data_type stringclasses 5
values | answer_start_char int64 18 266 ⌀ | tokens list | id int64 0 2.35k | answer_char_len int64 1 19 ⌀ | tokens_len int64 11 3.78k | shows_work bool 1
class | tokenizer stringclasses 1
value | char_len int64 19 5.75k | rule stringlengths 5 10 ⌀ | word_problem_type stringclasses 3
values | kind stringclasses 4
values | txt stringlengths 19 5.75k |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
boolean | null | [
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101,... | 1,800 | null | 1,893 | null | cl100k_base | 2,898 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((1 ∧ V) ∧ (V ∨ 1)) ∨ ((¬1) ∨ (1 ∨ S))
Options:
((¬1) ∨ (1 ∨ S)) ∨ ((1 ∧ V) ∧ (V ∨ 1))
(((1 ∧ V) ∧ (V ∨ 1)) ∨ (¬1)) ∨ (1 ∨ S)
((1 ∧ V) ∧ (V ∨ 1)) ∨ ((1 ∨ S) ∨ (¬1))
((1 ∧ V) ∧ (V ∨ 1)) ∨ (((¬1) ∨ 1) ∨ S)
((1 ∧ V) ∧ (V ∨ ... |
boolean | null | [
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51... | 1,801 | null | 869 | null | cl100k_base | 1,436 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬D) ∧ (0 ∧ W)) ∧ ((1 ∧ 1) ∨ (¬1))
Options:
((1 ∧ 1) ∨ (¬1)) ∧ ((¬D) ∧ (0 ∧ W))
(¬D) ∧ ((0 ∧ W) ∧ ((1 ∧ 1) ∨ (¬1)))
(((¬D) ∧ (0 ∧ W)) ∧ (1 ∧ 1)) ∨ (((¬D) ∧ (0 ∧ W)) ∧ (¬1))
((¬D) ∧ (0 ∧ W)) ∧ ((¬1) ∨ (1 ∧ 1))
((¬D) ∧ (0... |
boolean | null | [
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4489,
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512,
7,
... | 1,802 | null | 621 | null | cl100k_base | 1,040 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((Q ∧ 1) ∧ (Y ∧ Y)) ∨ (¬(0 ∧ 1))
Options:
(¬(0 ∧ 1)) ∨ ((Q ∧ 1) ∧ (Y ∧ Y))
((Q ∧ 1) ∧ (Y ∧ Y)) ∨ ((¬0) ∨ (¬1))
((Q ∧ 1) ∧ (Y ∧ Y)) ∨ (¬0)
((Q ∧ 1) ∧ (Y ∧ Y)) ∨ (¬(1 ∧ 0))
((Y ∧ Y) ∧ (Q ∧ 1)) ∨ (¬(0 ∧ 1))
(((Q ∧ 1) ∧ Y) ∧... |
boolean | null | [
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8,
7... | 1,803 | null | 529 | null | cl100k_base | 927 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(¬Q)) ∧ ((1 ∧ Q) ∧ (¬Q))
Options:
((1 ∧ Q) ∧ (¬Q)) ∧ (¬(¬Q))
((¬(¬Q)) ∧ (1 ∧ Q)) ∧ (¬Q)
(¬(¬Q)) ∧ ((¬Q) ∧ (1 ∧ Q))
(¬(¬Q)) ∧ (1 ∧ (Q ∧ (¬Q)))
(¬(¬Q)) ∧ (Q ∧ (¬Q))
(¬(¬Q)) ∧ ((Q ∧ 1) ∧ (¬Q))
Q ∧ ((1 ∧ Q) ∧ (¬Q))
Chosen:... |
boolean | null | [
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358,
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320,
47,
75078,
358,
4489,
388... | 1,804 | null | 1,326 | null | cl100k_base | 2,291 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬P) ∨ (P ∧ 1)) ∧ ((P ∧ I) ∧ (P ∧ I))
Options:
((P ∧ I) ∧ (P ∧ I)) ∧ ((¬P) ∨ (P ∧ 1))
(((¬P) ∨ (P ∧ 1)) ∧ (P ∧ I)) ∧ (P ∧ I)
((¬P) ∨ (P ∧ 1)) ∧ (((P ∧ I) ∧ P) ∧ I)
((¬P) ∨ (P ∧ 1)) ∧ (P ∧ (I ∧ (P ∧ I)))
((¬P) ∨ (P ∧ 1))... |
boolean | null | [
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1209,
15,
75078,
816,
8... | 1,805 | null | 425 | null | cl100k_base | 749 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(¬Y)) ∧ ((0 ∧ Y) ∨ (¬0))
Options:
((0 ∧ Y) ∨ (¬0)) ∧ (¬(¬Y))
((¬(¬Y)) ∧ (0 ∧ Y)) ∨ ((¬(¬Y)) ∧ (¬0))
(¬(¬Y)) ∧ ((¬0) ∨ (0 ∧ Y))
(¬(¬Y)) ∧ ((0 ∧ Y) ∨ 1)
(¬(¬Y)) ∧ (0 ∨ (¬0))
(¬(¬Y)) ∧ ((Y ∧ 0) ∨ (¬0))
Y ∧ ((0 ∧ Y) ∨ (¬0)... |
boolean | null | [
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3883,
512,
1209... | 1,806 | null | 904 | null | cl100k_base | 1,451 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(0 ∨ F)) ∧ ((F ∧ F) ∧ (1 ∨ 0))
Options:
((F ∧ F) ∧ (1 ∨ 0)) ∧ (¬(0 ∨ F))
((¬(0 ∨ F)) ∧ (F ∧ F)) ∧ (1 ∨ 0)
(¬(0 ∨ F)) ∧ ((1 ∨ 0) ∧ (F ∧ F))
(¬(0 ∨ F)) ∧ (F ∧ (F ∧ (1 ∨ 0)))
(¬(0 ∨ F)) ∧ (((F ∧ F) ∧ 1) ∨ ((F ∧ F) ∧ 0))
(... |
boolean | null | [
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8,
75078,
320,
83193,
15,
4489... | 1,807 | null | 1,253 | null | cl100k_base | 2,090 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((0 ∧ M) ∧ (1 ∧ M)) ∨ ((C ∨ 0) ∧ (¬0))
Options:
((C ∨ 0) ∧ (¬0)) ∨ ((0 ∧ M) ∧ (1 ∧ M))
(((0 ∧ M) ∧ (1 ∧ M)) ∨ (C ∨ 0)) ∧ (((0 ∧ M) ∧ (1 ∧ M)) ∨ (¬0))
((0 ∧ M) ∧ (1 ∧ M)) ∨ ((¬0) ∧ (C ∨ 0))
((0 ∧ M) ∧ (1 ∧ M)) ∨ ((C ∨ 0) ... |
boolean | null | [
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320,
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12264,
101,
1229... | 1,808 | null | 944 | null | cl100k_base | 1,457 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬T) ∨ (0 ∨ 1)) ∧ ((¬Q) ∨ (T ∨ Q))
Options:
((¬Q) ∨ (T ∨ Q)) ∧ ((¬T) ∨ (0 ∨ 1))
(((¬T) ∨ (0 ∨ 1)) ∧ (¬Q)) ∨ (((¬T) ∨ (0 ∨ 1)) ∧ (T ∨ Q))
((¬T) ∨ (0 ∨ 1)) ∧ ((T ∨ Q) ∨ (¬Q))
((¬T) ∨ (0 ∨ 1)) ∧ (((¬Q) ∨ T) ∨ Q)
((¬T) ∨ (0... |
boolean | null | [
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735,
8,
12264,
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320,
15,
12264,... | 1,809 | null | 2,246 | null | cl100k_base | 3,392 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((K ∧ 1) ∧ (T ∨ T)) ∧ ((0 ∨ K) ∨ (0 ∨ 0))
Options:
((0 ∨ K) ∨ (0 ∨ 0)) ∧ ((K ∧ 1) ∧ (T ∨ T))
