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96436e65ac29ece9 | 0c1e8b4c55df03d2 | Solve ((8 + 4) + (-8)). | Start by Evaluate 8 + 4 to get 12.
After that Evaluate (8 + 4) + (-8) to get 4.
That leaves us with 4. | 4 | [
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901681bbf988b826 | c21a7209c78fccaa | Find n: 2(n + 3) = 2. | Observe that Divide both sides by 2. We get n + 3 = 1. From this Subtract 3 on both sides to isolate n. We get n = -2. Hence, -2. | -2 | [
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5a045a19a670b414 | 1b63d3a072ef5696 | y/6 + 1 = 4/3. Determine the value of y. Assume all quantities are real numbers. | Start by Subtract 1 on both sides. We get y/6 = 1/3. After that Multiply both sides by 6. We get y = 2. That leaves us with 2. | 2 | [
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8e28274625dfe702 | c710a61d50fe6128 | Show ((((-1) + 6) - 13) - (14 * 13)). | 1. Observe that evaluate (-1) + 6 to get 5.
2. From this evaluate 14 * 13 to get 182.
3. Consequently evaluate (((-1) + 6) - 13) - (14 * 13) to get -190.
This proves the result is -190. | -190 | [
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aba7e76a6afcd52f | 627695b30c0fac33 | Use the following facts. Yorlingal is taller than Rinrin. Rinkelgal is taller than Denhaltar. Yorlinsol is taller than Yorlingal. Rinrin is taller than Rinkelgal. Question: Is Rinrin taller than Yorlingal? | Observe the ordering constraints. The facts show Yorlingal is taller than Rinrin via Yorlingal -> Rinrin, so the query is false. This proves the result is no. | no | [
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4106cf714099cf22 | 9856085193617ee8 | t/5 = 1. Solve for t. Assume all quantities are real numbers. | 1. First Multiply both sides by 5. We get t = 5.
Therefore the answer is 5. | 5 | [
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ededba3f2d7d8fed | 0f3df56bb0a06f7a | Using the order of operations, evaluate ((-7) * ((-5) * 11)). | First Evaluate (-5) * 11 to get -55. Next Evaluate (-7) * ((-5) * 11) to get 385. So the answer is 385. | 385 | [
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d5795c2ce63b73f1 | 387882b318285bfe | Determine this expression: ((7 - 2) * (15 + (13 - (-1)))). | 1. Observe that evaluate 7 - 2 to get 5.
2. From this evaluate 13 - (-1) to get 14.
3. Consequently evaluate 15 + (13 - (-1)) to get 29.
4. Consequently evaluate (7 - 2) * (15 + (13 - (-1))) to get 145.
This proves the result is 145. | 145 | [
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a474bab0a45679e5 | 7e2b0ee19e849149 | Find y: 2(y - 6) = -4. Assume all quantities are real numbers. | 1. Observe that Divide both sides by 2. We get y - 6 = -2.
2. From this Add 6 on both sides to isolate y. We get y = 4.
This proves the result is 4. | 4 | [
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f57da9cf66ab514d | 8429e6173a3ee783 | Determine the value of y: 5(y + 4) = -15. Assume all quantities are real numbers. | Observe that Divide both sides by 5. We get y + 4 = -3. From this Subtract 4 on both sides to isolate y. We get y = -7. Hence, -7. | -7 | [
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dcf4d3eb821393a8 | a5cb67cc34bcf2f6 | Use the following facts. - Baba is taller than Galzan.
- Galvelpel is taller than Halgal.
- Galzan is taller than Tarrinden.
- Tarrinden is taller than Galvelpel.
- Halgal is taller than Yoryor. Question: Is Tarrinden taller than Halgal? | Observe the ordering constraints. There is a chain Tarrinden -> Galvelpel -> Halgal, so Tarrinden is taller than Halgal.
Hence, yes. | yes | [
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3f4b891a6a707727 | e107e83d68ab5bd2 | Determine this expression: (5-(((-4)+(8+(-8)))*1)). | 1. Observe that evaluate 8 + (-8) to get 0.
2. From this evaluate (-4) + (8 + (-8)) to get -4.
3. Consequently evaluate ((-4) + (8 + (-8))) * 1 to get -4.
4. Consequently evaluate 5 - (((-4) + (8 + (-8))) * 1) to get 9.
Hence, 9. | 9 | [
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534f9dc23ca0dc44 | d9d348b9fc708397 | Try solving the value of (((13 - 7) - (8 * (-3))) * 5). | Start by Evaluate 13 - 7 to get 6.
After that Evaluate 8 * (-3) to get -24.
Now Evaluate (13 - 7) - (8 * (-3)) to get 30.
Now Evaluate ((13 - 7) - (8 * (-3))) * 5 to get 150.
