Solving ../../benchmarks/smtlib/false/list_delete_all_count.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}  ;  eltlist -> {cons, nil}  ;  nat -> {s, z}
}
definition:
{
(delete_one, F:
{
delete_one(x, nil, nil) <= True
delete_one(y, cons(y, r), r) <= True
eq_elt(x, y) \/ delete_one(x, cons(y, r), cons(y, _zab)) <= delete_one(x, r, _zab)
}
eq_eltlist(_cbb, _dbb) <= delete_one(_abb, _bbb, _cbb) /\ delete_one(_abb, _bbb, _dbb)
)
(delete_all, F:
{
delete_all(x, nil, nil) <= True
eq_elt(x, y) \/ delete_all(x, cons(y, r), cons(y, _fbb)) <= delete_all(x, r, _fbb)
delete_all(y, cons(y, r), _ebb) <= delete_all(y, r, _ebb)
}
eq_eltlist(_ibb, _jbb) <= delete_all(_gbb, _hbb, _ibb) /\ delete_all(_gbb, _hbb, _jbb)
)
(count, F:
{
count(x, nil, z) <= True
eq_elt(x, y) \/ count(x, cons(y, r), _lbb) <= count(x, r, _lbb)
count(y, cons(y, r), s(_kbb)) <= count(y, r, _kbb)
}
eq_nat(_obb, _pbb) <= count(_mbb, _nbb, _obb) /\ count(_mbb, _nbb, _pbb)
)
}

properties:
{
eq_nat(_sbb, s(z)) <= count(x, l, _sbb) /\ delete_all(x, l, _rbb) /\ delete_one(x, l, _rbb)
}


over-approximation: {count, delete_all, delete_one}
under-approximation: {}

Clause system for inference is:

{
count(x, nil, z) <= True -> 0
delete_all(x, nil, nil) <= True -> 0
delete_one(x, nil, nil) <= True -> 0
delete_one(y, cons(y, r), r) <= True -> 0
eq_nat(_sbb, s(z)) <= count(x, l, _sbb) /\ delete_all(x, l, _rbb) /\ delete_one(x, l, _rbb) -> 0
eq_elt(x, y) \/ count(x, cons(y, r), _lbb) <= count(x, r, _lbb) -> 0
count(y, cons(y, r), s(_kbb)) <= count(y, r, _kbb) -> 0
eq_elt(x, y) \/ delete_all(x, cons(y, r), cons(y, _fbb)) <= delete_all(x, r, _fbb) -> 0
delete_all(y, cons(y, r), _ebb) <= delete_all(y, r, _ebb) -> 0
eq_elt(x, y) \/ delete_one(x, cons(y, r), cons(y, _zab)) <= delete_one(x, r, _zab) -> 0
}


Solving took 0.021936 seconds.
No: Contradictory set of ground constraints:
{
False <= True
count(a, nil, z) <= True
count(b, cons(a, nil), z) <= True
count(b, cons(b, nil), s(z)) <= True
count(b, nil, z) <= True
delete_all(a, nil, nil) <= True
delete_all(b, cons(a, nil), cons(a, nil)) <= True
delete_all(b, cons(b, nil), nil) <= True
delete_all(b, nil, nil) <= True
delete_one(a, cons(a, nil), nil) <= True
delete_one(a, nil, nil) <= True
delete_one(b, cons(a, nil), cons(a, nil)) <= True
delete_one(b, cons(b, nil), nil) <= True
delete_one(b, nil, nil) <= True
}
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006749 s (model generation: 0.006576,  model checking: 0.000173):

Clauses:
{
count(x, nil, z) <= True -> 0
delete_all(x, nil, nil) <= True -> 0
delete_one(x, nil, nil) <= True -> 0
delete_one(y, cons(y, r), r) <= True -> 0
eq_nat(_sbb, s(z)) <= count(x, l, _sbb) /\ delete_all(x, l, _rbb) /\ delete_one(x, l, _rbb) -> 0
eq_elt(x, y) \/ count(x, cons(y, r), _lbb) <= count(x, r, _lbb) -> 0
count(y, cons(y, r), s(_kbb)) <= count(y, r, _kbb) -> 0
eq_elt(x, y) \/ delete_all(x, cons(y, r), cons(y, _fbb)) <= delete_all(x, r, _fbb) -> 0
delete_all(y, cons(y, r), _ebb) <= delete_all(y, r, _ebb) -> 0
eq_elt(x, y) \/ delete_one(x, cons(y, r), cons(y, _zab)) <= delete_one(x, r, _zab) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

count ->
[
count : <elt * eltlist * nat>
{
  
}
]


;
delete_all ->
[
delete_all : <elt * eltlist * eltlist>
{
  
}
]


;
delete_one ->
[
delete_one : <elt * eltlist * eltlist>
{
  
}
]



