Solving ../../benchmarks/smtlib/true/length_take_if.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: {
elist -> {econs, enil}  ;  elt -> {a, b}  ;  nat -> {s, z}
}
definition:
{
(take_elt, F:
{
take_elt(s(u), enil, enil) <= True
take_elt(z, y, enil) <= True
take_elt(s(u), econs(x2, x3), econs(x2, _jx)) <= take_elt(u, x3, _jx)
}
eq_elist(_mx, _nx) <= take_elt(_kx, _lx, _mx) /\ take_elt(_kx, _lx, _nx)
)
(length_elt, F:
{
length_elt(enil, z) <= True
length_elt(econs(x, ll), s(_ox)) <= length_elt(ll, _ox)
}
eq_nat(_qx, _rx) <= length_elt(_px, _qx) /\ length_elt(_px, _rx)
)
(leq_nat, P:
{
leq_nat(z, n2) <= True
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2)
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2))
False <= leq_nat(s(nn1), z)
}
)
}

properties:
{
eq_nat(_ux, n) <= length_elt(_tx, _ux) /\ length_elt(l, _sx) /\ leq_nat(n, _sx) /\ take_elt(n, l, _tx)
}


over-approximation: {length_elt, leq_nat, take_elt}
under-approximation: {}

Clause system for inference is:

{
length_elt(enil, z) <= True -> 0
leq_nat(z, n2) <= True -> 0
take_elt(s(u), enil, enil) <= True -> 0
take_elt(z, y, enil) <= True -> 0
eq_nat(_ux, n) <= length_elt(_tx, _ux) /\ length_elt(l, _sx) /\ leq_nat(n, _sx) /\ take_elt(n, l, _tx) -> 0
length_elt(econs(x, ll), s(_ox)) <= length_elt(ll, _ox) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
take_elt(s(u), econs(x2, x3), econs(x2, _jx)) <= take_elt(u, x3, _jx) -> 0
}


Solving took 0.068019 seconds.
Yes: |_
name: None

length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
leq_nat ->
[
leq_nat : <nat * nat>
{
  leq_nat(s(x_0_0), s(x_1_0)) <= leq_nat(x_0_0, x_1_0)
  leq_nat(z, s(x_1_0)) <= True
  leq_nat(z, z) <= True
}
]


;
take_elt ->
[
take_elt : <nat * elist * elist>
{
  take_elt(s(x_0_0), econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= take_elt(x_0_0, x_1_1, x_2_1)
  take_elt(s(x_0_0), enil, enil) <= True
  take_elt(z, econs(x_1_0, x_1_1), enil) <= True
  take_elt(z, enil, enil) <= True
}
]



--
Equality automata are defined for: {elist, elt, nat}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006005 s (model generation: 0.005944,  model checking: 0.000061):

Clauses:
{
length_elt(enil, z) <= True -> 0
leq_nat(z, n2) <= True -> 0
take_elt(s(u), enil, enil) <= True -> 0
take_elt(z, y, enil) <= True -> 0
eq_nat(_ux, n) <= length_elt(_tx, _ux) /\ length_elt(l, _sx) /\ leq_nat(n, _sx) /\ take_elt(n, l, _tx) -> 0
length_elt(econs(x, ll), s(_ox)) <= length_elt(ll, _ox) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
take_elt(s(u), econs(x2, x3), econs(x2, _jx)) <= take_elt(u, x3, _jx) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

length_elt ->
[
length_elt : <elist * nat>
{
  
}
]


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


;
take_elt ->
[
take_elt : <nat * elist * elist>
{
  
}
]



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




Answer of teacher:

length_elt(enil, z) <= True  :
Yes: {

}

leq_nat(z, n2) <= True  :
Yes: {
n2 -> z
}

take_elt(s(u), enil, enil) <= True  :
Yes: {

}

take_elt(z, y, enil) <= True  :
Yes: {
y -> enil
}

eq_nat(_ux, n) <= length_elt(_tx, _ux) /\ length_elt(l, _sx) /\ leq_nat(n, _sx) /\ take_elt(n, l, _tx)  :
No: ()

length_elt(econs(x, ll), s(_ox)) <= length_elt(ll, _ox)  :
No: ()

