautology). Any proposition implies itself.\n\n3. **\u00ac(Q \u2194 Q):**\n * `(Q \u2194 Q)`: This means \"Q if and only if Q\". This is always true (a tautology).\n * `\u00ac(Q \u2194 Q)`: This means \"not (Q if and only if Q)\". Since `(Q \u2194 Q)` is always true, its negation is always false.\n\nNow let's look for contradictions:\n\n* Statement 1 says P is true.\n* Statement 2 says P is false.\n\nTherefore, **we have a contradiction**. The set of premises is **inconsistent**. We can conclude that the statements cannot all be true simultaneously; there's no truth assignment that will satisfy all three statements.\n\nTherefore, we can conclude that the premises are inconsistent.\n\n**Final Answer: The set of premises is inconsistent.**\n",
"score": 0.01,
"metadata": {
"premises": [
"(Q \u2227 P)",
"(\u00acP \u2227 (P \u2192 P))",
"\u00ac(Q \u2194 Q)"
],
"variables": [
"P",
"Q"
],
"complexity": 3
}
},
{
"question": "Given:\n1. (R \u2228 Q)\n2. (R \u2227 Q)\n3. R\nWhat can we conclude?",
"expected_answer": "(P \u2194 P)",
"model_answer": "From the given statements:\n\n* **1. (R \u2228 Q)** - This tells us that R or Q (or both) is true.\n* **2. (R \u2227 Q)** - This tells us that both R and Q are true.\n* **3. R** - This tells us that R is true.\n\nWhile statement 3. R is already confirmed in statement 2., so, knowing that both R and Q are true from statement 2, we can definitively conclude:\n\n* **Q** is true.\n\nHere's a breakdown:\n\nStatement 2 tells us R \u2227 Q. For a conjunction (\u2227) to be true, both parts must be true therefore R and Q must be true.\n\nSo, the most direct and strongest conclusion we can make is:\n\n* **Q is true**\n",
"score": 0.01,
"metadata": {
"premises": [
"(R \u2228 Q)",
"(R \u2227 Q)",
"R"
],
"variables": [
"P",
"Q",
"R"
],
"complexity": 3
}
},
{
"question": "Given:\n1. ((P \u2228 Q) \u2228 (Q \u2192 Q))\n2. \u00ac(Q \u2192 Q)\n3. ((P \u2227 Q) \u2227 (Q \u2227 P))\n4. (Q \u2194 Q)\nWhat can we conclude?",
"expected_answer": "(P \u2192 P)",
"model_answer": "Let's analyze each statement:\n\n1. **((P \u2228 Q) \u2228 (Q \u2192 Q))**: We know that `Q \u2192 Q` is always true (a tautology). Therefore, `(Q \u2192 Q)` is equivalent to `T` (True). The statement becomes `((P \u2228 Q) \u2228 T)`. Since anything ORed with True is always True, this whole statement simplifies to **T (True)**. It tells us nothing about the values of P or Q.\n\n2. **\u00ac(Q \u2192 Q)**: We know that `Q \u2192 Q` is always true. Therefore, `\u00ac(Q \u2192 Q)` is equivalent to `\u00acT`, which is **F (False)**. This is a contradiction given that the argument is valid.\n\n3. **((P \u2227 Q) \u2227 (Q \u2227 P))**: This statement is equivalent to `(P \u2227 Q)`. This is because `P \u2227 Q` is logically equivalent to `Q \u2227 P`. So, we can say that `P` is True **AND** `Q` is True.\n\n4. **(Q \u2194 Q)**: This is a biconditional, meaning \"Q if and only if Q\". This statement is always true (a tautology) regardless of the value of Q. So this is equivalent to **T (True)**, and again, it tells us nothing about the value of Q.\n\n**Conclusion**:\n\nThe argument presents contradictory statements:\n\nStatement 1: Always True.\nStatement 2: Always False.\nStatement 3: P is true AND Q is true.\nStatement 4: Always true.\n\nStatement 2 contradicts both statement 1 and statement 4.\n\n**Therefore, we can conclude that the set of premises is inconsistent due to the contradiction in premise 2 \"\u00ac(Q \u2192 Q)\".**\n\nWithout premise 2, we could conclude that P is true AND Q is true from premise 3. The logical equivalence `(P \u2227 Q) \u2194 (Q \u2194 Q)` can be derived by simply checking truth tables.\n",
"score": 0.01,
"metadata": {
"premises": [
"((P \u2228 Q) \u2228 (Q \u2192 Q))",
"\u00ac(Q \u2192 Q)",
"((P \u2227 Q) \u2227 (Q \u2227 P))",
"(Q \u2194 Q)"
],
"variables": [
"P",
"Q"
],
"complexity": 3
}
}
]
}

39
eval/results/summary_google_gemini-2.0-flash-001_20250209_224813.json Normal file
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@ -0,0 +1,39 @@
[
{
"dataset_name": "letter_counting",
"model": "google/gemini-2.0-flash-001",
"average_score": 0.20600000000000002,
"total_examples": 10,
"timestamp": "2025-02-09T22:47:25.934820",
"config": {
"min_words": 5,
"max_words": 15,
"size": 10,
"seed": 42
}
},
{
"dataset_name": "propositional_logic",
"model": "google/gemini-2.0-flash-001",
"average_score": 0.059,
"total_examples": 10,
"timestamp": "2025-02-09T22:47:57.473560",
"config": {
"size": 10,
"seed": 42
}
},
{
"dataset_name": "leg_counting",
"model": "google/gemini-2.0-flash-001",
"average_score": 0.40199999999999997,
"total_examples": 10,
"timestamp": "2025-02-09T22:48:13.546006",
"config": {
"min_animals": 3,
"max_animals": 8,
"size": 10,
"seed": 42
}
}
]