So we can conclude the answer is 150. | 150 | [
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bcfcca1f42ff0adb | 1afefa72e68346b5 | Find n in the equation 3n - 2 = -11. | First Add 2 to both sides. This gives 3n = -9. We get 3n = -9. Next Divide both sides by 3 to isolate n. We get n = -3. So the answer is -3. | -3 | [
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9c467c9f679f7bb5 | 98e620d3abb54cb3 | Evaluate this expression: ((-1) * (0 + 7)). | First Evaluate 0 + 7 to get 7. Next Evaluate (-1) * (0 + 7) to get -7. So the answer is -7. | -7 | [
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d021c22e0c561b67 | 60f6dd969875b84a | Show (12*(((7*0)*(-2))*1)). | Observe that Evaluate 7 * 0 to get 0.
From this Evaluate ((7 * 0) * (-2)) * 1 to get 0.
Consequently Evaluate 12 * (((7 * 0) * (-2)) * 1) to get 0.
Hence, 0. | 0 | [
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a30bfc0691a1b289 | 4a82ce1a4d3c0161 | Determine the value of x: 6(x + 4) = 54. Assume all quantities are real numbers. | First Divide both sides by 6. We get x + 4 = 9. Next Subtract 4 on both sides to isolate x. We get x = 5. Therefore the answer is 5. | 5 | [
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15c73c30f1f55460 | c815b8e96f0b5338 | Work out this expression: (((-9) + 1) * 3). | First Evaluate (-9) + 1 to get -8. Next Evaluate ((-9) + 1) * 3 to get -24. So the answer is -24. | -24 | [
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b9889f8f89761da4 | 349ecbe67187c1ea | Find this expression: ((15*1)+(((-8)+13)*7)). | First Evaluate 15 * 1 to get 15. Next Evaluate (-8) + 13 to get 5. Then Evaluate ((-8) + 13) * 7 to get 35. Then Evaluate (15 * 1) + (((-8) + 13) * 7) to get 50. So the answer is 50. | 50 | [
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58bd0913883af3ee | d487281605420705 | Work through (5-(12*7)). | Start by Evaluate 12 * 7 to get 84.
After that Evaluate 5 - (12 * 7) to get -79.
So we can conclude the answer is -79. | -79 | [
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767d7ed5dac94426 | f3ce8e950553e08f | Compute ((10 + 11) + 11). | First Evaluate 10 + 11 to get 21.
Next Evaluate (10 + 11) + 11 to get 32.
So the answer is 32. | 32 | [
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451aa123212ca96c | 79ead67af6f48a22 | Without skipping steps, try solving ((((8-(-3))+0)+6)*(-9)). | 1. Start by evaluate 8 - (-3) to get 11.
2. After that evaluate (8 - (-3)) + 0 to get 11.
3. Now evaluate ((8 - (-3)) + 0) + 6 to get 17.
4. Now evaluate (((8 - (-3)) + 0) + 6) * (-9) to get -153.
So we can conclude the answer is -153. | -153 | [
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44ef6858c524ec63 | d300f6ae5a8485fa | m/4 - 5 = -11/4. Solve for m. Assume all quantities are real numbers. | Observe that Add 5 on both sides. We get m/4 = 9/4. From this Multiply both sides by 4. We get m = 9. This proves the result is 9. | 9 | [
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2fc17a947c2ead88 | 15ea91a338a8166b | Solve for x in the equation x/4 + 6 = 7. Assume all quantities are real numbers. | Observe that Subtract 6 on both sides. We get x/4 = 1. From this Multiply both sides by 4. We get x = 4. Hence, 4. | 4 | [
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cf7da22ced469090 | c329244d45584bb6 | Evaluate the value of (((-4) + 1) - 8). | 1. First evaluate (-4) + 1 to get -3.
2. Next evaluate ((-4) + 1) - 8 to get -11.
Therefore the answer is -11. | -11 | [
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c82117a1a0ba43f0 | f5467655ffd3f94e | Establish ((((-7)+(-1))+(3*11))*((-9)-(-5))). | Observe that Evaluate (-7) + (-1) to get -8. From this Evaluate 3 * 11 to get 33. Consequently Evaluate ((-7) + (-1)) + (3 * 11) to get 25. Consequently Evaluate (-9) - (-5) to get -4. Consequently Evaluate (((-7) + (-1)) + (3 * 11)) * ((-9) - (-5)) to get -100. This proves the result is -100. | -100 | [
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4bc367e25c3fed0f | 3bf3dcac578daa05 | Decide whether Denyorcor is older than Morgal. - Denyorcor is older than Galkel.
- Wenfi is older than Kelgal.
- Kelgal is older than Denyorcor.
- Galkel is older than Morgal. Question: Is Denyorcor older than Morgal? | There is a chain Denyorcor -> Galkel -> Morgal, so Denyorcor is older than Morgal.
