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

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


Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(double, F:
{() -> double([z, z])
(double([nn, _yja])) -> double([s(nn), s(s(_yja))])}
(double([_zja, _aka]) /\ double([_zja, _bka])) -> eq_nat([_aka, _bka])
)
(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, _cka])) -> le([n, _cka])}


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

Clause system for inference is:

{
() -> double([z, z]) -> 0
() -> le([z, s(nn2)]) -> 0
(double([n, _cka])) -> le([n, _cka]) -> 0
(double([nn, _yja])) -> double([s(nn), s(s(_yja))]) -> 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 0.078052 seconds.
Disproved
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006498 s (model generation: 0.006267,  model checking: 0.000231):

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> double([z, z]) -> 0
() -> le([z, s(nn2)]) -> 3
(double([n, _cka])) -> le([n, _cka]) -> 1
(double([nn, _yja])) -> double([s(nn), s(s(_yja))]) -> 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 0.010103 s (model generation: 0.010013,  model checking: 0.000090):

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

}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_6721, q_gen_6722},
Q_f={q_gen_6721},
Delta=
{
<z>() -> q_gen_6722
<z, s>(q_gen_6722) -> q_gen_6721
}

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

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

Teacher's answer:
New clause system:
{
() -> double([z, z]) -> 3
() -> le([z, s(nn2)]) -> 3
(double([n, _cka])) -> le([n, _cka]) -> 1
(double([nn, _yja])) -> double([s(nn), s(s(_yja))]) -> 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 0.011485 s (model generation: 0.011187,  model checking: 0.000298):

Model:
|_
{
double -> 
{{{
Q={q_gen_6723},
Q_f={q_gen_6723},
Delta=
{
<z, z>() -> q_gen_6723
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_6721, q_gen_6722},
Q_f={q_gen_6721},
Delta=
{
<z>() -> q_gen_6722
<z, s>(q_gen_6722) -> q_gen_6721
}

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

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

Teacher's answer:
New clause system:
{
() -> double([z, z]) -> 3
() -> le([z, s(nn2)]) -> 3
(double([n, _cka])) -> le([n, _cka]) -> 1
(double([nn, _yja])) -> double([s(nn), s(s(_yja))]) -> 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 0.011182 s (model generation: 0.011046,  model checking: 0.000136):

Model:
|_
{
double -> 
{{{
Q={q_gen_6723},
Q_f={q_gen_6723},
Delta=
{
<z, z>() -> q_gen_6723
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_6721, q_gen_6722},
Q_f={q_gen_6721},
Delta=
{
<z>() -> q_gen_6722
<s, s>(q_gen_6721) -> q_gen_6721
<z, s>(q_gen_6722) -> q_gen_6721
}

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

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

Teacher's answer:
New clause system:
{
() -> double([z, z]) -> 3
() -> le([z, s(nn2)]) -> 3
(double([n, _cka])) -> le([n, _cka]) -> 1
(double([nn, _yja])) -> double([s(nn), s(s(_yja))]) -> 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, _yja])) -> double([s(nn), s(s(_yja))]), {
_yja -> z  ;  nn -> z
})

-------------------------------------------
Step 4, which took 0.016013 s (model generation: 0.011706,  model checking: 0.004307):

Model:
|_
{
double -> 
{{{
Q={q_gen_6723, q_gen_6727},
Q_f={q_gen_6723},
Delta=
{
<z>() -> q_gen_6727
<s, s>(q_gen_6723) -> q_gen_6723
<z, s>(q_gen_6727) -> q_gen_6723
<z, z>() -> q_gen_6723
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_6721, q_gen_6722},
Q_f={q_gen_6721},
Delta=
{
<z>() -> q_gen_6722
<s, s>(q_gen_6721) -> q_gen_6721
<z, s>(q_gen_6722) -> q_gen_6721
}

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

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

Teacher's answer:
New clause system:
{
() -> double([z, z]) -> 3
() -> le([z, s(nn2)]) -> 3
(double([n, _cka])) -> le([n, _cka]) -> 4
(double([nn, _yja])) -> double([s(nn), s(s(_yja))]) -> 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, _cka])) -> le([n, _cka]), {
_cka -> z  ;  n -> z
})

-------------------------------------------
Step 5, which took 0.011770 s (model generation: 0.011737,  model checking: 0.000033):

Model:
|_
{
double -> 
{{{
Q={q_gen_6723, q_gen_6727},
Q_f={q_gen_6723},
Delta=
{
<z>() -> q_gen_6727
<s, s>(q_gen_6723) -> q_gen_6723
<z, s>(q_gen_6727) -> q_gen_6723
<z, z>() -> q_gen_6723
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_6721, q_gen_6722},
Q_f={q_gen_6721},
Delta=
{
<z>() -> q_gen_6722
<s, s>(q_gen_6721) -> q_gen_6721
<z, s>(q_gen_6722) -> q_gen_6721
<z, z>() -> q_gen_6721
}

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

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

Teacher's answer:
New clause system:
{
() -> double([z, z]) -> 3
() -> le([z, s(nn2)]) -> 3
(double([n, _cka])) -> le([n, _cka]) -> 4
(double([nn, _yja])) -> double([s(nn), s(s(_yja))]) -> 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: 0.078052
Reason for stopping: Disproved