Solving ../../benchmarks/smtlib/false/tree_taller_max.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)
}
)
(le_nat, P:
{
le_nat(z, s(nn2)) <= True
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2)
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2))
False <= le_nat(s(nn1), z)
False <= le_nat(z, z)
}
)
(subtree, P:
{
subtree(leaf, t) <= True
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2)
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))
False <= subtree(node(ea, ta1, ta2), leaf)
eq_elt(ea, eb) <= subtree(node(ea, ta1, ta2), node(eb, tb1, tb2))
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))
}
)
(max, F:
{
le_nat(n, m) \/ max(n, m, n) <= True
max(n, m, m) <= le_nat(n, m)
}
eq_nat(_wib, _xib) <= max(_uib, _vib, _wib) /\ max(_uib, _vib, _xib)
)
(min, F:
{
le_nat(n, m) \/ min(n, m, m) <= True
min(n, m, n) <= le_nat(n, m)
}
eq_nat(_ajb, _bjb) <= min(_yib, _zib, _ajb) /\ min(_yib, _zib, _bjb)
)
(height, F:
{
height(leaf, z) <= True
height(node(e, t1, t2), s(_fjb)) \/ le_nat(_cjb, _djb) <= height(t1, _cjb) /\ height(t1, _fjb) /\ height(t2, _djb)
height(node(e, t1, t2), s(_ejb)) <= height(t1, _cjb) /\ height(t2, _djb) /\ height(t2, _ejb) /\ le_nat(_cjb, _djb)
}
eq_nat(_hjb, _ijb) <= height(_gjb, _hjb) /\ height(_gjb, _ijb)
)
(shallower, P:
{
shallower(leaf, n) <= True
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m)
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m))
shallower(t1, m) <= shallower(node(e, t1, t2), s(m))
False <= shallower(node(e, t1, t2), z)
}
)
(taller, P:
{
taller(leaf, z) <= True
taller(node(e, t1, t2), z) <= True
taller(node(e, t1, t2), s(m)) <= taller(t1, m)
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m)
False <= taller(leaf, s(m))
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m))
}
)
}

properties:
{
taller(node(e, t1, t2), s(s(_jjb))) <= max(n1, n2, _jjb) /\ taller(t1, n1) /\ taller(t2, n2)
}


over-approximation: {height, leq_nat, max, min, shallower, subtree}
under-approximation: {height, leq_nat, min, shallower, subtree}

Clause system for inference is:

{
le_nat(n, m) \/ max(n, m, n) <= True -> 0
le_nat(z, s(nn2)) <= True -> 0
taller(leaf, z) <= True -> 0
taller(node(e, t1, t2), z) <= True -> 0
height(node(e, t1, t2), s(_fjb)) \/ le_nat(_cjb, _djb) <= height(t1, _cjb) /\ height(t1, _fjb) /\ height(t2, _djb) -> 0
height(node(e, t1, t2), s(_ejb)) <= height(t1, _cjb) /\ height(t2, _djb) /\ height(t2, _ejb) /\ le_nat(_cjb, _djb) -> 0
max(n, m, m) <= le_nat(n, m) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
taller(node(e, t1, t2), s(s(_jjb))) <= max(n1, n2, _jjb) /\ taller(t1, n1) /\ taller(t2, n2) -> 0
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m) -> 0
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m)) -> 0
shallower(t1, m) <= shallower(node(e, t1, t2), s(m)) -> 0
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2) -> 0
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
taller(node(e, t1, t2), s(m)) <= taller(t1, m) -> 0
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m) -> 0
False <= taller(leaf, s(m)) -> 0
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m)) -> 0
}


Solving took 0.167173 seconds.
No: Contradictory set of ground constraints:
{
False <= True
le_nat(s(z), s(s(z))) <= True
le_nat(z, 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
taller(leaf, z) <= True
taller(node(a, leaf, leaf), z) <= True
taller(node(a, leaf, node(a, leaf, leaf)), s(s(z))) <= True
taller(node(a, leaf, node(a, node(a, leaf, leaf), leaf)), s(s(z))) <= True
taller(node(a, node(a, leaf, leaf), leaf), s(s(z))) <= True
taller(node(a, node(a, leaf, leaf), leaf), s(z)) <= True
taller(node(a, node(a, leaf, leaf), node(a, leaf, leaf)), s(s(z))) <= True
False <= le_nat(s(z), s(z))
False <= le_nat(s(z), z)
False <= le_nat(z, z)
False <= taller(leaf, s(z))
False <= taller(node(a, leaf, leaf), s(s(z)))
taller(node(a, node(a, leaf, node(a, leaf, leaf)), leaf), s(s(z))) <= taller(node(a, leaf, node(a, leaf, leaf)), s(z))
}
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006443 s (model generation: 0.006221,  model checking: 0.000222):

