Solving ../../benchmarks/true/isaplanner_prop25.smt2...

Inference procedure has parameters:
Ice fuel: 200
Timeout: 30s
Convolution: complete


Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(leq, P:
{() -> leq([z, n2])
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)])
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2])
(leq([s(nn1), z])) -> BOT}
)
(max, F:
{() -> max([s(u), z, s(u)])
() -> max([z, y, y])
(max([u, x2, _kba])) -> max([s(u), s(x2), s(_kba)])}
(max([_lba, _mba, _nba]) /\ max([_lba, _mba, _oba])) -> eq_nat([_nba, _oba])
)
}

properties:
{(leq([i, j]) /\ max([i, j, _qba])) -> eq_nat([_qba, j]), (max([i, j, j])) -> leq([i, j])}


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

Clause system for inference is:

{
() -> leq([z, n2]) -> 0  ;  () -> max([s(u), z, s(u)]) -> 0  ;  () -> max([z, y, y]) -> 0  ;  (leq([i, j]) /\ max([i, j, _qba])) -> eq_nat([_qba, j]) -> 0  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 0  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 0  ;  (leq([s(nn1), z])) -> BOT -> 0  ;  (max([i, j, j])) -> leq([i, j]) -> 0  ;  (max([u, x2, _kba])) -> max([s(u), s(x2), s(_kba)]) -> 0
}


Solving took 0.107053 seconds.
Proved
Model:
|_
{
leq -> 
{{{
Q={q_gen_1612, q_gen_1619},
Q_f={q_gen_1612},
Delta=
{
<s>(q_gen_1619) -> q_gen_1619
<z>() -> q_gen_1619
<s, s>(q_gen_1612) -> q_gen_1612
<z, s>(q_gen_1619) -> q_gen_1612
<z, z>() -> q_gen_1612
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  max -> 
{{{
Q={q_gen_1609, q_gen_1611},
Q_f={q_gen_1609},
Delta=
{
<s, s>(q_gen_1611) -> q_gen_1611
<z, z>() -> q_gen_1611
<s, s, s>(q_gen_1609) -> q_gen_1609
<s, z, s>(q_gen_1611) -> q_gen_1609
<z, s, s>(q_gen_1611) -> q_gen_1609
<z, z, z>() -> q_gen_1609
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.010723 s (model generation: 0.010067,  model checking: 0.000656):

Model:
|_
{
leq -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  max -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 0  ;  () -> max([s(u), z, s(u)]) -> 0  ;  () -> max([z, y, y]) -> 3  ;  (leq([i, j]) /\ max([i, j, _qba])) -> eq_nat([_qba, j]) -> 1  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1  ;  (leq([s(nn1), z])) -> BOT -> 1  ;  (max([i, j, j])) -> leq([i, j]) -> 1  ;  (max([u, x2, _kba])) -> max([s(u), s(x2), s(_kba)]) -> 1
}
Sat witness: Yes: (() -> max([z, y, y]), {
y -> z
})

-------------------------------------------
Step 1, which took 0.010453 s (model generation: 0.010234,  model checking: 0.000219):

Model:
|_
{
leq -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  max -> 
{{{
Q={q_gen_1609},
Q_f={q_gen_1609},
Delta=
{
<z, z, z>() -> q_gen_1609
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 0  ;  () -> max([s(u), z, s(u)]) -> 3  ;  () -> max([z, y, y]) -> 3  ;  (leq([i, j]) /\ max([i, j, _qba])) -> eq_nat([_qba, j]) -> 1  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1  ;  (leq([s(nn1), z])) -> BOT -> 1  ;  (max([i, j, j])) -> leq([i, j]) -> 1  ;  (max([u, x2, _kba])) -> max([s(u), s(x2), s(_kba)]) -> 1
}
Sat witness: Yes: (() -> max([s(u), z, s(u)]), {
u -> z
})

-------------------------------------------
Step 2, which took 0.010501 s (model generation: 0.010389,  model checking: 0.000112):

