Solving ../../benchmarks/smtlib/false/tree_depth_max_error.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: {
elt -> {a, b}  ;  etree -> {leaf, node}  ;  nat -> {s, z}
}
definition:
{
(leq_nat, P:
{
leq_nat(z, n2) <= True
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2)
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2))
False <= leq_nat(s(nn1), z)
}
)
(max, F:
{
leq_nat(n, m) \/ max(n, m, n) <= True
max(n, m, m) <= leq_nat(n, m)
}
eq_nat(_vbb, _wbb) <= max(_tbb, _ubb, _vbb) /\ max(_tbb, _ubb, _wbb)
)
(height, F:
{
height(leaf, z) <= True
height(node(e, t1, t2), s(_acb)) \/ leq_nat(_xbb, _ybb) <= height(t1, _acb) /\ height(t1, _xbb) /\ height(t2, _ybb)
height(node(e, t1, t2), s(_zbb)) <= height(t1, _xbb) /\ height(t2, _ybb) /\ height(t2, _zbb) /\ leq_nat(_xbb, _ybb)
}
eq_nat(_ccb, _dcb) <= height(_bcb, _ccb) /\ height(_bcb, _dcb)
)
}

properties:
{
leq_nat(_hcb, _gcb) <= height(t1, _ecb) /\ height(t2, _fcb) /\ height(node(e, t1, t2), _hcb) /\ max(_ecb, _fcb, _gcb)
}


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

Clause system for inference is:

{
height(leaf, z) <= True -> 0
leq_nat(n, m) \/ max(n, m, n) <= True -> 0
leq_nat(z, n2) <= True -> 0
height(node(e, t1, t2), s(_acb)) \/ leq_nat(_xbb, _ybb) <= height(t1, _acb) /\ height(t1, _xbb) /\ height(t2, _ybb) -> 0
leq_nat(_hcb, _gcb) <= height(t1, _ecb) /\ height(t2, _fcb) /\ height(node(e, t1, t2), _hcb) /\ max(_ecb, _fcb, _gcb) -> 0
height(node(e, t1, t2), s(_zbb)) <= height(t1, _xbb) /\ height(t2, _ybb) /\ height(t2, _zbb) /\ leq_nat(_xbb, _ybb) -> 0
max(n, m, m) <= leq_nat(n, m) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
False <= leq_nat(s(nn1), z) -> 0
}


Solving took 0.038401 seconds.
No: Contradictory set of ground constraints:
{
False <= True
height(leaf, z) <= True
height(node(a, leaf, leaf), s(z)) <= True
leq_nat(s(z), s(z)) <= True
leq_nat(z, s(z)) <= True
leq_nat(z, z) <= True
max(s(z), z, s(z)) <= True
max(z, s(z), s(z)) <= True
max(z, z, z) <= True
False <= leq_nat(s(s(z)), s(z))
False <= leq_nat(s(z), z)
}
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006886 s (model generation: 0.006790,  model checking: 0.000096):

Clauses:
{
height(leaf, z) <= True -> 0
leq_nat(n, m) \/ max(n, m, n) <= True -> 0
leq_nat(z, n2) <= True -> 0
height(node(e, t1, t2), s(_acb)) \/ leq_nat(_xbb, _ybb) <= height(t1, _acb) /\ height(t1, _xbb) /\ height(t2, _ybb) -> 0
leq_nat(_hcb, _gcb) <= height(t1, _ecb) /\ height(t2, _fcb) /\ height(node(e, t1, t2), _hcb) /\ max(_ecb, _fcb, _gcb) -> 0
height(node(e, t1, t2), s(_zbb)) <= height(t1, _xbb) /\ height(t2, _ybb) /\ height(t2, _zbb) /\ leq_nat(_xbb, _ybb) -> 0
max(n, m, m) <= leq_nat(n, m) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
False <= leq_nat(s(nn1), z) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

height ->
[
height : <etree * nat>
{
  
}
]


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


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



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




Answer of teacher:

height(leaf, z) <= True  :
Yes: {

}

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

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

height(node(e, t1, t2), s(_acb)) \/ leq_nat(_xbb, _ybb) <= height(t1, _acb) /\ height(t1, _xbb) /\ height(t2, _ybb)  :
No: ()

leq_nat(_hcb, _gcb) <= height(t1, _ecb) /\ height(t2, _fcb) /\ height(node(e, t1, t2), _hcb) /\ max(_ecb, _fcb, _gcb)  :
No: ()

height(node(e, t1, t2), s(_zbb)) <= height(t1, _xbb) /\ height(t2, _ybb) /\ height(t2, _zbb) /\ leq_nat(_xbb, _ybb)  :
No: ()

