Solving ../../benchmarks/smtlib/true/timbuk_plus_even.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}
}
definition:
{
(is_even, P:
{
is_even(z) <= True
is_even(s(s(n3))) <= is_even(n3)
is_even(n3) <= is_even(s(s(n3)))
False <= is_even(s(z))
}
)
(plus, F:
{
plus(n, z, n) <= True
plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm)
}
eq_nat(_im, _jm) <= plus(_gm, _hm, _im) /\ plus(_gm, _hm, _jm)
)
}

properties:
{
is_even(_km) <= plus(x, x, _km)
}


over-approximation: {plus}
under-approximation: {is_even}

Clause system for inference is:

{
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm) -> 0
is_even(_km) <= plus(x, x, _km) -> 0
}


Solving took 0.325554 seconds.
Yes: |_
name: None

is_even ->
[
is_even : <nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0) /\ _r_1(x_1_0) /\ _r_1(x_2_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0) /\ is_even(x_1_0) /\ is_even(x_2_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_1_0) /\ is_even(x_0_0) /\ is_even(x_2_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_2_0) /\ is_even(x_0_0) /\ is_even(x_1_0)
  plus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_0_0) /\ _r_1(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_0_0) /\ is_even(x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



--
Equality automata are defined for: {nat}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.010937 s (model generation: 0.010895,  model checking: 0.000042):

Clauses:
{
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm) -> 0
is_even(_km) <= plus(x, x, _km) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  
}
]


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



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




Answer of teacher:

plus(n, z, n) <= True  :
Yes: {
n -> z
}

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm)  :
No: ()

is_even(_km) <= plus(x, x, _km)  :
No: ()


-------------------------------------------
Step 1, which took 0.013957 s (model generation: 0.013816,  model checking: 0.000141):

Clauses:
{
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm) -> 0
is_even(_km) <= plus(x, x, _km) -> 0
}

Accumulated learning constraints:
{
plus(z, z, z) <= True
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  
}
]


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



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




Answer of teacher:

plus(n, z, n) <= True  :
Yes: {
n -> s(_isnbd_0)
}

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm)  :
Yes: {
_fm -> z  ;  mm -> z  ;  n -> z
}

is_even(_km) <= plus(x, x, _km)  :
Yes: {
_km -> z  ;  x -> z
}


-------------------------------------------
Step 2, which took 0.018090 s (model generation: 0.017989,  model checking: 0.000101):

Clauses:
{
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm) -> 0
is_even(_km) <= plus(x, x, _km) -> 0
}

Accumulated learning constraints:
{
is_even(z) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



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




Answer of teacher:

plus(n, z, n) <= True  :
No: ()

is_even(s(s(n3))) <= is_even(n3)  :
Yes: {
n3 -> z
}

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm)  :
Yes: {
_fm -> s(_psnbd_0)  ;  mm -> z  ;  n -> s(_rsnbd_0)
}

is_even(_km) <= plus(x, x, _km)  :
No: ()


-------------------------------------------
Step 3, which took 0.017048 s (model generation: 0.016956,  model checking: 0.000092):

Clauses:
{
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm) -> 0
is_even(_km) <= plus(x, x, _km) -> 0
}

Accumulated learning constraints:
{
is_even(s(s(z))) <= True
is_even(z) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  is_even(s(x_0_0)) <= True
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= True
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



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




Answer of teacher:

plus(n, z, n) <= True  :
No: ()

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
Yes: {

}

plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm)  :
No: ()

is_even(_km) <= plus(x, x, _km)  :
No: ()


-------------------------------------------
Step 4, which took 0.031733 s (model generation: 0.031569,  model checking: 0.000164):

Clauses:
{
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm) -> 0
is_even(_km) <= plus(x, x, _km) -> 0
}

Accumulated learning constraints:
{
is_even(s(s(z))) <= True
is_even(z) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= is_even(s(z))
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  _r_1(s(x_0_0)) <= True
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= True
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



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




Answer of teacher:

plus(n, z, n) <= True  :
No: ()

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(n3) <= is_even(s(s(n3)))  :
Yes: {
n3 -> s(z)
}

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm)  :
No: ()

is_even(_km) <= plus(x, x, _km)  :
Yes: {
_km -> s(z)  ;  x -> s(_wsnbd_0)
}


-------------------------------------------
Step 5, which took 0.019717 s (model generation: 0.019557,  model checking: 0.000160):

Clauses:
{
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm) -> 0
is_even(_km) <= plus(x, x, _km) -> 0
}

Accumulated learning constraints:
{
is_even(s(s(z))) <= True
is_even(z) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= is_even(s(s(s(z))))
False <= is_even(s(z))
False <= plus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= True
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



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




Answer of teacher:

plus(n, z, n) <= True  :
No: ()