So the answer is yes. | yes | [
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a8e668acbbe702ef | d0d8e57e4f4380e7 | Work through this expression: (((-8) * (-9)) + ((-7) + (-1))). | Start by Evaluate (-8) * (-9) to get 72. After that Evaluate (-7) + (-1) to get -8. Now Evaluate ((-8) * (-9)) + ((-7) + (-1)) to get 64. So we can conclude the answer is 64. | 64 | [
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f920681dfa84a5a3 | 66f1e2a4d1a5c788 | Compute this expression: (0 + ((-2) + (-1))). | First Evaluate (-2) + (-1) to get -3.
Next Evaluate 0 + ((-2) + (-1)) to get -3.
So the answer is -3. | -3 | [
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f6f55ce97ea23b9b | cde25dec14f93a4d | Determine the value of t in the equation -5t + 3 = 33. Assume all quantities are real numbers. | First Subtract 3 from both sides. This gives -5t = 30. We get -5t = 30.
Next Divide both sides by -5 to isolate t. We get t = -6.
So the answer is -6. | -6 | [
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cab0332c7029f1d7 | 0eeba557b6bb0b38 | Decide whether Fiba is faster than Soldencor. - Rinpel is faster than Soldencor.
- Solfiyor is faster than Linden.
- Soldencor is faster than Pelnortar.
- Pelnortar is faster than Solfiyor.
- Linden is faster than Fiba. Question: Is Fiba faster than Soldencor? | The facts show Soldencor is faster than Fiba via Soldencor -> Pelnortar -> Solfiyor -> Linden -> Fiba, so the query is false.
Therefore the answer is no. | no | [
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f4d16e2cf2f77f23 | a0140976d75a201d | Use the following facts. - Bakel is faster than Morgal.
- Velhal is faster than Nornor.
- Veltar is faster than Velhal.
- Nornor is faster than Bakel.
- Velhal is faster than Bakel.
- Morgal is faster than Linsolvel. Question: Is Velhal faster than Veltar? | The facts show Veltar is faster than Velhal via Veltar -> Velhal, so the query is false.
So the answer is no. | no | [
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76037091982052dc | ac5310b328fe13e2 | Use the following facts. Tarkelyor is heavier than Mormor. Zanlinpel is heavier than Tarkelyor. Linjantar is heavier than Zanlinpel. Question: Is Linjantar heavier than Mormor? | There is a chain Linjantar -> Zanlinpel -> Tarkelyor -> Mormor, so Linjantar is heavier than Mormor. Therefore the answer is yes. | yes | [
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58298ddbca2407a7 | 866df47f5fbcfb3e | Decide whether Denpel is taller than Corjan. - Tarlin is taller than Corjan.
- Corjan is taller than Tarpel.
- Morkel is taller than Denpel.
- Denpel is taller than Tarlin. Question: Is Denpel taller than Corjan? | There is a chain Denpel -> Tarlin -> Corjan, so Denpel is taller than Corjan.
Therefore the answer is yes. | yes | [
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0b7108a6d0ca9c5a | 02f24cb8ba46668c | Decide whether Halrin is older than Solmormor. Halrin is older than Cormorzan. Yorgalyor is older than Halrin. Solmormor is older than Yorgalyor. Question: Is Halrin older than Solmormor? | The facts show Solmormor is older than Halrin via Solmormor -> Yorgalyor -> Halrin, so the query is false. So the answer is no. | no | [
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e5c33dd4a11d6e95 | 5d56fc67a5951e95 | Solve for t: 7t + 7 = 35. | Start by Subtract 7 from both sides. This gives 7t = 28. We get 7t = 28.
After that Divide both sides by 7 to isolate t. We get t = 4.
That leaves us with 4. | 4 | [
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fd7afb68881c4646 | 0dbf55a0378c1fd2 | Determine the value of m in the equation -6m - 5 = -29. | Start by Add 5 to both sides. This gives -6m = -24. We get -6m = -24. After that Divide both sides by -6 to isolate m. We get m = 4. That leaves us with 4. | 4 | [
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3888c5dba6456133 | 3864de2f15106496 | Using the order of operations, determine (((5 - 7) - 5) * (10 + ((-2) * 5))). | Observe that Evaluate 5 - 7 to get -2.
From this Evaluate (-2) * 5 to get -10.
Consequently Evaluate ((5 - 7) - 5) * (10 + ((-2) * 5)) to get 0.