(K ∧ 1) ∧ ((T ∨ T) ∧ ((0 ∨ K) ∨ (0 ∨ 0)))
(((K ∧ 1) ∧ (T ∨ T)) ∧ (0 ∨ K)) ∨ (((K ∧ 1) ∧ (T ∨ T)) ∧ (0 ∨ 0))
((K ∧ 1) ∧ (T ∨ T))... |
boolean | null | [
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3883,
512,
1209,
83193,
48,
8,
122... | 1,810 | null | 283 | null | cl100k_base | 480 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(¬0)) ∨ ((¬Q) ∨ (¬0))
Options:
((¬Q) ∨ (¬0)) ∨ (¬(¬0))
((¬(¬0)) ∨ (¬Q)) ∨ (¬0)
(¬(¬0)) ∨ ((¬0) ∨ (¬Q))
(¬(¬0)) ∨ ((¬Q) ∨ 1)
0 ∨ ((¬Q) ∨ (¬0))
(¬1) ∨ ((¬Q) ∨ (¬0))
Chosen: 0 ∨ ((¬Q) ∨ (¬0))
Options:
(¬Q) ∨ (¬0)
((¬Q) ∨... |
boolean | null | [
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264,
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7645,
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595,
75078,
320,
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7,
16,
75078,
735,
4489,
3883,
512,
7,
83193,... | 1,811 | null | 687 | null | cl100k_base | 1,091 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬K) ∨ (1 ∨ 1)) ∧ (¬(1 ∧ K))
Options:
(¬(1 ∧ K)) ∧ ((¬K) ∨ (1 ∨ 1))
((¬K) ∨ (1 ∨ 1)) ∧ ((¬1) ∨ (¬K))
((¬K) ∨ (1 ∨ 1)) ∧ (¬K)
((¬K) ∨ (1 ∨ 1)) ∧ (¬(K ∧ 1))
((1 ∨ 1) ∨ (¬K)) ∧ (¬(1 ∧ K))
(((¬K) ∨ 1) ∨ 1) ∧ (¬(1 ∧ K))
((¬K... |
boolean | null | [
39314,
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264,
2777,
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527,
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315,
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34,
8,
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320,
38,
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356,
595,
75078,
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101,
220,
16,
8,
12264,
101,
320,
83193,
34,... | 1,812 | null | 1,222 | null | cl100k_base | 1,862 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬C) ∨ (G ∨ C)) ∧ ((0 ∨ 1) ∨ (¬C))
Options:
((0 ∨ 1) ∨ (¬C)) ∧ ((¬C) ∨ (G ∨ C))
(((¬C) ∨ (G ∨ C)) ∧ (0 ∨ 1)) ∨ (((¬C) ∨ (G ∨ C)) ∧ (¬C))
((¬C) ∨ (G ∨ C)) ∧ ((¬C) ∨ (0 ∨ 1))
((¬C) ∨ (G ∨ C)) ∧ (0 ∨ (1 ∨ (¬C)))
((¬C) ∨ (G... |
boolean | null | [
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264,
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433,
527,
5897,
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315,
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1630,
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320,
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816,
595,
12264,
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320,
83193,
7,
16,
12264,
101,
1630,
4489,
38... | 1,813 | null | 1,748 | null | cl100k_base | 2,588 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((0 ∨ X) ∨ (1 ∨ Y)) ∨ (¬(1 ∨ X))
Options:
(¬(1 ∨ X)) ∨ ((0 ∨ X) ∨ (1 ∨ Y))
(0 ∨ X) ∨ ((1 ∨ Y) ∨ (¬(1 ∨ X)))
((0 ∨ X) ∨ (1 ∨ Y)) ∨ ((¬1) ∧ (¬X))
((0 ∨ X) ∨ (1 ∨ Y)) ∨ (¬1)
((0 ∨ X) ∨ (1 ∨ Y)) ∨ (¬(X ∨ 1))
((1 ∨ Y) ∨ (0 ∨ ... |
boolean | null | [
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264,
2777,
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315,
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12264,
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320,
83193,
7,
47,
75078,
432,
4489,
3883,
512,... | 1,814 | null | 594 | null | cl100k_base | 983 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((0 ∨ R) ∧ (1 ∨ 1)) ∨ (¬(P ∧ R))
Options:
(¬(P ∧ R)) ∨ ((0 ∨ R) ∧ (1 ∨ 1))
((0 ∨ R) ∧ (1 ∨ 1)) ∨ ((¬P) ∨ (¬R))
((0 ∨ R) ∧ (1 ∨ 1)) ∨ (¬(R ∧ P))
((1 ∨ 1) ∧ (0 ∨ R)) ∨ (¬(P ∧ R))
(((0 ∨ R) ∧ 1) ∨ ((0 ∨ R) ∧ 1)) ∨ (¬(P ∧ R)... |
boolean | null | [
39314,
374,
264,
2777,
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527,
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315,
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549,
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38,
75078,
480,
4489,
3883,
512,
1209... | 1,815 | null | 562 | null | cl100k_base | 942 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(1 ∧ 0)) ∨ ((1 ∨ U) ∧ (G ∧ G))
Options:
((1 ∨ U) ∧ (G ∧ G)) ∨ (¬(1 ∧ 0))
((¬(1 ∧ 0)) ∨ (1 ∨ U)) ∧ ((¬(1 ∧ 0)) ∨ (G ∧ G))
(¬(1 ∧ 0)) ∨ ((G ∧ G) ∧ (1 ∨ U))
(¬(1 ∧ 0)) ∨ (((1 ∨ U) ∧ G) ∧ G)
(¬(1 ∧ 0)) ∨ ((1 ∨ U) ∧ G)
(¬(1... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
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7645,
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18902,
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650,
4489,
3883,
512,
1209,
44,
12264,
1... | 1,816 | null | 520 | null | cl100k_base | 953 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(¬1)) ∧ ((M ∨ M) ∧ (V ∧ V))
Options:
((M ∨ M) ∧ (V ∧ V)) ∧ (¬(¬1))
((¬(¬1)) ∧ (M ∨ M)) ∧ (V ∧ V)
(¬(¬1)) ∧ ((V ∧ V) ∧ (M ∨ M))
(¬(¬1)) ∧ (((M ∨ M) ∧ V) ∧ V)
(¬(¬1)) ∧ ((M ∨ M) ∧ V)
(¬(¬1)) ∧ (M ∧ (V ∧ V))
1 ∧ ((M ∨ M) ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
