ABCDEFGHIJKLMNOPQRSTUVWXYZAA
1
Totals ==>72180000000000090
2
Ok?BPBSI
BSQ
IFIGOIWUEUXXRV
Scope
AnswerExplanationIDFormulaTraceExpected
3
1
Trace too short, the formula accepts no traces of its length.
No traces of size 1 can satisfy this formula as it has a next operator.
R_2PtHv3KdsGqQLoB
X(G(r)){r}*too short
4
1
Trace too short, the formula accepts no traces of its length.
R_3079Udc3BOxNquc
X(G(r)){r}*too short
5
1
Trace too short, the formula accepts no traces of its length.
R_2U5AqOKS1RFOYwc
X(G(r)){r}*too short
6
1
Trace too short, the formula accepts no traces of its length.
R_2yscxjylS1SXLu5
X(G(r)){r}*too short
7
1
Trace too short, the formula accepts no traces of its length.
R_oYU5yKiaqPgXzMd
X(G(r)){r}*too short
8
1
Trace too short, the formula accepts no traces of its length.
R_5vtXYvxyZKlCUx3
X(G(r)){r}*too short
9
1
Trace too short, the formula accepts no traces of its length.
R_2aenS9mNn6Dk4Cz
X(G(r)){r}*too short
10
1
Trace too short, the formula accepts no traces of its length.
We need at least two states because there's a next operator. There is no next state.
R_3s0nFuWCbCk5CjP
X(G(r)){r}*too short
11
1
Trace too short, the formula accepts no traces of its length.
There does not exist a next state for the formula G(Red) to hold.
R_2uWWZejY6DyOYaH
X(G(r)){r}*too short
12
1
Trace too short, the formula accepts no traces of its length.
A formula with 1 strong next operator requires traces of length at least 2
R_2WwptK2YPEgUAGJ
X(G(r)){r}*too short
13
1
Trace too short, the formula accepts no traces of its length.
R_sLorPWGMjcKuGYx
X(G(r)){r}*too short
14
1
Trace too short, the formula accepts no traces of its length.
the X at the start asserts traces must have a second state
R_2zeuLOxEmJflmcu
X(G(r)){r}*too short
15
1
Trace too short, the formula accepts no traces of its length.
R_1rjpSmO14SmyPCQ
X(G(r)){r}*too short
16
1
Trace too short, the formula accepts no traces of its length.
R_1FRNUwvnkvroHRF
X(G(r)){r}*too short
17
1
Trace too short, the formula accepts no traces of its length.
R_3IXnVYuOI9QeI10
X(G(r)){r}*too short
18
1
Trace too short, the formula accepts no traces of its length.
R_3KGxBOYYe7aGaXI
X(G(r)){r}*too short
19
1
Only an infinite trace can satisfy this formula
R_2QS5lE5zYMCL1s7
X(G(r)){r}*too short
20
1
Trace too short, the formula accepts no traces of its length.
R_31j7Jp3yQbqaZqk
X(G(r)){r}*too short
21
1
Trace content mismatch, wrong lights on/off in some state.
The trace has no Blue states but the formula requires a Blue state.
R_2PtHv3KdsGqQLoB
r U (!r & F(b)){r} {r} {}mismatch
22
1
Trace content mismatch, wrong lights on/off in some state.
R_3079Udc3BOxNquc
r U (!r & F(b)){r} {r} {}mismatch
23
1
Trace content mismatch, wrong lights on/off in some state.
R_2U5AqOKS1RFOYwc
r U (!r & F(b)){r} {r} {}mismatch
24
1
Trace content mismatch, wrong lights on/off in some state.
R_2yscxjylS1SXLu5
r U (!r & F(b)){r} {r} {}mismatch
25
1
Trace content mismatch, wrong lights on/off in some state.
F(Blue) never satisfied
R_oYU5yKiaqPgXzMd
r U (!r & F(b)){r} {r} {}mismatch
26
1
Trace content mismatch, wrong lights on/off in some state.
R_5vtXYvxyZKlCUx3
r U (!r & F(b)){r} {r} {}mismatch
27
1
Trace content mismatch, wrong lights on/off in some state.
R_2aenS9mNn6Dk4Cz
r U (!r & F(b)){r} {r} {}mismatch
28
1
Trace content mismatch, wrong lights on/off in some state.
There is no blue state and hence eventually blue isn't satisfied.
R_3s0nFuWCbCk5CjP
r U (!r & F(b)){r} {r} {}mismatch
29
1
Trace content mismatch, wrong lights on/off in some state.
