Solving ../../benchmarks/true/isaplanner_prop69.smt2...

Inference procedure has parameters:
Ice fuel: 200
Timeout: 30s
Convolution: complete


Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(plus, F:
{() -> plus([n, z, n])
(plus([n, mm, _pj])) -> plus([n, s(mm), s(_pj)])}
(plus([_qj, _rj, _sj]) /\ plus([_qj, _rj, _tj])) -> eq_nat([_sj, _tj])
)
(leq, P:
{() -> leq([z, n2])
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)])
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2])
(leq([s(nn1), z])) -> BOT}
)
}

properties:
{(plus([n, m, _uj])) -> leq([n, _uj])}


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

Clause system for inference is:

{
() -> leq([z, n2]) -> 0  ;  () -> plus([n, z, n]) -> 0  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 0  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 0  ;  (leq([s(nn1), z])) -> BOT -> 0  ;  (plus([n, m, _uj])) -> leq([n, _uj]) -> 0  ;  (plus([n, mm, _pj])) -> plus([n, s(mm), s(_pj)]) -> 0
}


Solving took 0.120055 seconds.
Proved
Model:
|_
{
leq -> 
{{{
Q={q_gen_2768, q_gen_2772},
Q_f={q_gen_2768},
Delta=
{
<s>(q_gen_2772) -> q_gen_2772
<z>() -> q_gen_2772
<s, s>(q_gen_2768) -> q_gen_2768
<z, s>(q_gen_2772) -> q_gen_2768
<z, z>() -> q_gen_2768
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2767, q_gen_2770, q_gen_2779},
Q_f={q_gen_2767},
Delta=
{
<s>(q_gen_2779) -> q_gen_2779
<z>() -> q_gen_2779
<s, s>(q_gen_2770) -> q_gen_2770
<z, s>(q_gen_2779) -> q_gen_2770
<z, z>() -> q_gen_2770
<s, s, s>(q_gen_2767) -> q_gen_2767
<s, z, s>(q_gen_2770) -> q_gen_2767
<z, s, s>(q_gen_2770) -> q_gen_2767
<z, z, s>(q_gen_2779) -> q_gen_2767
<z, z, z>() -> q_gen_2767
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.010518 s (model generation: 0.010032,  model checking: 0.000486):

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 0  ;  () -> plus([n, z, n]) -> 3  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1  ;  (leq([s(nn1), z])) -> BOT -> 1  ;  (plus([n, m, _uj])) -> leq([n, _uj]) -> 1  ;  (plus([n, mm, _pj])) -> plus([n, s(mm), s(_pj)]) -> 1
}
Sat witness: Yes: (() -> plus([n, z, n]), {
n -> z
})

-------------------------------------------
Step 1, which took 0.004961 s (model generation: 0.004931,  model checking: 0.000030):

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

}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2767},
Q_f={q_gen_2767},
Delta=
{
<z, z, z>() -> q_gen_2767
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3  ;  () -> plus([n, z, n]) -> 3  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1  ;  (leq([s(nn1), z])) -> BOT -> 1  ;  (plus([n, m, _uj])) -> leq([n, _uj]) -> 1  ;  (plus([n, mm, _pj])) -> plus([n, s(mm), s(_pj)]) -> 1
}
Sat witness: Yes: (() -> leq([z, n2]), {
n2 -> z
})

-------------------------------------------
Step 2, which took 0.003154 s (model generation: 0.003095,  model checking: 0.000059):

Model:
|_
{
leq -> 
{{{
Q={q_gen_2768},
Q_f={q_gen_2768},
Delta=
{
<z, z>() -> q_gen_2768
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2767},
Q_f={q_gen_2767},
Delta=
{
<z, z, z>() -> q_gen_2767
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3  ;  () -> plus([n, z, n]) -> 3  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1  ;  (leq([s(nn1), z])) -> BOT -> 1  ;  (plus([n, m, _uj])) -> leq([n, _uj]) -> 1  ;  (plus([n, mm, _pj])) -> plus([n, s(mm), s(_pj)]) -> 4
}
Sat witness: Yes: ((plus([n, mm, _pj])) -> plus([n, s(mm), s(_pj)]), {
_pj -> z  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 3, which took 0.003612 s (model generation: 0.003561,  model checking: 0.000051):

Model:
|_
{
leq -> 
{{{
Q={q_gen_2768},
Q_f={q_gen_2768},
Delta=
{
<z, z>() -> q_gen_2768
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2767, q_gen_2770},
Q_f={q_gen_2767},
Delta=
{
<z, z>() -> q_gen_2770
<z, s, s>(q_gen_2770) -> q_gen_2767
<z, z, z>() -> q_gen_2767
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3  ;  () -> plus([n, z, n]) -> 3  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1  ;  (leq([s(nn1), z])) -> BOT -> 1  ;  (plus([n, m, _uj])) -> leq([n, _uj]) -> 4  ;  (plus([n, mm, _pj])) -> plus([n, s(mm), s(_pj)]) -> 4
}
Sat witness: Yes: ((plus([n, m, _uj])) -> leq([n, _uj]), {
_uj -> s(z)  ;  m -> s(z)  ;  n -> z
})

