question_id stringlengths 22 24 | split stringclasses 3
values | domain stringclasses 1
value | task stringclasses 1
value | prompt stringlengths 308 347 | model_response stringlengths 244 577 | extracted_answer stringclasses 2
values | ground_truth stringclasses 2
values | correct bool 1
class | finish_reason stringclasses 1
value | token_count int64 86 214 |
|---|---|---|---|---|---|---|---|---|---|---|
formal_logic_test_3000 | test | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ¬(((Q → R) ∨ P ∧ Q))
Given: P=True, Q=False, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ¬(((Q → R) ∨ P ∧ Q))
Given: P=True, Q=False, R=True
Step 1: Evaluate next level
Q → R = False → True = True
P ∧ Q = True ∧ False = False
Step 2: Evaluate innermost subexpressions
Q → R ∨ P ∧ Q = True ∨ False = True
Step 3: Final negation
¬((Q → R) ∨ P ∧ Q) = ¬True = False
</think>
An... | False | False | true | stop | 121 |
formal_logic_test_3001 | test | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ↔ R ∧ (P ∧ Q))
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R ↔ R ∧ (P ∧ Q))
Given: P=True, Q=True, R=True
Step 1: Evaluate next level
P ∧ Q = True ∧ True = True
Step 2: Evaluate innermost subexpressions
R ∧ P ∧ Q = True ∧ True = True
Step 3: Final biconditional
R ↔ R ∧ (P ∧ Q) = True ↔ True = True
</think>
Answer: True | True | True | true | stop | 104 |
formal_logic_test_3002 | test | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ∨ (Q ∨ R ∨ P ∧ P))
Given: P=True, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R ∨ (Q ∨ R ∨ P ∧ P))
Given: P=True, Q=True, R=False
Step 1: Evaluate next level
Q ∨ R = True ∨ False = True
P ∧ P = True ∧ True = True
Step 2: Evaluate innermost subexpressions
Q ∨ R ∨ P ∧ P = True ∨ True = True
Step 3: Final disjunction
R ∨ Q ∨ R ∨ P ∧ P = False ∨ True = True
</thin... | True | True | true | stop | 129 |
formal_logic_test_3003 | test | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ∧ (Q ∧ P) → R)
Given: P=True, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P ∧ (Q ∧ P) → R)
Given: P=True, Q=False, R=False
Step 1: Evaluate next level
Q ∧ P = False ∧ True = False
Step 2: Evaluate innermost subexpressions
P ∧ Q ∧ P = True ∧ False = False
Step 3: Final implication
P ∧ (Q ∧ P) → R = False → False = True
</think>
Answer: True | True | True | true | stop | 102 |
formal_logic_test_3004 | test | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((Q → R ∨ Q ↔ R) ∧ P)
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((Q → R ∨ Q ↔ R) ∧ P)
Given: P=True, Q=True, R=True
Step 1: Evaluate next level
R ∨ Q = True ∨ True = True
Step 2: Evaluate innermost subexpressions
Q → R ∨ Q = True → True = True
Step 3: Evaluate next level
Q → R ∨ Q ↔ R = True ↔ True = True
Step 4: Final conjunction
Q → R ∨ Q ↔ R ∧ ... | True | True | true | stop | 132 |
formal_logic_test_3005 | test | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (¬Q → R ∧ P)
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (¬Q → R ∧ P)
Given: P=True, Q=True, R=True
Step 1: Evaluate atomic negations
¬Q = ¬True = False
Step 2: Evaluate innermost subexpressions
R ∧ P = True ∧ True = True
Step 3: Final implication
¬Q → R ∧ P = False → True = True
</think>
Answer: True | True | True | true | stop | 93 |
formal_logic_test_3006 | test | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ↔ (¬Q → P) ∧ R)
Given: P=False, Q=False, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R ↔ (¬Q → P) ∧ R)
Given: P=False, Q=False, R=True
Step 1: Evaluate atomic negations
¬Q = ¬False = True
Step 2: Evaluate innermost subexpressions
¬Q → P = True → False = False
Step 3: Evaluate next level
¬Q → P ∧ R = False ∧ True = False
Step 4: Final biconditional
R ↔ (¬Q → P) ∧ R = ... | False | False | true | stop | 127 |
formal_logic_test_3007 | test | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ∧ ¬((R ∨ Q)))
Given: P=True, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P ∧ ¬((R ∨ Q)))
Given: P=True, Q=True, R=False
Step 1: Evaluate next level
R ∨ Q = False ∨ True = True
Step 2: Evaluate innermost subexpressions
¬(R ∨ Q) = ¬True = False
Step 3: Final conjunction
P ∧ ¬((R ∨ Q)) = True ∧ False = False
</think>