The last state, since the Red light is not turned on, should have the Blue light turned on in order to satisfy the formula.
R_2uWWZejY6DyOYaH
r U (!r & F(b)){r} {r} {}mismatch
30
1
Trace content mismatch, wrong lights on/off in some state.
No state satisfies (!Red & F(Blue)) as the blue light is never on, and Red is not satisfied in the thrid timestep, and hence this formula is false
R_2WwptK2YPEgUAGJ
r U (!r & F(b)){r} {r} {}mismatch
31
1
Trace content mismatch, wrong lights on/off in some state.
R_sLorPWGMjcKuGYx
r U (!r & F(b)){r} {r} {}mismatch
32
1
Trace content mismatch, wrong lights on/off in some state.
If the blue light was on in state 3 it would be satisfied
R_2zeuLOxEmJflmcu
r U (!r & F(b)){r} {r} {}mismatch
33
1
Trace content mismatch, wrong lights on/off in some state.
3 should be blue
R_1rjpSmO14SmyPCQ
r U (!r & F(b)){r} {r} {}mismatch
34
1
Trace content mismatch, wrong lights on/off in some state.
R_1FRNUwvnkvroHRF
r U (!r & F(b)){r} {r} {}mismatch
35
1
Trace content mismatch, wrong lights on/off in some state.
R_3IXnVYuOI9QeI10
r U (!r & F(b)){r} {r} {}mismatch
36
1
Trace content mismatch, wrong lights on/off in some state.
R_3KGxBOYYe7aGaXI
r U (!r & F(b)){r} {r} {}mismatch
37
1
Only an infinite trace can satisfy this formula
R_2QS5lE5zYMCL1s7
r U (!r & F(b)){r} {r} {}mismatch
38
1
Trace content mismatch, wrong lights on/off in some state.
R_31j7Jp3yQbqaZqk
r U (!r & F(b)){r} {r} {}mismatch
39
1
Trace content mismatch, wrong lights on/off in some state.
The third state is Red but given Xw(Xw(!Red)) we expect it to not be Red.
R_2PtHv3KdsGqQLoB
G(r) & Xw(Xw(!r))
{r} {r} {r}too long
40
1
Trace content mismatch, wrong lights on/off in some state.
R_3079Udc3BOxNquc
G(r) & Xw(Xw(!r))
{r} {r} {r}too long
41
1
Trace content mismatch, wrong lights on/off in some state.
R_2U5AqOKS1RFOYwc
G(r) & Xw(Xw(!r))
{r} {r} {r}too long
42
1
Trace too long, the formula accepts no traces of its length.
R_2yscxjylS1SXLu5
G(r) & Xw(Xw(!r))
{r} {r} {r}too long
43
1
Trace content mismatch, wrong lights on/off in some state.
Xw(Xw(!Red)) Not satisfied, as Red on in state 3
R_oYU5yKiaqPgXzMd
G(r) & Xw(Xw(!r))
{r} {r} {r}too long
44
1
Trace content mismatch, wrong lights on/off in some state.
R_5vtXYvxyZKlCUx3
G(r) & Xw(Xw(!r))
{r} {r} {r}too long
45
1
Trace content mismatch, wrong lights on/off in some state.
R_2aenS9mNn6Dk4Cz
G(r) & Xw(Xw(!r))
{r} {r} {r}too long
46
1
Trace content mismatch, wrong lights on/off in some state.
Xw (Xw (!Red)) is equivalent to XX (!Red) here since both states exist and !Red is never satisfied here.
R_3s0nFuWCbCk5CjP
G(r) & Xw(Xw(!r))
{r} {r} {r}too long
47
1
Trace too long, the formula accepts no traces of its length.
In order to satisfy Xw(Xw(!Red)), the final state should not have the Red light turned on. The formula G(Red) & Xw(Xw(!Red) also cannot be satisfied for any finite traces with 3 or more states as they contradict one another.
R_2uWWZejY6DyOYaH
G(r) & Xw(Xw(!r))
{r} {r} {r}too long
48
1
Trace content mismatch, wrong lights on/off in some state.
The second clause is not satisfied as the third state exists and the Red light is on
R_2WwptK2YPEgUAGJ
G(r) & Xw(Xw(!r))
{r} {r} {r}too long
49
1
Trace too long, the formula accepts no traces of its length.
R_sLorPWGMjcKuGYx
G(r) & Xw(Xw(!r))
{r} {r} {r}too long
50
1
Trace too long, the formula accepts no traces of its length.
the third state need to be red and not red, or not exist at all. so only length <= 2 traces satisfy
R_2zeuLOxEmJflmcu
G(r) & Xw(Xw(!r))
{r} {r} {r}too long
51
1
Trace content mismatch, wrong lights on/off in some state.