Hence, 0. | 0 | [
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3b1b4f675e771406 | 56e36b6b8eeae06e | Try solving this expression: ((-8)*(((-9)-(-7))*((-3)*(-5)))). | Start by Evaluate (-9) - (-7) to get -2. After that Evaluate (-3) * (-5) to get 15. Now Evaluate ((-9) - (-7)) * ((-3) * (-5)) to get -30. Now Evaluate (-8) * (((-9) - (-7)) * ((-3) * (-5))) to get 240. That leaves us with 240. | 240 | [
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cb97502f651d920f | 674900d05be87ee0 | Use the following facts. Hallinfi is taller than Janhal. Peltar is taller than Hallinnor. Hallinnor is taller than Janhal. Norpel is taller than Peltar. Hallinnor is taller than Hallinfi. Janzanlin is taller than Norpel. Question: Is Hallinnor taller than Norpel? | The facts show Norpel is taller than Hallinnor via Norpel -> Peltar -> Hallinnor, so the query is false. Therefore the answer is no. | no | [
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694d6de0ef890222 | 1fe22d0202d0cb0f | Use the following facts. Solsolwen is taller than Corgalvel. Corba is taller than Solsolwen. Corba is taller than Kelgal. Corgalvel is taller than Kelgal. Question: Is Corba taller than Kelgal? | Start by linking the facts together. There is a chain Corba -> Kelgal, so Corba is taller than Kelgal. That leaves us with yes. | yes | [
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65ecf9fe911fd8d7 | c89112f58e33436a | Solve for y: y/5 + 6 = 31/5. Assume all quantities are real numbers. | First Subtract 6 on both sides. We get y/5 = 1/5. Next Multiply both sides by 5. We get y = 1. Therefore the answer is 1. | 1 | [
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d8d4d60fd747d875 | 8455ae35e9ef7d42 | 2(x + 3) = -2. Solve for x. | Start by Divide both sides by 2. We get x + 3 = -1. After that Subtract 3 on both sides to isolate x. We get x = -4. So we can conclude the answer is -4. | -4 | [
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fd3f5f02a7550be1 | a40ad34fc1297369 | Use the following facts. - Corfi is older than Filin.
- Dentarhal is older than Rinsol.
- Rinsol is older than Corfi. Question: Is Filin older than Rinsol? | The facts show Rinsol is older than Filin via Rinsol -> Corfi -> Filin, so the query is false.
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309aceb344547ce2 | 76fec5169e1070aa | Decide whether Janrinzan is taller than Velwenba. Solkel is taller than Norkelrin. Norkelrin is taller than Velwenba. Janrinzan is taller than Solkel. Question: Is Janrinzan taller than Velwenba? | There is a chain Janrinzan -> Solkel -> Norkelrin -> Velwenba, so Janrinzan is taller than Velwenba. So the answer is yes. | yes | [
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82185cf6a82ddd72 | 31e1b4664e2c87a6 | Work through the value of (((-3) + (15 + (6 - (-6)))) * (-5)). | Start by Evaluate 6 - (-6) to get 12. After that Evaluate 15 + (6 - (-6)) to get 27. Now Evaluate (-3) + (15 + (6 - (-6))) to get 24. Now Evaluate ((-3) + (15 + (6 - (-6)))) * (-5) to get -120. So we can conclude the answer is -120. | -120 | [
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d8a9c2dc4bb7653b | fa60f39c0e936c93 | Compute (4*((6*13)+(-8))). | First Evaluate 6 * 13 to get 78. Next Evaluate (6 * 13) + (-8) to get 70. Then Evaluate 4 * ((6 * 13) + (-8)) to get 280. Therefore the answer is 280. | 280 | [
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8203bad3c6cf58e1 | 04bc6961b1032eb1 | Work out the value of ((9 * (-4)) * 0). | First Evaluate 9 * (-4) to get -36.
Next Evaluate (9 * (-4)) * 0 to get 0.
So the answer is 0. | 0 | [
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198078663ab1e8b8 | 5156e49e71d42f25 | Use the following facts. Pelzan is older than Keltargal. Densolba is older than Wengaltar. Wengaltar is older than Pelzan. Wengaltar is older than Yorwenhal. Keltargal is older than Janmorlin. Yorwenhal is older than Keltargal. Yorwenhal is older than Pelzan. Question: Is Yorwenhal older than Densolba? | Start by linking the facts together. The facts show Densolba is older than Yorwenhal via Densolba -> Wengaltar -> Yorwenhal, so the query is false. That leaves us with no. | no | [
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83064d232f30d466 | a81976b6fbf56cfb | Use the following facts. Solwen is older than Norlinfi. Velficor is older than Kelrinhal. Norlinfi is older than Solveltar. Kelrinhal is older than Norba. Solveltar is older than Velficor. Question: Is Kelrinhal older than Solwen? | Observe the ordering constraints. The facts show Solwen is older than Kelrinhal via Solwen -> Norlinfi -> Solveltar -> Velficor -> Kelrinhal, so the query is false. Hence, no. | no | [
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76ad23d7728e950b | 3e40c94eda2e4789 | Decide whether Zanlinfi is heavier than Solsol. Solsol is heavier than Morrin. Zanlinfi is heavier than Rincorba. Rincorba is heavier than Solsol. Question: Is Zanlinfi heavier than Solsol? | Start by linking the facts together. There is a chain Zanlinfi -> Rincorba -> Solsol, so Zanlinfi is heavier than Solsol. That leaves us with yes. | yes | [
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86fb3db64211a8e0 | 4f071066514fad5c | Find t: 4(t) = 20. | Observe that Divide both sides by 4. We get t = 5. From this t is already isolated. We get t = 5. This proves the result is 5. | 5 | [
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6e67b76f73c0270d | 03367a04f845a1ba | n/2 + 3 = 0. Solve for n. Assume all quantities are real numbers. | First Subtract 3 on both sides. We get n/2 = -3. Next Multiply both sides by 2. We get n = -6. Therefore the answer is -6. | -6 | [
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6c6bb2e043618f69 | 196570845645af63 | Find y in the equation -2y - 5 = -19. | First Add 5 to both sides. This gives -2y = -14. We get -2y = -14. Next Divide both sides by -2 to isolate y. We get y = 7. So the answer is 7. | 7 | [
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6167e68cb0cf2818 | 5cb4b628362c0749 | Determine the value of t in the equation t/2 + 5 = 19/2. Assume all quantities are real numbers. | Observe that Subtract 5 on both sides. We get t/2 = 9/2. From this Multiply both sides by 2. We get t = 9. Hence, 9. | 9 | [
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41ca4868c4ed6260 | 7a83543f99922702 | Evaluate (((-4)*1)+5). | First Evaluate (-4) * 1 to get -4.