Answer: False | False | False | true | stop | 104 |
formal_logic_test_3008 | test | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ∨ Q → (P ↔ R ∨ P))
Given: P=True, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P ∨ Q → (P ↔ R ∨ P))
Given: P=True, Q=True, R=False
Step 1: Evaluate next level
P ∨ Q = True ∨ True = True
R ∨ P = False ∨ True = True
Step 2: Evaluate innermost subexpressions
P ↔ R ∨ P = True ↔ True = True
Step 3: Final implication
P ∨ Q → P ↔ R ∨ P = True → True = True
</think>
A... | True | True | true | stop | 123 |
formal_logic_test_3009 | test | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ¬((Q ∨ R → (P ↔ R)))
Given: P=True, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ¬((Q ∨ R → (P ↔ R)))
Given: P=True, Q=False, R=False
Step 1: Evaluate next level
Q ∨ R = False ∨ False = False
P ↔ R = True ↔ False = False
Step 2: Evaluate innermost subexpressions
Q ∨ R → P ↔ R = False → False = True
Step 3: Final negation
¬(Q ∨ R → (P ↔ R)) = ¬True = False
</think>... | False | False | true | stop | 122 |
formal_logic_test_3010 | test | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ↔ Q → (P ↔ P))
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R ↔ Q → (P ↔ P))
Given: P=True, Q=True, R=True
Step 1: Evaluate next level
P ↔ P = True ↔ True = True
Step 2: Evaluate innermost subexpressions
Q → P ↔ P = True → True = True
Step 3: Final biconditional
R ↔ Q → (P ↔ P) = True ↔ True = True
</think>
Answer: True | True | True | true | stop | 104 |
formal_logic_test_3011 | test | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((¬P ∨ (R → Q)) ∧ R)
Given: P=False, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ((¬P ∨ (R → Q)) ∧ R)
Given: P=False, Q=False, R=False
Step 1: Evaluate atomic negations
¬P = ¬False = True
Step 2: Evaluate innermost subexpressions
R → Q = False → False = True
Step 3: Evaluate next level
¬P ∨ R → Q = True ∨ True = True
Step 4: Final conjunction
¬P ∨ (R → Q) ∧ R = Tr... | False | False | true | stop | 127 |
formal_logic_test_3012 | test | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((R → Q) ∧ (P ∨ Q) ↔ R)
Given: P=False, Q=False, R=True<|im_end|>
<|im_start|>assistant... | <think>
Problem: Evaluate ((R → Q) ∧ (P ∨ Q) ↔ R)
Given: P=False, Q=False, R=True
Step 1: Evaluate next level
R → Q = True → False = False
P ∨ Q = False ∨ False = False
Step 2: Evaluate innermost subexpressions
R → Q ∧ P ∨ Q = False ∧ False = False
Step 3: Final biconditional
(R → Q) ∧ (P ∨ Q) ↔ R = False ↔ Tr... | False | False | true | stop | 130 |
formal_logic_test_3013 | test | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ∧ P ∧ (R → Q))
Given: P=True, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P ∧ P ∧ (R → Q))
Given: P=True, Q=True, R=False
Step 1: Evaluate next level
P ∧ P = True ∧ True = True
R → Q = False → True = True
Step 2: Final conjunction
P ∧ P ∧ R → Q = True ∧ True = True
</think>
Answer: True | True | True | true | stop | 86 |
formal_logic_test_3014 | test | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ¬((P ∨ (Q ∨ P ∨ R)))
Given: P=True, Q=False, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ¬((P ∨ (Q ∨ P ∨ R)))
Given: P=True, Q=False, R=True
Step 1: Evaluate next level
Q ∨ P = False ∨ True = True
Step 2: Evaluate innermost subexpressions
Q ∨ P ∨ R = True ∨ True = True
Step 3: Evaluate next level
P ∨ Q ∨ P ∨ R = True ∨ True = True
Step 4: Final negation
¬(P ∨ (Q ∨ P ∨ R))... | False | False | true | stop | 142 |
formal_logic_test_3015 | test | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ¬(((R ↔ Q) → P ↔ Q))
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ¬(((R ↔ Q) → P ↔ Q))
Given: P=True, Q=True, R=True
Step 1: Evaluate next level
R ↔ Q = True ↔ True = True
Step 2: Evaluate innermost subexpressions
R ↔ Q → P = True → True = True
Step 3: Evaluate next level
(R ↔ Q) → P ↔ Q = True ↔ True = True
Step 4: Final negation
¬((R ↔ Q) → P ↔ Q)... | False | False | true | stop | 129 |
formal_logic_test_3016 | test | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P → R ↔ P ↔ ¬Q)
Given: P=True, Q=False, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (P → R ↔ P ↔ ¬Q)
Given: P=True, Q=False, R=False