3 should not be red
R_1rjpSmO14SmyPCQ
G(r) & Xw(Xw(!r))
{r} {r} {r}too long
52
1
Trace content mismatch, wrong lights on/off in some state.
R_1FRNUwvnkvroHRF
G(r) & Xw(Xw(!r))
{r} {r} {r}too long
53
1
Trace content mismatch, wrong lights on/off in some state.
R_3IXnVYuOI9QeI10
G(r) & Xw(Xw(!r))
{r} {r} {r}too long
54
1
Trace content mismatch, wrong lights on/off in some state.
R_3KGxBOYYe7aGaXI
G(r) & Xw(Xw(!r))
{r} {r} {r}too long
55
1
Trace too long, the formula accepts no traces of its length.
R_2QS5lE5zYMCL1s7
G(r) & Xw(Xw(!r))
{r} {r} {r}too long
56
1
Trace content mismatch, wrong lights on/off in some state.
R_31j7Jp3yQbqaZqk
G(r) & Xw(Xw(!r))
{r} {r} {r}too long
57
1
Trace content mismatch, wrong lights on/off in some state.
We expect that the final state is not Red as this is a requirement of stability. However. the final state is Red.
R_2PtHv3KdsGqQLoB
F(G(!r)){g} {r}mismatch
58
1
Trace content mismatch, wrong lights on/off in some state.
R_3079Udc3BOxNquc
F(G(!r)){g} {r}mismatch
59
1
Trace content mismatch, wrong lights on/off in some state.
R_2U5AqOKS1RFOYwc
F(G(!r)){g} {r}mismatch
60
1
Trace content mismatch, wrong lights on/off in some state.
R_2yscxjylS1SXLu5
F(G(!r)){g} {r}mismatch
61
1
Trace content mismatch, wrong lights on/off in some state.
The final state has Red on
R_oYU5yKiaqPgXzMd
F(G(!r)){g} {r}mismatch
62
1
Trace content mismatch, wrong lights on/off in some state.
R_5vtXYvxyZKlCUx3
F(G(!r)){g} {r}mismatch
63
1
Trace content mismatch, wrong lights on/off in some state.
R_2aenS9mNn6Dk4Cz
F(G(!r)){g} {r}mismatch
64
1
Trace content mismatch, wrong lights on/off in some state.
We end up with Red being satisfied. We should have !Red being satisfied.
R_3s0nFuWCbCk5CjP
F(G(!r)){g} {r}mismatch
65
1
Trace content mismatch, wrong lights on/off in some state.
We will need state 2 to not have the Red light turned on in order for the formula to be satisfied.
R_2uWWZejY6DyOYaH
F(G(!r)){g} {r}mismatch
66
1
Trace content mismatch, wrong lights on/off in some state.
There is no state where the red light is never on subsequently.
R_2WwptK2YPEgUAGJ
F(G(!r)){g} {r}mismatch
67
1
Trace content mismatch, wrong lights on/off in some state.
R_sLorPWGMjcKuGYx
F(G(!r)){g} {r}mismatch
68
1
Trace content mismatch, wrong lights on/off in some state.
Any trace where the last state has no red would satisfy
R_2zeuLOxEmJflmcu
F(G(!r)){g} {r}mismatch
69
1
Trace content mismatch, wrong lights on/off in some state.
R_1rjpSmO14SmyPCQ
F(G(!r)){g} {r}mismatch
70
1
Trace content mismatch, wrong lights on/off in some state.
R_1FRNUwvnkvroHRF
F(G(!r)){g} {r}mismatch
71
1
Trace content mismatch, wrong lights on/off in some state.
R_3IXnVYuOI9QeI10
F(G(!r)){g} {r}mismatch
72
1
Trace content mismatch, wrong lights on/off in some state.
R_3KGxBOYYe7aGaXI
F(G(!r)){g} {r}mismatch
73
1
Only an infinite trace can satisfy this formula
R_2QS5lE5zYMCL1s7
F(G(!r)){g} {r}mismatch
74
1
Trace content mismatch, wrong lights on/off in some state.
R_31j7Jp3yQbqaZqk
F(G(!r)){g} {r}mismatch
75
1
Only an infinite trace can satisfy this formula
Given the formula, we can deduce that any trace satisfying it should have in odd positioned stated Red on. However, for a finite trace once we get to the last odd position with Red X(X(Red)) will be False so the formula cannot be satisfied.