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18902,
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16,
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3883,
512,
7,
83193,
7,
83193,
15,
595,
75078,
320,
8319... | 1,817 | null | 229 | null | cl100k_base | 440 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(1 ∧ W)) ∧ (¬(¬0))
Options:
(¬(¬0)) ∧ (¬(1 ∧ W))
(¬(1 ∧ W)) ∧ 0
(¬(1 ∧ W)) ∧ (¬1)
((¬1) ∨ (¬W)) ∧ (¬(¬0))
(¬W) ∧ (¬(¬0))
(¬(W ∧ 1)) ∧ (¬(¬0))
Chosen: (¬W) ∧ (¬(¬0))
Options:
(¬(¬0)) ∧ (¬W)
(¬W) ∧ 0
(¬W) ∧ (¬1)
Chosen:... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
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7645,
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1229,
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320,
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220,
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4489,
3883,
512,
7,
83193,
7,
48,
12264,
101,
1229,... | 1,818 | null | 328 | null | cl100k_base | 561 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((Q ∨ Q) ∨ (Q ∨ 1))
Options:
(¬(Q ∨ Q)) ∧ (¬(Q ∨ 1))
¬((Q ∨ 1) ∨ (Q ∨ Q))
¬(((Q ∨ Q) ∨ Q) ∨ 1)
¬(Q ∨ (Q ∨ (Q ∨ 1)))
¬((Q ∨ Q) ∨ 1)
¬((Q ∨ Q) ∨ (1 ∨ Q))
¬(Q ∨ (Q ∨ 1))
Chosen: ¬((Q ∨ Q) ∨ 1)
Options:
(¬(Q ∨ Q)) ∧ (¬1)
¬... |
boolean | null | [
39314,
374,
264,
2777,
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527,
5897,
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16,
12264,
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1901,
4489,
3883,
512,
16,
12264,
101,
1901,
198,
83193,
1209,
83193,
16,
8,
75078,
320,
83193,
... | 1,819 | null | 79 | null | cl100k_base | 198 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬(¬(1 ∨ Z))
Options:
1 ∨ Z
¬((¬1) ∧ (¬Z))
¬(¬1)
¬(¬(Z ∨ 1))
Chosen: ¬(¬1)
Options:
1
¬0
Chosen: 1 |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
83193,
46,
8,
75078,
320,
15,
75078,
220,
16,
595,
12264,
101,
1819,
15,
12264,
101,
220,
16,
8,
12264,
101,
320,
83193,
46,
... | 1,820 | null | 1,280 | null | cl100k_base | 1,889 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬O) ∧ (0 ∧ 1)) ∨ ((0 ∨ 1) ∨ (¬O))
Options:
((0 ∨ 1) ∨ (¬O)) ∨ ((¬O) ∧ (0 ∧ 1))
(((¬O) ∧ (0 ∧ 1)) ∨ (0 ∨ 1)) ∨ (¬O)
((¬O) ∧ (0 ∧ 1)) ∨ ((¬O) ∨ (0 ∨ 1))
((¬O) ∧ (0 ∧ 1)) ∨ (0 ∨ (1 ∨ (¬O)))
((¬O) ∧ (0 ∧ 1)) ∨ (1 ∨ (¬O))
(... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
46,
75078,
220,
16,
8,
75078,
320,
46,
12264,
101,
386,
595,
75078,
1819,
15,
12264,
101,
507,
8,
12264,
101,
320,
44,
12264,... | 1,821 | null | 1,805 | null | cl100k_base | 2,822 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((O ∧ 1) ∧ (O ∨ M)) ∧ ((0 ∨ O) ∨ (M ∨ 0))
Options:
((0 ∨ O) ∨ (M ∨ 0)) ∧ ((O ∧ 1) ∧ (O ∨ M))
(O ∧ 1) ∧ ((O ∨ M) ∧ ((0 ∨ O) ∨ (M ∨ 0)))
(((O ∧ 1) ∧ (O ∨ M)) ∧ (0 ∨ O)) ∨ (((O ∧ 1) ∧ (O ∨ M)) ∧ (M ∨ 0))
((O ∧ 1) ∧ (O ∨ M))... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
1209,
34,
75078,
356,
8,
12264,
101,
320,
15,
12264,
101,
350,
4489,
3883,
512,
7,
83193,
7,
34,
75078,
356,
595,
75078,
320... | 1,822 | null | 243 | null | cl100k_base | 470 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((C ∧ C) ∨ (0 ∨ T))
Options:
(¬(C ∧ C)) ∧ (¬(0 ∨ T))
¬((0 ∨ T) ∨ (C ∧ C))
¬(((C ∧ C) ∨ 0) ∨ T)
¬((C ∧ C) ∨ T)
¬((C ∧ C) ∨ (T ∨ 0))
¬(C ∨ (0 ∨ T))
Chosen: ¬((C ∧ C) ∨ T)
Options:
(¬(C ∧ C)) ∧ (¬T)
¬(T ∨ (C ∧ C))
¬(C ∨ T... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
320,
83193,
7,
16,
75078,
432,
595,
75078,
1819,
83193,
16,
8,
12264,
101,
320,
83193,
49,
4489,
3883,
512,
1209,
83193,
16,
8,
122... | 1,823 | null | 524 | null | cl100k_base | 884 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(1 ∧ R)) ∧ ((¬1) ∨ (¬R))
Options:
((¬1) ∨ (¬R)) ∧ (¬(1 ∧ R))
((¬(1 ∧ R)) ∧ (¬1)) ∨ ((¬(1 ∧ R)) ∧ (¬R))
(¬(1 ∧ R)) ∧ ((¬R) ∨ (¬1))
(¬(1 ∧ R)) ∧ (0 ∨ (¬R))
((¬1) ∨ (¬R)) ∧ ((¬1) ∨ (¬R))
(¬R) ∧ ((¬1) ∨ (¬R))
(¬(R ∧ 1)) ∧ ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
320,
83193,
7,
83193,
15,
595,
75078,
1819,
36,
12264,
101,
469,
8,
75078,
320,
36,
75078,
220,
16,
4489,
3883,
512,
1209,
36,
1226... | 1,824 | null | 881 | null | cl100k_base | 1,481 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(¬0)) ∧ ((E ∨ E) ∧ (E ∧ 1))
Options:
((E ∨ E) ∧ (E ∧ 1)) ∧ (¬(¬0))
((¬(¬0)) ∧ (E ∨ E)) ∧ (E ∧ 1)
(¬(¬0)) ∧ ((E ∧ 1) ∧ (E ∨ E))
(¬(¬0)) ∧ (((E ∨ E) ∧ E) ∧ 1)
(¬(¬0)) ∧ ((E ∨ E) ∧ E)
(¬(¬0)) ∧ ((E ∨ E) ∧ (1 ∧ E))
(¬(¬0))... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
44,
12264,
101,
1901,
8,
75078,
320,
83193,
44,
595,
75078,
1819,
15,
75078,
220,
16,
8,
12264,
101,
320,
83193,
16,
4489,
38... | 1,825 | null | 1,473 | null | cl100k_base | 2,351 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((M ∨ Z) ∧ (¬M)) ∧ ((0 ∧ 1) ∨ (¬1))
Options:
((0 ∧ 1) ∨ (¬1)) ∧ ((M ∨ Z) ∧ (¬M))
(M ∨ Z) ∧ ((¬M) ∧ ((0 ∧ 1) ∨ (¬1)))
