Solving ../../benchmarks/false/nat_double_is_le.smt2...

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


Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(double, F:
{() -> double([z, z])
(double([nn, _rka])) -> double([s(nn), s(s(_rka))])}
(double([_ska, _tka]) /\ double([_ska, _uka])) -> eq_nat([_tka, _uka])
)
(le, P:
{() -> le([z, s(nn2)])
(le([nn1, nn2])) -> le([s(nn1), s(nn2)])
(le([s(nn1), s(nn2)])) -> le([nn1, nn2])
(le([s(nn1), z])) -> BOT
(le([z, z])) -> BOT}
)
}

properties:
{(double([n, _vka])) -> le([n, _vka])}


over-approximation: {double}
under-approximation: {le}

Clause system for inference is:

{
() -> double([z, z]) -> 0
() -> le([z, s(nn2)]) -> 0
(double([n, _vka])) -> le([n, _vka]) -> 0
(double([nn, _rka])) -> double([s(nn), s(s(_rka))]) -> 0
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 0
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 0
(le([s(nn1), z])) -> BOT -> 0
(le([z, z])) -> BOT -> 0
}


Solving took 0.122949 seconds.
Disproved
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.016200 s (model generation: 0.015927,  model checking: 0.000273):

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> double([z, z]) -> 0
() -> le([z, s(nn2)]) -> 3
(double([n, _vka])) -> le([n, _vka]) -> 1
(double([nn, _rka])) -> double([s(nn), s(s(_rka))]) -> 1
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 1
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 1
(le([s(nn1), z])) -> BOT -> 1
(le([z, z])) -> BOT -> 1
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 1, which took 0.017226 s (model generation: 0.017133,  model checking: 0.000093):

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

}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_8990, q_gen_8991},
Q_f={q_gen_8990},
Delta=
{
<z>() -> q_gen_8991
<z, s>(q_gen_8991) -> q_gen_8990
}

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

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

Teacher's answer:
New clause system:
{
() -> double([z, z]) -> 3
() -> le([z, s(nn2)]) -> 3
(double([n, _vka])) -> le([n, _vka]) -> 1
(double([nn, _rka])) -> double([s(nn), s(s(_rka))]) -> 1
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 1
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 1
(le([s(nn1), z])) -> BOT -> 1
(le([z, z])) -> BOT -> 1
}
Sat witness: Found: (() -> double([z, z]), {

})

-------------------------------------------
Step 2, which took 0.016570 s (model generation: 0.016307,  model checking: 0.000263):

Model:
|_
{
double -> 
{{{
Q={q_gen_8992},
Q_f={q_gen_8992},
Delta=
{
<z, z>() -> q_gen_8992
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_8990, q_gen_8991},
Q_f={q_gen_8990},
Delta=
{
<z>() -> q_gen_8991
<z, s>(q_gen_8991) -> q_gen_8990
}

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

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

Teacher's answer:
New clause system:
{
() -> double([z, z]) -> 3
() -> le([z, s(nn2)]) -> 3
(double([n, _vka])) -> le([n, _vka]) -> 1
(double([nn, _rka])) -> double([s(nn), s(s(_rka))]) -> 1
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 2
(le([s(nn1), z])) -> BOT -> 2
(le([z, z])) -> BOT -> 2
}
Sat witness: Found: ((le([nn1, nn2])) -> le([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> s(z)
})

-------------------------------------------
Step 3, which took 0.017525 s (model generation: 0.017374,  model checking: 0.000151):

Model:
|_
{
double -> 
{{{
Q={q_gen_8992},
Q_f={q_gen_8992},
Delta=
{
<z, z>() -> q_gen_8992
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_8990, q_gen_8991},
Q_f={q_gen_8990},
Delta=
{
<z>() -> q_gen_8991
<s, s>(q_gen_8990) -> q_gen_8990
<z, s>(q_gen_8991) -> q_gen_8990
}

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

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

Teacher's answer:
New clause system:
{
() -> double([z, z]) -> 3
() -> le([z, s(nn2)]) -> 3
(double([n, _vka])) -> le([n, _vka]) -> 1
(double([nn, _rka])) -> double([s(nn), s(s(_rka))]) -> 4
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 2
(le([s(nn1), z])) -> BOT -> 2
(le([z, z])) -> BOT -> 2
}
Sat witness: Found: ((double([nn, _rka])) -> double([s(nn), s(s(_rka))]), {
_rka -> z  ;  nn -> z
})

-------------------------------------------
Step 4, which took 0.018238 s (model generation: 0.018074,  model checking: 0.000164):

Model:
|_
{
double -> 
{{{
Q={q_gen_8992, q_gen_8996},
Q_f={q_gen_8992},
Delta=
{
<z>() -> q_gen_8996
<s, s>(q_gen_8992) -> q_gen_8992
<z, s>(q_gen_8996) -> q_gen_8992
<z, z>() -> q_gen_8992
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_8990, q_gen_8991},
Q_f={q_gen_8990},
Delta=
{
<z>() -> q_gen_8991
<s, s>(q_gen_8990) -> q_gen_8990
<z, s>(q_gen_8991) -> q_gen_8990
}

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

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

Teacher's answer:
New clause system:
{
() -> double([z, z]) -> 3
() -> le([z, s(nn2)]) -> 3
(double([n, _vka])) -> le([n, _vka]) -> 4
(double([nn, _rka])) -> double([s(nn), s(s(_rka))]) -> 4
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 2
(le([s(nn1), z])) -> BOT -> 2
(le([z, z])) -> BOT -> 2
}
Sat witness: Found: ((double([n, _vka])) -> le([n, _vka]), {
_vka -> z  ;  n -> z
})

-------------------------------------------
Step 5, which took 0.018933 s (model generation: 0.018899,  model checking: 0.000034):

Model:
|_
{
double -> 
{{{
Q={q_gen_8992, q_gen_8996},
Q_f={q_gen_8992},
Delta=
{
<z>() -> q_gen_8996
<s, s>(q_gen_8992) -> q_gen_8992
<z, s>(q_gen_8996) -> q_gen_8992
<z, z>() -> q_gen_8992
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_8990, q_gen_8991},
Q_f={q_gen_8990},
Delta=
{
<z>() -> q_gen_8991
<s, s>(q_gen_8990) -> q_gen_8990
<z, s>(q_gen_8991) -> q_gen_8990
<z, z>() -> q_gen_8990
}

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

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

Teacher's answer:
New clause system:
{
() -> double([z, z]) -> 3
() -> le([z, s(nn2)]) -> 3
(double([n, _vka])) -> le([n, _vka]) -> 4
(double([nn, _rka])) -> double([s(nn), s(s(_rka))]) -> 4
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 2
(le([s(nn1), z])) -> BOT -> 2
(le([z, z])) -> BOT -> 5
}
Sat witness: Found: ((le([z, z])) -> BOT, {

})

Total time: 0.122949
Reason for stopping: Disproved