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm)  :
Yes: {
_fm -> s(s(z))  ;  mm -> z  ;  n -> s(_htnbd_0)
}

is_even(_km) <= plus(x, x, _km)  :
No: ()


-------------------------------------------
Step 6, which took 0.019986 s (model generation: 0.019670,  model checking: 0.000316):

Clauses:
{
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm) -> 0
is_even(_km) <= plus(x, x, _km) -> 0
}

Accumulated learning constraints:
{
is_even(s(s(z))) <= True
is_even(z) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= is_even(s(s(s(z))))
False <= is_even(s(z))
False <= plus(s(z), s(z), s(z))
plus(s(z), s(z), s(s(s(z)))) <= plus(s(z), z, s(s(z)))
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



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




Answer of teacher:

plus(n, z, n) <= True  :
Yes: {
n -> s(s(z))
}

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm)  :
Yes: {
_fm -> s(s(z))  ;  mm -> s(_ytnbd_0)  ;  n -> s(_ztnbd_0)
}

is_even(_km) <= plus(x, x, _km)  :
No: ()


-------------------------------------------
Step 7, which took 0.028299 s (model generation: 0.028039,  model checking: 0.000260):

Clauses:
{
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm) -> 0
is_even(_km) <= plus(x, x, _km) -> 0
}

Accumulated learning constraints:
{
is_even(s(s(z))) <= True
is_even(z) <= True
plus(s(s(z)), z, s(s(z))) <= True
plus(s(z), s(s(z)), s(s(s(z)))) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= is_even(s(s(s(z))))
False <= is_even(s(z))
False <= plus(s(z), s(z), s(z))
plus(s(z), s(z), s(s(s(z)))) <= plus(s(z), z, s(s(z)))
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_1_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_0_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



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




Answer of teacher:

plus(n, z, n) <= True  :
No: ()

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm)  :
Yes: {
_fm -> s(s(z))  ;  mm -> z  ;  n -> s(s(z))
}

is_even(_km) <= plus(x, x, _km)  :
Yes: {
_km -> s(z)  ;  x -> s(s(z))
}


-------------------------------------------
Step 8, which took 0.025728 s (model generation: 0.024709,  model checking: 0.001019):

Clauses:
{
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm) -> 0
is_even(_km) <= plus(x, x, _km) -> 0
}

Accumulated learning constraints:
{
is_even(s(s(z))) <= True
is_even(z) <= True
plus(s(s(z)), s(z), s(s(s(z)))) <= True
plus(s(s(z)), z, s(s(z))) <= True
plus(s(z), s(s(z)), s(s(s(z)))) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= is_even(s(s(s(z))))
False <= is_even(s(z))
False <= plus(s(s(z)), s(s(z)), s(z))
False <= plus(s(z), s(z), s(z))
plus(s(z), s(z), s(s(s(z)))) <= plus(s(z), z, s(s(z)))
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0) /\ is_even(x_1_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_1_0) /\ is_even(x_0_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_0_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



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




Answer of teacher:

plus(n, z, n) <= True  :
No: ()

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm)  :
Yes: {
_fm -> s(s(z))  ;  mm -> s(s(z))  ;  n -> s(z)
}

is_even(_km) <= plus(x, x, _km)  :
No: ()


-------------------------------------------
Step 9, which took 0.024971 s (model generation: 0.023086,  model checking: 0.001885):

Clauses:
{
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm) -> 0
is_even(_km) <= plus(x, x, _km) -> 0
}

Accumulated learning constraints:
{
is_even(s(s(z))) <= True
is_even(z) <= True
plus(s(s(z)), s(z), s(s(s(z)))) <= True
plus(s(s(z)), z, s(s(z))) <= True
plus(s(z), s(s(z)), s(s(s(z)))) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= is_even(s(s(s(z))))
False <= is_even(s(z))
False <= plus(s(s(z)), s(s(z)), s(z))
plus(s(z), s(s(s(z))), s(s(s(z)))) <= plus(s(z), s(s(z)), s(s(z)))
False <= plus(s(z), s(z), s(z))
plus(s(z), s(z), s(s(s(z)))) <= plus(s(z), z, s(s(z)))
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0) /\ is_even(x_1_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_1_0) /\ is_even(x_0_0) /\ is_even(x_2_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_2_0) /\ is_even(x_1_0)
  plus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_0_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



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




Answer of teacher:

plus(n, z, n) <= True  :
No: ()

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm)  :
Yes: {
_fm -> s(s(z))  ;  mm -> s(z)  ;  n -> s(s(z))
}

is_even(_km) <= plus(x, x, _km)  :
No: ()


-------------------------------------------
Step 10, which took 0.030584 s (model generation: 0.027517,  model checking: 0.003067):

Clauses:
{
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm) -> 0
is_even(_km) <= plus(x, x, _km) -> 0
}