Clauses:
{
le_nat(n, m) \/ max(n, m, n) <= True -> 0
le_nat(z, s(nn2)) <= True -> 0
taller(leaf, z) <= True -> 0
taller(node(e, t1, t2), z) <= True -> 0
height(node(e, t1, t2), s(_fjb)) \/ le_nat(_cjb, _djb) <= height(t1, _cjb) /\ height(t1, _fjb) /\ height(t2, _djb) -> 0
height(node(e, t1, t2), s(_ejb)) <= height(t1, _cjb) /\ height(t2, _djb) /\ height(t2, _ejb) /\ le_nat(_cjb, _djb) -> 0
max(n, m, m) <= le_nat(n, m) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
taller(node(e, t1, t2), s(s(_jjb))) <= max(n1, n2, _jjb) /\ taller(t1, n1) /\ taller(t2, n2) -> 0
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m) -> 0
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m)) -> 0
shallower(t1, m) <= shallower(node(e, t1, t2), s(m)) -> 0
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2) -> 0
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
taller(node(e, t1, t2), s(m)) <= taller(t1, m) -> 0
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m) -> 0
False <= taller(leaf, s(m)) -> 0
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m)) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

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


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


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


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


;
shallower ->
[
shallower : <etree * nat>
{
  
}
]


;
subtree ->
[
subtree : <etree * etree>
{
  
}
]


;
taller ->
[
taller : <etree * nat>
{
  
}
]



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




Answer of teacher:

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

le_nat(z, s(nn2)) <= True  :
Yes: {

}

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

}

taller(node(e, t1, t2), z) <= True  :
Yes: {

}

height(node(e, t1, t2), s(_fjb)) \/ le_nat(_cjb, _djb) <= height(t1, _cjb) /\ height(t1, _fjb) /\ height(t2, _djb)  :
No: ()

height(node(e, t1, t2), s(_ejb)) <= height(t1, _cjb) /\ height(t2, _djb) /\ height(t2, _ejb) /\ le_nat(_cjb, _djb)  :
No: ()

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

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

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

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

False <= le_nat(z, z)  :
No: ()

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

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

taller(node(e, t1, t2), s(s(_jjb))) <= max(n1, n2, _jjb) /\ taller(t1, n1) /\ taller(t2, n2)  :
No: ()

shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m)  :
No: ()

shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m))  :
No: ()

shallower(t1, m) <= shallower(node(e, t1, t2), s(m))  :
No: ()

subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2)  :
No: ()

subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

taller(node(e, t1, t2), s(m)) <= taller(t1, m)  :
No: ()

taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m)  :
No: ()

False <= taller(leaf, s(m))  :
No: ()

taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m))  :
No: ()


-------------------------------------------
Step 1, which took 0.007194 s (model generation: 0.006971,  model checking: 0.000223):

Clauses:
{
le_nat(n, m) \/ max(n, m, n) <= True -> 0
le_nat(z, s(nn2)) <= True -> 0
taller(leaf, z) <= True -> 0
taller(node(e, t1, t2), z) <= True -> 0
height(node(e, t1, t2), s(_fjb)) \/ le_nat(_cjb, _djb) <= height(t1, _cjb) /\ height(t1, _fjb) /\ height(t2, _djb) -> 0
height(node(e, t1, t2), s(_ejb)) <= height(t1, _cjb) /\ height(t2, _djb) /\ height(t2, _ejb) /\ le_nat(_cjb, _djb) -> 0
max(n, m, m) <= le_nat(n, m) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
taller(node(e, t1, t2), s(s(_jjb))) <= max(n1, n2, _jjb) /\ taller(t1, n1) /\ taller(t2, n2) -> 0
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m) -> 0
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m)) -> 0
shallower(t1, m) <= shallower(node(e, t1, t2), s(m)) -> 0
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2) -> 0
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
taller(node(e, t1, t2), s(m)) <= taller(t1, m) -> 0
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m) -> 0
False <= taller(leaf, s(m)) -> 0
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m)) -> 0
}

