Solving ../../benchmarks/smtlib/true/max_nat.smt2...

Inference procedure has parameters:
Ice fuel: 200
Timeout: Some(60.) (sec)
Teacher_type: Checks all clauses every time
Approximation method: remove every clause that can be safely removed



Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(leq, P:
{
leq(z, n2) <= True
leq(s(nn1), s(nn2)) <= leq(nn1, nn2)
leq(nn1, nn2) <= leq(s(nn1), s(nn2))
False <= leq(s(nn1), z)
}
)
(max, F:
{
leq(n, m) \/ max(n, m, n) <= True
max(n, m, m) <= leq(n, m)
}
eq_nat(_jaa, _kaa) <= max(_haa, _iaa, _jaa) /\ max(_haa, _iaa, _kaa)
)
}

properties:
{
leq(i, _laa) <= max(i, j, _laa)
leq(j, _maa) <= max(i, j, _maa)
}


over-approximation: {max}
under-approximation: {}

Clause system for inference is:

{
leq(n, m) \/ max(n, m, n) <= True -> 0
leq(z, n2) <= True -> 0
max(n, m, m) <= leq(n, m) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
leq(i, _laa) <= max(i, j, _laa) -> 0
leq(j, _maa) <= max(i, j, _maa) -> 0
}


Solving took 0.065780 seconds.
Yes: |_
name: None

leq ->
[
leq : <nat * nat>
{
  leq(s(x_0_0), s(x_1_0)) <= leq(x_0_0, x_1_0)
  leq(z, s(x_1_0)) <= True
  leq(z, z) <= True
}
]


;
max ->
[
max : <nat * nat * nat>
{
  leq(s(x_0_0), s(x_1_0)) <= leq(x_0_0, x_1_0)
  leq(z, s(x_1_0)) <= True
  leq(z, z) <= True
  max(s(x_0_0), s(x_1_0), s(x_2_0)) <= leq(x_0_0, x_2_0) /\ leq(x_1_0, x_2_0)
  max(s(x_0_0), z, s(x_2_0)) <= leq(x_0_0, x_2_0)
  max(z, s(x_1_0), s(x_2_0)) <= leq(x_1_0, x_2_0)
  max(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006045 s (model generation: 0.005973,  model checking: 0.000072):

Clauses:
{
leq(n, m) \/ max(n, m, n) <= True -> 0
leq(z, n2) <= True -> 0
max(n, m, m) <= leq(n, m) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
leq(i, _laa) <= max(i, j, _laa) -> 0
leq(j, _maa) <= max(i, j, _maa) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

leq ->
[
leq : <nat * nat>
{
  
}
]


;
max ->
[
max : <nat * nat * nat>
{
  
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

leq(n, m) \/ max(n, m, n) <= True  :
Yes: {
m -> z  ;  n -> z
}

leq(z, n2) <= True  :
Yes: {
n2 -> z
}

max(n, m, m) <= leq(n, m)  :
No: ()

leq(s(nn1), s(nn2)) <= leq(nn1, nn2)  :
No: ()

leq(nn1, nn2) <= leq(s(nn1), s(nn2))  :
No: ()

False <= leq(s(nn1), z)  :
No: ()

leq(i, _laa) <= max(i, j, _laa)  :
No: ()

leq(j, _maa) <= max(i, j, _maa)  :
No: ()


-------------------------------------------
Step 1, which took 0.006186 s (model generation: 0.006100,  model checking: 0.000086):

Clauses:
{
leq(n, m) \/ max(n, m, n) <= True -> 0
leq(z, n2) <= True -> 0
max(n, m, m) <= leq(n, m) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
leq(i, _laa) <= max(i, j, _laa) -> 0
leq(j, _maa) <= max(i, j, _maa) -> 0
}

Accumulated learning constraints:
{
leq(z, z) <= True
}

Current best model:
|_
name: None

leq ->
[
leq : <nat * nat>
{
  leq(z, z) <= True
}
]


;
max ->
[
max : <nat * nat * nat>
{
  
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

leq(n, m) \/ max(n, m, n) <= True  :
Yes: {
m -> z  ;  n -> s(_utus_0)
}

leq(z, n2) <= True  :
Yes: {
n2 -> s(_xtus_0)
}

max(n, m, m) <= leq(n, m)  :
Yes: {
m -> z  ;  n -> z
}

leq(s(nn1), s(nn2)) <= leq(nn1, nn2)  :
Yes: {
nn1 -> z  ;  nn2 -> z
}

leq(nn1, nn2) <= leq(s(nn1), s(nn2))  :
No: ()

