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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4489,... | 1,700 | null | 1,999 | null | cl100k_base | 3,155 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((0 ∧ 0) ∨ (1 ∧ 1)) ∧ ((0 ∧ J) ∧ (¬0))
Options:
((0 ∧ J) ∧ (¬0)) ∧ ((0 ∧ 0) ∨ (1 ∧ 1))
(((0 ∧ 0) ∨ (1 ∧ 1)) ∧ (0 ∧ J)) ∧ (¬0)
((0 ∧ 0) ∨ (1 ∧ 1)) ∧ ((¬0) ∧ (0 ∧ J))
((0 ∧ 0) ∨ (1 ∧ 1)) ∧ (0 ∧ (J ∧ (¬0)))
((0 ∧ 0) ∨ (1 ∧ ... |
boolean | null | [
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12... | 1,701 | null | 289 | null | cl100k_base | 482 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(S ∨ S)) ∨ (¬(S ∨ 0))
Options:
(¬(S ∨ 0)) ∨ (¬(S ∨ S))
(¬(S ∨ S)) ∨ ((¬S) ∧ (¬0))
(¬(S ∨ S)) ∨ (¬S)
(¬(S ∨ S)) ∨ (¬(0 ∨ S))
((¬S) ∧ (¬S)) ∨ (¬(S ∨ 0))
(¬S) ∨ (¬(S ∨ 0))
Chosen: (¬S) ∨ (¬(S ∨ 0))
Options:
(¬(S ∨ 0)) ∨ ... |
boolean | null | [
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41,
4489,
3883,
5... | 1,702 | null | 1,013 | null | cl100k_base | 1,694 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬0) ∧ (O ∧ J)) ∨ ((O ∨ J) ∧ (¬J))
Options:
((O ∨ J) ∧ (¬J)) ∨ ((¬0) ∧ (O ∧ J))
(((¬0) ∧ (O ∧ J)) ∨ (O ∨ J)) ∧ (((¬0) ∧ (O ∧ J)) ∨ (¬J))
((¬0) ∧ (O ∧ J)) ∨ ((¬J) ∧ (O ∨ J))
((¬0) ∧ (O ∧ J)) ∨ ((J ∨ O) ∧ (¬J))
((O ∧ J) ∧... |
boolean | null | [
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7,
83193,
7,
83193,
16,
595,
12264,
101,
320,... | 1,703 | null | 225 | null | cl100k_base | 411 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(¬N)) ∨ (¬(¬1))
Options:
(¬(¬1)) ∨ (¬(¬N))
(¬(¬N)) ∨ 1
(¬(¬N)) ∨ (¬0)
N ∨ (¬(¬1))
Chosen: (¬(¬1)) ∨ (¬(¬N))
Options:
(¬(¬1)) ∨ N
1 ∨ (¬(¬N))
(¬0) ∨ (¬(¬N))
Chosen: (¬0) ∨ (¬(¬N))
Options:
(¬(¬N)) ∨ (¬0)
(¬0) ∨ N
1 ∨ ... |
boolean | null | [
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47,
8,
12264,
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320,
34,
12264,
101,
220,
16,
4489,
3883,
... | 1,704 | null | 636 | null | cl100k_base | 917 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(0 ∨ 1)) ∨ ((¬P) ∨ (C ∨ 1))
Options:
((¬P) ∨ (C ∨ 1)) ∨ (¬(0 ∨ 1))
((¬(0 ∨ 1)) ∨ (¬P)) ∨ (C ∨ 1)
(¬(0 ∨ 1)) ∨ ((C ∨ 1) ∨ (¬P))
(¬(0 ∨ 1)) ∨ (((¬P) ∨ C) ∨ 1)
(¬(0 ∨ 1)) ∨ ((¬P) ∨ 1)
(¬(0 ∨ 1)) ∨ ((¬P) ∨ (1 ∨ C))
((¬0) ∧... |
boolean | null | [
39314,
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264,
2777,
7645,
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433,
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5897,
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1229,
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15,
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1229,
4489,
3883,
512,
7,
83193,
7,
15,
12264,
101,... | 1,705 | null | 343 | null | cl100k_base | 602 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(Q ∨ Q)) ∧ (¬(0 ∨ Q))
Options:
(¬(0 ∨ Q)) ∧ (¬(Q ∨ Q))
(¬(Q ∨ Q)) ∧ ((¬0) ∧ (¬Q))
(¬(Q ∨ Q)) ∧ (¬Q)
(¬(Q ∨ Q)) ∧ (¬(Q ∨ 0))
((¬Q) ∧ (¬Q)) ∧ (¬(0 ∨ Q))
(¬Q) ∧ (¬(0 ∨ Q))
Chosen: (¬(Q ∨ Q)) ∧ (¬(Q ∨ 0))
Options:
(¬(Q ∨ ... |
boolean | null | [
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264,
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7,
16,
75078,
480,
4489,
3883,
512,
7,
... | 1,706 | null | 956 | null | cl100k_base | 1,526 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((G ∧ 0) ∨ (G ∧ I)) ∨ (¬(1 ∧ G))
Options:
(¬(1 ∧ G)) ∨ ((G ∧ 0) ∨ (G ∧ I))
(G ∧ 0) ∨ ((G ∧ I) ∨ (¬(1 ∧ G)))
((G ∧ 0) ∨ (G ∧ I)) ∨ ((¬1) ∨ (¬G))
((G ∧ 0) ∨ (G ∧ I)) ∨ (¬G)
((G ∧ 0) ∨ (G ∧ I)) ∨ (¬(G ∧ 1))
((G ∧ I) ∨ (G ∧ ... |
boolean | null | [
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75078,
320,
83193,
46,
4489,
3883,
5... | 1,707 | null | 798 | null | cl100k_base | 1,367 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬1) ∨ (L ∧ L)) ∧ ((0 ∨ L) ∧ (¬O))
Options:
((0 ∨ L) ∧ (¬O)) ∧ ((¬1) ∨ (L ∧ L))
(((¬1) ∨ (L ∧ L)) ∧ (0 ∨ L)) ∧ (¬O)
((¬1) ∨ (L ∧ L)) ∧ ((¬O) ∧ (0 ∨ L))
((¬1) ∨ (L ∧ L)) ∧ (L ∧ (¬O))
((¬1) ∨ (L ∧ L)) ∧ ((L ∨ 0) ∧ (¬O))
(... |
boolean | null | [
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264,
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512,
7,
83193,
7,
83193,
16,
595,
75078,
320,
83193,
7... | 1,708 | null | 323 | null | cl100k_base | 545 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((¬1) ∨ (1 ∨ S))
Options:
(¬(¬1)) ∧ (¬(1 ∨ S))
¬((1 ∨ S) ∨ (¬1))
¬(((¬1) ∨ 1) ∨ S)
¬((¬1) ∨ 1)
¬((¬1) ∨ (S ∨ 1))
¬(0 ∨ (1 ∨ S))
Chosen: ¬(0 ∨ (1 ∨ S))
Options:
(¬0) ∧ (¬(1 ∨ S))
¬(1 ∨ S)
¬((1 ∨ S) ∨ 0)
¬((0 ∨ 1) ∨ S)
¬... |
boolean | null | [
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32,
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320,
83193,
32,
4489,
3883,
512,
1209,
32,
7507... | 1,709 | null | 448 | null | cl100k_base | 784 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(A ∨ A)) ∧ ((A ∧ 0) ∧ (¬A))
Options:
((A ∧ 0) ∧ (¬A)) ∧ (¬(A ∨ A))
((¬(A ∨ A)) ∧ (A ∧ 0)) ∧ (¬A)
(¬(A ∨ A)) ∧ ((¬A) ∧ (A ∧ 0))
(¬(A ∨ A)) ∧ (A ∧ (0 ∧ (¬A)))
(¬(A ∨ A)) ∧ (0 ∧ (¬A))
(¬(A ∨ A)) ∧ ((0 ∧ A) ∧ (¬A))
((¬A) ∧... |
boolean | null | [
39314,
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264,
2777,
7645,
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23548,
433,
527,
5897,
14951,
7607,
315,
430,
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12264,
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452,
595,
75078,
1819,
45,
75078,
452,
8,
12264,
101,
320,
16,
12264,... | 1,710 | null | 1,398 | null | cl100k_base | 2,168 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((N ∨ 0) ∧ (N ∨ N)) ∧ ((N ∧ N) ∨ (1 ∨ 0))
Options:
((N ∧ N) ∨ (1 ∨ 0)) ∧ ((N ∨ 0) ∧ (N ∨ N))
(N ∨ 0) ∧ ((N ∨ N) ∧ ((N ∧ N) ∨ (1 ∨ 0)))
(((N ∨ 0) ∧ (N ∨ N)) ∧ (N ∧ N)) ∨ (((N ∨ 0) ∧ (N ∨ N)) ∧ (1 ∨ 0))
((N ∨ 0) ∧ (N ∨ N))... |
boolean | null | [
39314,
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433,
527,
5897,
14951,
7607,
315,
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220,
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4489,
3883,
512,
1209,
83193,
3... | 1,711 | null | 1,325 | null | cl100k_base | 1,937 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(¬1)) ∨ ((¬B) ∧ (1 ∨ 0))
Options:
((¬B) ∧ (1 ∨ 0)) ∨ (¬(¬1))
((¬(¬1)) ∨ (¬B)) ∧ ((¬(¬1)) ∨ (1 ∨ 0))
(¬(¬1)) ∨ ((1 ∨ 0) ∧ (¬B))
(¬(¬1)) ∨ (((¬B) ∧ 1) ∨ ((¬B) ∧ 0))
(¬(¬1)) ∨ ((¬B) ∧ 1)
(¬(¬1)) ∨ ((¬B) ∧ (0 ∨ 1))
1 ∨ ((¬... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
