Solving ../../benchmarks/smtlib/true/append_not_null_cons_nat.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, _m)) <= append(t1, l2, _m)
}
eq_natlist(_p, _q) <= append(_n, _o, _p) /\ append(_n, _o, _q)
)
(not_null, P:
{
not_null(cons(x, ll)) <= True
False <= not_null(nil)
}
)
}

properties:
{
not_null(_r) <= append(cons(i, l1), l2, _r)
}


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

Clause system for inference is:

{
append(nil, l2, l2) <= True -> 0
append(cons(h1, t1), l2, cons(h1, _m)) <= append(t1, l2, _m) -> 0
not_null(_r) <= append(cons(i, l1), l2, _r) -> 0
False <= not_null(nil) -> 0
}


Solving took 0.032583 seconds.
Yes: |_
name: None

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



--
Equality automata are defined for: {nat, natlist}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006156 s (model generation: 0.006117,  model checking: 0.000039):

Clauses:
{
append(nil, l2, l2) <= True -> 0
append(cons(h1, t1), l2, cons(h1, _m)) <= append(t1, l2, _m) -> 0
not_null(_r) <= append(cons(i, l1), l2, _r) -> 0
False <= not_null(nil) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

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


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



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




Answer of teacher:

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

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

not_null(_r) <= append(cons(i, l1), l2, _r)  :
No: ()

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


-------------------------------------------
Step 1, which took 0.006157 s (model generation: 0.006118,  model checking: 0.000039):

Clauses:
{
append(nil, l2, l2) <= True -> 0
append(cons(h1, t1), l2, cons(h1, _m)) <= append(t1, l2, _m) -> 0
not_null(_r) <= append(cons(i, l1), l2, _r) -> 0
False <= not_null(nil) -> 0
}

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

Current best model:
|_
name: None

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


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



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




Answer of teacher:

append(nil, l2, l2) <= True  :
Yes: {
l2 -> cons(_ubud_0, _ubud_1)
}

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

not_null(_r) <= append(cons(i, l1), l2, _r)  :
No: ()

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


-------------------------------------------
Step 2, which took 0.007576 s (model generation: 0.007527,  model checking: 0.000049):

Clauses:
{
append(nil, l2, l2) <= True -> 0
append(cons(h1, t1), l2, cons(h1, _m)) <= append(t1, l2, _m) -> 0
not_null(_r) <= append(cons(i, l1), l2, _r) -> 0
False <= not_null(nil) -> 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
}

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>
{
  
}
]



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




Answer of teacher:

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

append(cons(h1, t1), l2, cons(h1, _m)) <= append(t1, l2, _m)  :
Yes: {
_m -> cons(_ybud_0, _ybud_1)  ;  l2 -> cons(_zbud_0, _zbud_1)  ;  t1 -> nil
}

not_null(_r) <= append(cons(i, l1), l2, _r)  :
Yes: {
_r -> cons(_bcud_0, _bcud_1)  ;  l2 -> nil
}

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


Total time: 0.032583
Learner time: 0.019762
Teacher time: 0.000127
Reasons for stopping: Yes: |_
name: None

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



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