Solving ../../benchmarks/false/plus_le.smt2...

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


Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(plus, F:
{() -> plus([n, z, n])
(plus([n, mm, _sla])) -> plus([n, s(mm), s(_sla)])}
(plus([_tla, _ula, _vla]) /\ plus([_tla, _ula, _wla])) -> eq_nat([_vla, _wla])
)
(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:
{(plus([n, m, _xla])) -> le([n, _xla])}


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

Clause system for inference is:

{
() -> le([z, s(nn2)]) -> 0
() -> plus([n, z, n]) -> 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
(plus([n, m, _xla])) -> le([n, _xla]) -> 0
(plus([n, mm, _sla])) -> plus([n, s(mm), s(_sla)]) -> 0
}


Solving took 0.063447 seconds.
Disproved
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.010213 s (model generation: 0.009827,  model checking: 0.000386):

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 0
() -> plus([n, z, n]) -> 3
(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
(plus([n, m, _xla])) -> le([n, _xla]) -> 1
(plus([n, mm, _sla])) -> plus([n, s(mm), s(_sla)]) -> 1
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> z
})

-------------------------------------------
Step 1, which took 0.010222 s (model generation: 0.010102,  model checking: 0.000120):

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

}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6841},
Q_f={q_gen_6841},
Delta=
{
<z, z, z>() -> q_gen_6841
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 3
() -> plus([n, z, n]) -> 3
(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
(plus([n, m, _xla])) -> le([n, _xla]) -> 1
(plus([n, mm, _sla])) -> plus([n, s(mm), s(_sla)]) -> 1
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 2, which took 0.010371 s (model generation: 0.010183,  model checking: 0.000188):

Model:
|_
{
le -> 
{{{
Q={q_gen_6842, q_gen_6843},
Q_f={q_gen_6842},
Delta=
{
<z>() -> q_gen_6843
<z, s>(q_gen_6843) -> q_gen_6842
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6841},
Q_f={q_gen_6841},
Delta=
{
<z, z, z>() -> q_gen_6841
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 3
() -> plus([n, z, n]) -> 3
(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
(plus([n, m, _xla])) -> le([n, _xla]) -> 1
(plus([n, mm, _sla])) -> plus([n, s(mm), s(_sla)]) -> 4
}
Sat witness: Found: ((plus([n, mm, _sla])) -> plus([n, s(mm), s(_sla)]), {
_sla -> z  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 3, which took 0.011284 s (model generation: 0.010584,  model checking: 0.000700):

Model:
|_
{
le -> 
{{{
Q={q_gen_6842, q_gen_6843},
Q_f={q_gen_6842},
Delta=
{
<z>() -> q_gen_6843
<z, s>(q_gen_6843) -> q_gen_6842
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6841, q_gen_6845},
Q_f={q_gen_6841},
Delta=
{
<z, z>() -> q_gen_6845
<z, s, s>(q_gen_6845) -> q_gen_6841
<z, z, z>() -> q_gen_6841
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 3
() -> plus([n, z, n]) -> 3
(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
(plus([n, m, _xla])) -> le([n, _xla]) -> 4
(plus([n, mm, _sla])) -> plus([n, s(mm), s(_sla)]) -> 4
}
Sat witness: Found: ((plus([n, m, _xla])) -> le([n, _xla]), {
_xla -> z  ;  m -> z  ;  n -> z
})

-------------------------------------------
Step 4, which took 0.010627 s (model generation: 0.010600,  model checking: 0.000027):

Model:
|_
{
le -> 
{{{
Q={q_gen_6842, q_gen_6843},
Q_f={q_gen_6842},
Delta=
{
<z>() -> q_gen_6843
<z, s>(q_gen_6843) -> q_gen_6842
<z, z>() -> q_gen_6842
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_6841, q_gen_6845},
Q_f={q_gen_6841},
Delta=
{
<z, z>() -> q_gen_6845
<z, s, s>(q_gen_6845) -> q_gen_6841
<z, z, z>() -> q_gen_6841
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 3
() -> plus([n, z, n]) -> 3
(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 -> 4
(plus([n, m, _xla])) -> le([n, _xla]) -> 4
(plus([n, mm, _sla])) -> plus([n, s(mm), s(_sla)]) -> 4
}
Sat witness: Found: ((le([z, z])) -> BOT, {

})

Total time: 0.063447
Reason for stopping: Disproved