Model:
|_
{
leq -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  max -> 
{{{
Q={q_gen_1609, q_gen_1611},
Q_f={q_gen_1609},
Delta=
{
<z, z>() -> q_gen_1611
<s, z, s>(q_gen_1611) -> q_gen_1609
<z, z, z>() -> q_gen_1609
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3  ;  () -> max([s(u), z, s(u)]) -> 3  ;  () -> max([z, y, y]) -> 3  ;  (leq([i, j]) /\ max([i, j, _qba])) -> eq_nat([_qba, j]) -> 1  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1  ;  (leq([s(nn1), z])) -> BOT -> 1  ;  (max([i, j, j])) -> leq([i, j]) -> 1  ;  (max([u, x2, _kba])) -> max([s(u), s(x2), s(_kba)]) -> 1
}
Sat witness: Yes: (() -> leq([z, n2]), {
n2 -> z
})

-------------------------------------------
Step 3, which took 0.011187 s (model generation: 0.010758,  model checking: 0.000429):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1612},
Q_f={q_gen_1612},
Delta=
{
<z, z>() -> q_gen_1612
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  max -> 
{{{
Q={q_gen_1609, q_gen_1611},
Q_f={q_gen_1609},
Delta=
{
<z, z>() -> q_gen_1611
<s, z, s>(q_gen_1611) -> q_gen_1609
<z, z, z>() -> q_gen_1609
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3  ;  () -> max([s(u), z, s(u)]) -> 3  ;  () -> max([z, y, y]) -> 3  ;  (leq([i, j]) /\ max([i, j, _qba])) -> eq_nat([_qba, j]) -> 1  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1  ;  (leq([s(nn1), z])) -> BOT -> 1  ;  (max([i, j, j])) -> leq([i, j]) -> 1  ;  (max([u, x2, _kba])) -> max([s(u), s(x2), s(_kba)]) -> 4
}
Sat witness: Yes: ((max([u, x2, _kba])) -> max([s(u), s(x2), s(_kba)]), {
_kba -> z  ;  u -> z  ;  x2 -> z
})

-------------------------------------------
Step 4, which took 0.011597 s (model generation: 0.011406,  model checking: 0.000191):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1612},
Q_f={q_gen_1612},
Delta=
{
<z, z>() -> q_gen_1612
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  max -> 
{{{
Q={q_gen_1609, q_gen_1611},
Q_f={q_gen_1609},
Delta=
{
<z, z>() -> q_gen_1611
<s, s, s>(q_gen_1609) -> q_gen_1609
<s, z, s>(q_gen_1611) -> q_gen_1609
<z, z, z>() -> q_gen_1609
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3  ;  () -> max([s(u), z, s(u)]) -> 3  ;  () -> max([z, y, y]) -> 3  ;  (leq([i, j]) /\ max([i, j, _qba])) -> eq_nat([_qba, j]) -> 1  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1  ;  (leq([s(nn1), z])) -> BOT -> 1  ;  (max([i, j, j])) -> leq([i, j]) -> 4  ;  (max([u, x2, _kba])) -> max([s(u), s(x2), s(_kba)]) -> 4
}
Sat witness: Yes: ((max([i, j, j])) -> leq([i, j]), {
i -> s(z)  ;  j -> s(z)
})

-------------------------------------------
Step 5, which took 0.012534 s (model generation: 0.011204,  model checking: 0.001330):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1612},
Q_f={q_gen_1612},
Delta=
{
<s, s>(q_gen_1612) -> q_gen_1612
<z, z>() -> q_gen_1612
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  max -> 
{{{
Q={q_gen_1609, q_gen_1611},
Q_f={q_gen_1609},
Delta=
{
<z, z>() -> q_gen_1611
<s, s, s>(q_gen_1609) -> q_gen_1609
<s, z, s>(q_gen_1611) -> q_gen_1609
<z, z, z>() -> q_gen_1609
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3  ;  () -> max([s(u), z, s(u)]) -> 3  ;  () -> max([z, y, y]) -> 6  ;  (leq([i, j]) /\ max([i, j, _qba])) -> eq_nat([_qba, j]) -> 2  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 2  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2  ;  (leq([s(nn1), z])) -> BOT -> 2  ;  (max([i, j, j])) -> leq([i, j]) -> 4  ;  (max([u, x2, _kba])) -> max([s(u), s(x2), s(_kba)]) -> 4
}
Sat witness: Yes: (() -> max([z, y, y]), {
y -> s(z)
})