-------------------------------------------
Step 4, which took 0.007220 s (model generation: 0.006871,  model checking: 0.000349):

Model:
|_
{
leq -> 
{{{
Q={q_gen_2768, q_gen_2772},
Q_f={q_gen_2768},
Delta=
{
<z>() -> q_gen_2772
<z, s>(q_gen_2772) -> q_gen_2768
<z, z>() -> q_gen_2768
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2767, q_gen_2770},
Q_f={q_gen_2767},
Delta=
{
<z, z>() -> q_gen_2770
<z, s, s>(q_gen_2770) -> q_gen_2767
<z, z, z>() -> q_gen_2767
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3  ;  () -> plus([n, z, n]) -> 3  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2  ;  (leq([s(nn1), z])) -> BOT -> 2  ;  (plus([n, m, _uj])) -> leq([n, _uj]) -> 4  ;  (plus([n, mm, _pj])) -> plus([n, s(mm), s(_pj)]) -> 4
}
Sat witness: Yes: ((leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 5, which took 0.011494 s (model generation: 0.011071,  model checking: 0.000423):

Model:
|_
{
leq -> 
{{{
Q={q_gen_2768, q_gen_2772},
Q_f={q_gen_2768},
Delta=
{
<z>() -> q_gen_2772
<s, s>(q_gen_2768) -> q_gen_2768
<z, s>(q_gen_2772) -> q_gen_2768
<z, z>() -> q_gen_2768
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2767, q_gen_2770},
Q_f={q_gen_2767},
Delta=
{
<z, z>() -> q_gen_2770
<z, s, s>(q_gen_2770) -> q_gen_2767
<z, z, z>() -> q_gen_2767
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3  ;  () -> plus([n, z, n]) -> 6  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 3  ;  (leq([s(nn1), z])) -> BOT -> 3  ;  (plus([n, m, _uj])) -> leq([n, _uj]) -> 4  ;  (plus([n, mm, _pj])) -> plus([n, s(mm), s(_pj)]) -> 4
}
Sat witness: Yes: (() -> plus([n, z, n]), {
n -> s(z)
})

-------------------------------------------
Step 6, which took 0.011919 s (model generation: 0.011609,  model checking: 0.000310):

Model:
|_
{
leq -> 
{{{
Q={q_gen_2768, q_gen_2772},
Q_f={q_gen_2768},
Delta=
{
<z>() -> q_gen_2772
<s, s>(q_gen_2768) -> q_gen_2768
<z, s>(q_gen_2772) -> q_gen_2768
<z, z>() -> q_gen_2768
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2767, q_gen_2770},
Q_f={q_gen_2767},
Delta=
{
<z, z>() -> q_gen_2770
<s, z, s>(q_gen_2770) -> q_gen_2767
<z, s, s>(q_gen_2770) -> q_gen_2767
<z, z, z>() -> q_gen_2767
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 6  ;  () -> plus([n, z, n]) -> 6  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4  ;  (leq([s(nn1), z])) -> BOT -> 4  ;  (plus([n, m, _uj])) -> leq([n, _uj]) -> 4  ;  (plus([n, mm, _pj])) -> plus([n, s(mm), s(_pj)]) -> 4
}
Sat witness: Yes: (() -> leq([z, n2]), {
n2 -> s(s(z))
})

-------------------------------------------
Step 7, which took 0.011976 s (model generation: 0.011668,  model checking: 0.000308):

Model:
|_
{
leq -> 
{{{
Q={q_gen_2768, q_gen_2772},
Q_f={q_gen_2768},
Delta=
{
<s>(q_gen_2772) -> q_gen_2772
<z>() -> q_gen_2772
<s, s>(q_gen_2768) -> q_gen_2768
<z, s>(q_gen_2772) -> q_gen_2768
<z, z>() -> q_gen_2768
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2767, q_gen_2770},
Q_f={q_gen_2767},
Delta=
{
<z, z>() -> q_gen_2770
<s, z, s>(q_gen_2770) -> q_gen_2767
<z, s, s>(q_gen_2770) -> q_gen_2767
<z, z, z>() -> q_gen_2767
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 6  ;  () -> plus([n, z, n]) -> 6  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4  ;  (leq([s(nn1), z])) -> BOT -> 4  ;  (plus([n, m, _uj])) -> leq([n, _uj]) -> 4  ;  (plus([n, mm, _pj])) -> plus([n, s(mm), s(_pj)]) -> 7
}
Sat witness: Yes: ((plus([n, mm, _pj])) -> plus([n, s(mm), s(_pj)]), {
_pj -> s(z)  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 8, which took 0.012845 s (model generation: 0.012186,  model checking: 0.000659):

