Solving ../../benchmarks/smtlib/true/timbuk_insertionSort_elt.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}
}
definition:
{
(leq, P:
{
leq(a, y) <= True
leq(b, b) <= True
False <= leq(b, a)
}
)
(insert, F:
{
insert(x, nil, cons(x, nil)) <= True
insert(x, cons(y, z), cons(y, _xi)) \/ leq(x, y) <= insert(x, z, _xi)
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)
}
eq_eltlist(_aj, _bj) <= insert(_yi, _zi, _aj) /\ insert(_yi, _zi, _bj)
)
(sort, F:
{
sort(nil, nil) <= True
sort(cons(y, z), _dj) <= insert(y, _cj, _dj) /\ sort(z, _cj)
}
eq_eltlist(_fj, _gj) <= sort(_ej, _fj) /\ sort(_ej, _gj)
)
(sorted, P:
{
sorted(cons(x, nil)) <= True
sorted(nil) <= True
}
)
}

properties:
{
sorted(_hj) <= sort(l, _hj)
}


over-approximation: {insert, sort}
under-approximation: {sorted}

Clause system for inference is:

{
insert(x, nil, cons(x, nil)) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
sort(nil, nil) <= True -> 0
insert(x, cons(y, z), cons(y, _xi)) \/ leq(x, y) <= insert(x, z, _xi) -> 0
sort(cons(y, z), _dj) <= insert(y, _cj, _dj) /\ sort(z, _cj) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
sorted(_hj) <= sort(l, _hj) -> 0
}


Solving took 0.046868 seconds.
Yes: |_
name: None

insert ->
[
insert : <elt * eltlist * eltlist>
{
  insert(a, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  insert(a, nil, cons(x_2_0, x_2_1)) <= True
  insert(b, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  insert(b, nil, cons(x_2_0, x_2_1)) <= True
}
]


;
leq ->
[
leq : <elt * elt>
{
  leq(a, a) <= True
  leq(a, b) <= True
  leq(b, b) <= True
}
]


;
sort ->
[
sort : <eltlist * eltlist>
{
  sort(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1)) <= True
  sort(nil, nil) <= True
}
]


;
sorted ->
[
sorted : <eltlist>
{
  sorted(cons(x_0_0, x_0_1)) <= True
  sorted(nil) <= True
}
]



--
Equality automata are defined for: {elt, eltlist}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006708 s (model generation: 0.006581,  model checking: 0.000127):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
sort(nil, nil) <= True -> 0
insert(x, cons(y, z), cons(y, _xi)) \/ leq(x, y) <= insert(x, z, _xi) -> 0
sort(cons(y, z), _dj) <= insert(y, _cj, _dj) /\ sort(z, _cj) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
sorted(_hj) <= sort(l, _hj) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

insert ->
[
insert : <elt * eltlist * eltlist>
{
  
}
]


;
leq ->
[
leq : <elt * elt>
{
  
}
]


;
sort ->
[
sort : <eltlist * eltlist>
{
  
}
]


;
sorted ->
[
sorted : <eltlist>
{
  
}
]



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




Answer of teacher:

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

leq(a, y) <= True  :
Yes: {
y -> b
}

leq(b, b) <= True  :
Yes: {

}

sort(nil, nil) <= True  :
Yes: {

}

insert(x, cons(y, z), cons(y, _xi)) \/ leq(x, y) <= insert(x, z, _xi)  :
No: ()

sort(cons(y, z), _dj) <= insert(y, _cj, _dj) /\ sort(z, _cj)  :
No: ()

insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)  :
No: ()

False <= leq(b, a)  :
No: ()

sorted(_hj) <= sort(l, _hj)  :
No: ()


-------------------------------------------
Step 1, which took 0.010162 s (model generation: 0.010064,  model checking: 0.000098):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
sort(nil, nil) <= True -> 0
insert(x, cons(y, z), cons(y, _xi)) \/ leq(x, y) <= insert(x, z, _xi) -> 0
sort(cons(y, z), _dj) <= insert(y, _cj, _dj) /\ sort(z, _cj) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
sorted(_hj) <= sort(l, _hj) -> 0
}

Accumulated learning constraints:
{
insert(b, nil, cons(b, nil)) <= True
leq(a, b) <= True
leq(b, b) <= True
sort(nil, nil) <= True
}

Current best model:
|_
name: None

insert ->
[
insert : <elt * eltlist * eltlist>
{
  insert(b, nil, cons(x_2_0, x_2_1)) <= True
}
]