320,
83193,
7,
32,
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595,
12264,
101,
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32,
12264,
101,
220,
16,
8,
75078,
320,
83193,
16,
4489,
3883,
512,
1209,... | 1,712 | null | 565 | null | cl100k_base | 876 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(A ∧ 0)) ∨ ((A ∨ 1) ∧ (¬1))
Options:
((A ∨ 1) ∧ (¬1)) ∨ (¬(A ∧ 0))
((¬(A ∧ 0)) ∨ (A ∨ 1)) ∧ ((¬(A ∧ 0)) ∨ (¬1))
(¬(A ∧ 0)) ∨ ((¬1) ∧ (A ∨ 1))
(¬(A ∧ 0)) ∨ ((A ∨ 1) ∧ 0)
(¬(A ∧ 0)) ∨ (1 ∧ (¬1))
(¬(A ∧ 0)) ∨ ((1 ∨ A) ∧ (... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
1209,
36,
12264,
101,
622,
8,
75078,
320,
41,
75078,
220,
15,
4489,
3883,
512,
7,
83193,
7,
36,
12264,
101,
622,
595,
12264,... | 1,713 | null | 515 | null | cl100k_base | 836 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((E ∨ J) ∧ (J ∧ 0))
Options:
(¬(E ∨ J)) ∨ (¬(J ∧ 0))
¬((J ∧ 0) ∧ (E ∨ J))
¬(((E ∨ J) ∧ J) ∧ 0)
¬((E ∨ J) ∧ 0)
¬((E ∨ J) ∧ (0 ∧ J))
¬((J ∨ E) ∧ (J ∧ 0))
Chosen: (¬(E ∨ J)) ∨ (¬(J ∧ 0))
Options:
(¬(J ∧ 0)) ∨ (¬(E ∨ J))
(... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
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16,
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358,
8,
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83193,
50,
4489,
3883,
512,
7,
83193,
7,
16,
12264,
101,
358,
595,
75078,
320... | 1,714 | null | 441 | null | cl100k_base | 746 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((1 ∨ I) ∨ (¬S))
Options:
(¬(1 ∨ I)) ∧ (¬(¬S))
¬((¬S) ∨ (1 ∨ I))
¬(1 ∨ (I ∨ (¬S)))
¬(1 ∨ (¬S))
¬((I ∨ 1) ∨ (¬S))
Chosen: ¬((I ∨ 1) ∨ (¬S))
Options:
(¬(I ∨ 1)) ∧ (¬(¬S))
¬((¬S) ∨ (I ∨ 1))
¬(I ∨ (1 ∨ (¬S)))
¬(1 ∨ (¬S))
C... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
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16,
12264,
101,
220,
15,
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12264,
101,
320,
83193,
35,
595,
12264,
101,
320,
83193,
7,
15,
12264,
101,
220,
16,
4489,
3883,
... | 1,715 | null | 510 | null | cl100k_base | 765 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((1 ∨ 0) ∨ (¬D)) ∨ (¬(0 ∨ 1))
Options:
(¬(0 ∨ 1)) ∨ ((1 ∨ 0) ∨ (¬D))
(1 ∨ 0) ∨ ((¬D) ∨ (¬(0 ∨ 1)))
((1 ∨ 0) ∨ (¬D)) ∨ ((¬0) ∧ (¬1))
((1 ∨ 0) ∨ (¬D)) ∨ (¬1)
((1 ∨ 0) ∨ (¬D)) ∨ (¬(1 ∨ 0))
((¬D) ∨ (1 ∨ 0)) ∨ (¬(0 ∨ 1))
(1 ∨... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
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83193,
7,
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3883,
512,
83193,
15,
198,
83193,
7,
83193,
16,
340,
1163,
8477,
25,
97265,
15,
271,
3883,
512... | 1,716 | null | 50 | null | cl100k_base | 159 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬(¬(¬0))
Options:
¬0
¬(¬1)
Chosen: ¬0
Options:
1
Chosen: 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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12264,
101,
220,
15,
8,
12264,
101,
... | 1,717 | null | 1,862 | null | cl100k_base | 2,660 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((H ∨ B) ∨ (H ∨ 0)) ∧ ((1 ∨ 0) ∨ (B ∧ 1))
Options:
((1 ∨ 0) ∨ (B ∧ 1)) ∧ ((H ∨ B) ∨ (H ∨ 0))
(((H ∨ B) ∨ (H ∨ 0)) ∧ (1 ∨ 0)) ∨ (((H ∨ B) ∨ (H ∨ 0)) ∧ (B ∧ 1))
((H ∨ B) ∨ (H ∨ 0)) ∧ ((B ∧ 1) ∨ (1 ∨ 0))
((H ∨ B) ∨ (H ∨ 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,
35,
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12264,
101,
1819,
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549,
8,
75078,
320,
35,
75078,
549,
4489,
3883,
512,
1209,
52,
75078,
5... | 1,718 | null | 502 | null | cl100k_base | 908 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(¬D)) ∨ ((U ∧ U) ∧ (D ∧ U))
Options:
((U ∧ U) ∧ (D ∧ U)) ∨ (¬(¬D))
((¬(¬D)) ∨ (U ∧ U)) ∧ ((¬(¬D)) ∨ (D ∧ U))
(¬(¬D)) ∨ ((D ∧ U) ∧ (U ∧ U))
(¬(¬D)) ∨ (((U ∧ U) ∧ D) ∧ U)
(¬(¬D)) ∨ (U ∧ (U ∧ (D ∧ U)))
(¬(¬D)) ∨ ((U ∧ U) ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
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7645,
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426,
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8,
12264,
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320,
83193,
35,... | 1,719 | null | 690 | null | cl100k_base | 1,036 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((0 ∧ 0) ∨ (1 ∨ B)) ∨ ((¬1) ∨ (¬D))
Options:
((¬1) ∨ (¬D)) ∨ ((0 ∧ 0) ∨ (1 ∨ B))
(((0 ∧ 0) ∨ (1 ∨ B)) ∨ (¬1)) ∨ (¬D)
(0 ∧ 0) ∨ ((1 ∨ B) ∨ ((¬1) ∨ (¬D)))
((0 ∧ 0) ∨ (1 ∨ B)) ∨ ((¬D) ∨ (¬1))
((0 ∧ 0) ∨ (1 ∨ B)) ∨ (0 ∨ (¬D)... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
33,
75078,
469,
8,
75078,
320,
16,
75078,
220,
15,
595,
75078,
320,
83193,
7,
33,
75078,
469,
4489,
3883,
512,
7,
83193,
7,
... | 1,720 | null | 890 | null | cl100k_base | 1,553 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((B ∧ E) ∧ (1 ∧ 0)) ∧ (¬(B ∧ E))
Options:
(¬(B ∧ E)) ∧ ((B ∧ E) ∧ (1 ∧ 0))
(B ∧ E) ∧ ((1 ∧ 0) ∧ (¬(B ∧ E)))
((B ∧ E) ∧ (1 ∧ 0)) ∧ ((¬B) ∨ (¬E))
((B ∧ E) ∧ (1 ∧ 0)) ∧ (¬(E ∧ B))
((1 ∧ 0) ∧ (B ∧ E)) ∧ (¬(B ∧ E))
(((B ∧ E) ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
83193,
37,
8,
12264,
101,
320,
16,
75078,
435,
595,
12264,
101,
1819,
83193,
16,
8,
75078,
320,
52,
12264,
101,
549,
4489,
38... | 1,721 | null | 946 | null | cl100k_base | 1,511 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬F) ∨ (1 ∧ F)) ∨ ((¬1) ∧ (U ∨ U))
Options:
((¬1) ∧ (U ∨ U)) ∨ ((¬F) ∨ (1 ∧ F))
(¬F) ∨ ((1 ∧ F) ∨ ((¬1) ∧ (U ∨ U)))
(((¬F) ∨ (1 ∧ F)) ∨ (¬1)) ∧ (((¬F) ∨ (1 ∧ F)) ∨ (U ∨ U))
((¬F) ∨ (1 ∧ F)) ∨ ((U ∨ U) ∧ (¬1))
((¬F) ∨ (1... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
83193,
50,
8,
75078,
320,
52,
12264,
101,
220,
15,
595,
75078,
1819,
50,
75078,
328,
8,
12264,
101,
320,
83193,
15,
4489,
388... | 1,722 | null | 780 | null | cl100k_base | 1,322 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬S) ∧ (U ∨ 0)) ∧ ((S ∧ S) ∨ (¬0))
Options:
((S ∧ S) ∨ (¬0)) ∧ ((¬S) ∧ (U ∨ 0))
(¬S) ∧ ((U ∨ 0) ∧ ((S ∧ S) ∨ (¬0)))
(((¬S) ∧ (U ∨ 0)) ∧ (S ∧ S)) ∨ (((¬S) ∧ (U ∨ 0)) ∧ (¬0))
((¬S) ∧ (U ∨ 0)) ∧ ((¬0) ∨ (S ∧ S))
((¬S) ∧ (U... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
1209,
42,
12264,
101,
735,
8,
12264,
101,
320,
15,
12264,
101,
220,
15,
4489,
3883,
512,
7,
83193,
7,
42,
12264,
101,
735,
... | 1,723 | null | 338 | null | cl100k_base | 554 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((K ∨ K) ∨ (0 ∨ 0))
Options:
(¬(K ∨ K)) ∧ (¬(0 ∨ 0))
