Solving ../../benchmarks/smtlib/false/tree_shallow_subtree_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)
}
)
(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(_vfb, _wfb) <= max(_tfb, _ufb, _vfb) /\ max(_tfb, _ufb, _wfb)
)
(height, F:
{
height(leaf, z) <= True
height(node(e, t1, t2), s(_agb)) \/ le_nat(_xfb, _yfb) <= height(t1, _agb) /\ height(t1, _xfb) /\ height(t2, _yfb)
height(node(e, t1, t2), s(_zfb)) <= height(t1, _xfb) /\ height(t2, _yfb) /\ height(t2, _zfb) /\ le_nat(_xfb, _yfb)
}
eq_nat(_cgb, _dgb) <= height(_bgb, _cgb) /\ height(_bgb, _dgb)
)
(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)
}
)
}

properties:
{
leq_nat(n1, n2) <= shallower(t1, n1) /\ shallower(t2, n2) /\ subtree(t1, t2)
}


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

Clause system for inference is:

{
shallower(leaf, n) <= True -> 0
subtree(leaf, t) <= True -> 0
height(node(e, t1, t2), s(_agb)) \/ le_nat(_xfb, _yfb) <= height(t1, _agb) /\ height(t1, _xfb) /\ height(t2, _yfb) -> 0
height(node(e, t1, t2), s(_zfb)) <= height(t1, _xfb) /\ height(t2, _yfb) /\ height(t2, _zfb) /\ le_nat(_xfb, _yfb) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 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
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
leq_nat(n1, n2) <= shallower(t1, n1) /\ shallower(t2, n2) /\ subtree(t1, t2) -> 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
}


Solving took 0.179416 seconds.
No: Contradictory set of ground constraints:
{
False <= True
leq_nat(s(z), s(z)) <= True
leq_nat(z, s(z)) <= True
leq_nat(z, z) <= True
shallower(leaf, s(z)) <= True
shallower(leaf, z) <= True
shallower(node(a, leaf, leaf), s(z)) <= True
subtree(leaf, leaf) <= True
subtree(leaf, node(a, leaf, leaf)) <= True
subtree(node(a, leaf, leaf), node(a, node(a, leaf, leaf), node(a, leaf, leaf))) <= True
False <= leq_nat(s(s(z)), s(z))
False <= leq_nat(s(z), z)
False <= shallower(node(a, leaf, leaf), z) /\ subtree(node(a, leaf, leaf), node(a, leaf, leaf))
shallower(node(a, leaf, leaf), z) <= shallower(node(a, leaf, node(a, leaf, leaf)), s(z))
shallower(node(a, leaf, leaf), z) <= shallower(node(a, node(a, leaf, leaf), leaf), s(z))
subtree(node(a, leaf, leaf), leaf) <= subtree(node(a, leaf, leaf), node(a, leaf, leaf)) /\ subtree(node(a, node(a, leaf, leaf), node(a, leaf, leaf)), node(a, node(a, leaf, leaf), leaf))
subtree(node(a, leaf, leaf), leaf) <= subtree(node(a, node(a, leaf, leaf), leaf), node(a, leaf, leaf))
}
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006334 s (model generation: 0.006233,  model checking: 0.000101):

Clauses:
{
shallower(leaf, n) <= True -> 0
subtree(leaf, t) <= True -> 0
height(node(e, t1, t2), s(_agb)) \/ le_nat(_xfb, _yfb) <= height(t1, _agb) /\ height(t1, _xfb) /\ height(t2, _yfb) -> 0
height(node(e, t1, t2), s(_zfb)) <= height(t1, _xfb) /\ height(t2, _yfb) /\ height(t2, _zfb) /\ le_nat(_xfb, _yfb) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 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
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
leq_nat(n1, n2) <= shallower(t1, n1) /\ shallower(t2, n2) /\ subtree(t1, t2) -> 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
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