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

Current best model:
|_
name: None

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


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


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


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


;
shallower ->
[
shallower : <etree * nat>
{
  
}
]


;
subtree ->
[
subtree : <etree * etree>
{
  
}
]


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



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




Answer of teacher:

le_nat(n, m) \/ max(n, m, n) <= True  :
Yes: {
m -> z  ;  n -> s(_hgnuw_0)
}

le_nat(z, s(nn2)) <= True  :
No: ()

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

taller(node(e, t1, t2), z) <= True  :
No: ()

height(node(e, t1, t2), s(_fjb)) \/ le_nat(_cjb, _djb) <= height(t1, _cjb) /\ height(t1, _fjb) /\ height(t2, _djb)  :
No: ()

height(node(e, t1, t2), s(_ejb)) <= height(t1, _cjb) /\ height(t2, _djb) /\ height(t2, _ejb) /\ le_nat(_cjb, _djb)  :
No: ()

max(n, m, m) <= le_nat(n, m)  :
Yes: {
m -> s(_ignuw_0)  ;  n -> z
}

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

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

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

False <= le_nat(z, z)  :
Yes: {

}

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

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

taller(node(e, t1, t2), s(s(_jjb))) <= max(n1, n2, _jjb) /\ taller(t1, n1) /\ taller(t2, n2)  :
Yes: {
_jjb -> z  ;  n1 -> z  ;  n2 -> z  ;  t1 -> node(_ghnuw_0, _ghnuw_1, _ghnuw_2)  ;  t2 -> node(_hhnuw_0, _hhnuw_1, _hhnuw_2)
}

shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m)  :
No: ()

shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m))  :
No: ()

shallower(t1, m) <= shallower(node(e, t1, t2), s(m))  :
No: ()

subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2)  :
No: ()

subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

taller(node(e, t1, t2), s(m)) <= taller(t1, m)  :
Yes: {
m -> z  ;  t1 -> node(_lhnuw_0, _lhnuw_1, _lhnuw_2)
}

taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m)  :
No: ()

False <= taller(leaf, s(m))  :
No: ()

taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m))  :
No: ()


-------------------------------------------
Step 2, which took 0.009411 s (model generation: 0.009159,  model checking: 0.000252):

Clauses:
{
le_nat(n, m) \/ max(n, m, n) <= True -> 0
le_nat(z, s(nn2)) <= True -> 0
taller(leaf, z) <= True -> 0
taller(node(e, t1, t2), z) <= True -> 0
height(node(e, t1, t2), s(_fjb)) \/ le_nat(_cjb, _djb) <= height(t1, _cjb) /\ height(t1, _fjb) /\ height(t2, _djb) -> 0
height(node(e, t1, t2), s(_ejb)) <= height(t1, _cjb) /\ height(t2, _djb) /\ height(t2, _ejb) /\ le_nat(_cjb, _djb) -> 0
max(n, m, m) <= le_nat(n, m) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
taller(node(e, t1, t2), s(s(_jjb))) <= max(n1, n2, _jjb) /\ taller(t1, n1) /\ taller(t2, n2) -> 0
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m) -> 0
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m)) -> 0
shallower(t1, m) <= shallower(node(e, t1, t2), s(m)) -> 0
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2) -> 0
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
taller(node(e, t1, t2), s(m)) <= taller(t1, m) -> 0
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m) -> 0
False <= taller(leaf, s(m)) -> 0
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m)) -> 0
}

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

Current best model:
|_
name: None

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


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


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


;
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
}
]


;
shallower ->
[
shallower : <etree * nat>
{
  
}
]


;
subtree ->
[
subtree : <etree * etree>
{
  
}
]


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



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




Answer of teacher:

le_nat(n, m) \/ max(n, m, n) <= True  :
Yes: {
m -> s(_mhnuw_0)  ;  n -> s(_nhnuw_0)
}

le_nat(z, s(nn2)) <= True  :
No: ()