Next Evaluate ((-4) * 1) + 5 to get 1.
Therefore the answer is 1. | 1 | [
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f0392c2f1dd89406 | 52524c11f3463121 | Find t: 6(t - 6) = -30. Assume all quantities are real numbers. | Observe that Divide both sides by 6. We get t - 6 = -5. From this Add 6 on both sides to isolate t. We get t = 1. This proves the result is 1. | 1 | [
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1fc977df91d16b16 | b4fd3583502516fd | Solve for m in the equation m/6 - 4 = -7. | First Add 4 on both sides. We get m/6 = -3.
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567921470c9dd187 | 2ae94717300f2af9 | Find y: y/4 - 4 = -2. | Start by Add 4 on both sides. We get y/4 = 2. After that Multiply both sides by 4. We get y = 8. That leaves us with 8. | 8 | [
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893dadf1351cf623 | 1b960c32928a3f4f | Compute this expression: ((-1) + (5 * 14)). | First Evaluate 5 * 14 to get 70. Next Evaluate (-1) + (5 * 14) to get 69. So the answer is 69. | 69 | [
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4ffeb6ca2f4e9767 | 009bc06d352da577 | Use the following facts. - Denrin is faster than Bacor.
- Morhalvel is faster than Norpel.
- Bacor is faster than Morhalvel. Question: Is Morhalvel faster than Denrin? | Start by linking the facts together. The facts show Denrin is faster than Morhalvel via Denrin -> Bacor -> Morhalvel, so the query is false.
So we can conclude the answer is no. | no | [
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ad6e9ec041dbc870 | 610321e14f5f1db2 | Without skipping steps, show ((3 - 3) - 12). | 1. Observe that evaluate 3 - 3 to get 0.
2. From this evaluate (3 - 3) - 12 to get -12.
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e8e44073e5760ed3 | 4efe8403269e851b | Decide whether Zangal is heavier than Rinjankel. Rinjankel is heavier than Corrintar. Yorvelpel is heavier than Zangal. Zangal is heavier than Yoryor. Corrintar is heavier than Yorvelpel. Question: Is Zangal heavier than Rinjankel? | The facts show Rinjankel is heavier than Zangal via Rinjankel -> Corrintar -> Yorvelpel -> Zangal, so the query is false. Therefore the answer is no. | no | [
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937020b195dd4550 | 2b5b31004e92abfc | Find t in the equation t/3 - 6 = -7. Assume all quantities are real numbers. | First Add 6 on both sides. We get t/3 = -1.
Next Multiply both sides by 3. We get t = -3.
Therefore the answer is -3. | -3 | [
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15d171dbb61bfbca | 12a04ac003f2474e | Use the following facts. Haltarhal is taller than Coryor. Kelkelhal is taller than Fidenlin. Coryor is taller than Kelkelhal. Zankelden is taller than Haltarhal. Tarvelden is taller than Zankelden. Question: Is Coryor taller than Fidenlin? | Observe the ordering constraints. There is a chain Coryor -> Kelkelhal -> Fidenlin, so Coryor is taller than Fidenlin. Hence, yes. | yes | [
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73c0d4354c023da2 | 888ce56d9ee52ffd | Use the following facts. Tarfi is faster than Rinhaltar. Denpel is faster than Jancorhal. Jancorhal is faster than Tarfi. Jancorhal is faster than Galba. Galba is faster than Tarfi. Question: Is Jancorhal faster than Tarfi? | Start by linking the facts together. There is a chain Jancorhal -> Tarfi, so Jancorhal is faster than Tarfi. That leaves us with yes. | yes | [
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15c5d0cf51f43b8d | 00e7b11b626a31cb | Use the following facts. Morfilin is older than Norhallin. Janyor is older than Figalwen. Norhallin is older than Pelsol. Figalwen is older than Morfilin. Pelsol is older than Finortar. Question: Is Janyor older than Pelsol? | There is a chain Janyor -> Figalwen -> Morfilin -> Norhallin -> Pelsol, so Janyor is older than Pelsol. Therefore the answer is yes. | yes | [
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43eeba6bc295fef6 | 3be1c23212778fa0 | Show this expression: ((-7) + (((-3) * (-5)) * 10)). | 1. Observe that evaluate (-3) * (-5) to get 15.
