Solving ../../benchmarks/true/isaplanner_prop24.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, _xfa])) -> max([s(u), s(x2), s(_xfa)])}
(max([_yfa, _zfa, _aga]) /\ max([_yfa, _zfa, _bga])) -> eq_nat([_aga, _bga])
)
}

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


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([j, i]) /\ max([i, j, _dga])) -> eq_nat([_dga, i]) -> 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, i])) -> leq([j, i]) -> 0  ;  (max([u, x2, _xfa])) -> max([s(u), s(x2), s(_xfa)]) -> 0
}


Solving took 0.119161 seconds.
Proved
Model:
|_
{
leq -> 
{{{
Q={q_gen_1599, q_gen_1602},
Q_f={q_gen_1599},
Delta=
{
<s>(q_gen_1602) -> q_gen_1602
<z>() -> q_gen_1602
<s, s>(q_gen_1599) -> q_gen_1599
<z, s>(q_gen_1602) -> q_gen_1599
<z, z>() -> q_gen_1599
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  max -> 
{{{
Q={q_gen_1596, q_gen_1598},
Q_f={q_gen_1596},
Delta=
{
<s, s>(q_gen_1598) -> q_gen_1598
<z, z>() -> q_gen_1598
<s, s, s>(q_gen_1596) -> q_gen_1596
<s, z, s>(q_gen_1598) -> q_gen_1596
<z, s, s>(q_gen_1598) -> q_gen_1596
<z, z, z>() -> q_gen_1596
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.010025 s (model generation: 0.009334,  model checking: 0.000691):

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([j, i]) /\ max([i, j, _dga])) -> eq_nat([_dga, i]) -> 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, i])) -> leq([j, i]) -> 1  ;  (max([u, x2, _xfa])) -> max([s(u), s(x2), s(_xfa)]) -> 1
}
Sat witness: Yes: (() -> max([z, y, y]), {
y -> z
})

-------------------------------------------
Step 1, which took 0.010813 s (model generation: 0.010602,  model checking: 0.000211):

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

}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  max -> 
{{{
Q={q_gen_1596},
Q_f={q_gen_1596},
Delta=
{
<z, z, z>() -> q_gen_1596
}

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([j, i]) /\ max([i, j, _dga])) -> eq_nat([_dga, i]) -> 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, i])) -> leq([j, i]) -> 1  ;  (max([u, x2, _xfa])) -> max([s(u), s(x2), s(_xfa)]) -> 1
}
Sat witness: Yes: (() -> max([s(u), z, s(u)]), {
u -> z
})

-------------------------------------------
Step 2, which took 0.011413 s (model generation: 0.011296,  model checking: 0.000117):

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

}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  max -> 
{{{
Q={q_gen_1596, q_gen_1598},
Q_f={q_gen_1596},
Delta=
{
<z, z>() -> q_gen_1598
<s, z, s>(q_gen_1598) -> q_gen_1596
<z, z, z>() -> q_gen_1596
}

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([j, i]) /\ max([i, j, _dga])) -> eq_nat([_dga, i]) -> 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, i])) -> leq([j, i]) -> 1  ;  (max([u, x2, _xfa])) -> max([s(u), s(x2), s(_xfa)]) -> 1
}
Sat witness: Yes: (() -> leq([z, n2]), {
n2 -> z
})

-------------------------------------------
Step 3, which took 0.011483 s (model generation: 0.011181,  model checking: 0.000302):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1599},
Q_f={q_gen_1599},
Delta=
{
<z, z>() -> q_gen_1599
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  max -> 
{{{
Q={q_gen_1596, q_gen_1598},
Q_f={q_gen_1596},
Delta=
{
<z, z>() -> q_gen_1598
<s, z, s>(q_gen_1598) -> q_gen_1596
<z, z, z>() -> q_gen_1596
}

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([j, i]) /\ max([i, j, _dga])) -> eq_nat([_dga, i]) -> 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, i])) -> leq([j, i]) -> 1  ;  (max([u, x2, _xfa])) -> max([s(u), s(x2), s(_xfa)]) -> 4
}
Sat witness: Yes: ((max([u, x2, _xfa])) -> max([s(u), s(x2), s(_xfa)]), {
_xfa -> z  ;  u -> z  ;  x2 -> z
})

-------------------------------------------
Step 4, which took 0.012105 s (model generation: 0.011905,  model checking: 0.000200):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1599},
Q_f={q_gen_1599},
Delta=
{
<z, z>() -> q_gen_1599
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  max -> 
{{{
Q={q_gen_1596, q_gen_1598},
Q_f={q_gen_1596},
Delta=
{
<z, z>() -> q_gen_1598
<s, s, s>(q_gen_1596) -> q_gen_1596
<s, z, s>(q_gen_1598) -> q_gen_1596
<z, z, z>() -> q_gen_1596
}