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

taller(node(e, t1, t2), z) <= True  :
No: ()

height(node(e, t1, t2), s(_fjb)) \/ le_nat(_cjb, _djb) <= height(t1, _cjb) /\ height(t1, _fjb) /\ height(t2, _djb)  :
No: ()

height(node(e, t1, t2), s(_ejb)) <= height(t1, _cjb) /\ height(t2, _djb) /\ height(t2, _ejb) /\ le_nat(_cjb, _djb)  :
No: ()

max(n, m, m) <= le_nat(n, m)  :
Yes: {
m -> z  ;  n -> s(_phnuw_0)
}

le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2)  :
Yes: {
nn1 -> z  ;  nn2 -> s(_thnuw_0)
}

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

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

}

False <= le_nat(z, z)  :
No: ()

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

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

taller(node(e, t1, t2), s(s(_jjb))) <= max(n1, n2, _jjb) /\ taller(t1, n1) /\ taller(t2, n2)  :
No: ()

shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m)  :
No: ()

shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m))  :
No: ()

shallower(t1, m) <= shallower(node(e, t1, t2), s(m))  :
No: ()

subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2)  :
No: ()

subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

taller(node(e, t1, t2), s(m)) <= taller(t1, m)  :
No: ()

taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m)  :
No: ()

False <= taller(leaf, s(m))  :
No: ()

taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m))  :
Yes: {
m -> s(_uhnuw_0)  ;  t1 -> leaf  ;  t2 -> leaf
}


-------------------------------------------
Step 3, which took 0.011023 s (model generation: 0.010858,  model checking: 0.000165):

Clauses:
{
le_nat(n, m) \/ max(n, m, n) <= True -> 0
le_nat(z, s(nn2)) <= True -> 0
taller(leaf, z) <= True -> 0
taller(node(e, t1, t2), z) <= True -> 0
height(node(e, t1, t2), s(_fjb)) \/ le_nat(_cjb, _djb) <= height(t1, _cjb) /\ height(t1, _fjb) /\ height(t2, _djb) -> 0
height(node(e, t1, t2), s(_ejb)) <= height(t1, _cjb) /\ height(t2, _djb) /\ height(t2, _ejb) /\ le_nat(_cjb, _djb) -> 0
max(n, m, m) <= le_nat(n, m) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
taller(node(e, t1, t2), s(s(_jjb))) <= max(n1, n2, _jjb) /\ taller(t1, n1) /\ taller(t2, n2) -> 0
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m) -> 0
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m)) -> 0
shallower(t1, m) <= shallower(node(e, t1, t2), s(m)) -> 0
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2) -> 0
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
taller(node(e, t1, t2), s(m)) <= taller(t1, m) -> 0
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m) -> 0
False <= taller(leaf, s(m)) -> 0
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m)) -> 0
}

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

Current best model:
|_
name: None

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


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


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


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


;
shallower ->
[
shallower : <etree * nat>
{
  
}
]


;
subtree ->
[
subtree : <etree * etree>
{
  
}
]


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



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




Answer of teacher:

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

le_nat(z, s(nn2)) <= True  :
No: ()

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

taller(node(e, t1, t2), z) <= True  :
No: ()

height(node(e, t1, t2), s(_fjb)) \/ le_nat(_cjb, _djb) <= height(t1, _cjb) /\ height(t1, _fjb) /\ height(t2, _djb)  :
No: ()

height(node(e, t1, t2), s(_ejb)) <= height(t1, _cjb) /\ height(t2, _djb) /\ height(t2, _ejb) /\ le_nat(_cjb, _djb)  :
No: ()

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

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

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

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

False <= le_nat(z, z)  :
No: ()

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

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

taller(node(e, t1, t2), s(s(_jjb))) <= max(n1, n2, _jjb) /\ taller(t1, n1) /\ taller(t2, n2)  :
No: ()

shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m)  :
No: ()

shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m))  :
No: ()

shallower(t1, m) <= shallower(node(e, t1, t2), s(m))  :
No: ()

subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2)  :
No: ()

subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

taller(node(e, t1, t2), s(m)) <= taller(t1, m)  :
No: ()

taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m)  :
No: ()

False <= taller(leaf, s(m))  :
Yes: {

}

taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m))  :
No: ()


-------------------------------------------
Step 4, which took 0.010830 s (model generation: 0.010228,  model checking: 0.000602):

