Solving ../../benchmarks/false/append_length_le.smt2...

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


Learning problem is:

env: {
nat -> {s, z}  ;  natlist -> {cons, nil}
}
definition:
{
(append, F:
{() -> append([nil, l2, l2])
(append([t1, l2, _kma])) -> append([cons(h1, t1), l2, cons(h1, _kma)])}
(append([_lma, _mma, _nma]) /\ append([_lma, _mma, _oma])) -> eq_natlist([_nma, _oma])
)
(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}
)
(length, F:
{() -> length([nil, z])
(length([ll, _pma])) -> length([cons(x, ll), s(_pma)])}
(length([_qma, _rma]) /\ length([_qma, _sma])) -> eq_nat([_rma, _sma])
)
}

properties:
{(append([l1, l2, _uma]) /\ length([_uma, _vma]) /\ length([l1, _tma])) -> le([_tma, _vma])}


over-approximation: {append, length}
under-approximation: {le}

Clause system for inference is:

{
() -> append([nil, l2, l2]) -> 0
() -> le([z, s(nn2)]) -> 0
() -> length([nil, z]) -> 0
(append([l1, l2, _uma]) /\ length([_uma, _vma]) /\ length([l1, _tma])) -> le([_tma, _vma]) -> 0
(append([t1, l2, _kma])) -> append([cons(h1, t1), l2, cons(h1, _kma)]) -> 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
(length([ll, _pma])) -> length([cons(x, ll), s(_pma)]) -> 0
}


Solving took 0.097906 seconds.
Disproved
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.010291 s (model generation: 0.009819,  model checking: 0.000472):

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

}

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> le([z, s(nn2)]) -> 0
() -> length([nil, z]) -> 3
(append([l1, l2, _uma]) /\ length([_uma, _vma]) /\ length([l1, _tma])) -> le([_tma, _vma]) -> 1
(append([t1, l2, _kma])) -> append([cons(h1, t1), l2, cons(h1, _kma)]) -> 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
(length([ll, _pma])) -> length([cons(x, ll), s(_pma)]) -> 1
}
Sat witness: Found: (() -> length([nil, z]), {

})

-------------------------------------------
Step 1, which took 0.010507 s (model generation: 0.010389,  model checking: 0.000118):

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

}

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

}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6863},
Q_f={q_gen_6863},
Delta=
{
<nil, z>() -> q_gen_6863
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(append([l1, l2, _uma]) /\ length([_uma, _vma]) /\ length([l1, _tma])) -> le([_tma, _vma]) -> 1
(append([t1, l2, _kma])) -> append([cons(h1, t1), l2, cons(h1, _kma)]) -> 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
(length([ll, _pma])) -> length([cons(x, ll), s(_pma)]) -> 1
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 2, which took 0.010434 s (model generation: 0.010142,  model checking: 0.000292):

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

}

Datatype: <natlist, natlist, natlist>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_6864, q_gen_6865},
Q_f={q_gen_6864},
Delta=
{
<z>() -> q_gen_6865
<z, s>(q_gen_6865) -> q_gen_6864
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6863},
Q_f={q_gen_6863},
Delta=
{
<nil, z>() -> q_gen_6863
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(append([l1, l2, _uma]) /\ length([_uma, _vma]) /\ length([l1, _tma])) -> le([_tma, _vma]) -> 1
(append([t1, l2, _kma])) -> append([cons(h1, t1), l2, cons(h1, _kma)]) -> 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
(length([ll, _pma])) -> length([cons(x, ll), s(_pma)]) -> 1
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> nil
})

-------------------------------------------
Step 3, which took 0.010420 s (model generation: 0.010221,  model checking: 0.000199):

Model:
|_
{
append -> 
{{{
Q={q_gen_6866},
Q_f={q_gen_6866},
Delta=
{
<nil, nil, nil>() -> q_gen_6866
}

Datatype: <natlist, natlist, natlist>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_6864, q_gen_6865},
Q_f={q_gen_6864},
Delta=
{
<z>() -> q_gen_6865
<z, s>(q_gen_6865) -> q_gen_6864
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6863},
Q_f={q_gen_6863},
Delta=
{
<nil, z>() -> q_gen_6863
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(append([l1, l2, _uma]) /\ length([_uma, _vma]) /\ length([l1, _tma])) -> le([_tma, _vma]) -> 1
(append([t1, l2, _kma])) -> append([cons(h1, t1), l2, cons(h1, _kma)]) -> 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
(length([ll, _pma])) -> length([cons(x, ll), s(_pma)]) -> 4
}
Sat witness: Found: ((length([ll, _pma])) -> length([cons(x, ll), s(_pma)]), {
_pma -> z  ;  ll -> nil  ;  x -> z
})

-------------------------------------------
Step 4, which took 0.010891 s (model generation: 0.010653,  model checking: 0.000238):

Model:
|_
{
append -> 
{{{
Q={q_gen_6866},
Q_f={q_gen_6866},
Delta=
{
<nil, nil, nil>() -> q_gen_6866
}