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

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

take_elt(s(u), econs(x2, x3), econs(x2, _jx)) <= take_elt(u, x3, _jx)  :
No: ()


-------------------------------------------
Step 1, which took 0.006544 s (model generation: 0.006450,  model checking: 0.000094):

Clauses:
{
length_elt(enil, z) <= True -> 0
leq_nat(z, n2) <= True -> 0
take_elt(s(u), enil, enil) <= True -> 0
take_elt(z, y, enil) <= True -> 0
eq_nat(_ux, n) <= length_elt(_tx, _ux) /\ length_elt(l, _sx) /\ leq_nat(n, _sx) /\ take_elt(n, l, _tx) -> 0
length_elt(econs(x, ll), s(_ox)) <= length_elt(ll, _ox) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
take_elt(s(u), econs(x2, x3), econs(x2, _jx)) <= take_elt(u, x3, _jx) -> 0
}

Accumulated learning constraints:
{
length_elt(enil, z) <= True
leq_nat(z, z) <= True
take_elt(s(z), enil, enil) <= True
take_elt(z, enil, enil) <= True
}

Current best model:
|_
name: None

length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(enil, z) <= True
}
]


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


;
take_elt ->
[
take_elt : <nat * elist * elist>
{
  take_elt(s(x_0_0), enil, enil) <= True
  take_elt(z, enil, enil) <= True
}
]



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




Answer of teacher:

length_elt(enil, z) <= True  :
No: ()

leq_nat(z, n2) <= True  :
Yes: {
n2 -> s(_ejfs_0)
}

take_elt(s(u), enil, enil) <= True  :
No: ()

take_elt(z, y, enil) <= True  :
Yes: {
y -> econs(_fjfs_0, _fjfs_1)
}

eq_nat(_ux, n) <= length_elt(_tx, _ux) /\ length_elt(l, _sx) /\ leq_nat(n, _sx) /\ take_elt(n, l, _tx)  :
No: ()

length_elt(econs(x, ll), s(_ox)) <= length_elt(ll, _ox)  :
Yes: {
_ox -> z  ;  ll -> enil
}

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

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

take_elt(s(u), econs(x2, x3), econs(x2, _jx)) <= take_elt(u, x3, _jx)  :
Yes: {
_jx -> enil  ;  u -> z  ;  x3 -> enil
}


-------------------------------------------
Step 2, which took 0.009953 s (model generation: 0.009854,  model checking: 0.000099):

Clauses:
{
length_elt(enil, z) <= True -> 0
leq_nat(z, n2) <= True -> 0
take_elt(s(u), enil, enil) <= True -> 0
take_elt(z, y, enil) <= True -> 0
eq_nat(_ux, n) <= length_elt(_tx, _ux) /\ length_elt(l, _sx) /\ leq_nat(n, _sx) /\ take_elt(n, l, _tx) -> 0
length_elt(econs(x, ll), s(_ox)) <= length_elt(ll, _ox) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
take_elt(s(u), econs(x2, x3), econs(x2, _jx)) <= take_elt(u, x3, _jx) -> 0
}

Accumulated learning constraints:
{
length_elt(econs(a, enil), s(z)) <= True
length_elt(enil, z) <= True
leq_nat(s(z), s(z)) <= True
leq_nat(z, s(z)) <= True
leq_nat(z, z) <= True
take_elt(s(z), econs(a, enil), econs(a, enil)) <= True
take_elt(s(z), enil, enil) <= True
take_elt(z, econs(a, enil), enil) <= True
take_elt(z, enil, enil) <= True
}

Current best model:
|_
name: None

length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= True
  length_elt(enil, z) <= True
}
]


;
leq_nat ->
[
leq_nat : <nat * nat>
{
  leq_nat(s(x_0_0), s(x_1_0)) <= True
  leq_nat(z, s(x_1_0)) <= True
  leq_nat(z, z) <= True
}
]