2. From this evaluate ((-3) * (-5)) * 10 to get 150.
3. Consequently evaluate (-7) + (((-3) * (-5)) * 10) to get 143.
Hence, 143. | 143 | [
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00cefc60696ff278 | 4331c7bfa14f246c | Work through the value of ((((-2)+(-4))*((-8)-(-4)))+(2*7)). | Start by Evaluate (-2) + (-4) to get -6. After that Evaluate (-8) - (-4) to get -4. Now Evaluate ((-2) + (-4)) * ((-8) - (-4)) to get 24. Now Evaluate 2 * 7 to get 14. Now Evaluate (((-2) + (-4)) * ((-8) - (-4))) + (2 * 7) to get 38. So we can conclude the answer is 38. | 38 | [
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cbedd046537bdc79 | b7e65babc3d07529 | Decide whether Fimor is taller than Kelhal. Bakel is taller than Wenyor. Fimor is taller than Veltar. Wenyor is taller than Yorbaba. Veltar is taller than Bakel. Kelhal is taller than Fimor. Question: Is Fimor taller than Kelhal? | Observe the ordering constraints. The facts show Kelhal is taller than Fimor via Kelhal -> Fimor, so the query is false. This proves the result is no. | no | [
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00567a4c4bdfdb90 | c0b050e826638912 | 3(m - 6) = -3. Determine the value of m. Assume all quantities are real numbers. | First Divide both sides by 3. We get m - 6 = -1. Next Add 6 on both sides to isolate m. We get m = 5. So the answer is 5. | 5 | [
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5af87f4376f796e0 | a44332422472e3c2 | Determine the value of n in the equation n/4 + 2 = 1/2. | 1. Observe that Subtract 2 on both sides. We get n/4 = -3/2.
2. From this Multiply both sides by 4. We get n = -6.
Hence, -6. | -6 | [
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978c9e0ee7d6a1a6 | 47183f0416e92ada | Use the following facts. - Filin is taller than Kelcormor.
- Galsol is taller than Tarcorcor.
- Tarcorcor is taller than Kelcormor.
- Wenba is taller than Galsol.
- Kelcormor is taller than Linlin.
- Filin is taller than Wenba. Question: Is Galsol taller than Wenba? | The facts show Wenba is taller than Galsol via Wenba -> Galsol, so the query is false.
Therefore the answer is no. | no | [
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f5c7b11c25c7a069 | 472eee0124ce587c | Determine this expression: (((((-2)+(-3))-(9-3))+(-9))-2). | Observe that Evaluate (-2) + (-3) to get -5. From this Evaluate ((-2) + (-3)) - (9 - 3) to get -11. Consequently Evaluate ((((-2) + (-3)) - (9 - 3)) + (-9)) - 2 to get -22. This proves the result is -22. | -22 | [
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20d953b2657c1dbf | 46adcc582d39eb8c | Determine the value of t in the equation 5(t + 1) = 50. Assume all quantities are real numbers. | 1. Observe that Divide both sides by 5. We get t + 1 = 10.
2. From this Subtract 1 on both sides to isolate t. We get t = 9.
Hence, 9. | 9 | [
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8fccf507df051c57 | 7b754cf48c8d80d1 | Decide whether Solyor is faster than Wenfivel. - Sollin is faster than Rintar.
- Velrin is faster than Galsolfi.
- Wenfivel is faster than Velrin.
- Galsolfi is faster than Sollin.
- Rintar is faster than Solyor. Question: Is Solyor faster than Wenfivel? | Observe the ordering constraints. The facts show Wenfivel is faster than Solyor via Wenfivel -> Velrin -> Galsolfi -> Sollin -> Rintar -> Solyor, so the query is false.
This proves the result is no. | no | [
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d4daed412eb4de76 | afe95b4795186312 | Find t in the equation t/2 - 6 = -6. Assume all quantities are real numbers. | Observe that Add 6 on both sides. We get t/2 = 0. From this Multiply both sides by 2. We get t = 0. This proves the result is 0. | 0 | [
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72f39b3b6800a38a | 872aec757193f72d | 2(n + 2) = -10. Solve for n. | Start by Divide both sides by 2. We get n + 2 = -5.
After that Subtract 2 on both sides to isolate n. We get n = -7.