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

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

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

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


-------------------------------------------
Step 1, which took 0.006113 s (model generation: 0.005986,  model checking: 0.000127):

Clauses:
{
height(leaf, z) <= True -> 0
leq_nat(n, m) \/ max(n, m, n) <= True -> 0
leq_nat(z, n2) <= True -> 0
height(node(e, t1, t2), s(_acb)) \/ leq_nat(_xbb, _ybb) <= height(t1, _acb) /\ height(t1, _xbb) /\ height(t2, _ybb) -> 0
leq_nat(_hcb, _gcb) <= height(t1, _ecb) /\ height(t2, _fcb) /\ height(node(e, t1, t2), _hcb) /\ max(_ecb, _fcb, _gcb) -> 0
height(node(e, t1, t2), s(_zbb)) <= height(t1, _xbb) /\ height(t2, _ybb) /\ height(t2, _zbb) /\ leq_nat(_xbb, _ybb) -> 0
max(n, m, m) <= leq_nat(n, m) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
False <= leq_nat(s(nn1), z) -> 0
}

Accumulated learning constraints:
{
height(leaf, z) <= True
leq_nat(z, z) <= True
}

Current best model:
|_
name: None

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


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


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



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




Answer of teacher:

height(leaf, z) <= True  :
No: ()

leq_nat(n, m) \/ max(n, m, n) <= True  :
Yes: {
m -> z  ;  n -> s(_pltqw_0)
}

leq_nat(z, n2) <= True  :
Yes: {
n2 -> s(_sltqw_0)
}

height(node(e, t1, t2), s(_acb)) \/ leq_nat(_xbb, _ybb) <= height(t1, _acb) /\ height(t1, _xbb) /\ height(t2, _ybb)  :
No: ()

leq_nat(_hcb, _gcb) <= height(t1, _ecb) /\ height(t2, _fcb) /\ height(node(e, t1, t2), _hcb) /\ max(_ecb, _fcb, _gcb)  :
No: ()

height(node(e, t1, t2), s(_zbb)) <= height(t1, _xbb) /\ height(t2, _ybb) /\ height(t2, _zbb) /\ leq_nat(_xbb, _ybb)  :
Yes: {
_xbb -> z  ;  _ybb -> z  ;  _zbb -> z  ;  t1 -> leaf  ;  t2 -> leaf
}

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

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

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

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


-------------------------------------------
Step 2, which took 0.008574 s (model generation: 0.008455,  model checking: 0.000119):

Clauses:
{
height(leaf, z) <= True -> 0
leq_nat(n, m) \/ max(n, m, n) <= True -> 0
leq_nat(z, n2) <= True -> 0
height(node(e, t1, t2), s(_acb)) \/ leq_nat(_xbb, _ybb) <= height(t1, _acb) /\ height(t1, _xbb) /\ height(t2, _ybb) -> 0
leq_nat(_hcb, _gcb) <= height(t1, _ecb) /\ height(t2, _fcb) /\ height(node(e, t1, t2), _hcb) /\ max(_ecb, _fcb, _gcb) -> 0
height(node(e, t1, t2), s(_zbb)) <= height(t1, _xbb) /\ height(t2, _ybb) /\ height(t2, _zbb) /\ leq_nat(_xbb, _ybb) -> 0
max(n, m, m) <= leq_nat(n, m) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
False <= leq_nat(s(nn1), z) -> 0
}

Accumulated learning constraints:
{
height(leaf, z) <= True
height(node(a, leaf, leaf), s(z)) <= True
leq_nat(s(z), s(z)) <= True
leq_nat(s(z), z) \/ max(s(z), z, s(z)) <= True
leq_nat(z, s(z)) <= True
leq_nat(z, z) <= True
max(z, z, z) <= True
}

Current best model:
|_
name: None

height ->
[
height : <etree * nat>
{
  height(leaf, z) <= True
  height(node(x_0_0, x_0_1, x_0_2), s(x_1_0)) <= True
}
]


;
leq_nat ->
[
leq_nat : <nat * nat>
{
  leq_nat(s(x_0_0), s(x_1_0)) <= True
  leq_nat(s(x_0_0), z) <= True
  leq_nat(z, s(x_1_0)) <= True
  leq_nat(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: {elt, etree, nat}
_|