¬((0 ∨ 0) ∨ (K ∨ K))
¬(((K ∨ K) ∨ 0) ∨ 0)
¬(K ∨ (K ∨ (0 ∨ 0)))
¬((K ∨ K) ∨ 0)
¬(K ∨ (0 ∨ 0))
Chosen: ¬(((K ∨ K) ∨ 0) ∨ 0)
Options:
(¬((K ∨ K) ∨ 0)) ∧ (¬0)
¬((K ∨ K) ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
39,
75078,
650,
8,
75078,
320,
83193,
53,
595,
12264,
101,
1819,
16,
75078,
220,
15,
8,
75078,
320,
53,
12264,
101,
650,
4489... | 1,724 | null | 1,009 | null | cl100k_base | 1,700 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((H ∧ V) ∧ (¬V)) ∨ ((1 ∧ 0) ∧ (V ∨ V))
Options:
((1 ∧ 0) ∧ (V ∨ V)) ∨ ((H ∧ V) ∧ (¬V))
(((H ∧ V) ∧ (¬V)) ∨ (1 ∧ 0)) ∧ (((H ∧ V) ∧ (¬V)) ∨ (V ∨ V))
((H ∧ V) ∧ (¬V)) ∨ ((V ∨ V) ∧ (1 ∧ 0))
((H ∧ V) ∧ (¬V)) ∨ (1 ∧ (0 ∧ (V ∨ ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
38,
12264,
101,
220,
16,
8,
12264,
101,
320,
83193,
16,
595,
12264,
101,
320,
83193,
7,
83193,
16,
4489,
3883,
512,
7,
83193,... | 1,725 | null | 359 | null | cl100k_base | 549 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((G ∨ 1) ∨ (¬1)) ∨ (¬(¬1))
Options:
(¬(¬1)) ∨ ((G ∨ 1) ∨ (¬1))
(G ∨ 1) ∨ ((¬1) ∨ (¬(¬1)))
((G ∨ 1) ∨ (¬1)) ∨ 1
((G ∨ 1) ∨ (¬1)) ∨ (¬0)
((¬1) ∨ (G ∨ 1)) ∨ (¬(¬1))
(G ∨ (1 ∨ (¬1))) ∨ (¬(¬1))
((G ∨ 1) ∨ 0) ∨ (¬(¬1))
(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,
47,
595,
75078,
1819,
15,
75078,
735,
8,
75078,
320,
16,
75078,
735,
4489,
3883,
512,
1209,
15,
75078,
735,
8... | 1,726 | null | 686 | null | cl100k_base | 1,250 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(¬P)) ∧ ((0 ∧ K) ∧ (1 ∧ K))
Options:
((0 ∧ K) ∧ (1 ∧ K)) ∧ (¬(¬P))
((¬(¬P)) ∧ (0 ∧ K)) ∧ (1 ∧ K)
(¬(¬P)) ∧ ((1 ∧ K) ∧ (0 ∧ K))
(¬(¬P)) ∧ (((0 ∧ K) ∧ 1) ∧ K)
(¬(¬P)) ∧ (0 ∧ (K ∧ (1 ∧ K)))
(¬(¬P)) ∧ ((0 ∧ K) ∧ K)
(¬(¬P))... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
43,
75078,
220,
16,
8,
12264,
101,
320,
15,
12264,
101,
445,
595,
75078,
1819,
16,
12264,
101,
445,
8,
75078,
320,
83193,
16,... | 1,727 | null | 877 | null | cl100k_base | 1,415 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((L ∧ 1) ∨ (0 ∨ L)) ∧ ((1 ∨ L) ∧ (¬1))
Options:
((1 ∨ L) ∧ (¬1)) ∧ ((L ∧ 1) ∨ (0 ∨ L))
(((L ∧ 1) ∨ (0 ∨ L)) ∧ (1 ∨ L)) ∧ (¬1)
((L ∧ 1) ∨ (0 ∨ L)) ∧ ((¬1) ∧ (1 ∨ L))
((L ∧ 1) ∨ (0 ∨ L)) ∧ ((1 ∨ L) ∧ 0)
((L ∧ 1) ∨ (0 ∨ L))... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
320,
83193,
7,
15,
12264,
101,
220,
16,
595,
75078,
320,
83193,
7,
15,
12264,
101,
816,
4489,
3883,
512,
7,
83193,
7,
15,
12264,
... | 1,728 | null | 724 | null | cl100k_base | 1,157 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(0 ∨ 1)) ∧ (¬(0 ∨ Y))
Options:
(¬(0 ∨ Y)) ∧ (¬(0 ∨ 1))
(¬(0 ∨ 1)) ∧ ((¬0) ∧ (¬Y))
(¬(0 ∨ 1)) ∧ (¬Y)
(¬(0 ∨ 1)) ∧ (¬(Y ∨ 0))
((¬0) ∧ (¬1)) ∧ (¬(0 ∨ Y))
(¬1) ∧ (¬(0 ∨ Y))
(¬(1 ∨ 0)) ∧ (¬(0 ∨ Y))
Chosen: (¬(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,
350,
595,
12264,
101,
1819,
16,
12264,
101,
432,
8,
75078,
320,
49,
75078,
220,
15,
4489,
3883,
512,... | 1,729 | null | 790 | null | cl100k_base | 1,232 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(R ∨ T)) ∨ ((1 ∨ R) ∧ (R ∧ 0))
Options:
((1 ∨ R) ∧ (R ∧ 0)) ∨ (¬(R ∨ T))
((¬(R ∨ T)) ∨ (1 ∨ R)) ∧ ((¬(R ∨ T)) ∨ (R ∧ 0))
(¬(R ∨ T)) ∨ ((R ∧ 0) ∧ (1 ∨ R))
(¬(R ∨ T)) ∨ (((1 ∨ R) ∧ R) ∧ 0)
(¬(R ∨ T)) ∨ ((1 ∨ R) ∧ 0)
(¬(R... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
55,
12264,
101,
1630,
8,
75078,
320,
83193,
55,
595,
12264,
101,
1819,
50,
12264,
101,
220,
15,
8,
75078,
320,
16,
75078,
163... | 1,730 | null | 1,230 | null | cl100k_base | 2,012 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((X ∨ X) ∧ (¬X)) ∨ ((S ∨ 0) ∧ (1 ∧ X))
Options:
((S ∨ 0) ∧ (1 ∧ X)) ∨ ((X ∨ X) ∧ (¬X))
(((X ∨ X) ∧ (¬X)) ∨ (S ∨ 0)) ∧ (((X ∨ X) ∧ (¬X)) ∨ (1 ∧ X))
((X ∨ X) ∧ (¬X)) ∨ ((1 ∧ X) ∧ (S ∨ 0))
((X ∨ X) ∧ (¬X)) ∨ (((S ∨ 0) ∧ 1) ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
47,
12264,
101,
650,
8,
75078,
320,
83193,
15,
595,
75078,
320,
83193,
7,
16,
75078,
650,
4489,
3883,
512,
7,
83193,
7,
16,
... | 1,731 | null | 690 | null | cl100k_base | 1,199 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((P ∨ V) ∧ (¬0)) ∧ (¬(1 ∧ V))
Options:
(¬(1 ∧ V)) ∧ ((P ∨ V) ∧ (¬0))
(P ∨ V) ∧ ((¬0) ∧ (¬(1 ∧ V)))
((P ∨ V) ∧ (¬0)) ∧ ((¬1) ∨ (¬V))
((P ∨ V) ∧ (¬0)) ∧ (¬V)
((P ∨ V) ∧ (¬0)) ∧ (¬(V ∧ 1))
((¬0) ∧ (P ∨ V)) ∧ (¬(1 ∧ V))
((P ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
1209,
83193,
16,
8,
12264,
101,
320,
83193,
16,
4489,
3883,
512,
7,
83193,
7,
83193,
16,
595,
75078,
320,
83193,
7,
83193,
1... | 1,732 | null | 151 | null | cl100k_base | 312 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((¬1) ∨ (¬1))
Options:
(¬(¬1)) ∧ (¬(¬1))
¬((¬1) ∨ 0)
¬(0 ∨ (¬1))
Chosen: ¬((¬1) ∨ 0)
Options:
(¬(¬1)) ∧ (¬0)
¬(¬1)
¬(0 ∨ (¬1))
¬(0 ∨ 0)
Chosen: ¬(0 ∨ 0)
Options:
(¬0) ∧ (¬0)
¬0
Chosen: ¬0
Options:
1
Chosen: 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,
75078,
320,
15,
12264,
101,
220,
15,
4489,
3883,
512,
7,
83193,
7,
83193,
15,
595,
12264,
101,
320,
8319... | 1,733 | null | 252 | null | cl100k_base | 440 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((¬0) ∧ (0 ∨ 0))
Options:
(¬(¬0)) ∨ (¬(0 ∨ 0))
¬((0 ∨ 0) ∧ (¬0))
¬(((¬0) ∧ 0) ∨ ((¬0) ∧ 0))
¬((¬0) ∧ 0)
¬(1 ∧ (0 ∨ 0))
Chosen: ¬((¬0) ∧ 0)
Options:
(¬(¬0)) ∨ (¬0)
¬0
¬(0 ∧ (¬0))
¬(1 ∧ 0)
Chosen: (¬(¬0)) ∨ (¬0)
Options... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
1209,
46,
75078,
220,
15,
8,
75078,
320,
46,
12264,
101,
220,
16,
4489,
3883,
512,
7,
83193,
7,
46,
75078,
220,
15,
595,
1... | 1,734 | null | 447 | null | cl100k_base | 714 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((O ∧ 0) ∧ (O ∨ 1))
Options:
(¬(O ∧ 0)) ∨ (¬(O ∨ 1))
¬((O ∨ 1) ∧ (O ∧ 0))
¬(O ∧ (0 ∧ (O ∨ 1)))
¬(((O ∧ 0) ∧ O) ∨ ((O ∧ 0) ∧ 1))
¬((O ∧ 0) ∧ 1)
¬((O ∧ 0) ∧ (1 ∨ O))
¬(0 ∧ (O ∨ 1))
¬((0 ∧ O) ∧ (O ∨ 1))
Chosen: ¬(0 ∧ (O ∨ ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
320,
83193,
7,
15,
12264,
101,
469,
595,
75078,
320,
83193,
7,
36,
75078,
469,
4489,
3883,
512,
7,
83193,
7,
36,
75078,
469,
595,
... | 1,735 | null | 590 | null | cl100k_base | 1,022 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(0 ∨ E)) ∧ (¬(E ∧ E))
Options:
(¬(E ∧ E)) ∧ (¬(0 ∨ E))
(¬(0 ∨ E)) ∧ ((¬E) ∨ (¬E))
(¬(0 ∨ E)) ∧ (¬E)
((¬0) ∧ (¬E)) ∧ (¬(E ∧ E))
(¬E) ∧ (¬(E ∧ E))
(¬(E ∨ 0)) ∧ (¬(E ∧ E))
Chosen: ((¬0) ∧ (¬E)) ∧ (¬(E ∧ E))
Options:
(¬(E... |
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,
15,
12264,
101,
220,
16,
4489,
3883,
512,
7,
83193,
7,
83193,
15,