So we can conclude the answer is -7. | -7 | [
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3b7e1920691c3fc4 | bbc8794c79a963b7 | 2(m - 4) = 10. Find m. Assume all quantities are real numbers. | 1. First Divide both sides by 2. We get m - 4 = 5.
2. Next Add 4 on both sides to isolate m. We get m = 9.
So the answer is 9. | 9 | [
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56ed0d927f66086d | 5137a0b806857b21 | Decide whether Solba is taller than Pelzan. - Pelzan is taller than Solba.
- Wenjan is taller than Halwenmor.
- Halwenmor is taller than Halcorzan.
- Solba is taller than Wenjan. Question: Is Solba taller than Pelzan? | The facts show Pelzan is taller than Solba via Pelzan -> Solba, so the query is false.
So the answer is no. | no | [
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30dabcf0e406524a | 24f6a68a87c02050 | Determine the value of m: 6(m) = 42. | First Divide both sides by 6. We get m = 7. Next m is already isolated. We get m = 7. Therefore the answer is 7. | 7 | [
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f7bb6d7f9f36a8bc | 2017c033d7e1afc2 | Work out the value of ((3 + 9) - 15). | First Evaluate 3 + 9 to get 12. Next Evaluate (3 + 9) - 15 to get -3. So the answer is -3. | -3 | [
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3f780e1d5c55a0e7 | 20480c49e3eb91c8 | Determine the value of (((-2) * 12) * (4 - 0)). | Observe that Evaluate (-2) * 12 to get -24. From this Evaluate 4 - 0 to get 4. Consequently Evaluate ((-2) * 12) * (4 - 0) to get -96. Hence, -96. | -96 | [
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de1d43f8d9f5cd6b | 3f12da160220677a | Compute this expression: ((-6) - (((-3) - 5) - (4 + (-8)))). | 1. First evaluate (-3) - 5 to get -8.
2. Next evaluate 4 + (-8) to get -4.
3. Then evaluate ((-3) - 5) - (4 + (-8)) to get -4.
4. Then evaluate (-6) - (((-3) - 5) - (4 + (-8))) to get -2.
So the answer is -2. | -2 | [
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58dd01f51b35eda4 | f17e698bf3aa929a | Use the following facts. - Rinrin is heavier than Keltar.
- Keltar is heavier than Morvel.
- Pelpel is heavier than Rinrin. Question: Is Morvel heavier than Pelpel? | The facts show Pelpel is heavier than Morvel via Pelpel -> Rinrin -> Keltar -> Morvel, so the query is false.
So the answer is no. | no | [
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acbd7a4573b4da7d | 0b49ed48626d1988 | Determine the value of x in the equation 2(x + 2) = -4. Assume all quantities are real numbers. | Observe that Divide both sides by 2. We get x + 2 = -2. From this Subtract 2 on both sides to isolate x. We get x = -4. Hence, -4. | -4 | [
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dcec7d8fc75b9ca0 | f7e4bb33e40cd485 | Find ((-9) * ((12 * 13) - 13)). | 1. First evaluate 12 * 13 to get 156.
2. Next evaluate (12 * 13) - 13 to get 143.
3. Then evaluate (-9) * ((12 * 13) - 13) to get -1287.
So the answer is -1287. | -1287 | [
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b553f1484efea603 | 37ce085ad48fbe77 | Show the value of (3 * (11 * 11)). | Observe that Evaluate 11 * 11 to get 121. From this Evaluate 3 * (11 * 11) to get 363. This proves the result is 363. | 363 | [
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"difficulty": 1,
"skill_tags": [
"math",
"arithme... |
d5ceb9e6c2b9dd4a | 87b69bc787209070 | Use the following facts. - Ficor is taller than Janpelden.
- Rinkellin is taller than Ficor.
- Corzancor is taller than Rinkellin. Question: Is Janpelden taller than Ficor? | Start by linking the facts together. The facts show Ficor is taller than Janpelden via Ficor -> Janpelden, so the query is false.