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


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


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


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


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



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




Answer of teacher:

shallower(leaf, n) <= True  :
Yes: {
n -> z
}

subtree(leaf, t) <= True  :
Yes: {
t -> node(_hnjuw_0, _hnjuw_1, _hnjuw_2)
}

height(node(e, t1, t2), s(_agb)) \/ le_nat(_xfb, _yfb) <= height(t1, _agb) /\ height(t1, _xfb) /\ height(t2, _yfb)  :
No: ()

height(node(e, t1, t2), s(_zfb)) <= height(t1, _xfb) /\ height(t2, _yfb) /\ height(t2, _zfb) /\ le_nat(_xfb, _yfb)  :
No: ()

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

le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2))  :
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: ()

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: ()

leq_nat(n1, n2) <= shallower(t1, n1) /\ shallower(t2, n2) /\ subtree(t1, t2)  :
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: ()


-------------------------------------------
Step 1, which took 0.006616 s (model generation: 0.006504,  model checking: 0.000112):

Clauses:
{
shallower(leaf, n) <= True -> 0
subtree(leaf, t) <= True -> 0
height(node(e, t1, t2), s(_agb)) \/ le_nat(_xfb, _yfb) <= height(t1, _agb) /\ height(t1, _xfb) /\ height(t2, _yfb) -> 0
height(node(e, t1, t2), s(_zfb)) <= height(t1, _xfb) /\ height(t2, _yfb) /\ height(t2, _zfb) /\ le_nat(_xfb, _yfb) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 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
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
leq_nat(n1, n2) <= shallower(t1, n1) /\ shallower(t2, n2) /\ subtree(t1, t2) -> 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
}

Accumulated learning constraints:
{
shallower(leaf, z) <= True
subtree(leaf, node(a, leaf, leaf)) <= True
}

Current best model:
|_
name: None

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


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


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


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


;
subtree ->
[
subtree : <etree * etree>
{
  subtree(leaf, node(x_1_0, x_1_1, x_1_2)) <= True
}
]



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




Answer of teacher:

shallower(leaf, n) <= True  :
Yes: {
n -> s(_injuw_0)
}

subtree(leaf, t) <= True  :
Yes: {
t -> leaf
}

height(node(e, t1, t2), s(_agb)) \/ le_nat(_xfb, _yfb) <= height(t1, _agb) /\ height(t1, _xfb) /\ height(t2, _yfb)  :
No: ()

height(node(e, t1, t2), s(_zfb)) <= height(t1, _xfb) /\ height(t2, _yfb) /\ height(t2, _zfb) /\ le_nat(_xfb, _yfb)  :
No: ()

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

le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2))  :
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: ()

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

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

leq_nat(n1, n2) <= shallower(t1, n1) /\ shallower(t2, n2) /\ subtree(t1, t2)  :
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)  :
Yes: {
ta1 -> leaf  ;  ta2 -> leaf  ;  tb1 -> node(_pnjuw_0, _pnjuw_1, _pnjuw_2)  ;  tb2 -> node(_qnjuw_0, _qnjuw_1, _qnjuw_2)
}

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: ()


-------------------------------------------
Step 2, which took 0.008201 s (model generation: 0.008038,  model checking: 0.000163):

Clauses:
{
shallower(leaf, n) <= True -> 0
subtree(leaf, t) <= True -> 0
height(node(e, t1, t2), s(_agb)) \/ le_nat(_xfb, _yfb) <= height(t1, _agb) /\ height(t1, _xfb) /\ height(t2, _yfb) -> 0
height(node(e, t1, t2), s(_zfb)) <= height(t1, _xfb) /\ height(t2, _yfb) /\ height(t2, _zfb) /\ le_nat(_xfb, _yfb) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 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
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
leq_nat(n1, n2) <= shallower(t1, n1) /\ shallower(t2, n2) /\ subtree(t1, t2) -> 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
}

Accumulated learning constraints:
{
shallower(leaf, s(z)) <= True
shallower(leaf, z) <= True
shallower(node(a, leaf, leaf), s(z)) <= True
subtree(leaf, leaf) <= True
subtree(leaf, node(a, leaf, leaf)) <= True
subtree(node(a, leaf, leaf), node(a, node(a, leaf, leaf), node(a, leaf, leaf))) <= True
}