595,
75078,
320,
8319... | 1,736 | null | 176 | null | cl100k_base | 330 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((¬0) ∨ (0 ∨ 1))
Options:
(¬(¬0)) ∧ (¬(0 ∨ 1))
¬((0 ∨ 1) ∨ (¬0))
¬(((¬0) ∨ 0) ∨ 1)
¬((¬0) ∨ 1)
¬((¬0) ∨ (1 ∨ 0))
¬(1 ∨ (0 ∨ 1))
Chosen: ¬((¬0) ∨ 1)
Options:
(¬(¬0)) ∧ (¬1)
¬1
¬(1 ∨ (¬0))
¬(1 ∨ 1)
Chosen: ¬1
Options:
0... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
1209,
83193,
48,
8,
75078,
320,
83193,
44,
4489,
3883,
512,
7,
83193,
7,
83193,
48,
595,
12264,
101,
320,
83193,
7,
83193,
4... | 1,737 | null | 177 | null | cl100k_base | 362 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((¬Q) ∧ (¬M))
Options:
(¬(¬Q)) ∨ (¬(¬M))
¬((¬M) ∧ (¬Q))
Chosen: (¬(¬Q)) ∨ (¬(¬M))
Options:
(¬(¬M)) ∨ (¬(¬Q))
(¬(¬Q)) ∨ M
Q ∨ (¬(¬M))
Chosen: Q ∨ (¬(¬M))
Options:
(¬(¬M)) ∨ Q
Q ∨ M
Chosen: (¬(¬M)) ∨ Q
Options:
M ∨ Q
C... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
1209,
83193,
16,
8,
75078,
320,
83193,
16,
4489,
3883,
512,
7,
83193,
7,
83193,
16,
595,
12264,
101,
320,
83193,
7,
83193,
1... | 1,738 | null | 235 | null | cl100k_base | 430 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((¬1) ∧ (¬1))
Options:
(¬(¬1)) ∨ (¬(¬1))
¬((¬1) ∧ 0)
¬(0 ∧ (¬1))
Chosen: ¬((¬1) ∧ 0)
Options:
(¬(¬1)) ∨ (¬0)
¬0
¬(0 ∧ (¬1))
¬(0 ∧ 0)
Chosen: ¬(0 ∧ (¬1))
Options:
(¬0) ∨ (¬(¬1))
¬0
¬(0 ∧ 0)
Chosen: (¬0) ∨ (¬(¬1))
Opti... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
1209,
53,
75078,
220,
16,
8,
75078,
320,
83193,
38,
4489,
3883,
512,
7,
83193,
7,
53,
75078,
220,
16,
595,
12264,
101,
320,
... | 1,739 | null | 252 | null | cl100k_base | 485 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((V ∧ 1) ∧ (¬G))
Options:
(¬(V ∧ 1)) ∨ (¬(¬G))
¬((¬G) ∧ (V ∧ 1))
¬(V ∧ (1 ∧ (¬G)))
¬(V ∧ (¬G))
¬((1 ∧ V) ∧ (¬G))
Chosen: ¬(V ∧ (1 ∧ (¬G)))
Options:
(¬V) ∨ (¬(1 ∧ (¬G)))
¬((1 ∧ (¬G)) ∧ V)
¬(V ∧ (¬G))
¬(V ∧ ((¬G) ∧ 1))
C... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
1209,
83193,
16,
8,
12264,
101,
320,
57,
75078,
220,
16,
4489,
3883,
512,
7,
83193,
7,
83193,
16,
595,
75078,
320,
83193,
7,... | 1,740 | null | 281 | null | cl100k_base | 509 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((¬1) ∨ (Z ∧ 1))
Options:
(¬(¬1)) ∧ (¬(Z ∧ 1))
¬((Z ∧ 1) ∨ (¬1))
¬(((¬1) ∨ Z) ∧ ((¬1) ∨ 1))
¬((¬1) ∨ Z)
¬((¬1) ∨ (1 ∧ Z))
¬(0 ∨ (Z ∧ 1))
Chosen: ¬((Z ∧ 1) ∨ (¬1))
Options:
(¬(Z ∧ 1)) ∧ (¬(¬1))
¬((Z ∧ 1) ∨ 0)
¬(Z ∨ (¬1)... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
1209,
43,
12264,
101,
426,
8,
12264,
101,
320,
43,
12264,
101,
426,
4489,
3883,
512,
7,
83193,
7,
43,
12264,
101,
426,
595,
... | 1,741 | null | 510 | null | cl100k_base | 842 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((L ∨ B) ∨ (L ∨ B))
Options:
(¬(L ∨ B)) ∧ (¬(L ∨ B))
¬(((L ∨ B) ∨ L) ∨ B)
¬(L ∨ (B ∨ (L ∨ B)))
¬((L ∨ B) ∨ (B ∨ L))
¬((B ∨ L) ∨ (L ∨ B))
Chosen: ¬((L ∨ B) ∨ (B ∨ L))
Options:
(¬(L ∨ B)) ∧ (¬(B ∨ L))
¬((B ∨ L) ∨ (L ∨ B)... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
1209,
15,
12264,
101,
220,
16,
8,
12264,
101,
320,
15,
12264,
101,
220,
15,
4489,
3883,
512,
7,
83193,
7,
15,
12264,
101,
... | 1,742 | null | 674 | null | cl100k_base | 971 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((0 ∨ 1) ∨ (0 ∨ 0))
Options:
(¬(0 ∨ 1)) ∧ (¬(0 ∨ 0))
¬((0 ∨ 0) ∨ (0 ∨ 1))
¬(((0 ∨ 1) ∨ 0) ∨ 0)
¬(0 ∨ (1 ∨ (0 ∨ 0)))
¬((0 ∨ 1) ∨ 0)
¬(1 ∨ (0 ∨ 0))
¬((1 ∨ 0) ∨ (0 ∨ 0))
Chosen: ¬((1 ∨ 0) ∨ (0 ∨ 0))
Options:
(¬(1 ∨ 0)) ∧ ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
83193,
52,
8,
12264,
101,
320,
52,
12264,
101,
473,
595,
75078,
1819,
83193,
16,
8,
75078,
320,
83193,
52,
4489,
3883,
512,
1... | 1,743 | null | 686 | null | cl100k_base | 1,122 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬U) ∨ (U ∨ H)) ∧ ((¬1) ∧ (¬U))
Options:
((¬1) ∧ (¬U)) ∧ ((¬U) ∨ (U ∨ H))
(((¬U) ∨ (U ∨ H)) ∧ (¬1)) ∧ (¬U)
((¬U) ∨ (U ∨ H)) ∧ ((¬U) ∧ (¬1))
((¬U) ∨ (U ∨ H)) ∧ (0 ∧ (¬U))
((U ∨ H) ∨ (¬U)) ∧ ((¬1) ∧ (¬U))
(((¬U) ∨ U) ∨ H)... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
15,
75078,
473,
8,
75078,
320,
83193,
16,
595,
12264,
101,
1819,
36,
12264,
101,
469,
8,
12264,
101,
320,
83193,
36,
4489,
38... | 1,744 | null | 939 | null | cl100k_base | 1,478 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((0 ∧ H) ∧ (¬1)) ∨ ((E ∨ E) ∨ (¬E))
Options:
((E ∨ E) ∨ (¬E)) ∨ ((0 ∧ H) ∧ (¬1))
(((0 ∧ H) ∧ (¬1)) ∨ (E ∨ E)) ∨ (¬E)
((0 ∧ H) ∧ (¬1)) ∨ ((¬E) ∨ (E ∨ E))
((0 ∧ H) ∧ (¬1)) ∨ (E ∨ (E ∨ (¬E)))
((0 ∧ H) ∧ (¬1)) ∨ (E ∨ (¬E))
(... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
15,
75078,
220,
15,
8,
12264,
101,
320,
15,
75078,
393,
595,
75078,
320,
83193,
7,
47,
75078,
735,
4489,
3883,
512,
7,
83193,... | 1,745 | null | 1,115 | null | cl100k_base | 1,772 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((0 ∧ 0) ∨ (0 ∧ P)) ∧ (¬(P ∧ K))
Options:
(¬(P ∧ K)) ∧ ((0 ∧ 0) ∨ (0 ∧ P))
((0 ∧ 0) ∨ (0 ∧ P)) ∧ ((¬P) ∨ (¬K))
((0 ∧ 0) ∨ (0 ∧ P)) ∧ (¬(K ∧ P))
((0 ∧ P) ∨ (0 ∧ 0)) ∧ (¬(P ∧ K))
(((0 ∧ 0) ∨ 0) ∧ ((0 ∧ 0) ∨ P)) ∧ (¬(P ∧ K)... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
55,
75078,
220,
15,
8,
75078,
320,
15,
12264,
101,
220,
16,
595,
75078,
320,
83193,
7,
55,
75078,
1630,
4489,
3883,
512,
7,
... | 1,746 | null | 852 | null | cl100k_base | 1,445 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((X ∧ 0) ∧ (0 ∨ 1)) ∧ (¬(X ∧ X))
Options:
(¬(X ∧ X)) ∧ ((X ∧ 0) ∧ (0 ∨ 1))
(X ∧ 0) ∧ ((0 ∨ 1) ∧ (¬(X ∧ X)))
((X ∧ 0) ∧ (0 ∨ 1)) ∧ ((¬X) ∨ (¬X))
((X ∧ 0) ∧ (0 ∨ 1)) ∧ (¬X)
((0 ∨ 1) ∧ (X ∧ 0)) ∧ (¬(X ∧ X))
(X ∧ (0 ∧ (0 ∨ 1... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
320,
83193,
7,
16,
12264,
101,
507,
595,
75078,
1819,
16,
12264,
101,
1229,
8,
75078,
320,
83193,
16,
4489,
3883,
512,
1209,
16,
12... | 1,747 | null | 1,039 | null | cl100k_base | 1,634 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(1 ∨ O)) ∧ ((1 ∨ Q) ∧ (¬1))
Options:
((1 ∨ Q) ∧ (¬1)) ∧ (¬(1 ∨ O))
((¬(1 ∨ O)) ∧ (1 ∨ Q)) ∧ (¬1)
(¬(1 ∨ O)) ∧ ((¬1) ∧ (1 ∨ Q))
(¬(1 ∨ O)) ∧ ((1 ∨ Q) ∧ 0)
(¬(1 ∨ O)) ∧ (1 ∧ (¬1))
(¬(1 ∨ O)) ∧ ((Q ∨ 1) ∧ (¬1))
((¬1) ∧ (¬... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
57,
12264,
101,
220,
16,
8,
75078,
320,
83193,
57,
595,
75078,
1819,
16,
75078,
328,
8,
75078,
320,
15,
12264,
101,
1901,
448... | 1,748 | null | 1,287 | null | cl100k_base | 2,060 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((Z ∨ 1) ∧ (¬Z)) ∧ ((1 ∧ S) ∧ (0 ∨ Z))
Options:
((1 ∧ S) ∧ (0 ∨ Z)) ∧ ((Z ∨ 1) ∧ (¬Z))