That leaves us with no. | no | [
"comparative-reasoning",
"comparison_logic",
"difficulty:1",
"format:numbered",
"logic",
"style:tutor",
"transitivity"
] | {
"accepted": true,
"correctness": true,
"trace_consistency": true,
"surface_diversity": 0.5,
"novelty": 0.28,
"leakage_risk": 0,
"readability": 0.869,
"reject_reasons": []
} | {
"family": "comparison_logic",
"difficulty": 1,
"feature_signature": [
"comparison_logic",
"difficulty=1",
"facts=3",
"answer=no",
"attribute=taller"
],
"spec": {
"family": "comparison_logic",
"difficulty": 1,
"skill_tags": [
"logic",
"comparative-reasoning",
... |
b8cb69b5bdf12493 | b8fbc1b353eaaafe | Try solving the value of ((9 * 9) * (((12 * 12) * (-5)) + 10)). | Start by Evaluate 9 * 9 to get 81. After that Evaluate 12 * 12 to get 144. Now Evaluate (12 * 12) * (-5) to get -720. Now Evaluate ((12 * 12) * (-5)) + 10 to get -710. Now Evaluate (9 * 9) * (((12 * 12) * (-5)) + 10) to get -57510. So we can conclude the answer is -57510. | -57510 | [
"arithmetic",
"arithmetic_expression",
"difficulty:3",
"expression-evaluation",
"format:paragraph",
"math",
"style:tutor"
] | {
"accepted": true,
"correctness": true,
"trace_consistency": true,
"surface_diversity": 0.4444,
"novelty": 0.4074,
"leakage_risk": 0,
"readability": 0.7622,
"reject_reasons": []
} | {
"family": "arithmetic_expression",
"difficulty": 3,
"feature_signature": [
"arithmetic_expression",
"difficulty=3",
"depth=4",
"mul=4",
"sub=0",
"notation=spaced"
],
"spec": {
"family": "arithmetic_expression",
"difficulty": 3,
"skill_tags": [
"math",
"arithme... |
aa84aec2f3b67ee3 | 30f099b1ff72e9f0 | Compute (((-4) - 8) - (5 + 15)). | 1. First evaluate (-4) - 8 to get -12.
2. Next evaluate 5 + 15 to get 20.
3. Then evaluate ((-4) - 8) - (5 + 15) to get -32.
So the answer is -32. | -32 | [
"arithmetic",
"arithmetic_expression",
"difficulty:2",
"expression-evaluation",
"format:numbered",
"math",
"style:direct"
] | {
"accepted": true,
"correctness": true,
"trace_consistency": true,
"surface_diversity": 0.5833,
"novelty": 0.2381,
"leakage_risk": 0,
"readability": 0.7498,
"reject_reasons": []
} | {
"family": "arithmetic_expression",
"difficulty": 2,
"feature_signature": [
"arithmetic_expression",
"difficulty=2",
"depth=2",
"mul=0",
"sub=2",
"notation=spaced"
],
"spec": {
"family": "arithmetic_expression",
"difficulty": 2,
"skill_tags": [
"math",
"arithme... |
afa3eaa5005a3b4c | ca562c804e370258 | Determine the value of m: m/3 - 5 = -14/3. | Start by Add 5 on both sides. We get m/3 = 1/3. After that Multiply both sides by 3. We get m = 1. So we can conclude the answer is 1. | 1 | [
"algebra",
"difficulty:4",
"format:paragraph",
"linear-equations",
"linear_equation",
"math",
"style:tutor"
] | {
"accepted": true,
"correctness": true,
"trace_consistency": true,
"surface_diversity": 0.5952,
"novelty": 0.3929,
"leakage_risk": 0,
"readability": 0.8094,
"reject_reasons": []
} | {
"family": "linear_equation",
"difficulty": 4,
"feature_signature": [
"linear_equation",
"difficulty=4",
"pattern=x_over_a_plus_b",
"depth=3",
"notation=spaced"
],
"spec": {
"family": "linear_equation",
"difficulty": 4,
"skill_tags": [
"math",
"algebra",
"lin... |
35ed1478ebe1cb31 | c90c4f913f578263 | Decide whether Norkelpel is taller than Yorpel. - Zanrin is taller than Kelcorcor.
- Kelcorcor is taller than Norkelpel.
- Norrinhal is taller than Yorpel.
- Yorpel is taller than Zanrin. Question: Is Norkelpel taller than Yorpel? | The facts show Yorpel is taller than Norkelpel via Yorpel -> Zanrin -> Kelcorcor -> Norkelpel, so the query is false.
Therefore the answer is no. | no | [
"comparative-reasoning",
"comparison_logic",
"difficulty:2",
"format:numbered",
"logic",
"style:direct",
"transitivity"
] | {
"accepted": true,
"correctness": true,
"trace_consistency": true,
"surface_diversity": 0.375,
"novelty": 0.3158,
"leakage_risk": 0,
"readability": 0.825,
"reject_reasons": []
} | {
"family": "comparison_logic",
"difficulty": 2,
"feature_signature": [
"comparison_logic",
"difficulty=2",
"facts=4",
"answer=no",
"attribute=taller"
],
"spec": {
"family": "comparison_logic",
"difficulty": 2,
"skill_tags": [
"logic",
"comparative-reasoning",
... |
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Synthetic Data Factory 5k
This dataset contains 5,000 synthetic math and logic examples generated without LLM-based generation.
File
generated_5000.jsonl: JSONL rows with problem text, explanation text, final answer, tags, metadata, and quality report.
Families
- arithmetic expression evaluation
- linear equation solving
- comparison logic / transitive reasoning
Generation approach
Examples are created through a world-model-first pipeline:
- latent structured problem specification
- exact symbolic or rule-based teacher
- controlled renderer for natural-language problems and explanations
- validation, deduplication, and quality gating
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