Solving ../../benchmarks/smtlib/true/member_equal_ab.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:
{
(memberl, P:
{
memberl(h1, cons(h1, t1)) <= True
eq_elt(e, h1) \/ memberl(e, cons(h1, t1)) <= memberl(e, t1)
eq_elt(e, h1) \/ memberl(e, t1) <= memberl(e, cons(h1, t1))
False <= memberl(e, nil)
}
)
}

properties:
{
memberl(i, l2) <= memberl(i, l2)
}


over-approximation: {}
under-approximation: {}

Clause system for inference is:

{
memberl(h1, cons(h1, t1)) <= True -> 0
eq_elt(e, h1) \/ memberl(e, cons(h1, t1)) <= memberl(e, t1) -> 0
eq_elt(e, h1) \/ memberl(e, t1) <= memberl(e, cons(h1, t1)) -> 0
False <= memberl(e, nil) -> 0
memberl(i, l2) <= memberl(i, l2) -> 0
}


Solving took 0.171609 seconds.
Yes: |_
name: None

memberl ->
[
memberl : <elt * eltlist>
{
  _r_1(cons(x_0_0, x_0_1)) <= _r_1(x_0_1)
  _r_1(cons(x_0_0, x_0_1)) <= _r_3(x_0_0)
  _r_2(cons(x_0_0, x_0_1)) <= _r_2(x_0_1)
  _r_2(cons(x_0_0, x_0_1)) <= _r_4(x_0_0)
  _r_3(b) <= True
  _r_4(a) <= True
  memberl(a, cons(x_1_0, x_1_1)) <= _r_2(x_1_1)
  memberl(a, cons(x_1_0, x_1_1)) <= _r_4(x_1_0)
  memberl(b, cons(x_1_0, x_1_1)) <= _r_1(x_1_1)
  memberl(b, cons(x_1_0, x_1_1)) <= _r_3(x_1_0)
}
]



--
Equality automata are defined for: {elt, eltlist}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.005927 s (model generation: 0.005879,  model checking: 0.000048):

Clauses:
{
memberl(h1, cons(h1, t1)) <= True -> 0
eq_elt(e, h1) \/ memberl(e, cons(h1, t1)) <= memberl(e, t1) -> 0
eq_elt(e, h1) \/ memberl(e, t1) <= memberl(e, cons(h1, t1)) -> 0
False <= memberl(e, nil) -> 0
memberl(i, l2) <= memberl(i, l2) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

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



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




Answer of teacher:

memberl(h1, cons(h1, t1)) <= True  :
Yes: {
h1 -> b
}

eq_elt(e, h1) \/ memberl(e, cons(h1, t1)) <= memberl(e, t1)  :
No: ()

eq_elt(e, h1) \/ memberl(e, t1) <= memberl(e, cons(h1, t1))  :
No: ()

False <= memberl(e, nil)  :
No: ()

memberl(i, l2) <= memberl(i, l2)  :
No: ()


-------------------------------------------
Step 1, which took 0.006475 s (model generation: 0.006412,  model checking: 0.000063):

Clauses:
{
memberl(h1, cons(h1, t1)) <= True -> 0
eq_elt(e, h1) \/ memberl(e, cons(h1, t1)) <= memberl(e, t1) -> 0
eq_elt(e, h1) \/ memberl(e, t1) <= memberl(e, cons(h1, t1)) -> 0
False <= memberl(e, nil) -> 0
memberl(i, l2) <= memberl(i, l2) -> 0
}

Accumulated learning constraints:
{
memberl(b, cons(b, nil)) <= True
}

Current best model:
|_
name: None

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



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




Answer of teacher:

memberl(h1, cons(h1, t1)) <= True  :
Yes: {
h1 -> a
}

eq_elt(e, h1) \/ memberl(e, cons(h1, t1)) <= memberl(e, t1)  :
No: ()

eq_elt(e, h1) \/ memberl(e, t1) <= memberl(e, cons(h1, t1))  :
Yes: {
e -> b  ;  h1 -> a  ;  t1 -> nil
}

False <= memberl(e, nil)  :
No: ()

memberl(i, l2) <= memberl(i, l2)  :
No: ()


-------------------------------------------
Step 2, which took 0.009390 s (model generation: 0.009337,  model checking: 0.000053):

Clauses:
{
memberl(h1, cons(h1, t1)) <= True -> 0
eq_elt(e, h1) \/ memberl(e, cons(h1, t1)) <= memberl(e, t1) -> 0
eq_elt(e, h1) \/ memberl(e, t1) <= memberl(e, cons(h1, t1)) -> 0
False <= memberl(e, nil) -> 0
memberl(i, l2) <= memberl(i, l2) -> 0
}

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

Current best model:
|_
name: None

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



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




Answer of teacher:

memberl(h1, cons(h1, t1)) <= True  :
No: ()

eq_elt(e, h1) \/ memberl(e, cons(h1, t1)) <= memberl(e, t1)  :
No: ()

eq_elt(e, h1) \/ memberl(e, t1) <= memberl(e, cons(h1, t1))  :
Yes: {
e -> a  ;  h1 -> b  ;  t1 -> nil
}