Current best model:
|_
name: None

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


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


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


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


;
subtree ->
[
subtree : <etree * etree>
{
  subtree(leaf, leaf) <= True
  subtree(leaf, node(x_1_0, x_1_1, x_1_2)) <= True
  subtree(node(x_0_0, x_0_1, x_0_2), node(x_1_0, x_1_1, x_1_2)) <= True
}
]



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




Answer of teacher:

shallower(leaf, n) <= True  :
No: ()

subtree(leaf, t) <= True  :
No: ()

height(node(e, t1, t2), s(_agb)) \/ le_nat(_xfb, _yfb) <= height(t1, _agb) /\ height(t1, _xfb) /\ height(t2, _yfb)  :
No: ()

height(node(e, t1, t2), s(_zfb)) <= height(t1, _xfb) /\ height(t2, _yfb) /\ height(t2, _zfb) /\ le_nat(_xfb, _yfb)  :
No: ()

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

le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2))  :
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: ()

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))  :
Yes: {
m -> z  ;  t1 -> leaf  ;  t2 -> node(_tnjuw_0, _tnjuw_1, _tnjuw_2)
}

leq_nat(n1, n2) <= shallower(t1, n1) /\ shallower(t2, n2) /\ subtree(t1, t2)  :
Yes: {
n1 -> z  ;  n2 -> z  ;  t1 -> leaf  ;  t2 -> leaf
}

shallower(t1, m) <= shallower(node(e, t1, t2), s(m))  :
Yes: {
m -> z  ;  t1 -> node(_xojuw_0, _xojuw_1, _xojuw_2)
}

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))  :
Yes: {
ta1 -> node(_gpjuw_0, _gpjuw_1, _gpjuw_2)  ;  ta2 -> node(_hpjuw_0, _hpjuw_1, _hpjuw_2)  ;  tb1 -> node(_ipjuw_0, _ipjuw_1, _ipjuw_2)  ;  tb2 -> leaf
}

subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
Yes: {
ta1 -> node(_kpjuw_0, _kpjuw_1, _kpjuw_2)  ;  tb1 -> leaf
}


-------------------------------------------
Step 3, which took 0.011244 s (model generation: 0.011016,  model checking: 0.000228):

Clauses:
{
shallower(leaf, n) <= True -> 0
subtree(leaf, t) <= True -> 0
height(node(e, t1, t2), s(_agb)) \/ le_nat(_xfb, _yfb) <= height(t1, _agb) /\ height(t1, _xfb) /\ height(t2, _yfb) -> 0
height(node(e, t1, t2), s(_zfb)) <= height(t1, _xfb) /\ height(t2, _yfb) /\ height(t2, _zfb) /\ le_nat(_xfb, _yfb) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 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
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
leq_nat(n1, n2) <= shallower(t1, n1) /\ shallower(t2, n2) /\ subtree(t1, t2) -> 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
}

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

Current best model:
|_
name: None

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


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


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


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


;
subtree ->
[
subtree : <etree * etree>
{
  subtree(leaf, leaf) <= True
  subtree(leaf, node(x_1_0, x_1_1, x_1_2)) <= True
  subtree(node(x_0_0, x_0_1, x_0_2), leaf) <= True
  subtree(node(x_0_0, x_0_1, x_0_2), node(x_1_0, x_1_1, x_1_2)) <= True
}
]



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




Answer of teacher:

shallower(leaf, n) <= True  :
No: ()

subtree(leaf, t) <= True  :
No: ()

height(node(e, t1, t2), s(_agb)) \/ le_nat(_xfb, _yfb) <= height(t1, _agb) /\ height(t1, _xfb) /\ height(t2, _yfb)  :
No: ()

height(node(e, t1, t2), s(_zfb)) <= height(t1, _xfb) /\ height(t2, _yfb) /\ height(t2, _zfb) /\ le_nat(_xfb, _yfb)  :
No: ()

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

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

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: ()

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: ()

leq_nat(n1, n2) <= shallower(t1, n1) /\ shallower(t2, n2) /\ subtree(t1, t2)  :
Yes: {
n1 -> z  ;  n2 -> s(_zqjuw_0)  ;  t1 -> leaf  ;  t2 -> node(_brjuw_0, _brjuw_1, _brjuw_2)
}