R_2PtHv3KdsGqQLoB
r & G(r => X(X(r)))
{r} {} {} {r} {} {} {r}
inf only
76
1
Trace content mismatch, wrong lights on/off in some state.
R_3079Udc3BOxNquc
r & G(r => X(X(r)))
{r} {} {} {r} {} {} {r}
inf only
77
1
Only an infinite trace can satisfy this formula
R_2U5AqOKS1RFOYwc
r & G(r => X(X(r)))
{r} {} {} {r} {} {} {r}
inf only
78
1
Only an infinite trace can satisfy this formula
R_2yscxjylS1SXLu5
r & G(r => X(X(r)))
{r} {} {} {r} {} {} {r}
inf only
79
1
Trace content mismatch, wrong lights on/off in some state.
State 1 does not satisfy Red => X(X(Red)) as state 3 is not red
R_oYU5yKiaqPgXzMd
r & G(r => X(X(r)))
{r} {} {} {r} {} {} {r}
inf only
80
1
Trace content mismatch, wrong lights on/off in some state.
R_5vtXYvxyZKlCUx3
r & G(r => X(X(r)))
{r} {} {} {r} {} {} {r}
inf only
81
1
Trace content mismatch, wrong lights on/off in some state.
R_2aenS9mNn6Dk4Cz
r & G(r => X(X(r)))
{r} {} {} {r} {} {} {r}
inf only
82
1
Only an infinite trace can satisfy this formula
Red is satisfied. \\ Then forever, whenever red is satisfied, two states along, red must also be satisfied. \\ \\ Only an infinite trace can satisfy this formula. Whenever state n satisfies Red, we must have that state n+2 satisfies Red also. Hence we must check n+2. But then we'd have to check that n+4 satisfies Red also, this continues forever and hence only an infinite trace can satisfy this formula.
R_3s0nFuWCbCk5CjP
r & G(r => X(X(r)))
{r} {} {} {r} {} {} {r}
inf only
83
1
Trace content mismatch, wrong lights on/off in some state.
Since the initial state has the red light turned on, G(Red => X(X(Red))) means that the Red light should be turned on at the 3rd time step, which is not the case.
R_2uWWZejY6DyOYaH
r & G(r => X(X(r)))
{r} {} {} {r} {} {} {r}
inf only
84
1
Only an infinite trace can satisfy this formula
The first clause enforces that the right light is on at the start. The second clause enforces that the next two timesteps exist and the third timestep has the red light on, which repeats so that no finite trace can satisfy this formula. \\ Furthermore, the Always operator already fails at the first timestep as the red light is not on at the thrid timestep.
R_2WwptK2YPEgUAGJ
r & G(r => X(X(r)))
{r} {} {} {r} {} {} {r}
inf only
85
1
Only an infinite trace can satisfy this formula
R_sLorPWGMjcKuGYx
r & G(r => X(X(r)))
{r} {} {} {r} {} {} {r}
inf only
86
1
Only an infinite trace can satisfy this formula
first state has to be red, but then this implies there always exists a state two states later, which is also red. since the X is strong, the sequence cannot end. There is also a content mismatch, since the alternation needs to be every other state, not every third state.
R_2zeuLOxEmJflmcu
r & G(r => X(X(r)))
{r} {} {} {r} {} {} {r}
inf only
87
1
Trace too short, the formula accepts no traces of its length.
R_1rjpSmO14SmyPCQ
r & G(r => X(X(r)))
{r} {} {} {r} {} {} {r}
inf only
88
1
Trace content mismatch, wrong lights on/off in some state.
R_1FRNUwvnkvroHRF
r & G(r => X(X(r)))
{r} {} {} {r} {} {} {r}
inf only
89
1
Only an infinite trace can satisfy this formula
R_3IXnVYuOI9QeI10
r & G(r => X(X(r)))
{r} {} {} {r} {} {} {r}
inf only
90
1
Trace content mismatch, wrong lights on/off in some state.
R_3KGxBOYYe7aGaXI
r & G(r => X(X(r)))
{r} {} {} {r} {} {} {r}
inf only
91
1
Trace too short, the formula accepts no traces of its length.
R_2QS5lE5zYMCL1s7
r & G(r => X(X(r)))
{r} {} {} {r} {} {} {r}
inf only
92
1
Trace content mismatch, wrong lights on/off in some state.
R_31j7Jp3yQbqaZqk
r & G(r => X(X(r)))
{r} {} {} {r} {} {} {r}
inf only
93
94
95
96
97
98
99
100
101
102
103
104
105
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107
108
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110
111
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115
116
117
118
119
120
121
122
123
124
125
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128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
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