False <= leq(s(nn1), z)  :
No: ()

leq(i, _laa) <= max(i, j, _laa)  :
No: ()

leq(j, _maa) <= max(i, j, _maa)  :
No: ()


-------------------------------------------
Step 2, which took 0.011881 s (model generation: 0.011734,  model checking: 0.000147):

Clauses:
{
leq(n, m) \/ max(n, m, n) <= True -> 0
leq(z, n2) <= True -> 0
max(n, m, m) <= leq(n, m) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
leq(i, _laa) <= max(i, j, _laa) -> 0
leq(j, _maa) <= max(i, j, _maa) -> 0
}

Accumulated learning constraints:
{
leq(s(z), s(z)) <= True
leq(s(z), z) \/ max(s(z), z, s(z)) <= True
leq(z, s(z)) <= True
leq(z, z) <= True
max(z, z, z) <= True
}

Current best model:
|_
name: None

leq ->
[
leq : <nat * nat>
{
  leq(s(x_0_0), s(x_1_0)) <= True
  leq(s(x_0_0), z) <= True
  leq(z, s(x_1_0)) <= True
  leq(z, z) <= True
}
]


;
max ->
[
max : <nat * nat * nat>
{
  max(s(x_0_0), z, s(x_2_0)) <= True
  max(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

leq(n, m) \/ max(n, m, n) <= True  :
No: ()

leq(z, n2) <= True  :
No: ()

max(n, m, m) <= leq(n, m)  :
Yes: {
m -> z  ;  n -> s(_fuus_0)
}

leq(s(nn1), s(nn2)) <= leq(nn1, nn2)  :
No: ()

leq(nn1, nn2) <= leq(s(nn1), s(nn2))  :
No: ()

False <= leq(s(nn1), z)  :
Yes: {

}

leq(i, _laa) <= max(i, j, _laa)  :
No: ()

leq(j, _maa) <= max(i, j, _maa)  :
No: ()


-------------------------------------------
Step 3, which took 0.011262 s (model generation: 0.011185,  model checking: 0.000077):

Clauses:
{
leq(n, m) \/ max(n, m, n) <= True -> 0
leq(z, n2) <= True -> 0
max(n, m, m) <= leq(n, m) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
leq(i, _laa) <= max(i, j, _laa) -> 0
leq(j, _maa) <= max(i, j, _maa) -> 0
}

Accumulated learning constraints:
{
leq(s(z), s(z)) <= True
leq(z, s(z)) <= True
leq(z, z) <= True
max(s(z), z, s(z)) <= True
max(z, z, z) <= True
False <= leq(s(z), z)
}

Current best model:
|_
name: None

leq ->
[
leq : <nat * nat>
{
  leq(s(x_0_0), s(x_1_0)) <= True
  leq(z, s(x_1_0)) <= True
  leq(z, z) <= True
}
]


;
max ->
[
max : <nat * nat * nat>
{
  max(s(x_0_0), z, s(x_2_0)) <= True
  max(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

leq(n, m) \/ max(n, m, n) <= True  :
No: ()

leq(z, n2) <= True  :
No: ()

max(n, m, m) <= leq(n, m)  :
Yes: {
m -> s(_kuus_0)  ;  n -> z
}

leq(s(nn1), s(nn2)) <= leq(nn1, nn2)  :
No: ()

leq(nn1, nn2) <= leq(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(_muus_0)  ;  nn2 -> z
}

False <= leq(s(nn1), z)  :
No: ()

leq(i, _laa) <= max(i, j, _laa)  :
No: ()

leq(j, _maa) <= max(i, j, _maa)  :
No: ()


-------------------------------------------
Step 4, which took 0.009876 s (model generation: 0.009640,  model checking: 0.000236):

Clauses:
{
leq(n, m) \/ max(n, m, n) <= True -> 0
leq(z, n2) <= True -> 0
max(n, m, m) <= leq(n, m) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
leq(i, _laa) <= max(i, j, _laa) -> 0
leq(j, _maa) <= max(i, j, _maa) -> 0
}

Accumulated learning constraints:
{
leq(s(z), s(z)) <= True
leq(z, s(z)) <= True
leq(z, z) <= True
max(s(z), z, s(z)) <= True
max(z, s(z), s(z)) <= True
max(z, z, z) <= True
False <= leq(s(s(z)), s(z))
False <= leq(s(z), z)
}

Current best model:
|_
name: None

leq ->
[
leq : <nat * nat>
{
  leq(s(x_0_0), s(x_1_0)) <= leq(x_0_0, x_1_0)
  leq(z, s(x_1_0)) <= True
  leq(z, z) <= True
}
]