Step 1: Evaluate atomic negations
¬Q = ¬False = True
Step 2: Evaluate innermost subexpressions
P → R = True → False = False
Step 3: Evaluate next level
P → R ↔ P = False ↔ True = False
Step 4: Final biconditional
P → R ↔ P ↔ ¬Q = False ... | False | False | true | stop | 121 |
formal_logic_test_3017 | test | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R → P → R ∨ Q)
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (R → P → R ∨ Q)
Given: P=True, Q=True, R=True
Step 1: Evaluate next level
R → P = True → True = True
R ∨ Q = True ∨ True = True
Step 2: Final implication
R → P → R ∨ Q = True → True = True
</think>
Answer: True | True | True | true | stop | 89 |
formal_logic_test_3018 | test | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (¬((R → Q)) ↔ Q ∨ P)
Given: P=False, Q=True, R=False<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate (¬((R → Q)) ↔ Q ∨ P)
Given: P=False, Q=True, R=False
Step 1: Evaluate next level
R → Q = False → True = True
Q ∨ P = True ∨ False = True
Step 2: Evaluate innermost subexpressions
¬(R → Q) = ¬True = False
Step 3: Final biconditional
¬((R → Q)) ↔ Q ∨ P = False ↔ True = False
</think>
A... | False | False | true | stop | 122 |
formal_logic_test_3019 | test | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ¬(((Q ↔ R) ∧ R ∨ P))
Given: P=True, Q=True, R=True<|im_end|>
<|im_start|>assistant
| <think>
Problem: Evaluate ¬(((Q ↔ R) ∧ R ∨ P))
Given: P=True, Q=True, R=True
Step 1: Evaluate next level
Q ↔ R = True ↔ True = True
Step 2: Evaluate innermost subexpressions
Q ↔ R ∧ R = True ∧ True = True
Step 3: Evaluate next level
(Q ↔ R) ∧ R ∨ P = True ∨ True = True
Step 4: Final negation
¬((Q ↔ R) ∧ R ∨ P)... | False | False | true | stop | 133 |
formal_logic_harder_7500 | harder | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (Q ∧ (P ∨ R) ∧ (¬S ↔ S))
Given: P=True, Q=True, R=True, S=False<|im_end|>
<|im_start|>a... | <think>
Problem: Evaluate (Q ∧ (P ∨ R) ∧ (¬S ↔ S))
Given: P=True, Q=True, R=True, S=False
Step 1: Evaluate atomic negations
¬S = ¬False = True
Step 2: Evaluate innermost subexpressions
P ∨ R = True ∨ True = True
Step 3: Evaluate next level
Q ∧ P ∨ R = True ∧ True = True
Step 4: Evaluate next level
¬S ↔ S = Tru... | False | False | true | stop | 155 |
formal_logic_harder_7501 | harder | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((S ∨ P ↔ Q) ∨ (R ↔ S) ∧ (P ↔ Q))
Given: P=True, Q=True, R=False, S=True<|im_end|>
<|im... | <think>
Problem: Evaluate ((S ∨ P ↔ Q) ∨ (R ↔ S) ∧ (P ↔ Q))
Given: P=True, Q=True, R=False, S=True
Step 1: Evaluate next level
S ∨ P = True ∨ True = True
P ↔ Q = True ↔ True = True
Step 2: Evaluate innermost subexpressions
R ↔ S = False ↔ True = False
Step 3: Evaluate next level
R ↔ S ∧ P ↔ Q = False ∧ True = ... | True | True | true | stop | 161 |
formal_logic_harder_7502 | harder | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ∨ (Q → S) ↔ P ∧ S)
Given: P=False, Q=False, R=True, S=False<|im_end|>
<|im_start|>as... | <think>
Problem: Evaluate (R ∨ (Q → S) ↔ P ∧ S)
Given: P=False, Q=False, R=True, S=False
Step 1: Evaluate next level
Q → S = False → False = True
P ∧ S = False ∧ False = False
Step 2: Evaluate innermost subexpressions
R ∨ Q → S = True ∨ True = True
Step 3: Final biconditional
R ∨ (Q → S) ↔ P ∧ S = True ↔ False... | False | False | true | stop | 127 |
formal_logic_harder_7503 | harder | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ¬((((S ↔ R) → Q) ∨ P))
Given: P=True, Q=True, R=True, S=True<|im_end|>
<|im_start|>assi... | <think>
Problem: Evaluate ¬((((S ↔ R) → Q) ∨ P))
Given: P=True, Q=True, R=True, S=True
Step 1: Evaluate next level
S ↔ R = True ↔ True = True
Step 2: Evaluate innermost subexpressions
S ↔ R → Q = True → True = True
Step 3: Evaluate next level
(S ↔ R) → Q ∨ P = True ∨ True = True
Step 4: Final negation
¬(((S ↔ ... | False | False | true | stop | 138 |
formal_logic_harder_7504 | harder | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (Q ↔ R ∧ (S ∨ (S ∨ P ↔ P)))
Given: P=False, Q=True, R=False, S=False<|im_end|>
<|im_sta... | <think>
Problem: Evaluate (Q ↔ R ∧ (S ∨ (S ∨ P ↔ P)))
Given: P=False, Q=True, R=False, S=False
Step 1: Evaluate next level
