Solving ../../benchmarks/smtlib/false/reverse_not_null.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: {
nat -> {s, z}  ;  natlist -> {cons, nil}
}
definition:
{
(append, F:
{
append(nil, l2, l2) <= True
append(cons(h1, t1), l2, cons(h1, _cab)) <= append(t1, l2, _cab)
}
eq_natlist(_fab, _gab) <= append(_dab, _eab, _fab) /\ append(_dab, _eab, _gab)
)
(reverse, F:
{
reverse(nil, nil) <= True
reverse(cons(h1, t1), _iab) <= append(_hab, cons(h1, nil), _iab) /\ reverse(t1, _hab)
}
eq_natlist(_kab, _lab) <= reverse(_jab, _kab) /\ reverse(_jab, _lab)
)
(not_null, P:
{
not_null(cons(x, ll)) <= True
False <= not_null(nil)
}
)
}

properties:
{
not_null(_mab) <= reverse(l1, _mab)
}


over-approximation: {append, reverse}
under-approximation: {not_null}

Clause system for inference is:

{
append(nil, l2, l2) <= True -> 0
reverse(nil, nil) <= True -> 0
reverse(cons(h1, t1), _iab) <= append(_hab, cons(h1, nil), _iab) /\ reverse(t1, _hab) -> 0
append(cons(h1, t1), l2, cons(h1, _cab)) <= append(t1, l2, _cab) -> 0
False <= not_null(nil) -> 0
not_null(_mab) <= reverse(l1, _mab) -> 0
}


Solving took 0.100415 seconds.
No: Contradictory set of ground constraints:
{
append(cons(z, nil), cons(z, nil), cons(z, cons(z, nil))) <= True
append(cons(z, nil), nil, cons(z, nil)) <= True
append(nil, cons(z, nil), cons(z, nil)) <= True
append(nil, nil, nil) <= True
not_null(nil) <= True
reverse(cons(z, nil), cons(z, nil)) <= True
reverse(nil, nil) <= True
False <= not_null(nil)
}
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006713 s (model generation: 0.006651,  model checking: 0.000062):

Clauses:
{
append(nil, l2, l2) <= True -> 0
reverse(nil, nil) <= True -> 0
reverse(cons(h1, t1), _iab) <= append(_hab, cons(h1, nil), _iab) /\ reverse(t1, _hab) -> 0
append(cons(h1, t1), l2, cons(h1, _cab)) <= append(t1, l2, _cab) -> 0
False <= not_null(nil) -> 0
not_null(_mab) <= reverse(l1, _mab) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

append ->
[
append : <natlist * natlist * natlist>
{
  
}
]


;
not_null ->
[
not_null : <natlist>
{
  
}
]


;
reverse ->
[
reverse : <natlist * natlist>
{
  
}
]



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




Answer of teacher:

append(nil, l2, l2) <= True  :
Yes: {
l2 -> nil
}

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

}

reverse(cons(h1, t1), _iab) <= append(_hab, cons(h1, nil), _iab) /\ reverse(t1, _hab)  :
No: ()

append(cons(h1, t1), l2, cons(h1, _cab)) <= append(t1, l2, _cab)  :
No: ()

False <= not_null(nil)  :
No: ()

not_null(_mab) <= reverse(l1, _mab)  :
No: ()


-------------------------------------------
Step 1, which took 0.006332 s (model generation: 0.006281,  model checking: 0.000051):

Clauses:
{
append(nil, l2, l2) <= True -> 0
reverse(nil, nil) <= True -> 0
reverse(cons(h1, t1), _iab) <= append(_hab, cons(h1, nil), _iab) /\ reverse(t1, _hab) -> 0
append(cons(h1, t1), l2, cons(h1, _cab)) <= append(t1, l2, _cab) -> 0
False <= not_null(nil) -> 0
not_null(_mab) <= reverse(l1, _mab) -> 0
}

Accumulated learning constraints:
{
append(nil, nil, nil) <= True
reverse(nil, nil) <= True
}

Current best model:
|_
name: None

append ->
[
append : <natlist * natlist * natlist>
{
  append(nil, nil, nil) <= True
}
]


;
not_null ->
[
not_null : <natlist>
{
  
}
]


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



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




Answer of teacher:

append(nil, l2, l2) <= True  :
Yes: {
l2 -> cons(_lhrqw_0, _lhrqw_1)
}

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

reverse(cons(h1, t1), _iab) <= append(_hab, cons(h1, nil), _iab) /\ reverse(t1, _hab)  :
No: ()

append(cons(h1, t1), l2, cons(h1, _cab)) <= append(t1, l2, _cab)  :
Yes: {
_cab -> nil  ;  l2 -> nil  ;  t1 -> nil
}

False <= not_null(nil)  :
No: ()

not_null(_mab) <= reverse(l1, _mab)  :
Yes: {
_mab -> nil  ;  l1 -> nil
}


-------------------------------------------
Step 2, which took 0.007950 s (model generation: 0.007893,  model checking: 0.000057):

Clauses:
{
append(nil, l2, l2) <= True -> 0
reverse(nil, nil) <= True -> 0
reverse(cons(h1, t1), _iab) <= append(_hab, cons(h1, nil), _iab) /\ reverse(t1, _hab) -> 0
append(cons(h1, t1), l2, cons(h1, _cab)) <= append(t1, l2, _cab) -> 0
False <= not_null(nil) -> 0
not_null(_mab) <= reverse(l1, _mab) -> 0
}

Accumulated learning constraints:
{
append(cons(z, nil), nil, cons(z, nil)) <= True
append(nil, cons(z, nil), cons(z, nil)) <= True
append(nil, nil, nil) <= True
not_null(nil) <= True
reverse(nil, nil) <= True
}

Current best model:
|_
name: None

append ->
[
append : <natlist * natlist * natlist>
{
  append(cons(x_0_0, x_0_1), nil, cons(x_2_0, x_2_1)) <= True
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  append(nil, nil, nil) <= True
}
]


;
not_null ->
[
not_null : <natlist>
{
  not_null(nil) <= True
}
]


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



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




Answer of teacher:

append(nil, l2, l2) <= True  :
No: ()

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

reverse(cons(h1, t1), _iab) <= append(_hab, cons(h1, nil), _iab) /\ reverse(t1, _hab)  :
Yes: {
_hab -> nil  ;  _iab -> cons(_shrqw_0, _shrqw_1)  ;  t1 -> nil
}

append(cons(h1, t1), l2, cons(h1, _cab)) <= append(t1, l2, _cab)  :
Yes: {
_cab -> cons(_uhrqw_0, _uhrqw_1)  ;  l2 -> cons(_vhrqw_0, _vhrqw_1)  ;  t1 -> nil
}

False <= not_null(nil)  :
Yes: {

}

not_null(_mab) <= reverse(l1, _mab)  :
No: ()


Total time: 0.100415
Learner time: 0.020825
Teacher time: 0.000170
Reasons for stopping: No: Contradictory set of ground constraints:
{
append(cons(z, nil), cons(z, nil), cons(z, cons(z, nil))) <= True
append(cons(z, nil), nil, cons(z, nil)) <= True
append(nil, cons(z, nil), cons(z, nil)) <= True
append(nil, nil, nil) <= True
not_null(nil) <= True
reverse(cons(z, nil), cons(z, nil)) <= True
reverse(nil, nil) <= True
False <= not_null(nil)
}