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




Answer of teacher:

count(x, nil, z) <= True  :
Yes: {
x -> b
}

delete_all(x, nil, nil) <= True  :
Yes: {
x -> b
}

delete_one(x, nil, nil) <= True  :
Yes: {
x -> b
}

delete_one(y, cons(y, r), r) <= True  :
Yes: {
r -> nil  ;  y -> b
}

eq_nat(_sbb, s(z)) <= count(x, l, _sbb) /\ delete_all(x, l, _rbb) /\ delete_one(x, l, _rbb)  :
No: ()

eq_elt(x, y) \/ count(x, cons(y, r), _lbb) <= count(x, r, _lbb)  :
No: ()

count(y, cons(y, r), s(_kbb)) <= count(y, r, _kbb)  :
No: ()

eq_elt(x, y) \/ delete_all(x, cons(y, r), cons(y, _fbb)) <= delete_all(x, r, _fbb)  :
No: ()

delete_all(y, cons(y, r), _ebb) <= delete_all(y, r, _ebb)  :
No: ()

eq_elt(x, y) \/ delete_one(x, cons(y, r), cons(y, _zab)) <= delete_one(x, r, _zab)  :
No: ()


-------------------------------------------
Step 1, which took 0.007062 s (model generation: 0.006931,  model checking: 0.000131):

Clauses:
{
count(x, nil, z) <= True -> 0
delete_all(x, nil, nil) <= True -> 0
delete_one(x, nil, nil) <= True -> 0
delete_one(y, cons(y, r), r) <= True -> 0
eq_nat(_sbb, s(z)) <= count(x, l, _sbb) /\ delete_all(x, l, _rbb) /\ delete_one(x, l, _rbb) -> 0
eq_elt(x, y) \/ count(x, cons(y, r), _lbb) <= count(x, r, _lbb) -> 0
count(y, cons(y, r), s(_kbb)) <= count(y, r, _kbb) -> 0
eq_elt(x, y) \/ delete_all(x, cons(y, r), cons(y, _fbb)) <= delete_all(x, r, _fbb) -> 0
delete_all(y, cons(y, r), _ebb) <= delete_all(y, r, _ebb) -> 0
eq_elt(x, y) \/ delete_one(x, cons(y, r), cons(y, _zab)) <= delete_one(x, r, _zab) -> 0
}

Accumulated learning constraints:
{
count(b, nil, z) <= True
delete_all(b, nil, nil) <= True
delete_one(b, cons(b, nil), nil) <= True
delete_one(b, nil, nil) <= True
}

Current best model:
|_
name: None

count ->
[
count : <elt * eltlist * nat>
{
  count(b, nil, z) <= True
}
]


;
delete_all ->
[
delete_all : <elt * eltlist * eltlist>
{
  delete_all(b, nil, nil) <= True
}
]


;
delete_one ->
[
delete_one : <elt * eltlist * eltlist>
{
  delete_one(b, cons(x_1_0, x_1_1), nil) <= True
  delete_one(b, nil, nil) <= True
}
]



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




Answer of teacher:

count(x, nil, z) <= True  :
Yes: {
x -> a
}

delete_all(x, nil, nil) <= True  :
Yes: {
x -> a
}

delete_one(x, nil, nil) <= True  :
Yes: {
x -> a
}

delete_one(y, cons(y, r), r) <= True  :
Yes: {
r -> nil  ;  y -> a
}

eq_nat(_sbb, s(z)) <= count(x, l, _sbb) /\ delete_all(x, l, _rbb) /\ delete_one(x, l, _rbb)  :
Yes: {
_rbb -> nil  ;  _sbb -> z  ;  l -> nil  ;  x -> b
}

eq_elt(x, y) \/ count(x, cons(y, r), _lbb) <= count(x, r, _lbb)  :
Yes: {
_lbb -> z  ;  r -> nil  ;  x -> b  ;  y -> a
}

count(y, cons(y, r), s(_kbb)) <= count(y, r, _kbb)  :
Yes: {
_kbb -> z  ;  r -> nil  ;  y -> b
}

eq_elt(x, y) \/ delete_all(x, cons(y, r), cons(y, _fbb)) <= delete_all(x, r, _fbb)  :
Yes: {
_fbb -> nil  ;  r -> nil  ;  x -> b  ;  y -> a
}

delete_all(y, cons(y, r), _ebb) <= delete_all(y, r, _ebb)  :
Yes: {
_ebb -> nil  ;  r -> nil  ;  y -> b
}

eq_elt(x, y) \/ delete_one(x, cons(y, r), cons(y, _zab)) <= delete_one(x, r, _zab)  :
Yes: {
_zab -> nil  ;  r -> nil  ;  x -> b  ;  y -> a
}


Total time: 0.021936
Learner time: 0.013507
Teacher time: 0.000304
Reasons for stopping: No: Contradictory set of ground constraints:
{
False <= True
count(a, nil, z) <= True
count(b, cons(a, nil), z) <= True
count(b, cons(b, nil), s(z)) <= True
count(b, nil, z) <= True
delete_all(a, nil, nil) <= True
delete_all(b, cons(a, nil), cons(a, nil)) <= True
delete_all(b, cons(b, nil), nil) <= True
delete_all(b, nil, nil) <= True
delete_one(a, cons(a, nil), nil) <= True
delete_one(a, nil, nil) <= True
delete_one(b, cons(a, nil), cons(a, nil)) <= True
delete_one(b, cons(b, nil), nil) <= True
delete_one(b, nil, nil) <= True
}