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: ()


-------------------------------------------
Step 4, which took 0.011167 s (model generation: 0.010973,  model checking: 0.000194):

Clauses:
{
shallower(leaf, n) <= True -> 0
subtree(leaf, t) <= True -> 0
height(node(e, t1, t2), s(_agb)) \/ le_nat(_xfb, _yfb) <= height(t1, _agb) /\ height(t1, _xfb) /\ height(t2, _yfb) -> 0
height(node(e, t1, t2), s(_zfb)) <= height(t1, _xfb) /\ height(t2, _yfb) /\ height(t2, _zfb) /\ le_nat(_xfb, _yfb) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 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
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
leq_nat(n1, n2) <= shallower(t1, n1) /\ shallower(t2, n2) /\ subtree(t1, t2) -> 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
}

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

Current best model:
|_
name: None

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


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


;
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
}
]


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


;
subtree ->
[
subtree : <etree * etree>
{
  subtree(leaf, leaf) <= True
  subtree(leaf, node(x_1_0, x_1_1, x_1_2)) <= True
  subtree(node(x_0_0, x_0_1, x_0_2), leaf) <= True
  subtree(node(x_0_0, x_0_1, x_0_2), node(x_1_0, x_1_1, x_1_2)) <= True
}
]



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




Answer of teacher:

shallower(leaf, n) <= True  :
No: ()

subtree(leaf, t) <= True  :
No: ()

height(node(e, t1, t2), s(_agb)) \/ le_nat(_xfb, _yfb) <= height(t1, _agb) /\ height(t1, _xfb) /\ height(t2, _yfb)  :
No: ()

height(node(e, t1, t2), s(_zfb)) <= height(t1, _xfb) /\ height(t2, _yfb) /\ height(t2, _zfb) /\ le_nat(_xfb, _yfb)  :
No: ()

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

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

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

leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(_krjuw_0)  ;  nn2 -> z
}

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

leq_nat(n1, n2) <= shallower(t1, n1) /\ shallower(t2, n2) /\ subtree(t1, t2)  :
Yes: {
n1 -> s(_yrjuw_0)  ;  n2 -> z  ;  t1 -> node(_asjuw_0, _asjuw_1, _asjuw_2)  ;  t2 -> node(_bsjuw_0, _bsjuw_1, _bsjuw_2)
}

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: ()


-------------------------------------------
Step 5, which took 0.010734 s (model generation: 0.010605,  model checking: 0.000129):

Clauses:
{
shallower(leaf, n) <= True -> 0
subtree(leaf, t) <= True -> 0
height(node(e, t1, t2), s(_agb)) \/ le_nat(_xfb, _yfb) <= height(t1, _agb) /\ height(t1, _xfb) /\ height(t2, _yfb) -> 0
height(node(e, t1, t2), s(_zfb)) <= height(t1, _xfb) /\ height(t2, _yfb) /\ height(t2, _zfb) /\ le_nat(_xfb, _yfb) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 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
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
leq_nat(n1, n2) <= shallower(t1, n1) /\ shallower(t2, n2) /\ subtree(t1, t2) -> 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
}

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

Current best model:
|_
name: None

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


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


;
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
}
]


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


;
subtree ->
[
subtree : <etree * etree>
{
  subtree(leaf, leaf) <= True
  subtree(leaf, node(x_1_0, x_1_1, x_1_2)) <= True
  subtree(node(x_0_0, x_0_1, x_0_2), leaf) <= True
  subtree(node(x_0_0, x_0_1, x_0_2), node(x_1_0, x_1_1, x_1_2)) <= True
}
]



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




Answer of teacher:

shallower(leaf, n) <= True  :
No: ()

subtree(leaf, t) <= True  :
No: ()

height(node(e, t1, t2), s(_agb)) \/ le_nat(_xfb, _yfb) <= height(t1, _agb) /\ height(t1, _xfb) /\ height(t2, _yfb)  :
No: ()

height(node(e, t1, t2), s(_zfb)) <= height(t1, _xfb) /\ height(t2, _yfb) /\ height(t2, _zfb) /\ le_nat(_xfb, _yfb)  :
No: ()

