Solving ../../benchmarks/smtlib/false/append_length_le.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, _alb)) <= append(t1, l2, _alb)
}
eq_natlist(_dlb, _elb) <= append(_blb, _clb, _dlb) /\ append(_blb, _clb, _elb)
)
(le, P:
{
le(z, s(nn2)) <= True
le(s(nn1), s(nn2)) <= le(nn1, nn2)
le(nn1, nn2) <= le(s(nn1), s(nn2))
False <= le(s(nn1), z)
False <= le(z, z)
}
)
(length, F:
{
length(nil, z) <= True
length(cons(x, ll), s(_flb)) <= length(ll, _flb)
}
eq_nat(_hlb, _ilb) <= length(_glb, _hlb) /\ length(_glb, _ilb)
)
}

properties:
{
le(_jlb, _llb) <= append(l1, l2, _klb) /\ length(_klb, _llb) /\ length(l1, _jlb)
}


over-approximation: {append, length}
under-approximation: {le}

Clause system for inference is:

{
append(nil, l2, l2) <= True -> 0
length(nil, z) <= True -> 0
le(_jlb, _llb) <= append(l1, l2, _klb) /\ length(_klb, _llb) /\ length(l1, _jlb) -> 0
append(cons(h1, t1), l2, cons(h1, _alb)) <= append(t1, l2, _alb) -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
length(cons(x, ll), s(_flb)) <= length(ll, _flb) -> 0
}


Solving took 0.127078 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
le(z, s(z)) <= True
le(z, z) <= True
length(cons(z, nil), s(z)) <= True
length(nil, z) <= True
False <= le(z, z)
}
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006443 s (model generation: 0.006367,  model checking: 0.000076):

Clauses:
{
append(nil, l2, l2) <= True -> 0
length(nil, z) <= True -> 0
le(_jlb, _llb) <= append(l1, l2, _klb) /\ length(_klb, _llb) /\ length(l1, _jlb) -> 0
append(cons(h1, t1), l2, cons(h1, _alb)) <= append(t1, l2, _alb) -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
length(cons(x, ll), s(_flb)) <= length(ll, _flb) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

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


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


;
length ->
[
length : <natlist * nat>
{
  
}
]



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




Answer of teacher:

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

length(nil, z) <= True  :
Yes: {

}

le(_jlb, _llb) <= append(l1, l2, _klb) /\ length(_klb, _llb) /\ length(l1, _jlb)  :
No: ()

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

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

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

False <= le(s(nn1), z)  :
No: ()

False <= le(z, z)  :
No: ()

length(cons(x, ll), s(_flb)) <= length(ll, _flb)  :
No: ()


-------------------------------------------
Step 1, which took 0.008135 s (model generation: 0.006847,  model checking: 0.001288):

Clauses:
{
append(nil, l2, l2) <= True -> 0
length(nil, z) <= True -> 0
le(_jlb, _llb) <= append(l1, l2, _klb) /\ length(_klb, _llb) /\ length(l1, _jlb) -> 0
append(cons(h1, t1), l2, cons(h1, _alb)) <= append(t1, l2, _alb) -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
length(cons(x, ll), s(_flb)) <= length(ll, _flb) -> 0
}

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

Current best model:
|_
name: None

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


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


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



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




Answer of teacher:

append(nil, l2, l2) <= True  :
Yes: {
l2 -> cons(_esoqw_0, _esoqw_1)
}

length(nil, z) <= True  :
No: ()

le(_jlb, _llb) <= append(l1, l2, _klb) /\ length(_klb, _llb) /\ length(l1, _jlb)  :
Yes: {
_jlb -> z  ;  _klb -> nil  ;  _llb -> z  ;  l1 -> nil  ;  l2 -> nil
}

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

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

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

False <= le(s(nn1), z)  :
No: ()

False <= le(z, z)  :
No: ()

length(cons(x, ll), s(_flb)) <= length(ll, _flb)  :
Yes: {
_flb -> z  ;  ll -> nil
}


-------------------------------------------
Step 2, which took 0.009068 s (model generation: 0.008808,  model checking: 0.000260):

Clauses:
{
append(nil, l2, l2) <= True -> 0
length(nil, z) <= True -> 0
le(_jlb, _llb) <= append(l1, l2, _klb) /\ length(_klb, _llb) /\ length(l1, _jlb) -> 0
append(cons(h1, t1), l2, cons(h1, _alb)) <= append(t1, l2, _alb) -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
length(cons(x, ll), s(_flb)) <= length(ll, _flb) -> 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
le(z, z) <= True
length(cons(z, nil), s(z)) <= True
length(nil, z) <= 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
}
]


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


;
length ->
[
length : <natlist * nat>
{
  length(cons(x_0_0, x_0_1), s(x_1_0)) <= True
  length(nil, z) <= True
}
]



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




Answer of teacher:

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

length(nil, z) <= True  :
No: ()

le(_jlb, _llb) <= append(l1, l2, _klb) /\ length(_klb, _llb) /\ length(l1, _jlb)  :
Yes: {
_jlb -> z  ;  _klb -> cons(_vsoqw_0, _vsoqw_1)  ;  _llb -> s(_wsoqw_0)  ;  l1 -> nil  ;  l2 -> cons(_ysoqw_0, _ysoqw_1)
}

append(cons(h1, t1), l2, cons(h1, _alb)) <= append(t1, l2, _alb)  :
Yes: {
_alb -> cons(_zsoqw_0, _zsoqw_1)  ;  l2 -> cons(_atoqw_0, _atoqw_1)  ;  t1 -> nil
}

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

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

False <= le(s(nn1), z)  :
No: ()

False <= le(z, z)  :
Yes: {

}

length(cons(x, ll), s(_flb)) <= length(ll, _flb)  :
No: ()


Total time: 0.127078
Learner time: 0.022022
Teacher time: 0.001624
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
le(z, s(z)) <= True
le(z, z) <= True
length(cons(z, nil), s(z)) <= True
length(nil, z) <= True
False <= le(z, z)
}