;
take_elt ->
[
take_elt : <nat * elist * elist>
{
  take_elt(s(x_0_0), econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= True
  take_elt(s(x_0_0), enil, enil) <= True
  take_elt(z, econs(x_1_0, x_1_1), enil) <= True
  take_elt(z, enil, enil) <= True
}
]



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




Answer of teacher:

length_elt(enil, z) <= True  :
No: ()

leq_nat(z, n2) <= True  :
No: ()

take_elt(s(u), enil, enil) <= True  :
No: ()

take_elt(z, y, enil) <= True  :
No: ()

eq_nat(_ux, n) <= length_elt(_tx, _ux) /\ length_elt(l, _sx) /\ leq_nat(n, _sx) /\ take_elt(n, l, _tx)  :
Yes: {
_sx -> s(_qjfs_0)  ;  _tx -> econs(_rjfs_0, _rjfs_1)  ;  _ux -> s(z)  ;  l -> econs(_tjfs_0, _tjfs_1)  ;  n -> s(s(_ckfs_0))
}

length_elt(econs(x, ll), s(_ox)) <= length_elt(ll, _ox)  :
No: ()

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

leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(_vjfs_0)  ;  nn2 -> z
}

take_elt(s(u), econs(x2, x3), econs(x2, _jx)) <= take_elt(u, x3, _jx)  :
No: ()


-------------------------------------------
Step 3, which took 0.014422 s (model generation: 0.014277,  model checking: 0.000145):

Clauses:
{
length_elt(enil, z) <= True -> 0
leq_nat(z, n2) <= True -> 0
take_elt(s(u), enil, enil) <= True -> 0
take_elt(z, y, enil) <= True -> 0
eq_nat(_ux, n) <= length_elt(_tx, _ux) /\ length_elt(l, _sx) /\ leq_nat(n, _sx) /\ take_elt(n, l, _tx) -> 0
length_elt(econs(x, ll), s(_ox)) <= length_elt(ll, _ox) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
take_elt(s(u), econs(x2, x3), econs(x2, _jx)) <= take_elt(u, x3, _jx) -> 0
}

Accumulated learning constraints:
{
length_elt(econs(a, enil), s(z)) <= True
length_elt(enil, z) <= True
leq_nat(s(z), s(z)) <= True
leq_nat(z, s(z)) <= True
leq_nat(z, z) <= True
take_elt(s(z), econs(a, enil), econs(a, enil)) <= True
take_elt(s(z), enil, enil) <= True
take_elt(z, econs(a, enil), enil) <= True
take_elt(z, enil, enil) <= True
leq_nat(s(z), z) <= leq_nat(s(s(z)), s(z))
False <= leq_nat(s(s(z)), s(z)) /\ take_elt(s(s(z)), econs(a, enil), econs(a, enil))
}

Current best model:
|_
name: None

length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= True
  length_elt(enil, z) <= True
}
]


;
leq_nat ->
[
leq_nat : <nat * nat>
{
  leq_nat(s(x_0_0), s(x_1_0)) <= leq_nat(x_0_0, x_1_0)
  leq_nat(z, s(x_1_0)) <= True
  leq_nat(z, z) <= True
}
]


;
take_elt ->
[
take_elt : <nat * elist * elist>
{
  take_elt(s(x_0_0), econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= True
  take_elt(s(x_0_0), enil, enil) <= True
  take_elt(z, econs(x_1_0, x_1_1), enil) <= True
  take_elt(z, enil, enil) <= True
}
]



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




Answer of teacher:

length_elt(enil, z) <= True  :
No: ()

leq_nat(z, n2) <= True  :
No: ()

take_elt(s(u), enil, enil) <= True  :
No: ()

take_elt(z, y, enil) <= True  :
No: ()

eq_nat(_ux, n) <= length_elt(_tx, _ux) /\ length_elt(l, _sx) /\ leq_nat(n, _sx) /\ take_elt(n, l, _tx)  :
Yes: {
_sx -> s(z)  ;  _tx -> econs(_ekfs_0, _ekfs_1)  ;  _ux -> s(s(_dlfs_0))  ;  l -> econs(_gkfs_0, _gkfs_1)  ;  n -> s(z)
}

length_elt(econs(x, ll), s(_ox)) <= length_elt(ll, _ox)  :
No: ()