(((M ∨ Z) ∧ (¬M)) ∧ (0 ∧ 1)) ∨ (((M ∨ Z) ∧ (¬M)) ∧ (¬1))
((M ∨ Z) ∧ (¬M)) ∧ ((¬1) ∨ (0 ∧ 1))
((M ∨ Z) ∧... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
7,
83193,
7,
52,
75078,
549,
4489,
3883,
512,
52,
75078,
549,
198,
83193,
1209,
83193,
52,
8,
12264,
101,
320,
83193,
52,
11... | 1,826 | null | 64 | null | cl100k_base | 183 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬(¬(U ∧ U))
Options:
U ∧ U
¬((¬U) ∨ (¬U))
¬(¬U)
Chosen: ¬(¬U)
Options:
U
Chosen: U |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
52,
75078,
816,
8,
75078,
320,
52,
12264,
101,
549,
595,
75078,
1819,
83193,
56,
8,
12264,
101,
320,
52,
75078,
549,
4489,
38... | 1,827 | null | 1,169 | null | cl100k_base | 2,039 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((U ∧ Y) ∧ (U ∨ U)) ∧ ((¬Y) ∨ (U ∧ U))
Options:
((¬Y) ∨ (U ∧ U)) ∧ ((U ∧ Y) ∧ (U ∨ U))
(U ∧ Y) ∧ ((U ∨ U) ∧ ((¬Y) ∨ (U ∧ U)))
(((U ∧ Y) ∧ (U ∨ U)) ∧ (¬Y)) ∨ (((U ∧ Y) ∧ (U ∨ U)) ∧ (U ∧ U))
((U ∧ Y) ∧ (U ∨ U)) ∧ ((U ∧ U) ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
7,
83193,
7,
83193,
15,
4489,
3883,
512,
83193,
15,
198,
83193,
7,
83193,
16,
340,
1163,
8477,
25,
97265,
7,
83193,
16,
696,... | 1,828 | null | 55 | null | cl100k_base | 165 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬(¬(¬0))
Options:
¬0
¬(¬1)
Chosen: ¬(¬1)
Options:
1
¬0
Chosen: 1 |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
1209,
39,
75078,
220,
15,
8,
12264,
101,
320,
44,
75078,
220,
16,
4489,
3883,
512,
7,
83193,
7,
39,
75078,
220,
15,
595,
7... | 1,829 | null | 386 | null | cl100k_base | 671 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((H ∧ 0) ∨ (M ∧ 1))
Options:
(¬(H ∧ 0)) ∧ (¬(M ∧ 1))
¬((M ∧ 1) ∨ (H ∧ 0))
¬(((H ∧ 0) ∨ M) ∧ ((H ∧ 0) ∨ 1))
¬((H ∧ 0) ∨ M)
¬((H ∧ 0) ∨ (1 ∧ M))
¬(0 ∨ (M ∧ 1))
¬((0 ∧ H) ∨ (M ∧ 1))
Chosen: ¬((0 ∧ H) ∨ (M ∧ 1))
Options:
(... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
83193,
51,
8,
75078,
320,
43,
12264,
101,
220,
15,
595,
75078,
320,
83193,
7,
16,
75078,
220,
15,
4489,
3883,
512,
7,
83193,
... | 1,830 | null | 1,940 | null | cl100k_base | 3,077 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬T) ∧ (L ∨ 0)) ∧ (¬(1 ∧ 0))
Options:
(¬(1 ∧ 0)) ∧ ((¬T) ∧ (L ∨ 0))
(¬T) ∧ ((L ∨ 0) ∧ (¬(1 ∧ 0)))
((¬T) ∧ (L ∨ 0)) ∧ ((¬1) ∨ (¬0))
((¬T) ∧ (L ∨ 0)) ∧ (¬0)
((¬T) ∧ (L ∨ 0)) ∧ (¬(0 ∧ 1))
((L ∨ 0) ∧ (¬T)) ∧ (¬(1 ∧ 0))
(((¬... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
15,
12264,
101,
480,
8,
12264,
101,
320,
33,
12264,
101,
426,
595,
75078,
1819,
15,
75078,
426,
8,
75078,
320,
16,
75078,
426... | 1,831 | null | 1,523 | null | cl100k_base | 2,582 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((0 ∨ G) ∨ (B ∨ B)) ∧ ((0 ∧ B) ∧ (1 ∧ B))
Options:
((0 ∧ B) ∧ (1 ∧ B)) ∧ ((0 ∨ G) ∨ (B ∨ B))
(((0 ∨ G) ∨ (B ∨ B)) ∧ (0 ∧ B)) ∧ (1 ∧ B)
((0 ∨ G) ∨ (B ∨ B)) ∧ ((1 ∧ B) ∧ (0 ∧ B))
((0 ∨ G) ∨ (B ∨ B)) ∧ (((0 ∧ B) ∧ 1) ∧ B)
(... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
83193,
47,
8,
12264,
101,
320,
83193,
47,
595,
75078,
1819,
46,
75078,
393,
8,
75078,
320,
16,
75078,
507,
4489,
3883,
512,
1... | 1,832 | null | 932 | null | cl100k_base | 1,646 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬P) ∨ (¬P)) ∧ ((O ∧ P) ∧ (1 ∧ O))
Options:
((O ∧ P) ∧ (1 ∧ O)) ∧ ((¬P) ∨ (¬P))
(((¬P) ∨ (¬P)) ∧ (O ∧ P)) ∧ (1 ∧ O)
((¬P) ∨ (¬P)) ∧ ((1 ∧ O) ∧ (O ∧ P))
((¬P) ∨ (¬P)) ∧ (((O ∧ P) ∧ 1) ∧ O)
((¬P) ∨ (¬P)) ∧ (O ∧ (P ∧ (1 ∧ ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
32,
12264,
101,
220,
16,
8,
12264,
101,
320,
16,
12264,
101,
220,
15,
595,
75078,
1819,
45,
12264,
101,
220,
15,
8,
12264,
... | 1,833 | null | 2,428 | null | cl100k_base | 3,404 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((A ∨ 1) ∨ (1 ∨ 0)) ∧ ((N ∨ 0) ∨ (A ∨ A))
Options:
((N ∨ 0) ∨ (A ∨ A)) ∧ ((A ∨ 1) ∨ (1 ∨ 0))
(((A ∨ 1) ∨ (1 ∨ 0)) ∧ (N ∨ 0)) ∨ (((A ∨ 1) ∨ (1 ∨ 0)) ∧ (A ∨ A))
((A ∨ 1) ∨ (1 ∨ 0)) ∧ ((A ∨ A) ∨ (N ∨ 0))
((A ∨ 1) ∨ (1 ∨ 0))... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
320,
83193,
7,
83193,
16,
595,
75078,
1819,
16,
12264,
101,
220,
15,
8,
12264,
101,
320,
16,
75078,
220,
15,
4489,
3883,
512,
1209,... | 1,834 | null | 857 | null | cl100k_base | 1,292 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(¬1)) ∧ ((1 ∨ 0) ∨ (1 ∧ 0))
Options:
((1 ∨ 0) ∨ (1 ∧ 0)) ∧ (¬(¬1))
((¬(¬1)) ∧ (1 ∨ 0)) ∨ ((¬(¬1)) ∧ (1 ∧ 0))
(¬(¬1)) ∧ ((1 ∧ 0) ∨ (1 ∨ 0))
(¬(¬1)) ∧ (1 ∨ (0 ∨ (1 ∧ 0)))
(¬(¬1)) ∧ (((1 ∨ 0) ∨ 1) ∧ ((1 ∨ 0) ∨ 0))
(¬(¬1))... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
83193,
48,
8,
12264,
101,
320,
39,
12264,
101,
220,
16,
595,
12264,
101,
1819,
16,
75078,
220,
15,
8,
12264,
101,
320,
83193,... | 1,835 | null | 1,126 | null | cl100k_base | 1,619 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬Q) ∨ (H ∨ 1)) ∨ ((1 ∧ 0) ∨ (¬Q))
Options:
((1 ∧ 0) ∨ (¬Q)) ∨ ((¬Q) ∨ (H ∨ 1))
(((¬Q) ∨ (H ∨ 1)) ∨ (1 ∧ 0)) ∨ (¬Q)