(((Z ∨ 1) ∧ (¬Z)) ∧ (1 ∧ S)) ∧ (0 ∨ Z)
(Z ∨ 1) ∧ ((¬Z) ∧ ((1 ∧ S) ∧ (0 ∨ Z)))
((Z ∨ 1) ∧ (¬Z)) ∧ ((0 ∨ Z) ∧ (1 ∧ S))
((Z ∨ 1) ∧ (¬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,
16,
12264,
101,
480,
4489,
3883,
512,
16,
12264,
101,
480,
198,
83193,
1209,
83193,
16,
8,
75078,
320,
83193,
3... | 1,749 | null | 254 | null | cl100k_base | 464 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬(¬(1 ∨ G))
Options:
1 ∨ G
¬((¬1) ∧ (¬G))
¬(¬1)
¬(¬(G ∨ 1))
Chosen: ¬((¬1) ∧ (¬G))
Options:
(¬(¬1)) ∨ (¬(¬G))
¬((¬G) ∧ (¬1))
¬(0 ∧ (¬G))
Chosen: ¬((¬G) ∧ (¬1))
Options:
(¬(¬G)) ∨ (¬(¬1))
¬((¬G) ∧ 0)
Chosen: (¬(¬G)) ∨ (... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
15,
75078,
220,
16,
8,
75078,
320,
51,
12264,
101,
220,
15,
595,
75078,
1819,
15,
12264,
101,
469,
8,
75078,
320,
51,
75078,
... | 1,750 | null | 1,843 | null | cl100k_base | 2,858 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((0 ∧ 1) ∧ (T ∨ 0)) ∧ ((0 ∨ E) ∧ (T ∧ 0))
Options:
((0 ∨ E) ∧ (T ∧ 0)) ∧ ((0 ∧ 1) ∧ (T ∨ 0))
(((0 ∧ 1) ∧ (T ∨ 0)) ∧ (0 ∨ E)) ∧ (T ∧ 0)
(0 ∧ 1) ∧ ((T ∨ 0) ∧ ((0 ∨ E) ∧ (T ∧ 0)))
((0 ∧ 1) ∧ (T ∨ 0)) ∧ ((T ∧ 0) ∧ (0 ∨ E))
(... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
50,
75078,
328,
8,
75078,
320,
16,
75078,
328,
595,
75078,
320,
83193,
7,
16,
12264,
101,
328,
4489,
3883,
512,
7,
83193,
7,
... | 1,751 | null | 598 | null | cl100k_base | 1,093 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((S ∧ S) ∧ (1 ∧ S)) ∧ (¬(1 ∨ S))
Options:
(¬(1 ∨ S)) ∧ ((S ∧ S) ∧ (1 ∧ S))
(S ∧ S) ∧ ((1 ∧ S) ∧ (¬(1 ∨ S)))
((S ∧ S) ∧ (1 ∧ S)) ∧ ((¬1) ∧ (¬S))
((S ∧ S) ∧ (1 ∧ S)) ∧ (¬1)
((S ∧ S) ∧ (1 ∧ S)) ∧ (¬(S ∨ 1))
((1 ∧ S) ∧ (S ∧ ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
7,
83193,
7,
16,
12264,
101,
220,
16,
4489,
3883,
512,
16,
12264,
101,
220,
16,
198,
83193,
1209,
83193,
16,
8,
75078,
320,
... | 1,752 | null | 70 | null | cl100k_base | 183 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬(¬(1 ∨ 1))
Options:
1 ∨ 1
¬((¬1) ∧ (¬1))
¬(¬1)
Chosen: 1 ∨ 1
Options:
1
Chosen: 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,
468,
8,
12264,
101,
320,
83193,
54,
595,
12264,
101,
1819,
54,
75078,
468,
8,
75078,
320,
83193,
54,
4489,
38... | 1,753 | null | 1,148 | null | cl100k_base | 1,784 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((1 ∨ W) ∨ (¬W)) ∨ ((W ∧ W) ∧ (¬W))
Options:
((W ∧ W) ∧ (¬W)) ∨ ((1 ∨ W) ∨ (¬W))
(1 ∨ W) ∨ ((¬W) ∨ ((W ∧ W) ∧ (¬W)))
(((1 ∨ W) ∨ (¬W)) ∨ (W ∧ W)) ∧ (((1 ∨ W) ∨ (¬W)) ∨ (¬W))
((1 ∨ W) ∨ (¬W)) ∨ ((¬W) ∧ (W ∧ W))
((1 ∨ W) ∨... |
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,
15,
8,
12264,
101,
320,
43,
12264,
101,
220,
15,
595,
12264,
101,
1819,
83193,
34,
8,
12264,
101,
320,
... | 1,754 | null | 1,565 | null | cl100k_base | 2,114 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((1 ∨ 0) ∨ (L ∨ 0)) ∨ ((¬C) ∨ (L ∧ 0))
Options:
((¬C) ∨ (L ∧ 0)) ∨ ((1 ∨ 0) ∨ (L ∨ 0))
(((1 ∨ 0) ∨ (L ∨ 0)) ∨ (¬C)) ∨ (L ∧ 0)
(1 ∨ 0) ∨ ((L ∨ 0) ∨ ((¬C) ∨ (L ∧ 0)))
((1 ∨ 0) ∨ (L ∨ 0)) ∨ ((L ∧ 0) ∨ (¬C))
((1 ∨ 0) ∨ (L ∨ ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
15,
12264,
101,
220,
15,
8,
12264,
101,
320,
83193,
41,
595,
75078,
1819,
41,
75078,
328,
8,
75078,
320,
16,
75078,
220,
16,
... | 1,755 | null | 1,172 | null | cl100k_base | 1,883 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((0 ∨ 0) ∨ (¬J)) ∧ ((J ∧ S) ∧ (1 ∧ 1))
Options:
((J ∧ S) ∧ (1 ∧ 1)) ∧ ((0 ∨ 0) ∨ (¬J))
(((0 ∨ 0) ∨ (¬J)) ∧ (J ∧ S)) ∧ (1 ∧ 1)
((0 ∨ 0) ∨ (¬J)) ∧ ((1 ∧ 1) ∧ (J ∧ S))
((0 ∨ 0) ∨ (¬J)) ∧ (((J ∧ S) ∧ 1) ∧ 1)
((0 ∨ 0) ∨ (¬J))... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
55,
75078,
426,
8,
12264,
101,
320,
83193,
16,
595,
75078,
1819,
33,
75078,
220,
15,
8,
75078,
320,
55,
75078,
1630,
4489,
38... | 1,756 | null | 1,154 | null | cl100k_base | 1,985 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((X ∧ B) ∨ (¬1)) ∧ ((B ∧ 0) ∧ (X ∧ X))
Options:
((B ∧ 0) ∧ (X ∧ X)) ∧ ((X ∧ B) ∨ (¬1))
(((X ∧ B) ∨ (¬1)) ∧ (B ∧ 0)) ∧ (X ∧ X)
((X ∧ B) ∨ (¬1)) ∧ ((X ∧ X) ∧ (B ∧ 0))
((X ∧ B) ∨ (¬1)) ∧ (((B ∧ 0) ∧ X) ∧ X)
((X ∧ B) ∨ (¬1))... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
1209,
83193,
51,
8,
12264,
101,
320,
43,
75078,
220,
16,
4489,
3883,
512,
7,
83193,
7,
83193,
51,
595,
75078,
320,
83193,
7,... | 1,757 | null | 372 | null | cl100k_base | 659 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((¬T) ∨ (L ∧ 1))
Options:
(¬(¬T)) ∧ (¬(L ∧ 1))
¬((L ∧ 1) ∨ (¬T))
¬(((¬T) ∨ L) ∧ ((¬T) ∨ 1))
¬((¬T) ∨ L)
¬((¬T) ∨ (1 ∧ L))
Chosen: ¬((¬T) ∨ (1 ∧ L))
Options:
(¬(¬T)) ∧ (¬(1 ∧ L))
¬((1 ∧ L) ∨ (¬T))
¬(((¬T) ∨ 1) ∧ ((¬T) ∨... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
15,
12264,
101,
220,
16,
8,
12264,
101,
320,
83193,
15,
595,
75078,
1819,
83193,
54,
8,
12264,
101,
320,
83193,
16,
4489,
388... | 1,758 | null | 1,789 | null | cl100k_base | 2,573 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((0 ∨ 1) ∨ (¬0)) ∧ ((¬W) ∨ (¬1))
Options:
((¬W) ∨ (¬1)) ∧ ((0 ∨ 1) ∨ (¬0))
(((0 ∨ 1) ∨ (¬0)) ∧ (¬W)) ∨ (((0 ∨ 1) ∨ (¬0)) ∧ (¬1))
((0 ∨ 1) ∨ (¬0)) ∧ ((¬1) ∨ (¬W))
((0 ∨ 1) ∨ (¬0)) ∧ ((¬W) ∨ 0)
((¬0) ∨ (0 ∨ 1)) ∧ ((¬W) ∨ (... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
1209,
15,
12264,
101,
220,
16,
8,
75078,
320,
39,
75078,
220,
16,
4489,
3883,
512,
7,
83193,
7,
15,
12264,
101,
220,
16,
5... | 1,759 | null | 573 | null | cl100k_base | 893 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((0 ∨ 1) ∧ (H ∧ 1))
Options:
(¬(0 ∨ 1)) ∨ (¬(H ∧ 1))
¬((H ∧ 1) ∧ (0 ∨ 1))
¬(((0 ∨ 1) ∧ H) ∧ 1)
¬((0 ∨ 1) ∧ H)
¬((0 ∨ 1) ∧ (1 ∧ H))
¬(1 ∧ (H ∧ 1))
¬((1 ∨ 0) ∧ (H ∧ 1))
Chosen: (¬(0 ∨ 1)) ∨ (¬(H ∧ 1))
Options:
(¬(H ∧ 1))... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
1209,
83193,
57,
8,
75078,
320,
35,
12264,
101,
220,
15,
4489,
3883,
512,
7,
83193,
7,
83193,
57,
595,
12264,
101,
320,
8319... | 1,760 | null | 260 | null | cl100k_base | 485 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((¬Z) ∧ (D ∨ 0))
Options:
(¬(¬Z)) ∨ (¬(D ∨ 0))
¬((D ∨ 0) ∧ (¬Z))
¬(((¬Z) ∧ D) ∨ ((¬Z) ∧ 0))
¬((¬Z) ∧ D)
¬((¬Z) ∧ (0 ∨ D))
Chosen: ¬((D ∨ 0) ∧ (¬Z))
Options:
(¬(D ∨ 0)) ∨ (¬(¬Z))
¬(D ∧ (¬Z))
¬((0 ∨ D) ∧ (¬Z))
Chosen: ¬(... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
1209,
16,
12264,
101,
220,
15,
8,
12264,
101,
320,
39,
12264,
101,
220,
16,
4489,
3883,
512,
7,
83193,
7,
16,
12264,
101,