Datatype: <natlist, natlist, natlist>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_6864, q_gen_6865},
Q_f={q_gen_6864},
Delta=
{
<z>() -> q_gen_6865
<z, s>(q_gen_6865) -> q_gen_6864
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6863, q_gen_6868},
Q_f={q_gen_6863},
Delta=
{
<z>() -> q_gen_6868
<cons, s>(q_gen_6868, q_gen_6863) -> q_gen_6863
<nil, z>() -> q_gen_6863
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(append([l1, l2, _uma]) /\ length([_uma, _vma]) /\ length([l1, _tma])) -> le([_tma, _vma]) -> 1
(append([t1, l2, _kma])) -> append([cons(h1, t1), l2, cons(h1, _kma)]) -> 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
(length([ll, _pma])) -> length([cons(x, ll), s(_pma)]) -> 4
}
Sat witness: Found: ((le([nn1, nn2])) -> le([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> s(z)
})

-------------------------------------------
Step 5, which took 0.011213 s (model generation: 0.010843,  model checking: 0.000370):

Model:
|_
{
append -> 
{{{
Q={q_gen_6866},
Q_f={q_gen_6866},
Delta=
{
<nil, nil, nil>() -> q_gen_6866
}

Datatype: <natlist, natlist, natlist>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_6864, q_gen_6865},
Q_f={q_gen_6864},
Delta=
{
<z>() -> q_gen_6865
<s, s>(q_gen_6864) -> q_gen_6864
<z, s>(q_gen_6865) -> q_gen_6864
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6863, q_gen_6868},
Q_f={q_gen_6863},
Delta=
{
<z>() -> q_gen_6868
<cons, s>(q_gen_6868, q_gen_6863) -> q_gen_6863
<nil, z>() -> q_gen_6863
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(append([l1, l2, _uma]) /\ length([_uma, _vma]) /\ length([l1, _tma])) -> le([_tma, _vma]) -> 1
(append([t1, l2, _kma])) -> append([cons(h1, t1), l2, cons(h1, _kma)]) -> 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
(length([ll, _pma])) -> length([cons(x, ll), s(_pma)]) -> 4
}
Sat witness: Found: ((append([t1, l2, _kma])) -> append([cons(h1, t1), l2, cons(h1, _kma)]), {
_kma -> nil  ;  h1 -> z  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 6, which took 0.011358 s (model generation: 0.011155,  model checking: 0.000203):

Model:
|_
{
append -> 
{{{
Q={q_gen_6866, q_gen_6871, q_gen_6872},
Q_f={q_gen_6866},
Delta=
{
<nil, nil>() -> q_gen_6871
<z, z>() -> q_gen_6872
<cons, nil, cons>(q_gen_6872, q_gen_6871) -> q_gen_6866
<nil, nil, nil>() -> q_gen_6866
}

Datatype: <natlist, natlist, natlist>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_6864, q_gen_6865},
Q_f={q_gen_6864},
Delta=
{
<z>() -> q_gen_6865
<s, s>(q_gen_6864) -> q_gen_6864
<z, s>(q_gen_6865) -> q_gen_6864
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6863, q_gen_6868},
Q_f={q_gen_6863},
Delta=
{
<z>() -> q_gen_6868
<cons, s>(q_gen_6868, q_gen_6863) -> q_gen_6863
<nil, z>() -> q_gen_6863
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(append([l1, l2, _uma]) /\ length([_uma, _vma]) /\ length([l1, _tma])) -> le([_tma, _vma]) -> 4
(append([t1, l2, _kma])) -> append([cons(h1, t1), l2, cons(h1, _kma)]) -> 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
(length([ll, _pma])) -> length([cons(x, ll), s(_pma)]) -> 4
}
Sat witness: Found: ((append([l1, l2, _uma]) /\ length([_uma, _vma]) /\ length([l1, _tma])) -> le([_tma, _vma]), {
_tma -> z  ;  _uma -> nil  ;  _vma -> z  ;  l1 -> nil  ;  l2 -> nil
})

-------------------------------------------
Step 7, which took 0.011548 s (model generation: 0.011517,  model checking: 0.000031):

Model:
|_
{
append -> 
{{{
Q={q_gen_6866, q_gen_6871, q_gen_6872},
Q_f={q_gen_6866},
Delta=
{
<nil, nil>() -> q_gen_6871
<z, z>() -> q_gen_6872
<cons, nil, cons>(q_gen_6872, q_gen_6871) -> q_gen_6866
<nil, nil, nil>() -> q_gen_6866
}

Datatype: <natlist, natlist, natlist>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_6864, q_gen_6865},
Q_f={q_gen_6864},
Delta=
{
<z>() -> q_gen_6865
<s, s>(q_gen_6864) -> q_gen_6864
<z, s>(q_gen_6865) -> q_gen_6864
<z, z>() -> q_gen_6864
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_6863, q_gen_6868},
Q_f={q_gen_6863},
Delta=
{
<z>() -> q_gen_6868
<cons, s>(q_gen_6868, q_gen_6863) -> q_gen_6863
<nil, z>() -> q_gen_6863
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(append([l1, l2, _uma]) /\ length([_uma, _vma]) /\ length([l1, _tma])) -> le([_tma, _vma]) -> 4
(append([t1, l2, _kma])) -> append([cons(h1, t1), l2, cons(h1, _kma)]) -> 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
(length([ll, _pma])) -> length([cons(x, ll), s(_pma)]) -> 4
}
Sat witness: Found: ((le([z, z])) -> BOT, {

})

Total time: 0.097906
Reason for stopping: Disproved