Solving ../../benchmarks/true/isaplanner_prop33.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}
)
(min, F:
{() -> min([s(u), z, z])
() -> min([z, y, z])
(min([u, y1, _im])) -> min([s(u), s(y1), s(_im)])}
(min([_jm, _km, _lm]) /\ min([_jm, _km, _mm])) -> eq_nat([_lm, _mm])
)
}

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


over-approximation: {min}
under-approximation: {}

Clause system for inference is:

{
() -> leq([z, n2]) -> 0  ;  () -> min([s(u), z, z]) -> 0  ;  () -> min([z, y, z]) -> 0  ;  (leq([i, j]) /\ min([i, j, _om])) -> eq_nat([_om, 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  ;  (min([i, j, i])) -> leq([i, j]) -> 0  ;  (min([u, y1, _im])) -> min([s(u), s(y1), s(_im)]) -> 0
}


Solving took 0.088576 seconds.
Proved
Model:
|_
{
leq -> 
{{{
Q={q_gen_1790, q_gen_1797},
Q_f={q_gen_1790},
Delta=
{
<s>(q_gen_1797) -> q_gen_1797
<z>() -> q_gen_1797
<s, s>(q_gen_1790) -> q_gen_1790
<z, s>(q_gen_1797) -> q_gen_1790
<z, z>() -> q_gen_1790
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  min -> 
{{{
Q={q_gen_1787, q_gen_1789},
Q_f={q_gen_1787},
Delta=
{
<s>(q_gen_1789) -> q_gen_1789
<z>() -> q_gen_1789
<s, s, s>(q_gen_1787) -> q_gen_1787
<s, z, z>(q_gen_1789) -> q_gen_1787
<z, s, z>(q_gen_1789) -> q_gen_1787
<z, z, z>() -> q_gen_1787
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.009980 s (model generation: 0.009506,  model checking: 0.000474):

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

}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  min -> 
{{{
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  ;  () -> min([s(u), z, z]) -> 0  ;  () -> min([z, y, z]) -> 3  ;  (leq([i, j]) /\ min([i, j, _om])) -> eq_nat([_om, 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  ;  (min([i, j, i])) -> leq([i, j]) -> 1  ;  (min([u, y1, _im])) -> min([s(u), s(y1), s(_im)]) -> 1
}
Sat witness: Yes: (() -> min([z, y, z]), {
y -> z
})

-------------------------------------------
Step 1, which took 0.007463 s (model generation: 0.007293,  model checking: 0.000170):

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

}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  min -> 
{{{
Q={q_gen_1787},
Q_f={q_gen_1787},
Delta=
{
<z, z, z>() -> q_gen_1787
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 0  ;  () -> min([s(u), z, z]) -> 3  ;  () -> min([z, y, z]) -> 3  ;  (leq([i, j]) /\ min([i, j, _om])) -> eq_nat([_om, 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  ;  (min([i, j, i])) -> leq([i, j]) -> 1  ;  (min([u, y1, _im])) -> min([s(u), s(y1), s(_im)]) -> 1
}
Sat witness: Yes: (() -> min([s(u), z, z]), {
u -> z
})

-------------------------------------------
Step 2, which took 0.007242 s (model generation: 0.007171,  model checking: 0.000071):

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

}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  min -> 
{{{
Q={q_gen_1787, q_gen_1789},
Q_f={q_gen_1787},
Delta=
{
<z>() -> q_gen_1789
<s, z, z>(q_gen_1789) -> q_gen_1787
<z, z, z>() -> q_gen_1787
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3  ;  () -> min([s(u), z, z]) -> 3  ;  () -> min([z, y, z]) -> 3  ;  (leq([i, j]) /\ min([i, j, _om])) -> eq_nat([_om, 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  ;  (min([i, j, i])) -> leq([i, j]) -> 1  ;  (min([u, y1, _im])) -> min([s(u), s(y1), s(_im)]) -> 1
}
Sat witness: Yes: (() -> leq([z, n2]), {
n2 -> z
})

-------------------------------------------
Step 3, which took 0.005094 s (model generation: 0.004956,  model checking: 0.000138):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1790},
Q_f={q_gen_1790},
Delta=
{
<z, z>() -> q_gen_1790
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  min -> 
{{{
Q={q_gen_1787, q_gen_1789},
Q_f={q_gen_1787},
Delta=
{
<z>() -> q_gen_1789
<s, z, z>(q_gen_1789) -> q_gen_1787
<z, z, z>() -> q_gen_1787
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3  ;  () -> min([s(u), z, z]) -> 3  ;  () -> min([z, y, z]) -> 3  ;  (leq([i, j]) /\ min([i, j, _om])) -> eq_nat([_om, 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  ;  (min([i, j, i])) -> leq([i, j]) -> 1  ;  (min([u, y1, _im])) -> min([s(u), s(y1), s(_im)]) -> 4
}
Sat witness: Yes: ((min([u, y1, _im])) -> min([s(u), s(y1), s(_im)]), {
_im -> z  ;  u -> z  ;  y1 -> z
})