(¬Q) ∨ ((H ∨ 1) ∨ ((1 ∧ 0) ∨ (¬Q)))
((¬Q) ∨ (H ∨ 1)) ∨ ((¬Q) ∨ (1 ∧ 0))
((¬Q) ∨ (H ∨ 1)) ∨ (0 ∨ (¬Q))
(... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
83193,
15,
8,
12264,
101,
320,
46,
75078,
220,
16,
595,
75078,
1819,
44,
75078,
386,
8,
12264,
101,
320,
83193,
46,
4489,
388... | 1,836 | null | 796 | null | cl100k_base | 1,292 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬0) ∨ (O ∧ 1)) ∧ ((M ∧ M) ∨ (¬O))
Options:
((M ∧ M) ∨ (¬O)) ∧ ((¬0) ∨ (O ∧ 1))
(((¬0) ∨ (O ∧ 1)) ∧ (M ∧ M)) ∨ (((¬0) ∨ (O ∧ 1)) ∧ (¬O))
((¬0) ∨ (O ∧ 1)) ∧ ((¬O) ∨ (M ∧ M))
((¬0) ∨ (O ∧ 1)) ∧ (M ∨ (¬O))
((O ∧ 1) ∨ (¬0))... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
83193,
16,
8,
12264,
101,
320,
40,
12264,
101,
358,
595,
12264,
101,
320,
83193,
7,
15,
75078,
426,
4489,
3883,
512,
7,
83193... | 1,837 | null | 659 | null | cl100k_base | 1,022 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬1) ∨ (I ∨ I)) ∨ (¬(0 ∧ B))
Options:
(¬(0 ∧ B)) ∨ ((¬1) ∨ (I ∨ I))
(¬1) ∨ ((I ∨ I) ∨ (¬(0 ∧ B)))
((¬1) ∨ (I ∨ I)) ∨ ((¬0) ∨ (¬B))
((¬1) ∨ (I ∨ I)) ∨ (¬0)
((¬1) ∨ (I ∨ I)) ∨ (¬(B ∧ 0))
((I ∨ I) ∨ (¬1)) ∨ (¬(0 ∧ B))
(((¬... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
16,
75078,
220,
15,
8,
75078,
320,
15,
75078,
220,
16,
595,
12264,
101,
1819,
16,
12264,
101,
423,
8,
12264,
101,
320,
16,
... | 1,838 | null | 1,296 | null | cl100k_base | 1,898 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((1 ∧ 0) ∧ (0 ∧ 1)) ∨ ((1 ∨ D) ∨ (1 ∨ 0))
Options:
((1 ∨ D) ∨ (1 ∨ 0)) ∨ ((1 ∧ 0) ∧ (0 ∧ 1))
(((1 ∧ 0) ∧ (0 ∧ 1)) ∨ (1 ∨ D)) ∨ (1 ∨ 0)
((1 ∧ 0) ∧ (0 ∧ 1)) ∨ ((1 ∨ 0) ∨ (1 ∨ D))
((1 ∧ 0) ∧ (0 ∧ 1)) ∨ (((1 ∨ D) ∨ 1) ∨ 0)
(... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
55,
12264,
101,
469,
8,
12264,
101,
320,
16,
12264,
101,
220,
15,
595,
12264,
101,
1819,
83193,
15,
8,
12264,
101,
320,
16,
... | 1,839 | null | 2,053 | null | cl100k_base | 2,735 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((X ∨ E) ∨ (1 ∨ 0)) ∨ ((¬0) ∨ (1 ∨ 0))
Options:
((¬0) ∨ (1 ∨ 0)) ∨ ((X ∨ E) ∨ (1 ∨ 0))
(((X ∨ E) ∨ (1 ∨ 0)) ∨ (¬0)) ∨ (1 ∨ 0)
(X ∨ E) ∨ ((1 ∨ 0) ∨ ((¬0) ∨ (1 ∨ 0)))
((X ∨ E) ∨ (1 ∨ 0)) ∨ ((1 ∨ 0) ∨ (¬0))
((X ∨ E) ∨ (1 ∨ ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
16,
12264,
101,
220,
16,
8,
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101,
320,
16,
75078,
220,
16,
595,
12264,
101,
1819,
16,
12264,
101,
622,
8,
75078,
320,
... | 1,840 | null | 1,198 | null | cl100k_base | 1,782 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((1 ∨ 1) ∨ (1 ∧ 1)) ∨ ((1 ∨ J) ∧ (S ∨ J))
Options:
((1 ∨ J) ∧ (S ∨ J)) ∨ ((1 ∨ 1) ∨ (1 ∧ 1))
(1 ∨ 1) ∨ ((1 ∧ 1) ∨ ((1 ∨ J) ∧ (S ∨ J)))
(((1 ∨ 1) ∨ (1 ∧ 1)) ∨ (1 ∨ J)) ∧ (((1 ∨ 1) ∨ (1 ∧ 1)) ∨ (S ∨ J))
((1 ∨ 1) ∨ (1 ∧ 1))... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
1209,
83193,
15,
8,
12264,
101,
320,
48,
75078,
220,
15,
4489,
3883,
512,
7,
83193,
7,
83193,
15,
595,
75078,
320,
83193,
7,... | 1,841 | null | 184 | null | cl100k_base | 351 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((¬0) ∨ (Q ∧ 0))
Options:
(¬(¬0)) ∧ (¬(Q ∧ 0))
¬((Q ∧ 0) ∨ (¬0))
¬(((¬0) ∨ Q) ∧ ((¬0) ∨ 0))
¬((¬0) ∨ 0)
¬((¬0) ∨ (0 ∧ Q))
¬(1 ∨ (Q ∧ 0))
Chosen: ¬((¬0) ∨ 0)
Options:
(¬(¬0)) ∧ (¬0)
¬(¬0)
¬1
¬(0 ∨ (¬0))
¬(1 ∨ 0)
Chosen:... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
7,
83193,
7,
44,
12264,
101,
650,
4489,
3883,
512,
44,
12264,
101,
650,
198,
83193,
1209,
83193,
44,
8,
75078,
320,
83193,
5... | 1,842 | null | 75 | null | cl100k_base | 197 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬(¬(M ∨ V))
Options:
M ∨ V
¬((¬M) ∧ (¬V))
¬(¬(V ∨ M))
Chosen: M ∨ V
Options:
V ∨ M
Chosen: V ∨ M |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
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7645,
382,
18902,
25,
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16,
75078,
220,
15,
8,
12264,
101,
320,
44,
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622,
595,
75078,
1819,
83193,
16,
8,
75078,
320,
15,
12264,
101,
220,
15,
... | 1,843 | null | 932 | null | cl100k_base | 1,509 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((1 ∧ 0) ∨ (M ∧ J)) ∧ ((¬1) ∧ (0 ∨ 0))
Options:
((¬1) ∧ (0 ∨ 0)) ∧ ((1 ∧ 0) ∨ (M ∧ J))
(((1 ∧ 0) ∨ (M ∧ J)) ∧ (¬1)) ∧ (0 ∨ 0)
((1 ∧ 0) ∨ (M ∧ J)) ∧ ((0 ∨ 0) ∧ (¬1))
((1 ∧ 0) ∨ (M ∧ J)) ∧ (((¬1) ∧ 0) ∨ ((¬1) ∧ 0))
((1 ∧ 0... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
320,
83193,
7,
49,
12264,
101,
432,
595,
12264,
101,
1819,
83193,
15,
8,
12264,
101,
320,
83193,
44,
4489,
3883,
512,
1209,
83193,
... | 1,844 | null | 407 | null | cl100k_base | 657 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(R ∨ R)) ∨ ((¬0) ∨ (¬M))
Options:
((¬0) ∨ (¬M)) ∨ (¬(R ∨ R))
((¬(R ∨ R)) ∨ (¬0)) ∨ (¬M)
(¬(R ∨ R)) ∨ ((¬M) ∨ (¬0))
(¬(R ∨ R)) ∨ (1 ∨ (¬M))
((¬R) ∧ (¬R)) ∨ ((¬0) ∨ (¬M))
(¬R) ∨ ((¬0) ∨ (¬M))