S ∨ P = False ∨ False = False
Step 2: Evaluate innermost subexpressions
S ∨ P ↔ P = False ↔ False = True
Step 3: Evaluate next level
S ∨ S ∨ P ↔ P = False ∨ True = True
Step 4: Final conjunc... | False | False | true | stop | 178 |
formal_logic_harder_7505 | harder | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (Q ∧ R → S ↔ R ∨ Q → P)
Given: P=False, Q=True, R=True, S=False<|im_end|>
<|im_start|>a... | <think>
Problem: Evaluate (Q ∧ R → S ↔ R ∨ Q → P)
Given: P=False, Q=True, R=True, S=False
Step 1: Evaluate next level
Q ∧ R = True ∧ True = True
R ∨ Q = True ∨ True = True
Step 2: Evaluate innermost subexpressions
Q ∧ R → S = True → False = False
Step 3: Evaluate next level
Q ∧ R → S ↔ R ∨ Q = False ↔ True = F... | True | True | true | stop | 150 |
formal_logic_harder_7506 | harder | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (((Q ↔ P) ∨ S ↔ R) → Q)
Given: P=False, Q=True, R=True, S=False<|im_end|>
<|im_start|>a... | <think>
Problem: Evaluate (((Q ↔ P) ∨ S ↔ R) → Q)
Given: P=False, Q=True, R=True, S=False
Step 1: Evaluate next level
Q ↔ P = True ↔ False = False
Step 2: Evaluate innermost subexpressions
Q ↔ P ∨ S = False ∨ False = False
Step 3: Evaluate next level
(Q ↔ P) ∨ S ↔ R = False ↔ True = False
Step 4: Final implicati... | True | True | true | stop | 139 |
formal_logic_harder_7507 | harder | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ¬((S → R → Q ∨ (S → P)))
Given: P=True, Q=False, R=True, S=False<|im_end|>
<|im_start|>... | <think>
Problem: Evaluate ¬((S → R → Q ∨ (S → P)))
Given: P=True, Q=False, R=True, S=False
Step 1: Evaluate next level
S → R = False → True = True
S → P = False → True = True
Step 2: Evaluate innermost subexpressions
Q ∨ S → P = False ∨ True = True
Step 3: Evaluate next level
S → R → Q ∨ (S → P) = True → True ... | False | False | true | stop | 154 |
formal_logic_harder_7508 | harder | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (¬P → S ∨ (¬R → Q → P))
Given: P=True, Q=False, R=True, S=False<|im_end|>
<|im_start|>a... | <think>
Problem: Evaluate (¬P → S ∨ (¬R → Q → P))
Given: P=True, Q=False, R=True, S=False
Step 1: Evaluate atomic negations
¬P = ¬True = False
¬R = ¬True = False
Step 2: Evaluate innermost subexpressions
¬R → Q = False → False = True
Step 3: Evaluate next level
¬R → Q → P = True → True = True
Step 4: Evaluate ... | True | True | true | stop | 169 |
formal_logic_harder_7509 | harder | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (Q ∧ (P → P) ∧ S ∧ (R ↔ S))
Given: P=False, Q=False, R=False, S=True<|im_end|>
<|im_sta... | <think>
Problem: Evaluate (Q ∧ (P → P) ∧ S ∧ (R ↔ S))
Given: P=False, Q=False, R=False, S=True
Step 1: Evaluate next level
P → P = False → False = True
R ↔ S = False ↔ True = False
Step 2: Evaluate innermost subexpressions
Q ∧ P → P = False ∧ True = False
Step 3: Evaluate next level
Q ∧ (P → P) ∧ S = False ∧ T... | False | False | true | stop | 150 |
formal_logic_harder_7510 | harder | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((R ↔ Q) ∧ (P → Q) ↔ (S ↔ Q ↔ Q))
Given: P=False, Q=False, R=True, S=True<|im_end|>
<|i... | <think>
Problem: Evaluate ((R ↔ Q) ∧ (P → Q) ↔ (S ↔ Q ↔ Q))
Given: P=False, Q=False, R=True, S=True
Step 1: Evaluate next level
R ↔ Q = True ↔ False = False
P → Q = False → False = True
S ↔ Q = True ↔ False = False
Step 2: Evaluate innermost subexpressions
S ↔ Q ↔ Q = False ↔ False = True
Step 3: Evaluate next... | False | False | true | stop | 169 |
formal_logic_harder_7511 | harder | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ¬((P ∧ (Q → R) → S))
Given: P=False, Q=False, R=True, S=True<|im_end|>
<|im_start|>assi... | <think>
Problem: Evaluate ¬((P ∧ (Q → R) → S))
Given: P=False, Q=False, R=True, S=True
Step 1: Evaluate next level
Q → R = False → True = True
Step 2: Evaluate innermost subexpressions
P ∧ Q → R = False ∧ True = False
Step 3: Evaluate next level
P ∧ (Q → R) → S = False → True = True
Step 4: Final negation
¬(P ... | False | False | true | stop | 134 |
formal_logic_harder_7512 | harder | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((P ∨ S → S) ∧ R → (Q → S))
Given: P=True, Q=True, R=True, S=False<|im_end|>
<|im_start... | <think>