False <= memberl(e, nil)  :
Yes: {
e -> b
}

memberl(i, l2) <= memberl(i, l2)  :
No: ()


-------------------------------------------
Step 3, which took 0.011431 s (model generation: 0.011339,  model checking: 0.000092):

Clauses:
{
memberl(h1, cons(h1, t1)) <= True -> 0
eq_elt(e, h1) \/ memberl(e, cons(h1, t1)) <= memberl(e, t1) -> 0
eq_elt(e, h1) \/ memberl(e, t1) <= memberl(e, cons(h1, t1)) -> 0
False <= memberl(e, nil) -> 0
memberl(i, l2) <= memberl(i, l2) -> 0
}

Accumulated learning constraints:
{
memberl(a, cons(a, nil)) <= True
memberl(b, cons(b, nil)) <= True
memberl(a, nil) <= memberl(a, cons(b, nil))
False <= memberl(b, cons(a, nil))
False <= memberl(b, nil)
}

Current best model:
|_
name: None

memberl ->
[
memberl : <elt * eltlist>
{
  _r_1(b) <= True
  memberl(a, cons(x_1_0, x_1_1)) <= True
  memberl(a, nil) <= True
  memberl(b, cons(x_1_0, x_1_1)) <= _r_1(x_1_0)
}
]



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




Answer of teacher:

memberl(h1, cons(h1, t1)) <= True  :
No: ()

eq_elt(e, h1) \/ memberl(e, cons(h1, t1)) <= memberl(e, t1)  :
Yes: {
e -> b  ;  h1 -> a  ;  t1 -> cons(b, _ceey_1)
}

eq_elt(e, h1) \/ memberl(e, t1) <= memberl(e, cons(h1, t1))  :
No: ()

False <= memberl(e, nil)  :
Yes: {
e -> a
}

memberl(i, l2) <= memberl(i, l2)  :
No: ()


-------------------------------------------
Step 4, which took 0.028666 s (model generation: 0.028327,  model checking: 0.000339):

Clauses:
{
memberl(h1, cons(h1, t1)) <= True -> 0
eq_elt(e, h1) \/ memberl(e, cons(h1, t1)) <= memberl(e, t1) -> 0
eq_elt(e, h1) \/ memberl(e, t1) <= memberl(e, cons(h1, t1)) -> 0
False <= memberl(e, nil) -> 0
memberl(i, l2) <= memberl(i, l2) -> 0
}

Accumulated learning constraints:
{
memberl(a, cons(a, nil)) <= True
memberl(b, cons(a, cons(b, nil))) <= True
memberl(b, cons(b, nil)) <= True
False <= memberl(a, cons(b, nil))
False <= memberl(a, nil)
False <= memberl(b, cons(a, nil))
False <= memberl(b, nil)
}

Current best model:
|_
name: None

memberl ->
[
memberl : <elt * eltlist>
{
  _r_1(cons(x_0_0, x_0_1)) <= True
  _r_2(b) <= True
  _r_3(a) <= True
  memberl(a, cons(x_1_0, x_1_1)) <= _r_3(x_1_0)
  memberl(b, cons(x_1_0, x_1_1)) <= _r_1(x_1_1)
  memberl(b, cons(x_1_0, x_1_1)) <= _r_2(x_1_0)
}
]



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




Answer of teacher:

memberl(h1, cons(h1, t1)) <= True  :
No: ()

eq_elt(e, h1) \/ memberl(e, cons(h1, t1)) <= memberl(e, t1)  :
Yes: {
e -> a  ;  h1 -> b  ;  t1 -> cons(a, _seey_1)
}

eq_elt(e, h1) \/ memberl(e, t1) <= memberl(e, cons(h1, t1))  :
Yes: {
e -> b  ;  h1 -> a  ;  t1 -> cons(a, nil)
}

False <= memberl(e, nil)  :
No: ()

memberl(i, l2) <= memberl(i, l2)  :
No: ()


-------------------------------------------
Step 5, which took 0.031168 s (model generation: 0.030784,  model checking: 0.000384):

Clauses:
{
memberl(h1, cons(h1, t1)) <= True -> 0
eq_elt(e, h1) \/ memberl(e, cons(h1, t1)) <= memberl(e, t1) -> 0
eq_elt(e, h1) \/ memberl(e, t1) <= memberl(e, cons(h1, t1)) -> 0
False <= memberl(e, nil) -> 0
memberl(i, l2) <= memberl(i, l2) -> 0
}

Accumulated learning constraints:
{
memberl(a, cons(a, nil)) <= True
memberl(a, cons(b, cons(a, nil))) <= True
memberl(b, cons(a, cons(b, nil))) <= True
memberl(b, cons(b, nil)) <= True
False <= memberl(a, cons(b, nil))
False <= memberl(a, nil)
False <= memberl(b, cons(a, cons(a, nil)))
False <= memberl(b, cons(a, nil))
False <= memberl(b, nil)
}