Chosen: (¬R) ∨ ((¬0) ∨ (¬M))... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
83193,
16,
8,
75078,
320,
83193,
39,
595,
75078,
320,
83193,
7,
39,
12264,
101,
220,
15,
4489,
3883,
512,
7,
83193,
7,
39,
... | 1,845 | null | 568 | null | cl100k_base | 968 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬1) ∧ (¬H)) ∧ (¬(H ∨ 0))
Options:
(¬(H ∨ 0)) ∧ ((¬1) ∧ (¬H))
(¬1) ∧ ((¬H) ∧ (¬(H ∨ 0)))
((¬1) ∧ (¬H)) ∧ ((¬H) ∧ (¬0))
((¬1) ∧ (¬H)) ∧ (¬H)
((¬1) ∧ (¬H)) ∧ (¬(0 ∨ H))
((¬H) ∧ (¬1)) ∧ (¬(H ∨ 0))
(0 ∧ (¬H)) ∧ (¬(H ∨ 0))
C... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
35,
75078,
220,
16,
8,
75078,
320,
83193,
15,
595,
75078,
320,
83193,
7,
34,
75078,
220,
15,
4489,
3883,
512,
7,
83193,
7,
... | 1,846 | null | 742 | null | cl100k_base | 1,259 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((D ∧ 1) ∧ (¬0)) ∧ (¬(C ∧ 0))
Options:
(¬(C ∧ 0)) ∧ ((D ∧ 1) ∧ (¬0))
(D ∧ 1) ∧ ((¬0) ∧ (¬(C ∧ 0)))
((D ∧ 1) ∧ (¬0)) ∧ ((¬C) ∨ (¬0))
((D ∧ 1) ∧ (¬0)) ∧ (¬0)
((D ∧ 1) ∧ (¬0)) ∧ (¬(0 ∧ C))
((¬0) ∧ (D ∧ 1)) ∧ (¬(C ∧ 0))
(D ∧... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
320,
83193,
7,
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16,
595,
12264,
101,
320,
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7,
39,
75078,
220,
15,
4489,
3883,
512,
7,
83193,
7,
39,
75078,
220,
15,
5... | 1,847 | null | 239 | null | cl100k_base | 422 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(¬1)) ∨ (¬(H ∧ 0))
Options:
(¬(H ∧ 0)) ∨ (¬(¬1))
(¬(¬1)) ∨ ((¬H) ∨ (¬0))
(¬(¬1)) ∨ (¬0)
(¬(¬1)) ∨ (¬(0 ∧ H))
1 ∨ (¬(H ∧ 0))
(¬0) ∨ (¬(H ∧ 0))
Chosen: 1 ∨ (¬(H ∧ 0))
Options:
1
(¬(H ∧ 0)) ∨ 1
1 ∨ ((¬H) ∨ (¬0))
1 ∨ (¬0)... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
1209,
39,
75078,
473,
8,
12264,
101,
320,
32,
75078,
220,
15,
4489,
3883,
512,
7,
83193,
7,
39,
75078,
473,
595,
75078,
320,... | 1,848 | null | 230 | null | cl100k_base | 431 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((H ∧ H) ∨ (A ∧ 0))
Options:
(¬(H ∧ H)) ∧ (¬(A ∧ 0))
¬((A ∧ 0) ∨ (H ∧ H))
¬(((H ∧ H) ∨ A) ∧ ((H ∧ H) ∨ 0))
¬((H ∧ H) ∨ 0)
¬((H ∧ H) ∨ (0 ∧ A))
¬(H ∨ (A ∧ 0))
Chosen: ¬(H ∨ (A ∧ 0))
Options:
(¬H) ∧ (¬(A ∧ 0))
¬((A ∧ 0) ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
320,
83193,
7,
54,
75078,
220,
15,
595,
12264,
101,
1819,
54,
12264,
101,
220,
16,
8,
75078,
320,
16,
12264,
101,
220,
15,
4489,
... | 1,849 | null | 804 | null | cl100k_base | 1,167 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(W ∧ 0)) ∨ ((W ∨ 1) ∧ (1 ∨ 0))
Options:
((W ∨ 1) ∧ (1 ∨ 0)) ∨ (¬(W ∧ 0))
((¬(W ∧ 0)) ∨ (W ∨ 1)) ∧ ((¬(W ∧ 0)) ∨ (1 ∨ 0))
(¬(W ∧ 0)) ∨ ((1 ∨ 0) ∧ (W ∨ 1))
(¬(W ∧ 0)) ∨ (((W ∨ 1) ∧ 1) ∨ ((W ∨ 1) ∧ 0))
(¬(W ∧ 0)) ∨ ((W ∨ ... |
factorization | null | [
791,
445,
10190,
320,
82916,
7874,
29911,
8,
374,
279,
25655,
1396,
8649,
1855,
315,
279,
2768,
5219,
439,
3512,
42314,
13,
35813,
25,
220,
806,
11,
2970,
11,
1490,
198,
8724,
44,
25,
220,
3192,
508
] | 1,850 | null | 37 | null | cl100k_base | 137 | null | null | LCM | The LCM (Least Common Multiple) is the smallest number containing each of the following numbers as divisors. Numbers: 11,58,80
LCM: 25520 |
factorization | null | [
845,
262,
220,
24,
198,
4314,
5219,
6,
445,
10190,
374,
25,
220,
8929
] | 1,851 | null | 14 | null | cl100k_base | 35 | null | null | LCM | 16 9
These numbers' LCM is: 144 |
factorization | null | [
35,
25296,
279,
445,
10190,
271,
868,
271,
975,
198,
791,
445,
10190,
25,
220,
8848
] | 1,852 | null | 16 | null | cl100k_base | 38 | null | null | LCM | Determine the LCM
15
14
The LCM: 210 |
factorization | null | [
35,
25296,
279,
445,
10190,
271,
972,
3929,
220,
2137,
3929,
220,
1490,
198,
791,
445,
10190,
25,
220,
25612,
15
] | 1,853 | null | 21 | null | cl100k_base | 49 | null | null | LCM | Determine the LCM
18 --> 39 --> 80
The LCM: 9360 |
factorization | null | [
28336,
25,
220,
23,
11,
777,
11,
845,
11,
2983,
198,
82916,
7874,
29911,
320,
8724,
44,
1680,
220,
24495,
19
] | 1,854 | null | 21 | null | cl100k_base | 53 | null | null | LCM | Numbers: 8,19,16,42
Least Common Multiple (LCM): 6384 |
factorization | null | [
28336,
25,
220,
972,
674,
220,
1272,
674,
220,
4103,
674,
220,
2148,
198,
82916,
7874,
29911,
320,
8724,
44,
1680,
220,
9591,
13837
] | 1,855 | null | 24 | null | cl100k_base | 62 | null | null | LCM | Numbers: 18 # 40 # 52 # 31
Least Common Multiple (LCM): 145080 |
factorization | null | [
28336,
25,
220,
1114,
220,
220,
17,
220,
220,
2397,
198,
8724,
44,
25,
220,
12425,
15
] | 1,856 | null | 17 | null | cl100k_base | 28 | null | null | LCM | Numbers: 17 2 65
LCM: 2210 |
factorization | null | [
10086,
279,
445,
10190,
25,
220,
1927,
201,
914,
198,
8724,
44,
25,
220,
7467
] | 1,857 | null | 15 | null | cl100k_base | 28 | null | null | LCM | Find the LCM: 36
25
LCM: 900 |
factorization | null | [