;
leq ->
[
leq : <elt * elt>
{
  leq(a, b) <= True
  leq(b, b) <= True
}
]


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


;
sorted ->
[
sorted : <eltlist>
{
  
}
]



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




Answer of teacher:

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

leq(a, y) <= True  :
Yes: {
y -> a
}

leq(b, b) <= True  :
No: ()

sort(nil, nil) <= True  :
No: ()

insert(x, cons(y, z), cons(y, _xi)) \/ leq(x, y) <= insert(x, z, _xi)  :
Yes: {
_xi -> cons(_mrnbd_0, _mrnbd_1)  ;  x -> b  ;  y -> a  ;  z -> nil
}

sort(cons(y, z), _dj) <= insert(y, _cj, _dj) /\ sort(z, _cj)  :
Yes: {
_cj -> nil  ;  _dj -> cons(_rrnbd_0, _rrnbd_1)  ;  y -> b  ;  z -> nil
}

insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)  :
Yes: {
x -> b  ;  y -> b
}

False <= leq(b, a)  :
No: ()

sorted(_hj) <= sort(l, _hj)  :
Yes: {
_hj -> nil  ;  l -> nil
}


-------------------------------------------
Step 2, which took 0.015720 s (model generation: 0.015633,  model checking: 0.000087):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
sort(nil, nil) <= True -> 0
insert(x, cons(y, z), cons(y, _xi)) \/ leq(x, y) <= insert(x, z, _xi) -> 0
sort(cons(y, z), _dj) <= insert(y, _cj, _dj) /\ sort(z, _cj) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
sorted(_hj) <= sort(l, _hj) -> 0
}

Accumulated learning constraints:
{
insert(a, nil, cons(a, nil)) <= True
insert(b, cons(b, nil), cons(b, cons(b, nil))) <= True
insert(b, nil, cons(b, nil)) <= True
leq(a, a) <= True
leq(a, b) <= True
leq(b, b) <= True
sort(nil, nil) <= True
sorted(nil) <= True
insert(b, cons(a, nil), cons(a, cons(a, nil))) \/ leq(b, a) <= insert(b, nil, cons(a, nil))
sort(cons(b, nil), cons(a, nil)) <= insert(b, nil, cons(a, nil))
}

Current best model:
|_
name: None

insert ->
[
insert : <elt * eltlist * eltlist>
{
  insert(a, nil, cons(x_2_0, x_2_1)) <= True
  insert(b, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  insert(b, nil, cons(x_2_0, x_2_1)) <= True
}
]


;
leq ->
[
leq : <elt * elt>
{
  leq(a, a) <= True
  leq(a, b) <= True
  leq(b, a) <= True
  leq(b, b) <= True
}
]


;
sort ->
[
sort : <eltlist * eltlist>
{
  sort(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1)) <= True
  sort(nil, nil) <= True
}
]


;
sorted ->
[
sorted : <eltlist>
{
  sorted(nil) <= True
}
]



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




Answer of teacher:

insert(x, nil, cons(x, nil)) <= True  :
No: ()

leq(a, y) <= True  :
No: ()

leq(b, b) <= True  :
No: ()

sort(nil, nil) <= True  :
No: ()

insert(x, cons(y, z), cons(y, _xi)) \/ leq(x, y) <= insert(x, z, _xi)  :
No: ()

sort(cons(y, z), _dj) <= insert(y, _cj, _dj) /\ sort(z, _cj)  :
No: ()

insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)  :
Yes: {
x -> a  ;  y -> b
}

False <= leq(b, a)  :
Yes: {

}

sorted(_hj) <= sort(l, _hj)  :
Yes: {
_hj -> cons(_esnbd_0, _esnbd_1)  ;  l -> cons(_fsnbd_0, _fsnbd_1)
}


Total time: 0.046868
Learner time: 0.032278
Teacher time: 0.000312
Reasons for stopping: Yes: |_
name: None

insert ->
[
insert : <elt * eltlist * eltlist>
{
  insert(a, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  insert(a, nil, cons(x_2_0, x_2_1)) <= True
  insert(b, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  insert(b, nil, cons(x_2_0, x_2_1)) <= True
}
]


;
leq ->
[
leq : <elt * elt>
{
  leq(a, a) <= True
  leq(a, b) <= True
  leq(b, b) <= True
}
]


;
sort ->
[
sort : <eltlist * eltlist>
{
  sort(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1)) <= True
  sort(nil, nil) <= True
}
]


;
sorted ->
[
sorted : <eltlist>
{
  sorted(cons(x_0_0, x_0_1)) <= True
  sorted(nil) <= True
}
]



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