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

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


Learning problem is:

env: {
nat -> {s, z}  ;  natlist -> {cons, nil}
}
definition:
{
(append, F:
{() -> append([nil, l2, l2])
(append([t1, l2, _wka])) -> append([cons(h1, t1), l2, cons(h1, _wka)])}
(append([_xka, _yka, _ala]) /\ append([_xka, _yka, _zka])) -> eq_natlist([_zka, _ala])
)
(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, _bla])) -> length([cons(x, ll), s(_bla)])}
(length([_cla, _dla]) /\ length([_cla, _ela])) -> eq_nat([_dla, _ela])
)
}

properties:
{(append([l1, l2, _gla]) /\ length([_gla, _hla]) /\ length([l1, _fla])) -> le([_fla, _hla])}


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, _gla]) /\ length([_gla, _hla]) /\ length([l1, _fla])) -> le([_fla, _hla]) -> 0
(append([t1, l2, _wka])) -> append([cons(h1, t1), l2, cons(h1, _wka)]) -> 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, _bla])) -> length([cons(x, ll), s(_bla)]) -> 0
}


Solving took 0.164853 seconds.
Disproved
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.017769 s (model generation: 0.016173,  model checking: 0.001596):

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

}

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

}

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

}

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

}
--
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, _gla]) /\ length([_gla, _hla]) /\ length([l1, _fla])) -> le([_fla, _hla]) -> 1
(append([t1, l2, _wka])) -> append([cons(h1, t1), l2, cons(h1, _wka)]) -> 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, _bla])) -> length([cons(x, ll), s(_bla)]) -> 1
}
Sat witness: Found: (() -> length([nil, z]), {

})

-------------------------------------------
Step 1, which took 0.016544 s (model generation: 0.016413,  model checking: 0.000131):

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

}

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

}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8998},
Q_f={q_gen_8998},
Delta=
{
<nil, z>() -> q_gen_8998
}

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

}
--
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, _gla]) /\ length([_gla, _hla]) /\ length([l1, _fla])) -> le([_fla, _hla]) -> 1
(append([t1, l2, _wka])) -> append([cons(h1, t1), l2, cons(h1, _wka)]) -> 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, _bla])) -> length([cons(x, ll), s(_bla)]) -> 1
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 2, which took 0.017406 s (model generation: 0.016973,  model checking: 0.000433):

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

}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_8999, q_gen_9000},
Q_f={q_gen_8999},
Delta=
{
<z>() -> q_gen_9000
<z, s>(q_gen_9000) -> q_gen_8999
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8998},
Q_f={q_gen_8998},
Delta=
{
<nil, z>() -> q_gen_8998
}

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

}
--
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, _gla]) /\ length([_gla, _hla]) /\ length([l1, _fla])) -> le([_fla, _hla]) -> 1
(append([t1, l2, _wka])) -> append([cons(h1, t1), l2, cons(h1, _wka)]) -> 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, _bla])) -> length([cons(x, ll), s(_bla)]) -> 1
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> nil
})

-------------------------------------------
Step 3, which took 0.017633 s (model generation: 0.017412,  model checking: 0.000221):

Model:
|_
{
append -> 
{{{
Q={q_gen_9001},
Q_f={q_gen_9001},
Delta=
{
<nil, nil, nil>() -> q_gen_9001
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_8999, q_gen_9000},
Q_f={q_gen_8999},
Delta=
{
<z>() -> q_gen_9000
<z, s>(q_gen_9000) -> q_gen_8999
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8998},
Q_f={q_gen_8998},
Delta=
{
<nil, z>() -> q_gen_8998
}

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

}
--
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, _gla]) /\ length([_gla, _hla]) /\ length([l1, _fla])) -> le([_fla, _hla]) -> 1
(append([t1, l2, _wka])) -> append([cons(h1, t1), l2, cons(h1, _wka)]) -> 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, _bla])) -> length([cons(x, ll), s(_bla)]) -> 4
}
Sat witness: Found: ((length([ll, _bla])) -> length([cons(x, ll), s(_bla)]), {
_bla -> z  ;  ll -> nil  ;  x -> z
})

-------------------------------------------
Step 4, which took 0.018355 s (model generation: 0.018089,  model checking: 0.000266):

Model:
|_
{
append -> 
{{{
Q={q_gen_9001},
Q_f={q_gen_9001},
Delta=
{
<nil, nil, nil>() -> q_gen_9001
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_8999, q_gen_9000},
Q_f={q_gen_8999},
Delta=
{
<z>() -> q_gen_9000
<z, s>(q_gen_9000) -> q_gen_8999
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8998, q_gen_9003, q_gen_9004},
Q_f={q_gen_8998},
Delta=
{
<nil>() -> q_gen_9003
<cons, s>(q_gen_9004, q_gen_9003) -> q_gen_8998
<nil, z>() -> q_gen_8998
<z, z>() -> q_gen_9004
}