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

le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2))  :
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)  :
Yes: {

}

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: ()

leq_nat(n1, n2) <= shallower(t1, n1) /\ shallower(t2, n2) /\ subtree(t1, t2)  :
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: ()


-------------------------------------------
Step 6, which took 0.114165 s (model generation: 0.011064,  model checking: 0.103101):

Clauses:
{
shallower(leaf, n) <= True -> 0
subtree(leaf, t) <= True -> 0
height(node(e, t1, t2), s(_agb)) \/ le_nat(_xfb, _yfb) <= height(t1, _agb) /\ height(t1, _xfb) /\ height(t2, _yfb) -> 0
height(node(e, t1, t2), s(_zfb)) <= height(t1, _xfb) /\ height(t2, _yfb) /\ height(t2, _zfb) /\ le_nat(_xfb, _yfb) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 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
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
leq_nat(n1, n2) <= shallower(t1, n1) /\ shallower(t2, n2) /\ subtree(t1, t2) -> 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
}

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

Current best model:
|_
name: None

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


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


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


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


;
subtree ->
[
subtree : <etree * etree>
{
  subtree(leaf, leaf) <= True
  subtree(leaf, node(x_1_0, x_1_1, x_1_2)) <= True
  subtree(node(x_0_0, x_0_1, x_0_2), leaf) <= True
  subtree(node(x_0_0, x_0_1, x_0_2), node(x_1_0, x_1_1, x_1_2)) <= True
}
]



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




Answer of teacher:

shallower(leaf, n) <= True  :
No: ()

subtree(leaf, t) <= True  :
No: ()

height(node(e, t1, t2), s(_agb)) \/ le_nat(_xfb, _yfb) <= height(t1, _agb) /\ height(t1, _xfb) /\ height(t2, _yfb)  :
No: ()

height(node(e, t1, t2), s(_zfb)) <= height(t1, _xfb) /\ height(t2, _yfb) /\ height(t2, _zfb) /\ le_nat(_xfb, _yfb)  :
No: ()

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

le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2))  :
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: ()

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: ()

leq_nat(n1, n2) <= shallower(t1, n1) /\ shallower(t2, n2) /\ subtree(t1, t2)  :
Yes: {
n1 -> s(_vujuw_0)  ;  n2 -> z  ;  t1 -> leaf  ;  t2 -> leaf
}

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: ()


Total time: 0.179416
Learner time: 0.064433
Teacher time: 0.104028
Reasons for stopping: No: Contradictory set of ground constraints:
{
False <= True
leq_nat(s(z), s(z)) <= True
leq_nat(z, s(z)) <= True
leq_nat(z, z) <= True
shallower(leaf, s(z)) <= True
shallower(leaf, z) <= True
shallower(node(a, leaf, leaf), s(z)) <= True
subtree(leaf, leaf) <= True
subtree(leaf, node(a, leaf, leaf)) <= True
subtree(node(a, leaf, leaf), node(a, node(a, leaf, leaf), node(a, leaf, leaf))) <= True
False <= leq_nat(s(s(z)), s(z))
False <= leq_nat(s(z), z)
False <= shallower(node(a, leaf, leaf), z) /\ subtree(node(a, leaf, leaf), node(a, leaf, leaf))
shallower(node(a, leaf, leaf), z) <= shallower(node(a, leaf, node(a, leaf, leaf)), s(z))
shallower(node(a, leaf, leaf), z) <= shallower(node(a, node(a, leaf, leaf), leaf), s(z))
subtree(node(a, leaf, leaf), leaf) <= subtree(node(a, leaf, leaf), node(a, leaf, leaf)) /\ subtree(node(a, node(a, leaf, leaf), node(a, leaf, leaf)), node(a, node(a, leaf, leaf), leaf))
subtree(node(a, leaf, leaf), leaf) <= subtree(node(a, node(a, leaf, leaf), leaf), node(a, leaf, leaf))
}