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

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


Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(plus, F:
{() -> plus([n, z, n])
(plus([n, mm, _cja])) -> plus([n, s(mm), s(_cja)])}
(plus([_dja, _eja, _fja]) /\ plus([_dja, _eja, _gja])) -> eq_nat([_fja, _gja])
)
(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, _hja])) -> le([n, _hja])}


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, _hja])) -> le([n, _hja]) -> 0
(plus([n, mm, _cja])) -> plus([n, s(mm), s(_cja)]) -> 0
}


Solving took 0.108536 seconds.
Disproved
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.017101 s (model generation: 0.016717,  model checking: 0.000384):

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

}

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

}

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

}
--
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, _hja])) -> le([n, _hja]) -> 1
(plus([n, mm, _cja])) -> plus([n, s(mm), s(_cja)]) -> 1
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> z
})

-------------------------------------------
Step 1, which took 0.016405 s (model generation: 0.016279,  model checking: 0.000126):

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

}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_8914},
Q_f={q_gen_8914},
Delta=
{
<z, z, z>() -> q_gen_8914
}

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

}
--
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, _hja])) -> le([n, _hja]) -> 1
(plus([n, mm, _cja])) -> plus([n, s(mm), s(_cja)]) -> 1
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 2, which took 0.021276 s (model generation: 0.016616,  model checking: 0.004660):

Model:
|_
{
le -> 
{{{
Q={q_gen_8915, q_gen_8916},
Q_f={q_gen_8915},
Delta=
{
<z>() -> q_gen_8916
<z, s>(q_gen_8916) -> q_gen_8915
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_8914},
Q_f={q_gen_8914},
Delta=
{
<z, z, z>() -> q_gen_8914
}

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

}
--
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, _hja])) -> le([n, _hja]) -> 1
(plus([n, mm, _cja])) -> plus([n, s(mm), s(_cja)]) -> 4
}
Sat witness: Found: ((plus([n, mm, _cja])) -> plus([n, s(mm), s(_cja)]), {
_cja -> z  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 3, which took 0.017820 s (model generation: 0.017654,  model checking: 0.000166):

Model:
|_
{
le -> 
{{{
Q={q_gen_8915, q_gen_8916},
Q_f={q_gen_8915},
Delta=
{
<z>() -> q_gen_8916
<z, s>(q_gen_8916) -> q_gen_8915
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_8914, q_gen_8918},
Q_f={q_gen_8914},
Delta=
{
<z, z>() -> q_gen_8918
<z, s, s>(q_gen_8918) -> q_gen_8914
<z, z, z>() -> q_gen_8914
}

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

}
--
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, _hja])) -> le([n, _hja]) -> 4
(plus([n, mm, _cja])) -> plus([n, s(mm), s(_cja)]) -> 4
}
Sat witness: Found: ((plus([n, m, _hja])) -> le([n, _hja]), {
_hja -> z  ;  m -> z  ;  n -> z
})

-------------------------------------------
Step 4, which took 0.018464 s (model generation: 0.018431,  model checking: 0.000033):

Model:
|_
{
le -> 
{{{
Q={q_gen_8915, q_gen_8916},
Q_f={q_gen_8915},
Delta=
{
<z>() -> q_gen_8916
<z, s>(q_gen_8916) -> q_gen_8915
<z, z>() -> q_gen_8915
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_8914, q_gen_8918},
Q_f={q_gen_8914},
Delta=
{
<z, z>() -> q_gen_8918
<z, s, s>(q_gen_8918) -> q_gen_8914
<z, z, z>() -> q_gen_8914
}

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

}
--
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, _hja])) -> le([n, _hja]) -> 4
(plus([n, mm, _cja])) -> plus([n, s(mm), s(_cja)]) -> 4
}
Sat witness: Found: ((le([z, z])) -> BOT, {

})

Total time: 0.108536
Reason for stopping: Disproved