Clauses:
{
le_nat(n, m) \/ max(n, m, n) <= True -> 0
le_nat(z, s(nn2)) <= True -> 0
taller(leaf, z) <= True -> 0
taller(node(e, t1, t2), z) <= True -> 0
height(node(e, t1, t2), s(_fjb)) \/ le_nat(_cjb, _djb) <= height(t1, _cjb) /\ height(t1, _fjb) /\ height(t2, _djb) -> 0
height(node(e, t1, t2), s(_ejb)) <= height(t1, _cjb) /\ height(t2, _djb) /\ height(t2, _ejb) /\ le_nat(_cjb, _djb) -> 0
max(n, m, m) <= le_nat(n, m) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
taller(node(e, t1, t2), s(s(_jjb))) <= max(n1, n2, _jjb) /\ taller(t1, n1) /\ taller(t2, n2) -> 0
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m) -> 0
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m)) -> 0
shallower(t1, m) <= shallower(node(e, t1, t2), s(m)) -> 0
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2) -> 0
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
taller(node(e, t1, t2), s(m)) <= taller(t1, m) -> 0
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m) -> 0
False <= taller(leaf, s(m)) -> 0
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m)) -> 0
}

Accumulated learning constraints:
{
le_nat(s(z), s(s(z))) <= True
le_nat(z, 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
taller(leaf, z) <= True
taller(node(a, leaf, leaf), z) <= True
taller(node(a, node(a, leaf, leaf), leaf), s(z)) <= True
taller(node(a, node(a, leaf, leaf), node(a, leaf, leaf)), s(s(z))) <= True
False <= le_nat(s(z), s(z))
False <= le_nat(s(z), z)
False <= le_nat(z, z)
False <= taller(leaf, s(z))
False <= taller(node(a, leaf, leaf), s(s(z)))
}

Current best model:
|_
name: None

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


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


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


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


;
shallower ->
[
shallower : <etree * nat>
{
  
}
]


;
subtree ->
[
subtree : <etree * etree>
{
  
}
]


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



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




Answer of teacher:

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

le_nat(z, s(nn2)) <= True  :
No: ()

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

taller(node(e, t1, t2), z) <= True  :
No: ()

height(node(e, t1, t2), s(_fjb)) \/ le_nat(_cjb, _djb) <= height(t1, _cjb) /\ height(t1, _fjb) /\ height(t2, _djb)  :
No: ()

height(node(e, t1, t2), s(_ejb)) <= height(t1, _cjb) /\ height(t2, _djb) /\ height(t2, _ejb) /\ le_nat(_cjb, _djb)  :
No: ()

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

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

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

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

False <= le_nat(z, z)  :
No: ()

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

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

taller(node(e, t1, t2), s(s(_jjb))) <= max(n1, n2, _jjb) /\ taller(t1, n1) /\ taller(t2, n2)  :
Yes: {
_jjb -> z  ;  n1 -> z  ;  n2 -> z  ;  t1 -> node(_xjnuw_0, _xjnuw_1, _xjnuw_2)  ;  t2 -> leaf
}

shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m)  :
No: ()

shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m))  :
No: ()

shallower(t1, m) <= shallower(node(e, t1, t2), s(m))  :
No: ()

subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2)  :
No: ()

subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

taller(node(e, t1, t2), s(m)) <= taller(t1, m)  :
Yes: {
m -> s(z)  ;  t1 -> node(_hknuw_0, _hknuw_1, node(_qlnuw_0, _qlnuw_1, _qlnuw_2))  ;  t2 -> leaf
}

taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m)  :
No: ()

False <= taller(leaf, s(m))  :
No: ()

taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m))  :
No: ()


-------------------------------------------
Step 5, which took 0.012121 s (model generation: 0.011517,  model checking: 0.000604):