35,
25296,
279,
445,
10190,
271,
1644,
765,
220,
17,
198,
791,
445,
10190,
25,
220,
2287
] | 1,858 | null | 17 | null | cl100k_base | 37 | null | null | LCM | Determine the LCM
33 | 2
The LCM: 66 |
factorization | null | [
35,
25296,
279,
445,
10190,
271,
3971,
405,
19,
405,
868,
405,
1114,
198,
791,
445,
10190,
25,
220,
4278,
15
] | 1,859 | null | 21 | null | cl100k_base | 46 | null | null | LCM | Determine the LCM
51->4->15->17
The LCM: 1020 |
factorization | null | [
791,
445,
10190,
320,
82916,
7874,
29911,
8,
374,
279,
25655,
1396,
8649,
1855,
315,
279,
2768,
5219,
439,
3512,
42314,
13,
35813,
25,
220,
1114,
11,
220,
975,
11,
220,
22,
198,
8724,
44,
25,
220,
13895
] | 1,860 | null | 38 | null | cl100k_base | 136 | null | null | LCM | The LCM (Least Common Multiple) is the smallest number containing each of the following numbers as divisors. Numbers: 17, 14, 7
LCM: 238 |
factorization | null | [
10086,
279,
445,
10190,
25,
220,
22,
765,
220,
806,
198,
8724,
44,
25,
220,
2813
] | 1,861 | null | 16 | null | cl100k_base | 28 | null | null | LCM | Find the LCM: 7 | 11
LCM: 77 |
factorization | null | [
28336,
25,
220,
1313,
197,
2096,
198,
82916,
7874,
29911,
320,
8724,
44,
1680,
220,
2096
] | 1,862 | null | 16 | null | cl100k_base | 46 | null | null | LCM | Numbers: 22 44
Least Common Multiple (LCM): 44 |
factorization | null | [
39314,
374,
264,
1160,
315,
5219,
13,
7531,
872,
3325,
4279,
5361,
382,
24,
765,
220,
914,
1432,
8724,
44,
25,
11057
] | 1,863 | null | 22 | null | cl100k_base | 79 | null | null | LCM | Below is a list of numbers. Find their least common multiple.
9 | 25
LCM:225 |
factorization | null | [
28336,
25,
220,
972,
11,
220,
21,
11,
220,
2137,
11,
220,
972,
11,
220,
717,
11,
220,
2031,
198,
8724,
44,
25,
220,
9892,
1490
] | 1,864 | null | 26 | null | cl100k_base | 41 | null | null | LCM | Numbers: 18, 6, 39, 18, 12, 70
LCM: 16380 |
factorization | null | [
35,
25296,
279,
87179,
25,
220,
1591,
1174,
220,
1682,
198,
82916,
4279,
5361,
271,
19270
] | 1,865 | null | 16 | null | cl100k_base | 53 | null | null | LCM | Determine the lcm: 28 , 29
Least common multiple
812 |
factorization | null | [
28336,
25,
220,
1806,
198,
975,
198,
8724,
44,
25,
220,
21312
] | 1,866 | null | 12 | null | cl100k_base | 23 | null | null | LCM | Numbers: 37
14
LCM: 518 |
factorization | null | [
39314,
374,
264,
1160,
315,
5219,
13,
7531,
872,
3325,
4279,
5361,
382,
6028,
220,
1114,
220,
1644,
220,
1419,
220,
777,
220,
2983,
1432,
8724,
44,
25,
14052,
22347,
24824
] | 1,867 | null | 31 | null | cl100k_base | 96 | null | null | LCM | Below is a list of numbers. Find their least common multiple.
71 17 33 23 19 42
LCM:243686058 |
factorization | null | [
4370,
91,
1682,
198,
50828,
445,
10190,
374,
25,
220,
10132,
21
] | 1,868 | null | 12 | null | cl100k_base | 24 | null | null | LCM | 54|29
their LCM is: 1566 |
factorization | null | [
10086,
279,
445,
10190,
25,
220,
1032,
11,
220,
1419,
198,
8724,
44,
25,
220,
15531
] | 1,869 | null | 16 | null | cl100k_base | 29 | null | null | LCM | Find the LCM: 13, 23
LCM: 299 |
factorization | null | [
21,
262,
220,
5332,
262,
220,
23,
262,
220,
24,
198,
50828,
445,
10190,
374,
25,
220,
5332
] | 1,870 | null | 18 | null | cl100k_base | 34 | null | null | LCM | 6 72 8 9
their LCM is: 72 |
factorization | null | [
3990,
279,
87179,
18,
405,
975,
405,
24,
198,
75,
6358,
25,
220,
9390
] | 1,871 | null | 14 | null | cl100k_base | 29 | null | null | LCM | find the lcm3->14->9
lcm: 126 |
factorization | null | [
2491,
220,
220,
22,
220,
220,
4578,
198,
4314,
5219,
6,
445,
10190,
374,
25,
220,
21299,
16
] | 1,872 | null | 18 | null | cl100k_base | 38 | null | null | LCM | 49 7 89
These numbers' LCM is: 4361 |
factorization | null | [
10086,
279,
445,
10190,
25,
220,
3487,
405,
2970,
198,
8724,
44,
25,
220,
10674,
19
] | 1,873 | null | 16 | null | cl100k_base | 30 | null | null | LCM | Find the LCM: 56->58
LCM: 1624 |
factorization | null | [
10086,
279,
91616,
7874,
29911,
1990,
279,
2768,
5219,
271,
1774,
11,
220,
1114,
271,
16533,
25,
220,
22240
] | 1,874 | null | 19 | null | cl100k_base | 81 | null | null | LCM | Find the Least Common Multiple between the following numbers
45, 17
Answer: 765 |
factorization | null | [
10086,
279,
91616,
7874,
29911,
1990,
279,
2768,
5219,
271,
777,
198,
17,
271,
16533,
25,
220,
1987
] | 1,875 | null | 18 | null | cl100k_base | 78 | null | null | LCM | Find the Least Common Multiple between the following numbers
19
2
Answer: 38 |
factorization | null | [
39314,
374,
264,
1160,
315,
5219,
13,
7531,
872,
3325,
4279,
5361,
382,
975,
405,
20,
1432,
8724,
44,
25,
2031
] | 1,876 | null | 21 | null | cl100k_base | 77 | null | null | LCM | Below is a list of numbers. Find their least common multiple.