... | 1,761 | null | 429 | null | cl100k_base | 674 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((1 ∨ 0) ∨ (H ∨ 1))
Options:
(¬(1 ∨ 0)) ∧ (¬(H ∨ 1))
¬((H ∨ 1) ∨ (1 ∨ 0))
¬(((1 ∨ 0) ∨ H) ∨ 1)
¬(1 ∨ (0 ∨ (H ∨ 1)))
¬((1 ∨ 0) ∨ 1)
¬((1 ∨ 0) ∨ (1 ∨ H))
¬(1 ∨ (H ∨ 1))
¬((0 ∨ 1) ∨ (H ∨ 1))
Chosen: ¬(1 ∨ (H ∨ 1))
Options... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
15,
75078,
220,
15,
8,
75078,
320,
36,
75078,
220,
15,
595,
12264,
101,
1819,
55,
12264,
101,
1630,
8,
75078,
320,
83193,
55,... | 1,762 | null | 1,176 | null | cl100k_base | 1,904 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((0 ∧ 0) ∧ (E ∧ 0)) ∨ ((X ∨ X) ∧ (¬X))
Options:
((X ∨ X) ∧ (¬X)) ∨ ((0 ∧ 0) ∧ (E ∧ 0))
(((0 ∧ 0) ∧ (E ∧ 0)) ∨ (X ∨ X)) ∧ (((0 ∧ 0) ∧ (E ∧ 0)) ∨ (¬X))
((0 ∧ 0) ∧ (E ∧ 0)) ∨ ((¬X) ∧ (X ∨ X))
((0 ∧ 0) ∧ (E ∧ 0)) ∨ (X ∧ (¬X)... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
55,
75078,
426,
8,
75078,
320,
33,
12264,
101,
220,
15,
595,
12264,
101,
320,
83193,
7,
33,
75078,
426,
4489,
3883,
512,
7,
... | 1,763 | null | 695 | null | cl100k_base | 1,193 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((X ∧ B) ∧ (B ∨ 0)) ∨ (¬(B ∧ B))
Options:
(¬(B ∧ B)) ∨ ((X ∧ B) ∧ (B ∨ 0))
((X ∧ B) ∧ (B ∨ 0)) ∨ ((¬B) ∨ (¬B))
((X ∧ B) ∧ (B ∨ 0)) ∨ (¬B)
((B ∨ 0) ∧ (X ∧ B)) ∨ (¬(B ∧ B))
(X ∧ (B ∧ (B ∨ 0))) ∨ (¬(B ∧ B))
(((X ∧ B) ∧ B) ∨... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
43,
12264,
101,
220,
15,
8,
75078,
320,
43,
75078,
220,
16,
595,
12264,
101,
1819,
43,
12264,
101,
356,
8,
12264,
101,
320,
... | 1,764 | null | 1,285 | null | cl100k_base | 1,991 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((L ∨ 0) ∧ (L ∧ 1)) ∨ ((L ∨ C) ∨ (¬0))
Options:
((L ∨ C) ∨ (¬0)) ∨ ((L ∨ 0) ∧ (L ∧ 1))
(((L ∨ 0) ∧ (L ∧ 1)) ∨ (L ∨ C)) ∨ (¬0)
((L ∨ 0) ∧ (L ∧ 1)) ∨ ((¬0) ∨ (L ∨ C))
((L ∨ 0) ∧ (L ∧ 1)) ∨ (L ∨ (C ∨ (¬0)))
((L ∨ 0) ∧ (L ∧ ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
320,
83193,
7,
83193,
38,
595,
12264,
101,
1819,
83193,
38,
8,
75078,
320,
83193,
15,
4489,
3883,
512,
1209,
83193,
38,
8,
75078,
3... | 1,765 | null | 280 | null | cl100k_base | 507 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(¬G)) ∨ ((¬G) ∧ (¬0))
Options:
((¬G) ∧ (¬0)) ∨ (¬(¬G))
((¬(¬G)) ∨ (¬G)) ∧ ((¬(¬G)) ∨ (¬0))
(¬(¬G)) ∨ ((¬0) ∧ (¬G))
(¬(¬G)) ∨ ((¬G) ∧ 1)
G ∨ ((¬G) ∧ (¬0))
Chosen: G ∨ ((¬G) ∧ (¬0))
Options:
((¬G) ∧ (¬0)) ∨ G
(G ∨ (¬G))... |
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,
12264,
101,
320,
83193,
15,
595,
12264,
101,
1819,
56,
12264,
101,
220,
16,
8,
75078,
320,
16,
... | 1,766 | null | 915 | null | cl100k_base | 1,368 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((1 ∨ 1) ∨ (¬0)) ∨ ((Y ∨ 1) ∧ (1 ∧ C))
Options:
((Y ∨ 1) ∧ (1 ∧ C)) ∨ ((1 ∨ 1) ∨ (¬0))
(1 ∨ 1) ∨ ((¬0) ∨ ((Y ∨ 1) ∧ (1 ∧ C)))
(((1 ∨ 1) ∨ (¬0)) ∨ (Y ∨ 1)) ∧ (((1 ∨ 1) ∨ (¬0)) ∨ (1 ∧ C))
((1 ∨ 1) ∨ (¬0)) ∨ ((1 ∧ C) ∧ (Y ∨... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
52,
75078,
622,
8,
12264,
101,
320,
41,
75078,
549,
595,
12264,
101,
1819,
52,
12264,
101,
220,
16,
8,
75078,
320,
41,
75078,... | 1,767 | null | 2,650 | null | cl100k_base | 4,424 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((U ∧ J) ∨ (J ∧ U)) ∨ ((U ∨ 1) ∧ (J ∧ U))
Options:
((U ∨ 1) ∧ (J ∧ U)) ∨ ((U ∧ J) ∨ (J ∧ U))
(U ∧ J) ∨ ((J ∧ U) ∨ ((U ∨ 1) ∧ (J ∧ U)))
(((U ∧ J) ∨ (J ∧ U)) ∨ (U ∨ 1)) ∧ (((U ∧ J) ∨ (J ∧ U)) ∨ (J ∧ U))
((U ∧ J) ∨ (J ∧ U))... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
1209,
83193,
53,
8,
12264,
101,
320,
83193,
53,
4489,
3883,
512,
7,
83193,
7,
83193,
53,
595,
75078,
320,
83193,
7,
83193,
5... | 1,768 | null | 138 | null | cl100k_base | 321 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((¬V) ∨ (¬V))
Options:
(¬(¬V)) ∧ (¬(¬V))
Chosen: (¬(¬V)) ∧ (¬(¬V))
Options:
(¬(¬V)) ∧ V
V ∧ (¬(¬V))
Chosen: V ∧ (¬(¬V))
Options:
(¬(¬V)) ∧ V
V ∧ V
Chosen: (¬(¬V)) ∧ V
Options:
V ∧ V
Chosen: V ∧ V
Options:
V
Chosen: ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
320,
83193,
7,
43,
75078,
735,
595,
75078,
320,
83193,
7,
43,
12264,
101,
735,
4489,
3883,
512,
7,
83193,
7,
43,
12264,
101,
735,
... | 1,769 | null | 480 | null | cl100k_base | 845 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(L ∧ K)) ∧ (¬(L ∨ K))
Options:
(¬(L ∨ K)) ∧ (¬(L ∧ K))
(¬(L ∧ K)) ∧ ((¬L) ∧ (¬K))
(¬(L ∧ K)) ∧ (¬(K ∨ L))
((¬L) ∨ (¬K)) ∧ (¬(L ∨ K))
(¬(K ∧ L)) ∧ (¬(L ∨ K))
Chosen: (¬(L ∨ K)) ∧ (¬(L ∧ K))
Options:
(¬(L ∨ K)) ∧ ((¬L) ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
320,
83193,
7,
15,
75078,
549,
595,
75078,
1819,
83193,
53,
8,
75078,
320,
15,
75078,
220,
16,
4489,
3883,
512,
1209,
83193,
53,
8,... | 1,770 | null | 746 | null | cl100k_base | 1,253 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(0 ∧ U)) ∧ ((¬V) ∧ (0 ∧ 1))
Options:
((¬V) ∧ (0 ∧ 1)) ∧ (¬(0 ∧ U))
((¬(0 ∧ U)) ∧ (¬V)) ∧ (0 ∧ 1)
(¬(0 ∧ U)) ∧ ((0 ∧ 1) ∧ (¬V))
(¬(0 ∧ U)) ∧ (((¬V) ∧ 0) ∧ 1)
(¬(0 ∧ U)) ∧ ((¬V) ∧ 0)
(¬(0 ∧ U)) ∧ ((¬V) ∧ (1 ∧ 0))
((¬0) ∨... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
33,
12264,
101,
426,
8,
12264,
101,
320,
15,
75078,
423,
595,
75078,
320,
83193,
7,
15,
75078,
426,
4489,
3883,
512,
7,
83193... | 1,771 | null | 817 | null | cl100k_base | 1,340 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((B ∨ B) ∨ (0 ∧ D)) ∧ (¬(0 ∧ B))
Options:
(¬(0 ∧ B)) ∧ ((B ∨ B) ∨ (0 ∧ D))
((B ∨ B) ∨ (0 ∧ D)) ∧ ((¬0) ∨ (¬B))
((B ∨ B) ∨ (0 ∧ D)) ∧ (¬0)
((B ∨ B) ∨ (0 ∧ D)) ∧ (¬(B ∧ 0))
((0 ∧ D) ∨ (B ∨ B)) ∧ (¬(0 ∧ B))
(B ∨ (B ∨ (0 ∧ D... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
83193,
36,
8,
75078,
320,
16,
75078,
468,
595,
12264,
101,
320,
83193,
7,
83193,
54,
4489,
3883,
512,
7,
83193,
7,
83193,
54,... | 1,772 | null | 487 | null | cl100k_base | 842 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬E) ∧ (1 ∧ W)) ∨ (¬(¬W))
Options:
(¬(¬W)) ∨ ((¬E) ∧ (1 ∧ W))
((¬E) ∧ (1 ∧ W)) ∨ W
((1 ∧ W) ∧ (¬E)) ∨ (¬(¬W))
(((¬E) ∧ 1) ∧ W) ∨ (¬(¬W))
((¬E) ∧ W) ∨ (¬(¬W))
((¬E) ∧ (W ∧ 1)) ∨ (¬(¬W))
Chosen: (((¬E) ∧ 1) ∧ W) ∨ (¬(¬W))... |
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,
15,
8,
12264,
101,
320,
83193,
16,
595,
75078,
1819,
35,
75078,
220,
16,
8,
12264,
101,
320,
15,
75078,
... | 1,773 | null | 3,776 | null | cl100k_base | 5,492 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((A ∨ 0) ∨ (¬1)) ∧ ((D ∧ 1) ∨ (0 ∧ 1))
Options:
((D ∧ 1) ∨ (0 ∧ 1)) ∧ ((A ∨ 0) ∨ (¬1))
(((A ∨ 0) ∨ (¬1)) ∧ (D ∧ 1)) ∨ (((A ∨ 0) ∨ (¬1)) ∧ (0 ∧ 1))