Clauses:
{
le_nat(n, m) \/ max(n, m, n) <= True -> 0
le_nat(z, s(nn2)) <= True -> 0
taller(leaf, z) <= True -> 0
taller(node(e, t1, t2), z) <= True -> 0
height(node(e, t1, t2), s(_fjb)) \/ le_nat(_cjb, _djb) <= height(t1, _cjb) /\ height(t1, _fjb) /\ height(t2, _djb) -> 0
height(node(e, t1, t2), s(_ejb)) <= height(t1, _cjb) /\ height(t2, _djb) /\ height(t2, _ejb) /\ le_nat(_cjb, _djb) -> 0
max(n, m, m) <= le_nat(n, m) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
taller(node(e, t1, t2), s(s(_jjb))) <= max(n1, n2, _jjb) /\ taller(t1, n1) /\ taller(t2, n2) -> 0
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m) -> 0
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m)) -> 0
shallower(t1, m) <= shallower(node(e, t1, t2), s(m)) -> 0
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2) -> 0
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
taller(node(e, t1, t2), s(m)) <= taller(t1, m) -> 0
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m) -> 0
False <= taller(leaf, s(m)) -> 0
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m)) -> 0
}

Accumulated learning constraints:
{
le_nat(s(z), s(s(z))) <= True
le_nat(z, 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
taller(leaf, z) <= True
taller(node(a, leaf, leaf), z) <= True
taller(node(a, node(a, leaf, leaf), leaf), s(s(z))) <= True
taller(node(a, node(a, leaf, leaf), leaf), s(z)) <= True
taller(node(a, node(a, leaf, leaf), node(a, leaf, leaf)), s(s(z))) <= True
False <= le_nat(s(z), s(z))
False <= le_nat(s(z), z)
False <= le_nat(z, z)
False <= taller(leaf, s(z))
False <= taller(node(a, leaf, leaf), s(s(z)))
taller(node(a, node(a, leaf, node(a, leaf, leaf)), leaf), s(s(z))) <= taller(node(a, leaf, node(a, leaf, leaf)), s(z))
}

Current best model:
|_
name: None

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


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


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


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


;
shallower ->
[
shallower : <etree * nat>
{
  
}
]


;
subtree ->
[
subtree : <etree * etree>
{
  
}
]


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



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




Answer of teacher:

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

le_nat(z, s(nn2)) <= True  :
No: ()

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

taller(node(e, t1, t2), z) <= True  :
No: ()

height(node(e, t1, t2), s(_fjb)) \/ le_nat(_cjb, _djb) <= height(t1, _cjb) /\ height(t1, _fjb) /\ height(t2, _djb)  :
No: ()

height(node(e, t1, t2), s(_ejb)) <= height(t1, _cjb) /\ height(t2, _djb) /\ height(t2, _ejb) /\ le_nat(_cjb, _djb)  :
No: ()

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

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

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

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

False <= le_nat(z, z)  :
No: ()

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

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

taller(node(e, t1, t2), s(s(_jjb))) <= max(n1, n2, _jjb) /\ taller(t1, n1) /\ taller(t2, n2)  :
Yes: {
_jjb -> z  ;  n1 -> z  ;  n2 -> z  ;  t1 -> leaf  ;  t2 -> node(_oonuw_0, _oonuw_1, _oonuw_2)
}

shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m)  :
No: ()

shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m))  :
No: ()

shallower(t1, m) <= shallower(node(e, t1, t2), s(m))  :
No: ()

subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2)  :
No: ()

subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

taller(node(e, t1, t2), s(m)) <= taller(t1, m)  :
No: ()

taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m)  :
Yes: {
m -> s(z)  ;  t1 -> leaf  ;  t2 -> node(_hpnuw_0, node(_cqnuw_0, _cqnuw_1, _cqnuw_2), _hpnuw_2)
}

False <= taller(leaf, s(m))  :
No: ()

taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m))  :
No: ()


-------------------------------------------
Step 6, which took 0.098106 s (model generation: 0.012445,  model checking: 0.085661):

Clauses:
{
le_nat(n, m) \/ max(n, m, n) <= True -> 0
le_nat(z, s(nn2)) <= True -> 0
taller(leaf, z) <= True -> 0
taller(node(e, t1, t2), z) <= True -> 0
height(node(e, t1, t2), s(_fjb)) \/ le_nat(_cjb, _djb) <= height(t1, _cjb) /\ height(t1, _fjb) /\ height(t2, _djb) -> 0
height(node(e, t1, t2), s(_ejb)) <= height(t1, _cjb) /\ height(t2, _djb) /\ height(t2, _ejb) /\ le_nat(_cjb, _djb) -> 0
max(n, m, m) <= le_nat(n, m) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
taller(node(e, t1, t2), s(s(_jjb))) <= max(n1, n2, _jjb) /\ taller(t1, n1) /\ taller(t2, n2) -> 0
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m) -> 0
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m)) -> 0
shallower(t1, m) <= shallower(node(e, t1, t2), s(m)) -> 0
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2) -> 0
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
taller(node(e, t1, t2), s(m)) <= taller(t1, m) -> 0
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m) -> 0
False <= taller(leaf, s(m)) -> 0
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m)) -> 0
}