-------------------------------------------
Step 6, which took 0.012017 s (model generation: 0.011527,  model checking: 0.000490):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1612},
Q_f={q_gen_1612},
Delta=
{
<s, s>(q_gen_1612) -> q_gen_1612
<z, z>() -> q_gen_1612
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  max -> 
{{{
Q={q_gen_1609, q_gen_1611},
Q_f={q_gen_1609},
Delta=
{
<z, z>() -> q_gen_1611
<s, s, s>(q_gen_1609) -> q_gen_1609
<s, z, s>(q_gen_1611) -> q_gen_1609
<z, s, s>(q_gen_1611) -> q_gen_1609
<z, z, z>() -> q_gen_1609
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3  ;  () -> max([s(u), z, s(u)]) -> 6  ;  () -> max([z, y, y]) -> 6  ;  (leq([i, j]) /\ max([i, j, _qba])) -> eq_nat([_qba, j]) -> 3  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 3  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 3  ;  (leq([s(nn1), z])) -> BOT -> 3  ;  (max([i, j, j])) -> leq([i, j]) -> 4  ;  (max([u, x2, _kba])) -> max([s(u), s(x2), s(_kba)]) -> 4
}
Sat witness: Yes: (() -> max([s(u), z, s(u)]), {
u -> s(z)
})

-------------------------------------------
Step 7, which took 0.012062 s (model generation: 0.011327,  model checking: 0.000735):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1612},
Q_f={q_gen_1612},
Delta=
{
<s, s>(q_gen_1612) -> q_gen_1612
<z, z>() -> q_gen_1612
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  max -> 
{{{
Q={q_gen_1609, q_gen_1611},
Q_f={q_gen_1609},
Delta=
{
<s, s>(q_gen_1611) -> q_gen_1611
<z, z>() -> q_gen_1611
<s, s, s>(q_gen_1609) -> q_gen_1609
<s, z, s>(q_gen_1611) -> q_gen_1609
<z, s, s>(q_gen_1611) -> q_gen_1609
<z, z, z>() -> q_gen_1609
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 6  ;  () -> max([s(u), z, s(u)]) -> 6  ;  () -> max([z, y, y]) -> 6  ;  (leq([i, j]) /\ max([i, j, _qba])) -> eq_nat([_qba, j]) -> 4  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4  ;  (leq([s(nn1), z])) -> BOT -> 4  ;  (max([i, j, j])) -> leq([i, j]) -> 4  ;  (max([u, x2, _kba])) -> max([s(u), s(x2), s(_kba)]) -> 4
}
Sat witness: Yes: (() -> leq([z, n2]), {
n2 -> s(z)
})

-------------------------------------------
Step 8, which took 0.008890 s (model generation: 0.008727,  model checking: 0.000163):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1612, q_gen_1619},
Q_f={q_gen_1612},
Delta=
{
<z>() -> q_gen_1619
<s, s>(q_gen_1612) -> q_gen_1612
<z, s>(q_gen_1619) -> q_gen_1612
<z, z>() -> q_gen_1612
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  max -> 
{{{
Q={q_gen_1609, q_gen_1611},
Q_f={q_gen_1609},
Delta=
{
<s, s>(q_gen_1611) -> q_gen_1611
<z, z>() -> q_gen_1611
<s, s, s>(q_gen_1609) -> q_gen_1609
<s, z, s>(q_gen_1611) -> q_gen_1609
<z, s, s>(q_gen_1611) -> q_gen_1609
<z, z, z>() -> q_gen_1609
}

Datatype: <nat, nat, nat>
Convolution form: complete
}}}

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 6  ;  () -> max([s(u), z, s(u)]) -> 6  ;  () -> max([z, y, y]) -> 6  ;  (leq([i, j]) /\ max([i, j, _qba])) -> eq_nat([_qba, j]) -> 4  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4  ;  (leq([s(nn1), z])) -> BOT -> 4  ;  (max([i, j, j])) -> leq([i, j]) -> 7  ;  (max([u, x2, _kba])) -> max([s(u), s(x2), s(_kba)]) -> 5
}
Sat witness: Yes: ((max([i, j, j])) -> leq([i, j]), {
i -> z  ;  j -> s(s(z))
})

Total time: 0.107053
Reason for stopping: Proved