((A ∨ 0) ∨ (¬1)) ∧ ((0 ∧ 1) ∨ (D ∧ 1))
((A ∨ 0) ∨ (¬1)) ∧ (((D ∧ 1) ∨ 0) ... |
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,
44,
4489,
3883,
512,
83193,
44,
198,
1163,
8477,
25,
97265,
44
] | 1,774 | null | 35 | null | cl100k_base | 131 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬(¬(¬M))
Options:
¬M
Chosen: ¬M |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
7,
83193,
7,
15,
12264,
101,
220,
15,
4489,
3883,
512,
15,
12264,
101,
220,
15,
198,
83193,
1209,
83193,
15,
8,
75078,
320,
... | 1,775 | null | 71 | null | cl100k_base | 186 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬(¬(0 ∨ 0))
Options:
0 ∨ 0
¬((¬0) ∧ (¬0))
¬(¬0)
Chosen: ¬(¬0)
Options:
0
¬1
Chosen: 0 |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
83193,
50,
8,
75078,
320,
35,
75078,
328,
595,
75078,
1819,
15,
75078,
423,
8,
75078,
320,
83193,
35,
4489,
3883,
512,
1209,
... | 1,776 | null | 864 | null | cl100k_base | 1,529 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬S) ∧ (D ∧ S)) ∧ ((0 ∧ D) ∧ (¬D))
Options:
((0 ∧ D) ∧ (¬D)) ∧ ((¬S) ∧ (D ∧ S))
(((¬S) ∧ (D ∧ S)) ∧ (0 ∧ D)) ∧ (¬D)
(¬S) ∧ ((D ∧ S) ∧ ((0 ∧ D) ∧ (¬D)))
((¬S) ∧ (D ∧ S)) ∧ ((¬D) ∧ (0 ∧ D))
((¬S) ∧ (D ∧ S)) ∧ (0 ∧ (D ∧ (¬... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
16,
75078,
468,
8,
12264,
101,
320,
54,
75078,
650,
595,
12264,
101,
320,
83193,
7,
15,
75078,
650,
4489,
3883,
512,
7,
83193... | 1,777 | null | 629 | null | cl100k_base | 1,050 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((1 ∧ W) ∨ (W ∧ V)) ∨ (¬(0 ∧ V))
Options:
(¬(0 ∧ V)) ∨ ((1 ∧ W) ∨ (W ∧ V))
(1 ∧ W) ∨ ((W ∧ V) ∨ (¬(0 ∧ V)))
((1 ∧ W) ∨ (W ∧ V)) ∨ ((¬0) ∨ (¬V))
((1 ∧ W) ∨ (W ∧ V)) ∨ (¬0)
((1 ∧ W) ∨ (W ∧ V)) ∨ (¬(V ∧ 0))
((W ∧ V) ∨ (1 ∧ ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
16,
75078,
473,
8,
12264,
101,
320,
53,
12264,
101,
650,
595,
12264,
101,
320,
83193,
7,
15,
12264,
101,
220,
16,
4489,
3883,... | 1,778 | null | 739 | null | cl100k_base | 1,124 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((1 ∧ H) ∨ (V ∨ V)) ∨ (¬(0 ∨ 1))
Options:
(¬(0 ∨ 1)) ∨ ((1 ∧ H) ∨ (V ∨ V))
(1 ∧ H) ∨ ((V ∨ V) ∨ (¬(0 ∨ 1)))
((1 ∧ H) ∨ (V ∨ V)) ∨ ((¬0) ∧ (¬1))
((1 ∧ H) ∨ (V ∨ V)) ∨ (¬1)
((1 ∧ H) ∨ (V ∨ V)) ∨ (¬(1 ∨ 0))
((V ∨ V) ∨ (1 ∧ ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
50,
75078,
328,
8,
75078,
320,
16,
12264,
101,
328,
595,
75078,
1819,
16,
12264,
101,
328,
8,
12264,
101,
320,
83193,
50,
448... | 1,779 | null | 1,508 | null | cl100k_base | 2,477 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((S ∧ S) ∧ (1 ∨ S)) ∧ ((1 ∨ S) ∨ (¬S))
Options:
((1 ∨ S) ∨ (¬S)) ∧ ((S ∧ S) ∧ (1 ∨ S))
(S ∧ S) ∧ ((1 ∨ S) ∧ ((1 ∨ S) ∨ (¬S)))
(((S ∧ S) ∧ (1 ∨ S)) ∧ (1 ∨ S)) ∨ (((S ∧ S) ∧ (1 ∨ S)) ∧ (¬S))
((S ∧ S) ∧ (1 ∨ S)) ∧ ((¬S) ∨ (... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
320,
83193,
7,
83193,
45,
595,
12264,
101,
320,
83193,
7,
83193,
15,
4489,
3883,
512,
7,
83193,
7,
83193,
15,
595,
12264,
101,
320,... | 1,780 | null | 139 | null | cl100k_base | 282 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(¬N)) ∨ (¬(¬0))
Options:
(¬(¬0)) ∨ (¬(¬N))
(¬(¬N)) ∨ 0
(¬(¬N)) ∨ (¬1)
N ∨ (¬(¬0))
Chosen: N ∨ (¬(¬0))
Options:
(¬(¬0)) ∨ N
N ∨ 0
N ∨ (¬1)
Chosen: N ∨ 0
Options:
N
0 ∨ N
Chosen: N |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
45,
75078,
220,
16,
8,
12264,
101,
320,
83193,
37,
595,
12264,
101,
320,
83193,
7,
83193,
37,
4489,
3883,
512,
7,
83193,
7,
... | 1,781 | null | 347 | null | cl100k_base | 591 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((N ∧ 1) ∨ (¬F)) ∨ (¬(¬F))
Options:
(¬(¬F)) ∨ ((N ∧ 1) ∨ (¬F))
(N ∧ 1) ∨ ((¬F) ∨ (¬(¬F)))
((N ∧ 1) ∨ (¬F)) ∨ F
((¬F) ∨ (N ∧ 1)) ∨ (¬(¬F))
(N ∨ (¬F)) ∨ (¬(¬F))
((1 ∧ N) ∨ (¬F)) ∨ (¬(¬F))
Chosen: (N ∨ (¬F)) ∨ (¬(¬F))
Opti... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
16,
12264,
101,
423,
8,
12264,
101,
320,
83193,
16,
595,
12264,
101,
1819,
35,
12264,
101,
220,
16,
8,
12264,
101,
320,
83193... | 1,782 | null | 1,277 | null | cl100k_base | 1,752 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((1 ∨ D) ∨ (¬1)) ∨ ((D ∨ 1) ∨ (¬0))
Options:
((D ∨ 1) ∨ (¬0)) ∨ ((1 ∨ D) ∨ (¬1))
(((1 ∨ D) ∨ (¬1)) ∨ (D ∨ 1)) ∨ (¬0)
(1 ∨ D) ∨ ((¬1) ∨ ((D ∨ 1) ∨ (¬0)))
((1 ∨ D) ∨ (¬1)) ∨ ((¬0) ∨ (D ∨ 1))
((1 ∨ D) ∨ (¬1)) ∨ (D ∨ (1 ∨ (¬... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
41,
75078,
220,
16,
8,
12264,
101,
320,
83193,
46,
595,
75078,
1819,
15,
75078,
622,
8,
12264,
101,
320,
15,
75078,
507,
4489... | 1,783 | null | 1,582 | null | cl100k_base | 2,537 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((J ∧ 1) ∨ (¬O)) ∧ ((0 ∧ J) ∨ (0 ∧ O))
Options:
((0 ∧ J) ∨ (0 ∧ O)) ∧ ((J ∧ 1) ∨ (¬O))
(((J ∧ 1) ∨ (¬O)) ∧ (0 ∧ J)) ∨ (((J ∧ 1) ∨ (¬O)) ∧ (0 ∧ O))
((J ∧ 1) ∨ (¬O)) ∧ ((0 ∧ O) ∨ (0 ∧ J))
((J ∧ 1) ∨ (¬O)) ∧ (((0 ∧ J) ∨ 0) ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
320,
83193,
7,
39,
75078,
622,
595,
12264,
101,
1819,
83193,
41,
8,
12264,
101,
320,
83193,
15,
4489,
3883,
512,
1209,
83193,
41,
8... | 1,784 | null | 644 | null | cl100k_base | 1,036 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(H ∧ J)) ∨ ((¬J) ∨ (¬0))
Options:
((¬J) ∨ (¬0)) ∨ (¬(H ∧ J))
((¬(H ∧ J)) ∨ (¬J)) ∨ (¬0)
(¬(H ∧ J)) ∨ ((¬0) ∨ (¬J))
(¬(H ∧ J)) ∨ ((¬J) ∨ 1)
((¬H) ∨ (¬J)) ∨ ((¬J) ∨ (¬0))
(¬(J ∧ H)) ∨ ((¬J) ∨ (¬0))
Chosen: (¬(H ∧ J)) ∨ (... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
83193,
15,
8,
75078,
320,
83193,
38,
595,
75078,
1819,
42,
75078,
735,
8,
75078,
320,
15,
75078,
220,
16,
4489,
3883,
512,
12... | 1,785 | null | 1,058 | null | cl100k_base | 1,826 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬0) ∧ (¬G)) ∧ ((K ∧ K) ∧ (0 ∧ 1))
Options:
((K ∧ K) ∧ (0 ∧ 1)) ∧ ((¬0) ∧ (¬G))
(((¬0) ∧ (¬G)) ∧ (K ∧ K)) ∧ (0 ∧ 1)
(¬0) ∧ ((¬G) ∧ ((K ∧ K) ∧ (0 ∧ 1)))
((¬0) ∧ (¬G)) ∧ ((0 ∧ 1) ∧ (K ∧ K))
((¬0) ∧ (¬G)) ∧ (((K ∧ K) ∧ 0) ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
1209,
16,
12264,
101,
468,
8,
12264,
101,
320,
56,
75078,
816,
4489,
3883,
512,
7,
83193,
7,
16,
12264,
101,
468,
595,
75078... | 1,786 | null | 391 | null | cl100k_base | 671 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((1 ∨ W) ∨ (Y ∧ Y))
Options:
(¬(1 ∨ W)) ∧ (¬(Y ∧ Y))
¬((Y ∧ Y) ∨ (1 ∨ W))
¬(1 ∨ (W ∨ (Y ∧ Y)))
¬(((1 ∨ W) ∨ Y) ∧ ((1 ∨ W) ∨ Y))
¬((1 ∨ W) ∨ Y)
¬(1 ∨ (Y ∧ Y))
¬((W ∨ 1) ∨ (Y ∧ Y))
Chosen: ¬((W ∨ 1) ∨ (Y ∧ Y))
Options:
(... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