Model:
|_
{
leq -> 
{{{
Q={q_gen_2768, q_gen_2772},
Q_f={q_gen_2768},
Delta=
{
<s>(q_gen_2772) -> q_gen_2772
<z>() -> q_gen_2772
<s, s>(q_gen_2768) -> q_gen_2768
<z, s>(q_gen_2772) -> q_gen_2768
<z, z>() -> q_gen_2768
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2767, q_gen_2770, q_gen_2779},
Q_f={q_gen_2767},
Delta=
{
<z>() -> q_gen_2779
<z, z>() -> q_gen_2770
<s, s, s>(q_gen_2767) -> q_gen_2767
<s, z, s>(q_gen_2770) -> q_gen_2767
<z, s, s>(q_gen_2770) -> q_gen_2767
<z, z, s>(q_gen_2779) -> q_gen_2767
<z, z, z>() -> q_gen_2767
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 6  ;  () -> plus([n, z, n]) -> 9  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5  ;  (leq([s(nn1), z])) -> BOT -> 5  ;  (plus([n, m, _uj])) -> leq([n, _uj]) -> 5  ;  (plus([n, mm, _pj])) -> plus([n, s(mm), s(_pj)]) -> 7
}
Sat witness: Yes: (() -> plus([n, z, n]), {
n -> s(s(z))
})

-------------------------------------------
Step 9, which took 0.015865 s (model generation: 0.012634,  model checking: 0.003231):

Model:
|_
{
leq -> 
{{{
Q={q_gen_2768, q_gen_2772},
Q_f={q_gen_2768},
Delta=
{
<s>(q_gen_2772) -> q_gen_2772
<z>() -> q_gen_2772
<s, s>(q_gen_2768) -> q_gen_2768
<z, s>(q_gen_2772) -> q_gen_2768
<z, z>() -> q_gen_2768
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2767, q_gen_2770, q_gen_2779},
Q_f={q_gen_2767},
Delta=
{
<z>() -> q_gen_2779
<s, s>(q_gen_2770) -> q_gen_2770
<z, z>() -> q_gen_2770
<s, s, s>(q_gen_2767) -> q_gen_2767
<s, z, s>(q_gen_2770) -> q_gen_2767
<z, s, s>(q_gen_2770) -> q_gen_2767
<z, z, s>(q_gen_2779) -> q_gen_2767
<z, z, z>() -> q_gen_2767
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 7  ;  () -> plus([n, z, n]) -> 9  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 6  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 6  ;  (leq([s(nn1), z])) -> BOT -> 6  ;  (plus([n, m, _uj])) -> leq([n, _uj]) -> 6  ;  (plus([n, mm, _pj])) -> plus([n, s(mm), s(_pj)]) -> 10
}
Sat witness: Yes: ((plus([n, mm, _pj])) -> plus([n, s(mm), s(_pj)]), {
_pj -> s(z)  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 10, which took 0.014889 s (model generation: 0.013309,  model checking: 0.001580):

Model:
|_
{
leq -> 
{{{
Q={q_gen_2768, q_gen_2772},
Q_f={q_gen_2768},
Delta=
{
<s>(q_gen_2772) -> q_gen_2772
<z>() -> q_gen_2772
<s, s>(q_gen_2768) -> q_gen_2768
<z, s>(q_gen_2772) -> q_gen_2768
<z, z>() -> q_gen_2768
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_2767, q_gen_2770, q_gen_2779},
Q_f={q_gen_2767},
Delta=
{
<z>() -> q_gen_2779
<s, s>(q_gen_2770) -> q_gen_2770
<z, s>(q_gen_2779) -> q_gen_2770
<z, z>() -> q_gen_2770
<s, s, s>(q_gen_2767) -> q_gen_2767
<s, z, s>(q_gen_2770) -> q_gen_2767
<z, s, s>(q_gen_2770) -> q_gen_2767
<z, z, s>(q_gen_2779) -> q_gen_2767
<z, z, z>() -> q_gen_2767
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 8  ;  () -> plus([n, z, n]) -> 10  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 7  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 7  ;  (leq([s(nn1), z])) -> BOT -> 7  ;  (plus([n, m, _uj])) -> leq([n, _uj]) -> 7  ;  (plus([n, mm, _pj])) -> plus([n, s(mm), s(_pj)]) -> 13
}
Sat witness: Yes: ((plus([n, mm, _pj])) -> plus([n, s(mm), s(_pj)]), {
_pj -> s(s(z))  ;  mm -> z  ;  n -> s(z)
})

Total time: 0.120055
Reason for stopping: Proved