Solving ../../benchmarks/smtlib/false/max_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}
}
definition:
{
(leq, P:
{
leq(z, n2) <= True
leq(s(nn1), s(nn2)) <= leq(nn1, nn2)
leq(nn1, nn2) <= leq(s(nn1), s(nn2))
False <= leq(s(nn1), z)
}
)
(max, F:
{
leq(n, m) \/ max(n, m, n) <= True
max(n, m, m) <= leq(n, m)
}
eq_nat(_neb, _oeb) <= max(_leb, _meb, _neb) /\ max(_leb, _meb, _oeb)
)
}

properties:
{
eq_nat(i, _peb) <= max(i, j, _peb)
}


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

Clause system for inference is:

{
leq(n, m) \/ max(n, m, n) <= True -> 0
leq(z, n2) <= True -> 0
max(n, m, m) <= leq(n, m) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
eq_nat(i, _peb) <= max(i, j, _peb) -> 0
}


Solving took 0.091581 seconds.
No: Contradictory set of ground constraints:
{
leq(s(s(z)), z) \/ max(s(s(z)), z, s(s(z))) <= True
leq(s(z), s(s(z))) <= True
leq(s(z), s(z)) <= True
leq(z, s(z)) <= True
leq(z, z) <= True
max(s(z), s(s(z)), s(s(z))) <= True
max(s(z), s(z), s(z)) <= True
max(s(z), z, s(z)) <= True
max(z, s(z), s(z)) <= True
max(z, z, z) <= True
False <= leq(s(s(z)), s(z))
False <= leq(s(z), z)
False <= max(s(s(z)), z, s(z))
False <= max(s(z), s(z), s(s(z)))
False <= max(s(z), z, s(s(z)))
False <= max(z, s(z), s(z))
}
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006039 s (model generation: 0.005956,  model checking: 0.000083):

Clauses:
{
leq(n, m) \/ max(n, m, n) <= True -> 0
leq(z, n2) <= True -> 0
max(n, m, m) <= leq(n, m) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
eq_nat(i, _peb) <= max(i, j, _peb) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

leq ->
[
leq : <nat * nat>
{
  
}
]


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



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




Answer of teacher:

leq(n, m) \/ max(n, m, n) <= True  :
Yes: {
m -> z  ;  n -> z
}

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

max(n, m, m) <= leq(n, m)  :
No: ()

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

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

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

eq_nat(i, _peb) <= max(i, j, _peb)  :
No: ()


-------------------------------------------
Step 1, which took 0.006093 s (model generation: 0.006008,  model checking: 0.000085):

Clauses:
{
leq(n, m) \/ max(n, m, n) <= True -> 0
leq(z, n2) <= True -> 0
max(n, m, m) <= leq(n, m) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
eq_nat(i, _peb) <= max(i, j, _peb) -> 0
}

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

Current best model:
|_
name: None

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


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



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




Answer of teacher:

leq(n, m) \/ max(n, m, n) <= True  :
Yes: {
m -> z  ;  n -> s(_ayoqw_0)
}

leq(z, n2) <= True  :
Yes: {
n2 -> s(_dyoqw_0)
}

max(n, m, m) <= leq(n, m)  :
Yes: {
m -> z  ;  n -> z
}

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

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

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

eq_nat(i, _peb) <= max(i, j, _peb)  :
No: ()


-------------------------------------------
Step 2, which took 0.007867 s (model generation: 0.007775,  model checking: 0.000092):

Clauses:
{
leq(n, m) \/ max(n, m, n) <= True -> 0
leq(z, n2) <= True -> 0
max(n, m, m) <= leq(n, m) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
eq_nat(i, _peb) <= max(i, j, _peb) -> 0
}

Accumulated learning constraints:
{
leq(s(z), s(z)) <= True
leq(s(z), z) \/ max(s(z), z, s(z)) <= True
leq(z, s(z)) <= True
leq(z, z) <= True
max(z, z, z) <= True
}

Current best model:
|_
name: None

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


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



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




Answer of teacher:

leq(n, m) \/ max(n, m, n) <= True  :
No: ()

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

max(n, m, m) <= leq(n, m)  :
Yes: {
m -> z  ;  n -> s(_lyoqw_0)
}

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

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

False <= leq(s(nn1), z)  :
Yes: {

}

eq_nat(i, _peb) <= max(i, j, _peb)  :
Yes: {
_peb -> s(s(_wyoqw_0))  ;  i -> s(z)  ;  j -> z
}


-------------------------------------------
Step 3, which took 0.009143 s (model generation: 0.009037,  model checking: 0.000106):

Clauses:
{
leq(n, m) \/ max(n, m, n) <= True -> 0
leq(z, n2) <= True -> 0
max(n, m, m) <= leq(n, m) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
eq_nat(i, _peb) <= max(i, j, _peb) -> 0
}