7,
83193,
7,
16,
12264,
101,
220,
16,
4489,
3883,
512,
16,
12264,
101,
220,
16,
198,
83193,
1209,
83193,
16,
8,
75078,
320,
... | 1,787 | null | 156 | null | cl100k_base | 324 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬(¬(1 ∨ 1))
Options:
1 ∨ 1
¬((¬1) ∧ (¬1))
¬(¬1)
Chosen: ¬((¬1) ∧ (¬1))
Options:
(¬(¬1)) ∨ (¬(¬1))
¬((¬1) ∧ 0)
¬(0 ∧ (¬1))
Chosen: ¬((¬1) ∧ 0)
Options:
(¬(¬1)) ∨ (¬0)
¬0
¬(0 ∧ (¬1))
¬(0 ∧ 0)
Chosen: ¬0
Options:
1
Chose... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
55,
75078,
1630,
8,
12264,
101,
320,
83193,
15,
595,
75078,
1819,
16,
12264,
101,
220,
16,
8,
12264,
101,
320,
83193,
35,
448... | 1,788 | null | 891 | null | cl100k_base | 1,382 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((X ∧ X) ∨ (¬0)) ∧ ((1 ∨ 1) ∨ (¬D))
Options:
((1 ∨ 1) ∨ (¬D)) ∧ ((X ∧ X) ∨ (¬0))
(((X ∧ X) ∨ (¬0)) ∧ (1 ∨ 1)) ∨ (((X ∧ X) ∨ (¬0)) ∧ (¬D))
((X ∧ X) ∨ (¬0)) ∧ ((¬D) ∨ (1 ∨ 1))
((X ∧ X) ∨ (¬0)) ∧ (1 ∨ (1 ∨ (¬D)))
((X ∧ X) ∨... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
83193,
39,
8,
75078,
320,
39,
12264,
101,
220,
16,
595,
75078,
1819,
83193,
15,
8,
75078,
320,
15,
75078,
468,
4489,
3883,
51... | 1,789 | null | 1,255 | null | cl100k_base | 2,120 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬H) ∧ (H ∨ 1)) ∧ ((¬0) ∧ (0 ∧ W))
Options:
((¬0) ∧ (0 ∧ W)) ∧ ((¬H) ∧ (H ∨ 1))
(((¬H) ∧ (H ∨ 1)) ∧ (¬0)) ∧ (0 ∧ W)
(¬H) ∧ ((H ∨ 1) ∧ ((¬0) ∧ (0 ∧ W)))
((¬H) ∧ (H ∨ 1)) ∧ ((0 ∧ W) ∧ (¬0))
((¬H) ∧ (H ∨ 1)) ∧ (((¬0) ∧ 0) ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
7,
83193,
7,
15,
75078,
507,
4489,
3883,
512,
15,
75078,
507,
198,
83193,
1209,
83193,
15,
8,
12264,
101,
320,
83193,
46,
11... | 1,790 | null | 79 | null | cl100k_base | 201 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬(¬(0 ∧ O))
Options:
0 ∧ O
¬((¬0) ∨ (¬O))
¬(¬0)
¬(¬(O ∧ 0))
Chosen: 0 ∧ O
Options:
0
O ∧ 0
Chosen: 0 |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
32,
12264,
101,
362,
8,
12264,
101,
320,
43,
75078,
220,
15,
595,
75078,
1819,
16,
75078,
220,
15,
8,
75078,
320,
15,
75078,
... | 1,791 | null | 1,403 | null | cl100k_base | 2,196 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((A ∨ A) ∨ (L ∧ 0)) ∧ ((1 ∧ 0) ∧ (0 ∧ 0))
Options:
((1 ∧ 0) ∧ (0 ∧ 0)) ∧ ((A ∨ A) ∨ (L ∧ 0))
(((A ∨ A) ∨ (L ∧ 0)) ∧ (1 ∧ 0)) ∧ (0 ∧ 0)
((A ∨ A) ∨ (L ∧ 0)) ∧ ((0 ∧ 0) ∧ (1 ∧ 0))
((A ∨ A) ∨ (L ∧ 0)) ∧ (((1 ∧ 0) ∧ 0) ∧ 0)
(... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
7,
83193,
7,
45,
12264,
101,
220,
16,
4489,
3883,
512,
45,
12264,
101,
220,
16,
198,
83193,
1209,
83193,
45,
8,
75078,
320,
... | 1,792 | null | 96 | null | cl100k_base | 227 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬(¬(N ∨ 1))
Options:
N ∨ 1
¬((¬N) ∧ (¬1))
¬(¬1)
¬(¬(1 ∨ N))
Chosen: N ∨ 1
Options:
1
1 ∨ N
Chosen: 1 ∨ N
Options:
1
Chosen: 1 |
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,
15,
271,
3883,
512... | 1,793 | null | 50 | null | cl100k_base | 159 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬(¬(¬0))
Options:
¬0
¬(¬1)
Chosen: ¬0
Options:
1
Chosen: 1 |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
320,
83193,
7,
16,
12264,
101,
469,
595,
12264,
101,
1819,
83193,
55,
8,
12264,
101,
320,
55,
12264,
101,
469,
4489,
3883,
512,
120... | 1,794 | null | 896 | null | cl100k_base | 1,355 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: (¬(1 ∨ E)) ∨ ((¬X) ∨ (X ∨ E))
Options:
((¬X) ∨ (X ∨ E)) ∨ (¬(1 ∨ E))
((¬(1 ∨ E)) ∨ (¬X)) ∨ (X ∨ E)
(¬(1 ∨ E)) ∨ ((X ∨ E) ∨ (¬X))
(¬(1 ∨ E)) ∨ (((¬X) ∨ X) ∨ E)
(¬(1 ∨ E)) ∨ ((¬X) ∨ (E ∨ X))
((¬1) ∧ (¬E)) ∨ ((¬X) ∨ (X ∨ E)... |
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,
15,
8,
75078,
320,
44,
12264,
101,
507,
595,
12264,
101,
1819,
16,
12264,
101,
220,
15,
8,
75078,
320,
... | 1,795 | null | 1,141 | null | cl100k_base | 1,727 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((1 ∨ 0) ∧ (M ∨ O)) ∨ ((1 ∨ 0) ∧ (¬1))
Options:
((1 ∨ 0) ∧ (¬1)) ∨ ((1 ∨ 0) ∧ (M ∨ O))
(((1 ∨ 0) ∧ (M ∨ O)) ∨ (1 ∨ 0)) ∧ (((1 ∨ 0) ∧ (M ∨ O)) ∨ (¬1))
((1 ∨ 0) ∧ (M ∨ O)) ∨ ((¬1) ∧ (1 ∨ 0))
((1 ∨ 0) ∧ (M ∨ O)) ∨ ((1 ∨ 0) ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
97265,
1209,
16,
75078,
220,
16,
8,
75078,
320,
15,
12264,
101,
220,
15,
4489,
3883,
512,
7,
83193,
7,
16,
75078,
220,
16,
595,
1... | 1,796 | null | 203 | null | cl100k_base | 384 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ¬((1 ∧ 1) ∧ (0 ∨ 0))
Options:
(¬(1 ∧ 1)) ∨ (¬(0 ∨ 0))
¬((0 ∨ 0) ∧ (1 ∧ 1))
¬(1 ∧ (1 ∧ (0 ∨ 0)))
¬(((1 ∧ 1) ∧ 0) ∨ ((1 ∧ 1) ∧ 0))
¬((1 ∧ 1) ∧ 0)
¬(1 ∧ (0 ∨ 0))
Chosen: ¬((1 ∧ 1) ∧ 0)
Options:
(¬(1 ∧ 1)) ∨ (¬0)
¬0
¬(0 ∧ (... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
83193,
57,
8,
75078,
320,
83193,
57,
595,
75078,
1819,
35,
75078,
220,
15,
8,
75078,
320,
16,
12264,
101,
423,
4489,
3883,
51... | 1,797 | null | 822 | null | cl100k_base | 1,406 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((¬Z) ∧ (¬Z)) ∧ ((D ∧ 0) ∧ (1 ∨ D))
Options:
((D ∧ 0) ∧ (1 ∨ D)) ∧ ((¬Z) ∧ (¬Z))
(((¬Z) ∧ (¬Z)) ∧ (D ∧ 0)) ∧ (1 ∨ D)
(¬Z) ∧ ((¬Z) ∧ ((D ∧ 0) ∧ (1 ∨ D)))
((¬Z) ∧ (¬Z)) ∧ ((1 ∨ D) ∧ (D ∧ 0))
((¬Z) ∧ (¬Z)) ∧ (D ∧ (0 ∧ (1 ∨ ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
15,
75078,
220,
15,
8,
12264,
101,
320,
16,
75078,
220,
16,
595,
12264,
101,
1819,
83193,
16,
8,
75078,
320,
16,
12264,
101,
... | 1,798 | null | 3,665 | null | cl100k_base | 5,285 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((0 ∧ 0) ∨ (1 ∧ 1)) ∨ ((¬1) ∧ (1 ∨ 1))
Options:
((¬1) ∧ (1 ∨ 1)) ∨ ((0 ∧ 0) ∨ (1 ∧ 1))
(0 ∧ 0) ∨ ((1 ∧ 1) ∨ ((¬1) ∧ (1 ∨ 1)))
(((0 ∧ 0) ∨ (1 ∧ 1)) ∨ (¬1)) ∧ (((0 ∧ 0) ∨ (1 ∧ 1)) ∨ (1 ∨ 1))
((0 ∧ 0) ∨ (1 ∧ 1)) ∨ ((1 ∨ 1) ... |
boolean | null | [
39314,
374,
264,
2777,
7645,
13,
23548,
433,
527,
5897,
14951,
7607,
315,
430,
7645,
382,
18902,
25,
1819,
38,
12264,
101,
220,
15,
8,
75078,
320,
53,
12264,
101,
220,
15,
595,
75078,
1819,
16,
75078,
220,
15,
8,
12264,
101,
320,
... | 1,799 | null | 1,763 | null | cl100k_base | 2,705 | null | null | null | Below is a boolean expression. Following it are legal manipulations of that expression.
Original: ((G ∨ 0) ∧ (V ∨ 0)) ∧ ((1 ∧ 0) ∨ (¬0))
Options:
((1 ∧ 0) ∨ (¬0)) ∧ ((G ∨ 0) ∧ (V ∨ 0))
(G ∨ 0) ∧ ((V ∨ 0) ∧ ((1 ∧ 0) ∨ (¬0)))
(((G ∨ 0) ∧ (V ∨ 0)) ∧ (1 ∧ 0)) ∨ (((G ∨ 0) ∧ (V ∨ 0)) ∧ (¬0))
((G ∨ 0) ∧ (V ∨ 0)) ∧ ((¬0) ∨ (... |
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