Accumulated learning constraints:
{
le_nat(s(z), s(s(z))) <= True
le_nat(z, 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
taller(leaf, z) <= True
taller(node(a, leaf, leaf), z) <= True
taller(node(a, leaf, node(a, leaf, leaf)), s(s(z))) <= True
taller(node(a, leaf, node(a, node(a, leaf, leaf), leaf)), s(s(z))) <= True
taller(node(a, node(a, leaf, leaf), leaf), s(s(z))) <= True
taller(node(a, node(a, leaf, leaf), leaf), s(z)) <= True
taller(node(a, node(a, leaf, leaf), node(a, leaf, leaf)), s(s(z))) <= True
False <= le_nat(s(z), s(z))
False <= le_nat(s(z), z)
False <= le_nat(z, z)
False <= taller(leaf, s(z))
False <= taller(node(a, leaf, leaf), s(s(z)))
taller(node(a, node(a, leaf, node(a, leaf, leaf)), leaf), s(s(z))) <= taller(node(a, leaf, node(a, leaf, leaf)), s(z))
}

Current best model:
|_
name: None

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


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


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


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


;
shallower ->
[
shallower : <etree * nat>
{
  
}
]


;
subtree ->
[
subtree : <etree * etree>
{
  
}
]


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



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




Answer of teacher:

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

le_nat(z, s(nn2)) <= True  :
No: ()

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

taller(node(e, t1, t2), z) <= True  :
No: ()

height(node(e, t1, t2), s(_fjb)) \/ le_nat(_cjb, _djb) <= height(t1, _cjb) /\ height(t1, _fjb) /\ height(t2, _djb)  :
No: ()

height(node(e, t1, t2), s(_ejb)) <= height(t1, _cjb) /\ height(t2, _djb) /\ height(t2, _ejb) /\ le_nat(_cjb, _djb)  :
No: ()

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

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

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

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

False <= le_nat(z, z)  :
No: ()

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

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

taller(node(e, t1, t2), s(s(_jjb))) <= max(n1, n2, _jjb) /\ taller(t1, n1) /\ taller(t2, n2)  :
Yes: {
_jjb -> z  ;  n1 -> z  ;  n2 -> z  ;  t1 -> leaf  ;  t2 -> leaf
}

shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m)  :
No: ()

shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m))  :
No: ()

shallower(t1, m) <= shallower(node(e, t1, t2), s(m))  :
No: ()

subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2)  :
No: ()

subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

taller(node(e, t1, t2), s(m)) <= taller(t1, m)  :
No: ()

taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m)  :
No: ()

False <= taller(leaf, s(m))  :
No: ()

taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m))  :
No: ()


Total time: 0.167173
Learner time: 0.067399
Teacher time: 0.087729
Reasons for stopping: No: Contradictory set of ground constraints:
{
False <= True
le_nat(s(z), s(s(z))) <= True
le_nat(z, 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
taller(leaf, z) <= True
taller(node(a, leaf, leaf), z) <= True
taller(node(a, leaf, node(a, leaf, leaf)), s(s(z))) <= True
taller(node(a, leaf, node(a, node(a, leaf, leaf), leaf)), s(s(z))) <= True
taller(node(a, node(a, leaf, leaf), leaf), s(s(z))) <= True
taller(node(a, node(a, leaf, leaf), leaf), s(z)) <= True
taller(node(a, node(a, leaf, leaf), node(a, leaf, leaf)), s(s(z))) <= True
False <= le_nat(s(z), s(z))
False <= le_nat(s(z), z)
False <= le_nat(z, z)
False <= taller(leaf, s(z))
False <= taller(node(a, leaf, leaf), s(s(z)))
taller(node(a, node(a, leaf, node(a, leaf, leaf)), leaf), s(s(z))) <= taller(node(a, leaf, node(a, leaf, leaf)), s(z))
}