;
max ->
[
max : <nat * nat * nat>
{
  max(s(x_0_0), z, s(x_2_0)) <= True
  max(z, s(x_1_0), s(x_2_0)) <= True
  max(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

leq(n, m) \/ max(n, m, n) <= True  :
Yes: {
m -> s(z)  ;  n -> s(s(_kvus_0))
}

leq(z, n2) <= True  :
No: ()

max(n, m, m) <= leq(n, m)  :
Yes: {
m -> s(z)  ;  n -> s(z)
}

leq(s(nn1), s(nn2)) <= leq(nn1, nn2)  :
No: ()

leq(nn1, nn2) <= leq(s(nn1), s(nn2))  :
No: ()

False <= leq(s(nn1), z)  :
No: ()

leq(i, _laa) <= max(i, j, _laa)  :
Yes: {
_laa -> s(z)  ;  i -> s(s(_kvus_0))  ;  j -> z
}

leq(j, _maa) <= max(i, j, _maa)  :
Yes: {
_maa -> s(z)  ;  i -> z  ;  j -> s(s(_kvus_0))
}


-------------------------------------------
Step 5, which took 0.009934 s (model generation: 0.009474,  model checking: 0.000460):

Clauses:
{
leq(n, m) \/ max(n, m, n) <= True -> 0
leq(z, n2) <= True -> 0
max(n, m, m) <= leq(n, m) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
leq(i, _laa) <= max(i, j, _laa) -> 0
leq(j, _maa) <= max(i, j, _maa) -> 0
}

Accumulated learning constraints:
{
leq(s(z), s(z)) <= True
leq(z, s(z)) <= True
leq(z, z) <= True
max(s(s(z)), s(z), s(s(z))) <= True
max(s(z), s(z), s(z)) <= True
max(s(z), z, s(z)) <= True
max(z, s(z), s(z)) <= True
max(z, z, z) <= True
False <= leq(s(s(z)), s(z))
False <= leq(s(z), z)
False <= max(s(s(z)), z, s(z))
False <= max(z, s(s(z)), s(z))
}

Current best model:
|_
name: None

leq ->
[
leq : <nat * nat>
{
  leq(s(x_0_0), s(x_1_0)) <= leq(x_0_0, x_1_0)
  leq(z, s(x_1_0)) <= True
  leq(z, z) <= True
}
]


;
max ->
[
max : <nat * nat * nat>
{
  leq(s(x_0_0), s(x_1_0)) <= leq(x_0_0, x_1_0)
  leq(z, s(x_1_0)) <= True
  leq(z, z) <= True
  max(s(x_0_0), s(x_1_0), s(x_2_0)) <= True
  max(s(x_0_0), z, s(x_2_0)) <= leq(x_0_0, x_2_0)
  max(z, s(x_1_0), s(x_2_0)) <= leq(x_1_0, x_2_0)
  max(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|




Answer of teacher:

leq(n, m) \/ max(n, m, n) <= True  :
No: ()

leq(z, n2) <= True  :
No: ()

max(n, m, m) <= leq(n, m)  :
No: ()

leq(s(nn1), s(nn2)) <= leq(nn1, nn2)  :
No: ()

leq(nn1, nn2) <= leq(s(nn1), s(nn2))  :
No: ()

False <= leq(s(nn1), z)  :
No: ()

leq(i, _laa) <= max(i, j, _laa)  :
Yes: {
_laa -> s(z)  ;  i -> s(s(_vwus_0))  ;  j -> s(_iwus_0)
}

leq(j, _maa) <= max(i, j, _maa)  :
Yes: {
_maa -> s(z)  ;  i -> s(_nwus_0)  ;  j -> s(s(_vwus_0))
}


Total time: 0.065780
Learner time: 0.054106
Teacher time: 0.001078
Reasons for stopping: Yes: |_
name: None

leq ->
[
leq : <nat * nat>
{
  leq(s(x_0_0), s(x_1_0)) <= leq(x_0_0, x_1_0)
  leq(z, s(x_1_0)) <= True
  leq(z, z) <= True
}
]


;
max ->
[
max : <nat * nat * nat>
{
  leq(s(x_0_0), s(x_1_0)) <= leq(x_0_0, x_1_0)
  leq(z, s(x_1_0)) <= True
  leq(z, z) <= True
  max(s(x_0_0), s(x_1_0), s(x_2_0)) <= leq(x_0_0, x_2_0) /\ leq(x_1_0, x_2_0)
  max(s(x_0_0), z, s(x_2_0)) <= leq(x_0_0, x_2_0)
  max(z, s(x_1_0), s(x_2_0)) <= leq(x_1_0, x_2_0)
  max(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|