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

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

take_elt(s(u), econs(x2, x3), econs(x2, _jx)) <= take_elt(u, x3, _jx)  :
No: ()


-------------------------------------------
Step 4, which took 0.012091 s (model generation: 0.011787,  model checking: 0.000304):

Clauses:
{
length_elt(enil, z) <= True -> 0
leq_nat(z, n2) <= True -> 0
take_elt(s(u), enil, enil) <= True -> 0
take_elt(z, y, enil) <= True -> 0
eq_nat(_ux, n) <= length_elt(_tx, _ux) /\ length_elt(l, _sx) /\ leq_nat(n, _sx) /\ take_elt(n, l, _tx) -> 0
length_elt(econs(x, ll), s(_ox)) <= length_elt(ll, _ox) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
take_elt(s(u), econs(x2, x3), econs(x2, _jx)) <= take_elt(u, x3, _jx) -> 0
}

Accumulated learning constraints:
{
length_elt(econs(a, enil), s(z)) <= True
length_elt(enil, z) <= True
leq_nat(s(z), s(z)) <= True
leq_nat(z, s(z)) <= True
leq_nat(z, z) <= True
take_elt(s(z), econs(a, enil), econs(a, enil)) <= True
take_elt(s(z), enil, enil) <= True
take_elt(z, econs(a, enil), enil) <= True
take_elt(z, enil, enil) <= True
False <= length_elt(econs(a, enil), s(s(z)))
leq_nat(s(z), z) <= leq_nat(s(s(z)), s(z))
False <= leq_nat(s(s(z)), s(z)) /\ take_elt(s(s(z)), econs(a, enil), econs(a, enil))
}

Current best model:
|_
name: None

length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
leq_nat ->
[
leq_nat : <nat * nat>
{
  leq_nat(s(x_0_0), s(x_1_0)) <= leq_nat(x_0_0, x_1_0)
  leq_nat(z, s(x_1_0)) <= True
  leq_nat(z, z) <= True
}
]


;
take_elt ->
[
take_elt : <nat * elist * elist>
{
  take_elt(s(x_0_0), econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= True
  take_elt(s(x_0_0), enil, enil) <= True
  take_elt(z, econs(x_1_0, x_1_1), enil) <= True
  take_elt(z, enil, enil) <= True
}
]



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




Answer of teacher:

length_elt(enil, z) <= True  :
No: ()

leq_nat(z, n2) <= True  :
No: ()

take_elt(s(u), enil, enil) <= True  :
No: ()

take_elt(z, y, enil) <= True  :
No: ()

eq_nat(_ux, n) <= length_elt(_tx, _ux) /\ length_elt(l, _sx) /\ leq_nat(n, _sx) /\ take_elt(n, l, _tx)  :
Yes: {
_sx -> s(z)  ;  _tx -> econs(_flfs_0, econs(_omfs_0, enil))  ;  _ux -> s(s(z))  ;  l -> econs(_hlfs_0, enil)  ;  n -> s(z)
}

length_elt(econs(x, ll), s(_ox)) <= length_elt(ll, _ox)  :
No: ()

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

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

take_elt(s(u), econs(x2, x3), econs(x2, _jx)) <= take_elt(u, x3, _jx)  :
No: ()


Total time: 0.068019
Learner time: 0.048312
Teacher time: 0.000703
Reasons for stopping: Yes: |_
name: None

length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
leq_nat ->
[
leq_nat : <nat * nat>
{
  leq_nat(s(x_0_0), s(x_1_0)) <= leq_nat(x_0_0, x_1_0)
  leq_nat(z, s(x_1_0)) <= True
  leq_nat(z, z) <= True
}
]


;
take_elt ->
[
take_elt : <nat * elist * elist>
{
  take_elt(s(x_0_0), econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= take_elt(x_0_0, x_1_1, x_2_1)
  take_elt(s(x_0_0), enil, enil) <= True
  take_elt(z, econs(x_1_0, x_1_1), enil) <= True
  take_elt(z, enil, enil) <= True
}
]



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