Problem: Evaluate ((P ∨ S → S) ∧ R → (Q → S))
Given: P=True, Q=True, R=True, S=False
Step 1: Evaluate next level
P ∨ S = True ∨ False = True
Q → S = True → False = False
Step 2: Evaluate innermost subexpressions
P ∨ S → S = True → False = False
Step 3: Evaluate next level
P ∨ S → S ∧ R = False ∧ True =... | True | True | true | stop | 153 |
formal_logic_harder_7513 | harder | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (S ∧ R → ¬((Q → P)))
Given: P=True, Q=False, R=False, S=False<|im_end|>
<|im_start|>ass... | <think>
Problem: Evaluate (S ∧ R → ¬((Q → P)))
Given: P=True, Q=False, R=False, S=False
Step 1: Evaluate next level
S ∧ R = False ∧ False = False
Q → P = False → True = True
Step 2: Evaluate innermost subexpressions
¬(Q → P) = ¬True = False
Step 3: Final implication
S ∧ R → ¬((Q → P)) = False → False = True
</... | True | True | true | stop | 117 |
formal_logic_harder_7514 | harder | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (¬((Q ∧ P)) → (S ↔ R))
Given: P=False, Q=True, R=True, S=False<|im_end|>
<|im_start|>as... | <think>
Problem: Evaluate (¬((Q ∧ P)) → (S ↔ R))
Given: P=False, Q=True, R=True, S=False
Step 1: Evaluate next level
Q ∧ P = True ∧ False = False
S ↔ R = False ↔ True = False
Step 2: Evaluate innermost subexpressions
¬(Q ∧ P) = ¬False = True
Step 3: Final implication
¬((Q ∧ P)) → S ↔ R = True → False = False
<... | False | False | true | stop | 119 |
formal_logic_harder_7515 | harder | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (Q ∨ (¬P → S) ↔ R → ¬R)
Given: P=False, Q=False, R=False, S=False<|im_end|>
<|im_start|... | <think>
Problem: Evaluate (Q ∨ (¬P → S) ↔ R → ¬R)
Given: P=False, Q=False, R=False, S=False
Step 1: Evaluate atomic negations
¬P = ¬False = True
¬R = ¬False = True
Step 2: Evaluate innermost subexpressions
¬P → S = True → False = False
Step 3: Evaluate next level
Q ∨ ¬P → S = False ∨ False = False
Step 4: Eval... | False | False | true | stop | 169 |
formal_logic_harder_7516 | harder | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((P ↔ R ∧ S) ∧ (P ∧ Q))
Given: P=False, Q=True, R=True, S=True<|im_end|>
<|im_start|>as... | <think>
Problem: Evaluate ((P ↔ R ∧ S) ∧ (P ∧ Q))
Given: P=False, Q=True, R=True, S=True
Step 1: Evaluate next level
R ∧ S = True ∧ True = True
P ∧ Q = False ∧ True = False
Step 2: Evaluate innermost subexpressions
P ↔ R ∧ S = False ↔ True = False
Step 3: Final conjunction
P ↔ R ∧ S ∧ P ∧ Q = False ∧ False = F... | False | False | true | stop | 118 |
formal_logic_harder_7517 | harder | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (Q → ¬((P ∨ R ∧ Q ∧ S)))
Given: P=False, Q=False, R=True, S=True<|im_end|>
<|im_start|>... | <think>
Problem: Evaluate (Q → ¬((P ∨ R ∧ Q ∧ S)))
Given: P=False, Q=False, R=True, S=True
Step 1: Evaluate next level
R ∧ Q = True ∧ False = False
Step 2: Evaluate innermost subexpressions
P ∨ R ∧ Q = False ∨ False = False
Step 3: Evaluate next level
¬(P ∨ R ∧ Q ∧ S) = ¬(False ∧ True) = ¬False = True
Step 4: Fi... | True | True | true | stop | 147 |
formal_logic_harder_7518 | harder | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((R ∧ S ∧ Q → (R ↔ P)) ∧ S)
Given: P=True, Q=False, R=False, S=False<|im_end|>
<|im_sta... | <think>
Problem: Evaluate ((R ∧ S ∧ Q → (R ↔ P)) ∧ S)
Given: P=True, Q=False, R=False, S=False
Step 1: Evaluate next level
R ∧ S = False ∧ False = False
R ↔ P = False ↔ True = False
Step 2: Evaluate innermost subexpressions
R ∧ S ∧ Q = False ∧ False = False
Step 3: Evaluate next level
R ∧ S ∧ Q → R ↔ P = False... | False | False | true | stop | 149 |
formal_logic_harder_7519 | harder | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ¬(((S ↔ Q ∨ P) ∧ Q ↔ R ∧ S))
Given: P=True, Q=True, R=False, S=False<|im_end|>
<|im_sta... | <think>
Problem: Evaluate ¬(((S ↔ Q ∨ P) ∧ Q ↔ R ∧ S))
Given: P=True, Q=True, R=False, S=False
Step 1: Evaluate next level
Q ∨ P = True ∨ True = True
R ∧ S = False ∧ False = False
Step 2: Evaluate innermost subexpressions
S ↔ Q ∨ P = False ↔ True = False
Step 3: Evaluate next level
S ↔ Q ∨ P ∧ Q = False ∧ True... | False | False | true | stop | 185 |
formal_logic_ood_10000 | ood | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((S → T ∧ (P ∨ Q)) ∨ R)