Answer of teacher:

height(leaf, z) <= True  :
No: ()

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

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

height(node(e, t1, t2), s(_acb)) \/ leq_nat(_xbb, _ybb) <= height(t1, _acb) /\ height(t1, _xbb) /\ height(t2, _ybb)  :
No: ()

leq_nat(_hcb, _gcb) <= height(t1, _ecb) /\ height(t2, _fcb) /\ height(node(e, t1, t2), _hcb) /\ max(_ecb, _fcb, _gcb)  :
No: ()

height(node(e, t1, t2), s(_zbb)) <= height(t1, _xbb) /\ height(t2, _ybb) /\ height(t2, _zbb) /\ leq_nat(_xbb, _ybb)  :
No: ()

max(n, m, m) <= leq_nat(n, m)  :
Yes: {
m -> z  ;  n -> s(_fmtqw_0)
}

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

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

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

}


-------------------------------------------
Step 3, which took 0.008163 s (model generation: 0.008052,  model checking: 0.000111):

Clauses:
{
height(leaf, z) <= True -> 0
leq_nat(n, m) \/ max(n, m, n) <= True -> 0
leq_nat(z, n2) <= True -> 0
height(node(e, t1, t2), s(_acb)) \/ leq_nat(_xbb, _ybb) <= height(t1, _acb) /\ height(t1, _xbb) /\ height(t2, _ybb) -> 0
leq_nat(_hcb, _gcb) <= height(t1, _ecb) /\ height(t2, _fcb) /\ height(node(e, t1, t2), _hcb) /\ max(_ecb, _fcb, _gcb) -> 0
height(node(e, t1, t2), s(_zbb)) <= height(t1, _xbb) /\ height(t2, _ybb) /\ height(t2, _zbb) /\ leq_nat(_xbb, _ybb) -> 0
max(n, m, m) <= leq_nat(n, m) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
False <= leq_nat(s(nn1), z) -> 0
}

Accumulated learning constraints:
{
height(leaf, z) <= True
height(node(a, leaf, leaf), s(z)) <= True
leq_nat(s(z), s(z)) <= True
leq_nat(z, s(z)) <= True
leq_nat(z, z) <= True
max(s(z), z, s(z)) <= True
max(z, z, z) <= True
False <= leq_nat(s(z), z)
}

Current best model:
|_
name: None

height ->
[
height : <etree * nat>
{
  height(leaf, z) <= True
  height(node(x_0_0, x_0_1, x_0_2), s(x_1_0)) <= True
}
]


;
leq_nat ->
[
leq_nat : <nat * nat>
{
  leq_nat(s(x_0_0), s(x_1_0)) <= True
  leq_nat(z, s(x_1_0)) <= True
  leq_nat(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: {elt, etree, nat}
_|




Answer of teacher:

height(leaf, z) <= True  :
No: ()

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

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

height(node(e, t1, t2), s(_acb)) \/ leq_nat(_xbb, _ybb) <= height(t1, _acb) /\ height(t1, _xbb) /\ height(t2, _ybb)  :
No: ()

leq_nat(_hcb, _gcb) <= height(t1, _ecb) /\ height(t2, _fcb) /\ height(node(e, t1, t2), _hcb) /\ max(_ecb, _fcb, _gcb)  :
Yes: {
_ecb -> z  ;  _fcb -> z  ;  _gcb -> z  ;  _hcb -> s(_lmtqw_0)  ;  t1 -> leaf  ;  t2 -> leaf
}

height(node(e, t1, t2), s(_zbb)) <= height(t1, _xbb) /\ height(t2, _ybb) /\ height(t2, _zbb) /\ leq_nat(_xbb, _ybb)  :
No: ()

max(n, m, m) <= leq_nat(n, m)  :
Yes: {
m -> s(_qmtqw_0)  ;  n -> z
}

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

leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(_smtqw_0)  ;  nn2 -> z
}

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


Total time: 0.038401
Learner time: 0.029283
Teacher time: 0.000453
Reasons for stopping: No: Contradictory set of ground constraints:
{
False <= True
height(leaf, z) <= True
height(node(a, leaf, leaf), s(z)) <= True
leq_nat(s(z), s(z)) <= True
leq_nat(z, s(z)) <= True
leq_nat(z, z) <= True
max(s(z), z, s(z)) <= True
max(z, s(z), s(z)) <= True
max(z, z, z) <= True
False <= leq_nat(s(s(z)), s(z))
False <= leq_nat(s(z), z)
}