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

}
--
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, _gla]) /\ length([_gla, _hla]) /\ length([l1, _fla])) -> le([_fla, _hla]) -> 1
(append([t1, l2, _wka])) -> append([cons(h1, t1), l2, cons(h1, _wka)]) -> 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, _bla])) -> length([cons(x, ll), s(_bla)]) -> 4
}
Sat witness: Found: ((le([nn1, nn2])) -> le([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> s(z)
})

-------------------------------------------
Step 5, which took 0.019356 s (model generation: 0.018942,  model checking: 0.000414):

Model:
|_
{
append -> 
{{{
Q={q_gen_9001},
Q_f={q_gen_9001},
Delta=
{
<nil, nil, nil>() -> q_gen_9001
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_8999, q_gen_9000},
Q_f={q_gen_8999},
Delta=
{
<z>() -> q_gen_9000
<s, s>(q_gen_8999) -> q_gen_8999
<z, s>(q_gen_9000) -> q_gen_8999
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8998, q_gen_9003, q_gen_9004},
Q_f={q_gen_8998},
Delta=
{
<nil>() -> q_gen_9003
<cons, s>(q_gen_9004, q_gen_9003) -> q_gen_8998
<nil, z>() -> q_gen_8998
<z, z>() -> q_gen_9004
}

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

}
--
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, _gla]) /\ length([_gla, _hla]) /\ length([l1, _fla])) -> le([_fla, _hla]) -> 1
(append([t1, l2, _wka])) -> append([cons(h1, t1), l2, cons(h1, _wka)]) -> 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, _bla])) -> length([cons(x, ll), s(_bla)]) -> 4
}
Sat witness: Found: ((append([t1, l2, _wka])) -> append([cons(h1, t1), l2, cons(h1, _wka)]), {
_wka -> nil  ;  h1 -> z  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 6, which took 0.019114 s (model generation: 0.018897,  model checking: 0.000217):

Model:
|_
{
append -> 
{{{
Q={q_gen_9001, q_gen_9007, q_gen_9008},
Q_f={q_gen_9001},
Delta=
{
<nil, nil>() -> q_gen_9007
<z, z>() -> q_gen_9008
<cons, nil, cons>(q_gen_9008, q_gen_9007) -> q_gen_9001
<nil, nil, nil>() -> q_gen_9001
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_8999, q_gen_9000},
Q_f={q_gen_8999},
Delta=
{
<z>() -> q_gen_9000
<s, s>(q_gen_8999) -> q_gen_8999
<z, s>(q_gen_9000) -> q_gen_8999
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8998, q_gen_9003, q_gen_9004},
Q_f={q_gen_8998},
Delta=
{
<nil>() -> q_gen_9003
<cons, s>(q_gen_9004, q_gen_9003) -> q_gen_8998
<nil, z>() -> q_gen_8998
<z, z>() -> q_gen_9004
}

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

}
--
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, _gla]) /\ length([_gla, _hla]) /\ length([l1, _fla])) -> le([_fla, _hla]) -> 4
(append([t1, l2, _wka])) -> append([cons(h1, t1), l2, cons(h1, _wka)]) -> 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, _bla])) -> length([cons(x, ll), s(_bla)]) -> 4
}
Sat witness: Found: ((append([l1, l2, _gla]) /\ length([_gla, _hla]) /\ length([l1, _fla])) -> le([_fla, _hla]), {
_fla -> z  ;  _gla -> nil  ;  _hla -> z  ;  l1 -> nil  ;  l2 -> nil
})

-------------------------------------------
Step 7, which took 0.020088 s (model generation: 0.020054,  model checking: 0.000034):

Model:
|_
{
append -> 
{{{
Q={q_gen_9001, q_gen_9007, q_gen_9008},
Q_f={q_gen_9001},
Delta=
{
<nil, nil>() -> q_gen_9007
<z, z>() -> q_gen_9008
<cons, nil, cons>(q_gen_9008, q_gen_9007) -> q_gen_9001
<nil, nil, nil>() -> q_gen_9001
}

Datatype: <natlist, natlist, natlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_8999, q_gen_9000},
Q_f={q_gen_8999},
Delta=
{
<z>() -> q_gen_9000
<s, s>(q_gen_8999) -> q_gen_8999
<z, s>(q_gen_9000) -> q_gen_8999
<z, z>() -> q_gen_8999
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_8998, q_gen_9003, q_gen_9004},
Q_f={q_gen_8998},
Delta=
{
<nil>() -> q_gen_9003
<cons, s>(q_gen_9004, q_gen_9003) -> q_gen_8998
<nil, z>() -> q_gen_8998
<z, z>() -> q_gen_9004
}

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

}
--
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, _gla]) /\ length([_gla, _hla]) /\ length([l1, _fla])) -> le([_fla, _hla]) -> 4
(append([t1, l2, _wka])) -> append([cons(h1, t1), l2, cons(h1, _wka)]) -> 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, _bla])) -> length([cons(x, ll), s(_bla)]) -> 4
}
Sat witness: Found: ((le([z, z])) -> BOT, {

})

Total time: 0.164853
Reason for stopping: Disproved