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([j, i]) /\ max([i, j, _dga])) -> eq_nat([_dga, i]) -> 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, i])) -> leq([j, i]) -> 4  ;  (max([u, x2, _xfa])) -> max([s(u), s(x2), s(_xfa)]) -> 4
}
Sat witness: Yes: ((max([i, j, i])) -> leq([j, i]), {
i -> s(z)  ;  j -> z
})

-------------------------------------------
Step 5, which took 0.011597 s (model generation: 0.011353,  model checking: 0.000244):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1599, q_gen_1602},
Q_f={q_gen_1599},
Delta=
{
<z>() -> q_gen_1602
<z, s>(q_gen_1602) -> q_gen_1599
<z, z>() -> q_gen_1599
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  max -> 
{{{
Q={q_gen_1596, q_gen_1598},
Q_f={q_gen_1596},
Delta=
{
<z, z>() -> q_gen_1598
<s, s, s>(q_gen_1596) -> q_gen_1596
<s, z, s>(q_gen_1598) -> q_gen_1596
<z, z, z>() -> q_gen_1596
}

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([j, i]) /\ max([i, j, _dga])) -> eq_nat([_dga, i]) -> 1  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2  ;  (leq([s(nn1), z])) -> BOT -> 2  ;  (max([i, j, i])) -> leq([j, i]) -> 4  ;  (max([u, x2, _xfa])) -> max([s(u), s(x2), s(_xfa)]) -> 4
}
Sat witness: Yes: ((leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 6, which took 0.012981 s (model generation: 0.011432,  model checking: 0.001549):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1599, q_gen_1602},
Q_f={q_gen_1599},
Delta=
{
<z>() -> q_gen_1602
<s, s>(q_gen_1599) -> q_gen_1599
<z, s>(q_gen_1602) -> q_gen_1599
<z, z>() -> q_gen_1599
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  max -> 
{{{
Q={q_gen_1596, q_gen_1598},
Q_f={q_gen_1596},
Delta=
{
<z, z>() -> q_gen_1598
<s, s, s>(q_gen_1596) -> q_gen_1596
<s, z, s>(q_gen_1598) -> q_gen_1596
<z, z, z>() -> q_gen_1596
}

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([j, i]) /\ max([i, j, _dga])) -> eq_nat([_dga, i]) -> 2  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 3  ;  (leq([s(nn1), z])) -> BOT -> 3  ;  (max([i, j, i])) -> leq([j, i]) -> 4  ;  (max([u, x2, _xfa])) -> max([s(u), s(x2), s(_xfa)]) -> 4
}
Sat witness: Yes: (() -> max([z, y, y]), {
y -> s(z)
})

-------------------------------------------
Step 7, which took 0.012232 s (model generation: 0.011556,  model checking: 0.000676):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1599, q_gen_1602},
Q_f={q_gen_1599},
Delta=
{
<z>() -> q_gen_1602
<s, s>(q_gen_1599) -> q_gen_1599
<z, s>(q_gen_1602) -> q_gen_1599
<z, z>() -> q_gen_1599
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  max -> 
{{{
Q={q_gen_1596, q_gen_1598},
Q_f={q_gen_1596},
Delta=
{
<z, z>() -> q_gen_1598
<s, s, s>(q_gen_1596) -> q_gen_1596
<s, z, s>(q_gen_1598) -> q_gen_1596
<z, s, s>(q_gen_1598) -> q_gen_1596
<z, z, z>() -> q_gen_1596
}

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([j, i]) /\ max([i, j, _dga])) -> eq_nat([_dga, i]) -> 3  ;  (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, i])) -> leq([j, i]) -> 4  ;  (max([u, x2, _xfa])) -> max([s(u), s(x2), s(_xfa)]) -> 4
}
Sat witness: Yes: (() -> max([s(u), z, s(u)]), {
u -> s(z)
})

-------------------------------------------
Step 8, which took 0.012952 s (model generation: 0.012322,  model checking: 0.000630):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1599, q_gen_1602},
Q_f={q_gen_1599},
Delta=
{
<z>() -> q_gen_1602
<s, s>(q_gen_1599) -> q_gen_1599
<z, s>(q_gen_1602) -> q_gen_1599
<z, z>() -> q_gen_1599
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  max -> 
{{{
Q={q_gen_1596, q_gen_1598},
Q_f={q_gen_1596},
Delta=
{
<s, s>(q_gen_1598) -> q_gen_1598
<z, z>() -> q_gen_1598
<s, s, s>(q_gen_1596) -> q_gen_1596
<s, z, s>(q_gen_1598) -> q_gen_1596
<z, s, s>(q_gen_1598) -> q_gen_1596
<z, z, z>() -> q_gen_1596
}

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([j, i]) /\ max([i, j, _dga])) -> eq_nat([_dga, i]) -> 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, i])) -> leq([j, i]) -> 4  ;  (max([u, x2, _xfa])) -> max([s(u), s(x2), s(_xfa)]) -> 4
}
Sat witness: Yes: (() -> leq([z, n2]), {
n2 -> s(s(z))
})

Total time: 0.119161
Reason for stopping: Proved