Current best model:
|_
name: None

memberl ->
[
memberl : <elt * eltlist>
{
  _r_1(cons(x_0_0, x_0_1)) <= _r_4(x_0_0)
  _r_2(cons(x_0_0, x_0_1)) <= True
  _r_3(a) <= True
  _r_4(b) <= True
  memberl(a, cons(x_1_0, x_1_1)) <= _r_2(x_1_1)
  memberl(a, cons(x_1_0, x_1_1)) <= _r_3(x_1_0)
  memberl(b, cons(x_1_0, x_1_1)) <= _r_1(x_1_1)
  memberl(b, cons(x_1_0, x_1_1)) <= _r_4(x_1_0)
}
]



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




Answer of teacher:

memberl(h1, cons(h1, t1)) <= True  :
No: ()

eq_elt(e, h1) \/ memberl(e, cons(h1, t1)) <= memberl(e, t1)  :
Yes: {
e -> b  ;  h1 -> a  ;  t1 -> cons(a, cons(b, _diey_1))
}

eq_elt(e, h1) \/ memberl(e, t1) <= memberl(e, cons(h1, t1))  :
Yes: {
e -> a  ;  h1 -> b  ;  t1 -> cons(b, nil)
}

False <= memberl(e, nil)  :
No: ()

memberl(i, l2) <= memberl(i, l2)  :
No: ()


-------------------------------------------
Step 6, which took 0.035855 s (model generation: 0.035430,  model checking: 0.000425):

Clauses:
{
memberl(h1, cons(h1, t1)) <= True -> 0
eq_elt(e, h1) \/ memberl(e, cons(h1, t1)) <= memberl(e, t1) -> 0
eq_elt(e, h1) \/ memberl(e, t1) <= memberl(e, cons(h1, t1)) -> 0
False <= memberl(e, nil) -> 0
memberl(i, l2) <= memberl(i, l2) -> 0
}

Accumulated learning constraints:
{
memberl(a, cons(a, nil)) <= True
memberl(a, cons(b, cons(a, nil))) <= True
memberl(b, cons(a, cons(a, cons(b, nil)))) <= True
memberl(b, cons(a, cons(b, nil))) <= True
memberl(b, cons(b, nil)) <= True
False <= memberl(a, cons(b, cons(b, nil)))
False <= memberl(a, cons(b, nil))
False <= memberl(a, nil)
False <= memberl(b, cons(a, cons(a, nil)))
False <= memberl(b, cons(a, nil))
False <= memberl(b, nil)
}

Current best model:
|_
name: None

memberl ->
[
memberl : <elt * eltlist>
{
  _r_1(cons(x_0_0, x_0_1)) <= _r_4(x_0_0)
  _r_2(cons(x_0_0, x_0_1)) <= _r_2(x_0_1)
  _r_2(cons(x_0_0, x_0_1)) <= _r_3(x_0_0)
  _r_3(b) <= True
  _r_4(a) <= True
  memberl(a, cons(x_1_0, x_1_1)) <= _r_1(x_1_1)
  memberl(a, cons(x_1_0, x_1_1)) <= _r_4(x_1_0)
  memberl(b, cons(x_1_0, x_1_1)) <= _r_2(x_1_1)
  memberl(b, cons(x_1_0, x_1_1)) <= _r_3(x_1_0)
}
]



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




Answer of teacher:

memberl(h1, cons(h1, t1)) <= True  :
No: ()

eq_elt(e, h1) \/ memberl(e, cons(h1, t1)) <= memberl(e, t1)  :
Yes: {
e -> a  ;  h1 -> b  ;  t1 -> cons(b, cons(a, _qkey_1))
}

eq_elt(e, h1) \/ memberl(e, t1) <= memberl(e, cons(h1, t1))  :
No: ()

False <= memberl(e, nil)  :
No: ()

memberl(i, l2) <= memberl(i, l2)  :
No: ()


Total time: 0.171609
Learner time: 0.127507
Teacher time: 0.001405
Reasons for stopping: Yes: |_
name: None

memberl ->
[
memberl : <elt * eltlist>
{
  _r_1(cons(x_0_0, x_0_1)) <= _r_1(x_0_1)
  _r_1(cons(x_0_0, x_0_1)) <= _r_3(x_0_0)
  _r_2(cons(x_0_0, x_0_1)) <= _r_2(x_0_1)
  _r_2(cons(x_0_0, x_0_1)) <= _r_4(x_0_0)
  _r_3(b) <= True
  _r_4(a) <= True
  memberl(a, cons(x_1_0, x_1_1)) <= _r_2(x_1_1)
  memberl(a, cons(x_1_0, x_1_1)) <= _r_4(x_1_0)
  memberl(b, cons(x_1_0, x_1_1)) <= _r_1(x_1_1)
  memberl(b, cons(x_1_0, x_1_1)) <= _r_3(x_1_0)
}
]



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