Inference procedure has parameters:
Ice fuel: 200
Timeout: 60s
Convolution: left


Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(min, F:
{() -> min([s(u), z, z])
() -> min([z, y, z])
(min([u, y1, _qb])) -> min([s(u), s(y1), s(_qb)])}
(min([_rb, _sb, _tb]) /\ min([_rb, _sb, _ub])) -> eq_nat([_tb, _ub])
)
}

properties:
{(min([_vb, c, _wb]) /\ min([a, _xb, _yb]) /\ min([a, b, _vb]) /\ min([b, c, _xb])) -> eq_nat([_wb, _yb])}


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

Clause system for inference is:

{
() -> min([s(u), z, z]) -> 0
() -> min([z, y, z]) -> 0
(min([_vb, c, _wb]) /\ min([a, _xb, _yb]) /\ min([a, b, _vb]) /\ min([b, c, _xb])) -> eq_nat([_wb, _yb]) -> 0
(min([u, y1, _qb])) -> min([s(u), s(y1), s(_qb)]) -> 0
}


Solving took 0.046555 seconds.
Proved
Model:
|_
{
min -> 
{{{
Q={q_gen_602, q_gen_604},
Q_f={q_gen_602},
Delta=
{
<s>(q_gen_604) -> q_gen_604
<z>() -> q_gen_604
<s, s, s>(q_gen_602) -> q_gen_602
<s, z, z>(q_gen_604) -> q_gen_602
<z, s, z>(q_gen_604) -> q_gen_602
<z, z, z>() -> q_gen_602
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.007751 s (model generation: 0.007575,  model checking: 0.000176):

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

}

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

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

Teacher's answer:
New clause system:
{
() -> min([s(u), z, z]) -> 0
() -> min([z, y, z]) -> 3
(min([_vb, c, _wb]) /\ min([a, _xb, _yb]) /\ min([a, b, _vb]) /\ min([b, c, _xb])) -> eq_nat([_wb, _yb]) -> 1
(min([u, y1, _qb])) -> min([s(u), s(y1), s(_qb)]) -> 1
}
Sat witness: Found: (() -> min([z, y, z]), {
y -> z
})

-------------------------------------------
Step 1, which took 0.008159 s (model generation: 0.008063,  model checking: 0.000096):

Model:
|_
{
min -> 
{{{
Q={q_gen_602},
Q_f={q_gen_602},
Delta=
{
<z, z, z>() -> q_gen_602
}

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

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

Teacher's answer:
New clause system:
{
() -> min([s(u), z, z]) -> 3
() -> min([z, y, z]) -> 3
(min([_vb, c, _wb]) /\ min([a, _xb, _yb]) /\ min([a, b, _vb]) /\ min([b, c, _xb])) -> eq_nat([_wb, _yb]) -> 1
(min([u, y1, _qb])) -> min([s(u), s(y1), s(_qb)]) -> 1
}
Sat witness: Found: (() -> min([s(u), z, z]), {
u -> z
})

-------------------------------------------
Step 2, which took 0.007805 s (model generation: 0.007646,  model checking: 0.000159):

Model:
|_
{
min -> 
{{{
Q={q_gen_602, q_gen_604},
Q_f={q_gen_602},
Delta=
{
<z>() -> q_gen_604
<s, z, z>(q_gen_604) -> q_gen_602
<z, z, z>() -> q_gen_602
}

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

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

Teacher's answer:
New clause system:
{
() -> min([s(u), z, z]) -> 3
() -> min([z, y, z]) -> 3
(min([_vb, c, _wb]) /\ min([a, _xb, _yb]) /\ min([a, b, _vb]) /\ min([b, c, _xb])) -> eq_nat([_wb, _yb]) -> 1
(min([u, y1, _qb])) -> min([s(u), s(y1), s(_qb)]) -> 4
}
Sat witness: Found: ((min([u, y1, _qb])) -> min([s(u), s(y1), s(_qb)]), {
_qb -> z  ;  u -> z  ;  y1 -> z
})

-------------------------------------------
Step 3, which took 0.007601 s (model generation: 0.007405,  model checking: 0.000196):

Model:
|_
{
min -> 
{{{
Q={q_gen_602, q_gen_604},
Q_f={q_gen_602},
Delta=
{
<z>() -> q_gen_604
<s, s, s>(q_gen_602) -> q_gen_602
<s, z, z>(q_gen_604) -> q_gen_602
<z, z, z>() -> q_gen_602
}

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

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

Teacher's answer:
New clause system:
{
() -> min([s(u), z, z]) -> 3
() -> min([z, y, z]) -> 6
(min([_vb, c, _wb]) /\ min([a, _xb, _yb]) /\ min([a, b, _vb]) /\ min([b, c, _xb])) -> eq_nat([_wb, _yb]) -> 2
(min([u, y1, _qb])) -> min([s(u), s(y1), s(_qb)]) -> 4
}
Sat witness: Found: (() -> min([z, y, z]), {
y -> s(s(z))
})

Total time: 0.046555
Reason for stopping: Proved