Accumulated learning constraints:
{
is_even(s(s(z))) <= True
is_even(z) <= True
plus(s(s(z)), s(z), s(s(s(z)))) <= True
plus(s(s(z)), z, s(s(z))) <= True
plus(s(z), s(s(z)), s(s(s(z)))) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= is_even(s(s(s(z))))
False <= is_even(s(z))
False <= plus(s(s(z)), s(s(z)), s(z))
plus(s(s(z)), s(s(z)), s(s(s(z)))) <= plus(s(s(z)), s(z), s(s(z)))
plus(s(z), s(s(s(z))), s(s(s(z)))) <= plus(s(z), s(s(z)), s(s(z)))
False <= plus(s(z), s(z), s(z))
plus(s(z), s(z), s(s(s(z)))) <= plus(s(z), z, s(s(z)))
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0) /\ is_even(x_1_0) /\ is_even(x_2_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_1_0) /\ is_even(x_0_0) /\ is_even(x_2_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_2_0) /\ is_even(x_0_0) /\ is_even(x_1_0)
  plus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_0_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



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




Answer of teacher:

plus(n, z, n) <= True  :
No: ()

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm)  :
Yes: {
_fm -> s(z)  ;  mm -> s(z)  ;  n -> s(s(z))
}

is_even(_km) <= plus(x, x, _km)  :
No: ()


-------------------------------------------
Step 11, which took 0.038789 s (model generation: 0.033280,  model checking: 0.005509):

Clauses:
{
plus(n, z, n) <= True -> 0
is_even(s(s(n3))) <= is_even(n3) -> 0
is_even(n3) <= is_even(s(s(n3))) -> 0
False <= is_even(s(z)) -> 0
plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm) -> 0
is_even(_km) <= plus(x, x, _km) -> 0
}

Accumulated learning constraints:
{
is_even(s(s(z))) <= True
is_even(z) <= True
plus(s(s(z)), s(z), s(s(s(z)))) <= True
plus(s(s(z)), z, s(s(z))) <= True
plus(s(z), s(s(z)), s(s(s(z)))) <= True
plus(s(z), s(z), s(s(z))) <= True
plus(s(z), z, s(z)) <= True
plus(z, s(z), s(z)) <= True
plus(z, z, z) <= True
False <= is_even(s(s(s(z))))
False <= is_even(s(z))
False <= plus(s(s(z)), s(s(z)), s(z))
plus(s(s(z)), s(s(z)), s(s(s(z)))) <= plus(s(s(z)), s(z), s(s(z)))
plus(s(s(z)), s(s(z)), s(s(z))) <= plus(s(s(z)), s(z), s(z))
plus(s(z), s(s(s(z))), s(s(s(z)))) <= plus(s(z), s(s(z)), s(s(z)))
False <= plus(s(z), s(z), s(z))
plus(s(z), s(z), s(s(s(z)))) <= plus(s(z), z, s(s(z)))
}

Current best model:
|_
name: None

is_even ->
[
is_even : <nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0) /\ _r_1(x_1_0) /\ _r_1(x_2_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0) /\ is_even(x_1_0) /\ is_even(x_2_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_1_0) /\ is_even(x_0_0) /\ is_even(x_2_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_2_0) /\ is_even(x_0_0) /\ is_even(x_1_0)
  plus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_0_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



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




Answer of teacher:

plus(n, z, n) <= True  :
No: ()

is_even(s(s(n3))) <= is_even(n3)  :
No: ()

is_even(n3) <= is_even(s(s(n3)))  :
No: ()

False <= is_even(s(z))  :
No: ()

plus(n, s(mm), s(_fm)) <= plus(n, mm, _fm)  :
Yes: {
_fm -> s(z)  ;  mm -> z  ;  n -> s(s(z))
}

is_even(_km) <= plus(x, x, _km)  :
No: ()


Total time: 0.325554
Learner time: 0.267083
Teacher time: 0.012756
Reasons for stopping: Yes: |_
name: None

is_even ->
[
is_even : <nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
}
]


;
plus ->
[
plus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= is_even(x_0_0)
  is_even(s(x_0_0)) <= _r_1(x_0_0)
  is_even(z) <= True
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0) /\ _r_1(x_1_0) /\ _r_1(x_2_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0) /\ is_even(x_1_0) /\ is_even(x_2_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_1_0) /\ is_even(x_0_0) /\ is_even(x_2_0)
  plus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_2_0) /\ is_even(x_0_0) /\ is_even(x_1_0)
  plus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_0_0) /\ _r_1(x_2_0)
  plus(s(x_0_0), z, s(x_2_0)) <= is_even(x_0_0) /\ is_even(x_2_0)
  plus(z, s(x_1_0), s(x_2_0)) <= True
  plus(z, z, z) <= True
}
]



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