-------------------------------------------
Step 4, which took 0.005599 s (model generation: 0.005412,  model checking: 0.000187):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1790},
Q_f={q_gen_1790},
Delta=
{
<z, z>() -> q_gen_1790
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  min -> 
{{{
Q={q_gen_1787, q_gen_1789},
Q_f={q_gen_1787},
Delta=
{
<z>() -> q_gen_1789
<s, s, s>(q_gen_1787) -> q_gen_1787
<s, z, z>(q_gen_1789) -> q_gen_1787
<z, z, z>() -> q_gen_1787
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3  ;  () -> min([s(u), z, z]) -> 3  ;  () -> min([z, y, z]) -> 3  ;  (leq([i, j]) /\ min([i, j, _om])) -> eq_nat([_om, 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  ;  (min([i, j, i])) -> leq([i, j]) -> 4  ;  (min([u, y1, _im])) -> min([s(u), s(y1), s(_im)]) -> 4
}
Sat witness: Yes: ((min([i, j, i])) -> leq([i, j]), {
i -> s(z)  ;  j -> s(z)
})

-------------------------------------------
Step 5, which took 0.005341 s (model generation: 0.004584,  model checking: 0.000757):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1790},
Q_f={q_gen_1790},
Delta=
{
<s, s>(q_gen_1790) -> q_gen_1790
<z, z>() -> q_gen_1790
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  min -> 
{{{
Q={q_gen_1787, q_gen_1789},
Q_f={q_gen_1787},
Delta=
{
<z>() -> q_gen_1789
<s, s, s>(q_gen_1787) -> q_gen_1787
<s, z, z>(q_gen_1789) -> q_gen_1787
<z, z, z>() -> q_gen_1787
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3  ;  () -> min([s(u), z, z]) -> 3  ;  () -> min([z, y, z]) -> 6  ;  (leq([i, j]) /\ min([i, j, _om])) -> eq_nat([_om, i]) -> 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  ;  (min([i, j, i])) -> leq([i, j]) -> 4  ;  (min([u, y1, _im])) -> min([s(u), s(y1), s(_im)]) -> 4
}
Sat witness: Yes: (() -> min([z, y, z]), {
y -> s(z)
})

-------------------------------------------
Step 6, which took 0.006204 s (model generation: 0.005813,  model checking: 0.000391):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1790},
Q_f={q_gen_1790},
Delta=
{
<s, s>(q_gen_1790) -> q_gen_1790
<z, z>() -> q_gen_1790
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  min -> 
{{{
Q={q_gen_1787, q_gen_1789},
Q_f={q_gen_1787},
Delta=
{
<z>() -> q_gen_1789
<s, s, s>(q_gen_1787) -> q_gen_1787
<s, z, z>(q_gen_1789) -> q_gen_1787
<z, s, z>(q_gen_1789) -> q_gen_1787
<z, z, z>() -> q_gen_1787
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3  ;  () -> min([s(u), z, z]) -> 6  ;  () -> min([z, y, z]) -> 6  ;  (leq([i, j]) /\ min([i, j, _om])) -> eq_nat([_om, i]) -> 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  ;  (min([i, j, i])) -> leq([i, j]) -> 4  ;  (min([u, y1, _im])) -> min([s(u), s(y1), s(_im)]) -> 4
}
Sat witness: Yes: (() -> min([s(u), z, z]), {
u -> s(z)
})

-------------------------------------------
Step 7, which took 0.011786 s (model generation: 0.011319,  model checking: 0.000467):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1790},
Q_f={q_gen_1790},
Delta=
{
<s, s>(q_gen_1790) -> q_gen_1790
<z, z>() -> q_gen_1790
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  min -> 
{{{
Q={q_gen_1787, q_gen_1789},
Q_f={q_gen_1787},
Delta=
{
<s>(q_gen_1789) -> q_gen_1789
<z>() -> q_gen_1789
<s, s, s>(q_gen_1787) -> q_gen_1787
<s, z, z>(q_gen_1789) -> q_gen_1787
<z, s, z>(q_gen_1789) -> q_gen_1787
<z, z, z>() -> q_gen_1787
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 6  ;  () -> min([s(u), z, z]) -> 6  ;  () -> min([z, y, z]) -> 6  ;  (leq([i, j]) /\ min([i, j, _om])) -> eq_nat([_om, 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  ;  (min([i, j, i])) -> leq([i, j]) -> 4  ;  (min([u, y1, _im])) -> min([s(u), s(y1), s(_im)]) -> 4
}
Sat witness: Yes: (() -> leq([z, n2]), {
n2 -> s(z)
})

-------------------------------------------
Step 8, which took 0.014555 s (model generation: 0.013114,  model checking: 0.001441):

Model:
|_
{
leq -> 
{{{
Q={q_gen_1790, q_gen_1797},
Q_f={q_gen_1790},
Delta=
{
<z>() -> q_gen_1797
<s, s>(q_gen_1790) -> q_gen_1790
<z, s>(q_gen_1797) -> q_gen_1790
<z, z>() -> q_gen_1790
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  min -> 
{{{
Q={q_gen_1787, q_gen_1789},
Q_f={q_gen_1787},
Delta=
{
<s>(q_gen_1789) -> q_gen_1789
<z>() -> q_gen_1789
<s, s, s>(q_gen_1787) -> q_gen_1787
<s, z, z>(q_gen_1789) -> q_gen_1787
<z, s, z>(q_gen_1789) -> q_gen_1787
<z, z, z>() -> q_gen_1787
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 6  ;  () -> min([s(u), z, z]) -> 6  ;  () -> min([z, y, z]) -> 6  ;  (leq([i, j]) /\ min([i, j, _om])) -> eq_nat([_om, 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  ;  (min([i, j, i])) -> leq([i, j]) -> 7  ;  (min([u, y1, _im])) -> min([s(u), s(y1), s(_im)]) -> 5
}
Sat witness: Yes: ((min([i, j, i])) -> leq([i, j]), {
i -> z  ;  j -> s(s(z))
})

Total time: 0.088576
Reason for stopping: Proved