Given: P=False, Q=True, R=False, S=False, T=True<|im_end|>
<|im... | <think>
Problem: Evaluate ((S → T ∧ (P ∨ Q)) ∨ R)
Given: P=False, Q=True, R=False, S=False, T=True
Step 1: Evaluate next level
P ∨ Q = False ∨ True = True
Step 2: Evaluate innermost subexpressions
T ∧ P ∨ Q = True ∧ True = True
Step 3: Evaluate next level
S → T ∧ (P ∨ Q) = False → True = True
Step 4: Final disju... | True | True | true | stop | 147 |
formal_logic_ood_10001 | ood | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (P ∨ Q → Q ∧ (S ∧ (T ∧ R)))
Given: P=False, Q=True, R=False, S=True, T=False<|im_end|>
... | <think>
Problem: Evaluate (P ∨ Q → Q ∧ (S ∧ (T ∧ R)))
Given: P=False, Q=True, R=False, S=True, T=False
Step 1: Evaluate next level
P ∨ Q = False ∨ True = True
T ∧ R = False ∧ False = False
Step 2: Evaluate innermost subexpressions
S ∧ T ∧ R = True ∧ False = False
Step 3: Evaluate next level
Q ∧ S ∧ (T ∧ R) = T... | False | False | true | stop | 157 |
formal_logic_ood_10002 | ood | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((P ∧ S ↔ Q) ∨ T ∨ R)
Given: P=False, Q=False, R=True, S=False, T=False<|im_end|>
<|im_... | <think>
Problem: Evaluate ((P ∧ S ↔ Q) ∨ T ∨ R)
Given: P=False, Q=False, R=True, S=False, T=False
Step 1: Evaluate next level
P ∧ S = False ∧ False = False
Step 2: Evaluate innermost subexpressions
P ∧ S ↔ Q = False ↔ False = True
Step 3: Evaluate next level
P ∧ S ↔ Q ∨ T = True ∨ False = True
Step 4: Final disj... | True | True | true | stop | 142 |
formal_logic_ood_10003 | ood | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((¬P → T ↔ S ∧ (Q ↔ R)) → Q)
Given: P=True, Q=False, R=False, S=False, T=True<|im_end|>... | <think>
Problem: Evaluate ((¬P → T ↔ S ∧ (Q ↔ R)) → Q)
Given: P=True, Q=False, R=False, S=False, T=True
Step 1: Evaluate atomic negations
¬P = ¬True = False
Step 2: Evaluate innermost subexpressions
Q ↔ R = False ↔ False = True
Step 3: Evaluate next level
S ∧ Q ↔ R = False ∧ True = False
Step 4: Evaluate next le... | True | True | true | stop | 184 |
formal_logic_ood_10004 | ood | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ¬(((S → T ∨ (R ↔ (Q ↔ P))) ∧ Q))
Given: P=True, Q=False, R=True, S=False, T=False<|im_e... | <think>
Problem: Evaluate ¬(((S → T ∨ (R ↔ (Q ↔ P))) ∧ Q))
Given: P=True, Q=False, R=True, S=False, T=False
Step 1: Evaluate next level
Q ↔ P = False ↔ True = False
Step 2: Evaluate innermost subexpressions
R ↔ Q ↔ P = True ↔ False = False
Step 3: Evaluate next level
T ∨ R ↔ (Q ↔ P) = False ∨ False = False
Step ... | True | True | true | stop | 214 |
formal_logic_ood_10005 | ood | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (T ∧ (P ↔ R ∧ S ↔ S) ↔ Q)
Given: P=False, Q=True, R=True, S=True, T=False<|im_end|>
<|i... | <think>
Problem: Evaluate (T ∧ (P ↔ R ∧ S ↔ S) ↔ Q)
Given: P=False, Q=True, R=True, S=True, T=False
Step 1: Evaluate next level
R ∧ S = True ∧ True = True
Step 2: Evaluate innermost subexpressions
P ↔ R ∧ S = False ↔ True = False
Step 3: Evaluate next level
P ↔ R ∧ S ↔ S = False ↔ True = False
Step 4: Evaluate n... | False | False | true | stop | 167 |
formal_logic_ood_10006 | ood | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (¬((Q → S → R)) → (T → R) → P)
Given: P=True, Q=False, R=False, S=True, T=False<|im_end... | <think>
Problem: Evaluate (¬((Q → S → R)) → (T → R) → P)
Given: P=True, Q=False, R=False, S=True, T=False
Step 1: Evaluate next level
Q → S = False → True = True
T → R = False → False = True
Step 2: Evaluate innermost subexpressions
¬(Q → S → R) = ¬True = False
Step 3: Evaluate next level
¬((Q → S → R)) → T → ... | True | True | true | stop | 163 |
formal_logic_ood_10007 | ood | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ∨ S → T ∨ P ∧ Q)
Given: P=False, Q=True, R=False, S=False, T=False<|im_end|>
<|im_st... | <think>
Problem: Evaluate (R ∨ S → T ∨ P ∧ Q)
Given: P=False, Q=True, R=False, S=False, T=False
Step 1: Evaluate next level
R ∨ S = False ∨ False = False
P ∧ Q = False ∧ True = False
Step 2: Evaluate innermost subexpressions
T ∨ P ∧ Q = False ∨ False = False
Step 3: Final implication
R ∨ S → T ∨ P ∧ Q = False ... | True | True | true | stop | 127 |