14->5
LCM:70 |
factorization | null | [
20,
262,
220,
508,
262,
220,
18,
198,
50828,
445,
10190,
374,
25,
220,
1399
] | 1,877 | null | 15 | null | cl100k_base | 29 | null | null | LCM | 5 20 3
their LCM is: 60 |
factorization | null | [
3990,
279,
87179,
20,
198,
1032,
198,
1987,
198,
75,
6358,
25,
220,
14125,
15
] | 1,878 | null | 15 | null | cl100k_base | 29 | null | null | LCM | find the lcm5
13
38
lcm: 2470 |
factorization | null | [
35,
25296,
279,
445,
10190,
271,
22,
3929,
220,
9892,
198,
791,
445,
10190,
25,
220,
8011,
16
] | 1,879 | null | 18 | null | cl100k_base | 42 | null | null | LCM | Determine the LCM
7 --> 163
The LCM: 1141 |
factorization | null | [
35,
25296,
279,
87179,
25,
220,
1544,
198,
2491,
198,
82916,
4279,
5361,
271,
9413,
18
] | 1,880 | null | 16 | null | cl100k_base | 52 | null | null | LCM | Determine the lcm: 27
49
Least common multiple
1323 |
factorization | null | [
28336,
25,
220,
6549,
3929,
220,
868,
3929,
220,
605,
198,
82916,
7874,
29911,
320,
8724,
44,
1680,
220,
11711
] | 1,881 | null | 20 | null | cl100k_base | 59 | null | null | LCM | Numbers: 125 --> 15 --> 10
Least Common Multiple (LCM): 750 |
factorization | null | [
10086,
279,
91616,
7874,
29911,
1990,
279,
2768,
5219,
271,
717,
674,
220,
508,
271,
16533,
25,
220,
1399
] | 1,882 | null | 19 | null | cl100k_base | 81 | null | null | LCM | Find the Least Common Multiple between the following numbers
12 # 20
Answer: 60 |
factorization | null | [
39314,
374,
264,
1160,
315,
5219,
13,
7531,
872,
3325,
4279,
5361,
382,
914,
201,
24,
1432,
8724,
44,
25,
11057
] | 1,883 | null | 21 | null | cl100k_base | 77 | null | null | LCM | Below is a list of numbers. Find their least common multiple.
25
9
LCM:225 |
factorization | null | [
18257,
704,
279,
445,
10190,
25,
220,
1682,
201,
717,
198,
75,
6358,
25,
220,
19746
] | 1,884 | null | 16 | null | cl100k_base | 34 | null | null | LCM | figure out the LCM: 29
12
lcm: 348 |
factorization | null | [
18257,
704,
279,
445,
10190,
25,
220,
966,
674,
220,
5547,
198,
75,
6358,
25,
220,
10750,
15
] | 1,885 | null | 18 | null | cl100k_base | 37 | null | null | LCM | figure out the LCM: 30 # 61
lcm: 1830 |
factorization | null | [
972,
11,
220,
1758,
198,
50828,
445,
10190,
374,
25,
220,
18660
] | 1,886 | null | 12 | null | cl100k_base | 24 | null | null | LCM | 18, 35
their LCM is: 630 |
factorization | null | [
10086,
279,
91616,
7874,
29911,
1990,
279,
2768,
5219,
271,
966,
765,
220,
1272,
765,
220,
1627,
271,
16533,
25,
220,
10132,
15
] | 1,887 | null | 23 | null | cl100k_base | 88 | null | null | LCM | Find the Least Common Multiple between the following numbers
30 | 40 | 26
Answer: 1560 |
factorization | null | [
28336,
25,
220,
24,
1174,
220,
20,
198,
82916,
7874,
29911,
320,
8724,
44,
1680,
220,
1774
] | 1,888 | null | 17 | null | cl100k_base | 46 | null | null | LCM | Numbers: 9 , 5
Least Common Multiple (LCM): 45 |
factorization | null | [
4044,
11,
23,
11,
23,
198,
4314,
5219,
6,
445,
10190,
374,
25,
220,
23578
] | 1,889 | null | 15 | null | cl100k_base | 34 | null | null | LCM | 87,8,8
These numbers' LCM is: 696 |
factorization | null | [
20,
11,
220,
22,
198,
50828,
445,
10190,
374,
25,
220,
1758
] | 1,890 | null | 12 | null | cl100k_base | 21 | null | null | LCM | 5, 7
their LCM is: 35 |
factorization | null | [
791,
445,
10190,
320,
82916,
7874,
29911,
8,
374,
279,
25655,
1396,
8649,
1855,
315,
279,
2768,
5219,
439,
3512,
42314,
13,
35813,
25,
220,
21,
3929,
220,
1591,
198,
8724,
44,
25,
220,
5833
] | 1,891 | null | 35 | null | cl100k_base | 134 | null | null | LCM | The LCM (Least Common Multiple) is the smallest number containing each of the following numbers as divisors. Numbers: 6 --> 28
LCM: 84 |
factorization | null | [
791,
445,
10190,
320,
82916,
7874,
29911,
8,
374,
279,
25655,
1396,
8649,
1855,
315,
279,
2768,
5219,
439,
3512,
42314,
13,
35813,
25,
220,
605,
11,
1187,
11,
1627,
11,
1958,
198,
8724,
44,
25,
220,
14374,
508
] | 1,892 | null | 39 | null | cl100k_base | 140 | null | null | LCM | The LCM (Least Common Multiple) is the smallest number containing each of the following numbers as divisors. Numbers: 10,24,26,34
LCM: 26520 |
factorization | null | [
10086,
279,
445,
10190,
25,
220,
22,
91,
1313,
198,
8724,
44,
25,
220,
10559
] | 1,893 | null | 15 | null | cl100k_base | 27 | null | null | LCM | Find the LCM: 7|22
LCM: 154 |
factorization | null | [
18257,
704,
279,
445,
10190,
25,
220,
1399,
271,
24,
198,
75,
6358,
25,
220,
5245
] | 1,894 | null | 16 | null | cl100k_base | 34 | null | null | LCM | figure out the LCM: 60
9
lcm: 180 |
factorization | null | [
10086,
279,
445,
10190,
25,
220,
1691,
91,
20,
91,
1806,
91,
1114,
91,
1927,
91,
972,
198,
8724,
44,
25,
220,
24763,
17048
] | 1,895 | null | 24 | null | cl100k_base | 42 | null | null | LCM | Find the LCM: 21|5|37|17|36|18
LCM: 792540 |
factorization | null | [
791,
445,
10190,
320,
82916,
7874,
29911,
8,
374,
279,
25655,
1396,
8649,
1855,
315,
279,
2768,
5219,
439,
3512,
42314,
13,
35813,
25,
220,
24,
197,
1806,
198,
8724,
44,
25,
220,
8765
] | 1,896 | null | 34 | null | cl100k_base | 131 | null | null | LCM | The LCM (Least Common Multiple) is the smallest number containing each of the following numbers as divisors. Numbers: 9 37
LCM: 333 |
factorization | null | [
28336,
25,
220,
19,
201,
1958,
198,
8724,
44,
25,
220,
2614
] | 1,897 | null | 12 | null | cl100k_base | 21 | null | null | LCM | Numbers: 4
34
LCM: 68 |
factorization | null | [
28336,
25,
220,
717,
262,
220,
845,
198,
82916,
7874,
29911,
320,
8724,
44,
1680,
220,
2166
] | 1,898 | null | 17 | null | cl100k_base | 49 | null | null | LCM | Numbers: 12 16
Least Common Multiple (LCM): 48 |
factorization | null | [
28336,
25,
220,
21,
197,
20,
198,
8724,
44,
25,
220,
966
] | 1,899 | null | 12 | null | cl100k_base | 20 | null | null | LCM | Numbers: 6 5
LCM: 30 |
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