Accumulated learning constraints:
{
leq(s(z), s(z)) <= True
leq(z, s(z)) <= True
leq(z, z) <= True
max(s(z), z, s(z)) <= True
max(z, z, z) <= True
False <= leq(s(z), z)
False <= max(s(z), z, s(s(z)))
}

Current best model:
|_
name: None

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


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



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




Answer of teacher:

leq(n, m) \/ max(n, m, n) <= True  :
Yes: {
m -> z  ;  n -> s(s(_izoqw_0))
}

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

max(n, m, m) <= leq(n, m)  :
Yes: {
m -> s(_zyoqw_0)  ;  n -> s(_azoqw_0)
}

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

leq(nn1, nn2) <= leq(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(_dzoqw_0)  ;  nn2 -> z
}

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

eq_nat(i, _peb) <= max(i, j, _peb)  :
Yes: {
_peb -> s(z)  ;  i -> s(s(_kzoqw_0))  ;  j -> z
}


-------------------------------------------
Step 4, which took 0.012805 s (model generation: 0.012657,  model checking: 0.000148):

Clauses:
{
leq(n, m) \/ max(n, m, n) <= True -> 0
leq(z, n2) <= True -> 0
max(n, m, m) <= leq(n, m) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
eq_nat(i, _peb) <= max(i, j, _peb) -> 0
}

Accumulated learning constraints:
{
leq(s(s(z)), z) \/ max(s(s(z)), z, s(s(z))) <= True
leq(s(z), s(z)) <= True
leq(z, s(z)) <= True
leq(z, z) <= True
max(s(z), s(z), s(z)) <= True
max(s(z), z, s(z)) <= True
max(z, z, z) <= True
False <= leq(s(s(z)), s(z))
False <= leq(s(z), z)
False <= max(s(s(z)), z, s(z))
False <= max(s(z), z, s(s(z)))
}

Current best model:
|_
name: None

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


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



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




Answer of teacher:

leq(n, m) \/ max(n, m, n) <= True  :
No: ()

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

max(n, m, m) <= leq(n, m)  :
Yes: {
m -> s(_nzoqw_0)  ;  n -> z
}

leq(s(nn1), s(nn2)) <= leq(nn1, nn2)  :
Yes: {
nn1 -> z  ;  nn2 -> s(_szoqw_0)
}

leq(nn1, nn2) <= leq(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(z)  ;  nn2 -> s(s(_oapqw_0))
}

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

eq_nat(i, _peb) <= max(i, j, _peb)  :
Yes: {
_peb -> s(s(_kapqw_0))  ;  i -> s(z)  ;  j -> s(_bapqw_0)
}


-------------------------------------------
Step 5, which took 0.014235 s (model generation: 0.013975,  model checking: 0.000260):

Clauses:
{
leq(n, m) \/ max(n, m, n) <= True -> 0
leq(z, n2) <= True -> 0
max(n, m, m) <= leq(n, m) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
eq_nat(i, _peb) <= max(i, j, _peb) -> 0
}

Accumulated learning constraints:
{
leq(s(s(z)), z) \/ max(s(s(z)), z, s(s(z))) <= True
leq(s(z), s(s(z))) <= True
leq(s(z), s(z)) <= True
leq(z, s(z)) <= True
leq(z, z) <= True
max(s(z), s(z), s(z)) <= True
max(s(z), z, s(z)) <= True
max(z, s(z), s(z)) <= True
max(z, z, z) <= True
False <= leq(s(s(z)), s(z))
False <= leq(s(z), z)
False <= max(s(s(z)), z, s(z))
False <= max(s(z), s(z), s(s(z)))
False <= max(s(z), z, s(s(z)))
}

Current best model:
|_
name: None

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


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



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




Answer of teacher:

leq(n, m) \/ max(n, m, n) <= True  :
No: ()

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

max(n, m, m) <= leq(n, m)  :
Yes: {
m -> s(s(_pbpqw_0))  ;  n -> s(z)
}

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

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

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

eq_nat(i, _peb) <= max(i, j, _peb)  :
Yes: {
_peb -> s(_lbpqw_0)  ;  i -> z  ;  j -> s(_nbpqw_0)
}


Total time: 0.091581
Learner time: 0.055408
Teacher time: 0.000774
Reasons for stopping: No: Contradictory set of ground constraints:
{
leq(s(s(z)), z) \/ max(s(s(z)), z, s(s(z))) <= True
leq(s(z), s(s(z))) <= True
leq(s(z), s(z)) <= True
leq(z, s(z)) <= True
leq(z, z) <= True
max(s(z), s(s(z)), s(s(z))) <= True
max(s(z), s(z), s(z)) <= True
max(s(z), z, s(z)) <= True
max(z, s(z), s(z)) <= True
max(z, z, z) <= True
False <= leq(s(s(z)), s(z))
False <= leq(s(z), z)
False <= max(s(s(z)), z, s(z))
False <= max(s(z), s(z), s(s(z)))
False <= max(s(z), z, s(s(z)))
False <= max(z, s(z), s(z))
}