formal_logic_ood_10008 | ood | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (¬S ∧ (T ∨ (Q ↔ R ∨ P)))
Given: P=False, Q=False, R=False, S=False, T=True<|im_end|>
<|... | <think>
Problem: Evaluate (¬S ∧ (T ∨ (Q ↔ R ∨ P)))
Given: P=False, Q=False, R=False, S=False, T=True
Step 1: Evaluate atomic negations
¬S = ¬False = True
Step 2: Evaluate innermost subexpressions
R ∨ P = False ∨ False = False
Step 3: Evaluate next level
Q ↔ R ∨ P = False ↔ False = True
Step 4: Evaluate next leve... | True | True | true | stop | 165 |
formal_logic_ood_10009 | ood | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (T ∨ P ∧ S ∨ Q → R)
Given: P=True, Q=False, R=True, S=True, T=True<|im_end|>
<|im_start... | <think>
Problem: Evaluate (T ∨ P ∧ S ∨ Q → R)
Given: P=True, Q=False, R=True, S=True, T=True
Step 1: Evaluate next level
P ∧ S = True ∧ True = True
Step 2: Evaluate innermost subexpressions
T ∨ P ∧ S = True ∨ True = True
Step 3: Evaluate next level
T ∨ P ∧ S ∨ Q = True ∨ False = True
Step 4: Final implication
... | True | True | true | stop | 140 |
formal_logic_ood_10010 | ood | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ∧ (Q ↔ P ∧ S ↔ T ↔ Q))
Given: P=False, Q=False, R=True, S=True, T=True<|im_end|>
<|i... | <think>
Problem: Evaluate (R ∧ (Q ↔ P ∧ S ↔ T ↔ Q))
Given: P=False, Q=False, R=True, S=True, T=True
Step 1: Evaluate next level
P ∧ S = False ∧ True = False
Step 2: Evaluate innermost subexpressions
Q ↔ P ∧ S = False ↔ False = True
Step 3: Evaluate next level
Q ↔ P ∧ S ↔ T = True ↔ True = True
Step 4: Final conj... | False | False | true | stop | 136 |
formal_logic_ood_10011 | ood | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (Q ∧ (R ∨ P → (S ↔ T → S)))
Given: P=False, Q=True, R=False, S=True, T=True<|im_end|>
<... | <think>
Problem: Evaluate (Q ∧ (R ∨ P → (S ↔ T → S)))
Given: P=False, Q=True, R=False, S=True, T=True
Step 1: Evaluate next level
R ∨ P = False ∨ False = False
T → S = True → True = True
Step 2: Evaluate innermost subexpressions
S ↔ T → S = True ↔ True = True
Step 3: Evaluate next level
R ∨ P → S ↔ T → S = Fal... | True | True | true | stop | 157 |
formal_logic_ood_10012 | ood | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (¬(((Q ∨ P ∨ S) ∧ (T ∧ R))) → R)
Given: P=True, Q=False, R=True, S=True, T=False<|im_en... | <think>
Problem: Evaluate (¬(((Q ∨ P ∨ S) ∧ (T ∧ R))) → R)
Given: P=True, Q=False, R=True, S=True, T=False
Step 1: Evaluate next level
Q ∨ P = False ∨ True = True
T ∧ R = False ∧ True = False
Step 2: Evaluate innermost subexpressions
Q ∨ P ∨ S = True ∨ True = True
Step 3: Evaluate next level
Q ∨ P ∨ S ∧ T ∧ R ... | True | True | true | stop | 200 |
formal_logic_ood_10013 | ood | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (T ∨ (Q ∨ (R → (T ↔ (P ↔ S)))))
Given: P=False, Q=True, R=False, S=True, T=True<|im_end... | <think>
Problem: Evaluate (T ∨ (Q ∨ (R → (T ↔ (P ↔ S)))))
Given: P=False, Q=True, R=False, S=True, T=True
Step 1: Evaluate next level
P ↔ S = False ↔ True = False
Step 2: Evaluate innermost subexpressions
T ↔ P ↔ S = True ↔ False = False
Step 3: Evaluate next level
R → T ↔ (P ↔ S) = False → False = True
Step 4: ... | True | True | true | stop | 184 |
formal_logic_ood_10014 | ood | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (¬((R ↔ T)) ∨ (S ∨ Q) ↔ P)
Given: P=False, Q=False, R=False, S=False, T=True<|im_end|>
... | <think>
Problem: Evaluate (¬((R ↔ T)) ∨ (S ∨ Q) ↔ P)
Given: P=False, Q=False, R=False, S=False, T=True
Step 1: Evaluate next level
R ↔ T = False ↔ True = False
S ∨ Q = False ∨ False = False
Step 2: Evaluate innermost subexpressions
¬(R ↔ T) = ¬False = True
Step 3: Evaluate next level
¬((R ↔ T)) ∨ S ∨ Q = True ... | False | False | true | stop | 167 |
formal_logic_ood_10015 | ood | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ↔ ¬((S ∨ Q ∧ T)) → T → P)
Given: P=False, Q=False, R=False, S=True, T=True<|im_end|>... | <think>
Problem: Evaluate (R ↔ ¬((S ∨ Q ∧ T)) → T → P)
Given: P=False, Q=False, R=False, S=True, T=True
Step 1: Evaluate next level
Q ∧ T = False ∧ True = False
Step 2: Evaluate innermost subexpressions
S ∨ Q ∧ T = True ∨ False = True
Step 3: Evaluate next level
¬(S ∨ Q ∧ T) = ¬True = False
Step 4: Evaluate inne... | True | True | true | stop | 208 |
formal_logic_ood_10016 | ood | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate (R ∨ S ∨ (T ↔ P ∨ Q))
Given: P=False, Q=False, R=False, S=True, T=False<|im_end|>
<|im_... | <think>
Problem: Evaluate (R ∨ S ∨ (T ↔ P ∨ Q))
Given: P=False, Q=False, R=False, S=True, T=False
Step 1: Evaluate next level
R ∨ S = False ∨ True = True
P ∨ Q = False ∨ False = False
Step 2: Evaluate innermost subexpressions
T ↔ P ∨ Q = False ↔ False = True
Step 3: Final disjunction
R ∨ S ∨ T ↔ P ∨ Q = True ∨... | True | True | true | stop | 133 |
formal_logic_ood_10017 | ood | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((R ↔ Q) → (S → T → P))
Given: P=True, Q=False, R=True, S=True, T=True<|im_end|>
<|im_s... | <think>
Problem: Evaluate ((R ↔ Q) → (S → T → P))
Given: P=True, Q=False, R=True, S=True, T=True
Step 1: Evaluate next level
R ↔ Q = True ↔ False = False
S → T = True → True = True
Step 2: Evaluate innermost subexpressions
S → T → P = True → True = True
Step 3: Final implication
R ↔ Q → S → T → P = False → Tru... | True | True | true | stop | 121 |
formal_logic_ood_10018 | ood | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((T → S) ∨ (R → (Q ↔ P)))
Given: P=False, Q=False, R=False, S=False, T=True<|im_end|>
<... | <think>
Problem: Evaluate ((T → S) ∨ (R → (Q ↔ P)))
Given: P=False, Q=False, R=False, S=False, T=True
Step 1: Evaluate next level
T → S = True → False = False
Q ↔ P = False ↔ False = True
Step 2: Evaluate innermost subexpressions
R → Q ↔ P = False → True = True
Step 3: Final disjunction
T → S ∨ R → (Q ↔ P) = F... | True | True | true | stop | 128 |
formal_logic_ood_10019 | ood | formal_logic | formal_logic_bottom_up | <|im_start|>system
You are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>
<|im_start|>user
Solve the following problem. Show your work, then give your final answer on a line starting with "Answer:".
Evaluate ((Q ↔ (R ↔ T)) ∨ (P → S))
Given: P=True, Q=False, R=True, S=True, T=True<|im_end|>
<|im... | <think>
Problem: Evaluate ((Q ↔ (R ↔ T)) ∨ (P → S))
Given: P=True, Q=False, R=True, S=True, T=True
Step 1: Evaluate next level
R ↔ T = True ↔ True = True
P → S = True → True = True
Step 2: Evaluate innermost subexpressions
Q ↔ R ↔ T = False ↔ True = False
Step 3: Final disjunction
Q ↔ (R ↔ T) ∨ P → S = False ∨... | True | True | true | stop | 128 |
algo-sft-eval-traces-formal-logic-bottom-up-v4
Full eval traces for algo-sft-formal-logic-bottom-up across test/harder/ood splits
Dataset Info
- Rows: 60
- Columns: 11
Columns
| Column | Type | Description |
|---|---|---|
| question_id | Value('string') | Unique question identifier from eval set |
| split | Value('string') | Evaluation split: test (in-distribution), harder (scaled up), ood (structural out-of-distribution) |
| domain | Value('string') | Task domain: formal_logic, conlang_morphology, cellular_automata, long_arithmetic |
| task | Value('string') | Specific task variant (e.g., formal_logic_bottom_up) |
| prompt | Value('string') | Full prompt sent to the model |
| model_response | Value('string') | Complete untruncated model output |
| extracted_answer | Value('string') | Answer extracted by domain-specific parser |
| ground_truth | Value('string') | Expected correct answer |
| correct | Value('bool') | Whether extracted_answer matched ground_truth |
| finish_reason | Value('string') | vLLM finish reason: stop (natural end) or length (hit max_tokens) |
| token_count | Value('int64') | Number of tokens in model_response |
Generation Parameters
{
"script_name": "eval_model.py",
"model": "reasoning-degeneration-dev/algo-sft-formal-logic-bottom-up",
"description": "Full eval traces for algo-sft-formal-logic-bottom-up across test/harder/ood splits",
"hyperparameters": {
"max_tokens": 32768,
"max_model_len": 32768,
"temperature": 0.0,
"base_model": "Qwen/Qwen2.5-1.5B-Instruct"
},
"input_datasets": []
}
Usage
from datasets import load_dataset
dataset = load_dataset("zsprague/algo-sft-eval-traces-formal-logic-bottom-up-v4", split="train")
print(f"Loaded {len(dataset)} rows")
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