Solving ../../benchmarks/true/isaplanner_prop18.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, _eba])) -> plus([n, s(mm), s(_eba)])}
(plus([_fba, _gba, _hba]) /\ plus([_fba, _gba, _iba])) -> eq_nat([_hba, _iba])
)
(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([i, m, _jba])) -> le([i, s(_jba)])}


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([i, m, _jba])) -> le([i, s(_jba)]) -> 0  ;  (plus([n, mm, _eba])) -> plus([n, s(mm), s(_eba)]) -> 0
}


Solving took 0.054337 seconds.
Proved
Model:
|_
{
le -> 
{{{
Q={q_gen_1329, q_gen_1330},
Q_f={q_gen_1329},
Delta=
{
<s>(q_gen_1330) -> q_gen_1330
<z>() -> q_gen_1330
<s, s>(q_gen_1329) -> q_gen_1329
<z, s>(q_gen_1330) -> q_gen_1329
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_1328, q_gen_1332, q_gen_1339},
Q_f={q_gen_1328},
Delta=
{
<s>(q_gen_1339) -> q_gen_1339
<z>() -> q_gen_1339
<s, s>(q_gen_1332) -> q_gen_1332
<z, s>(q_gen_1339) -> q_gen_1332
<z, z>() -> q_gen_1332
<s, s, s>(q_gen_1328) -> q_gen_1328
<s, z, s>(q_gen_1332) -> q_gen_1328
<z, s, s>(q_gen_1332) -> q_gen_1328
<z, z, s>(q_gen_1339) -> q_gen_1328
<z, z, z>() -> q_gen_1328
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.003642 s (model generation: 0.003508,  model checking: 0.000134):

Model:
|_
{
le -> 
{{{
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:
{
() -> 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([i, m, _jba])) -> le([i, s(_jba)]) -> 1  ;  (plus([n, mm, _eba])) -> plus([n, s(mm), s(_eba)]) -> 1
}
Sat witness: Yes: (() -> plus([n, z, n]), {
n -> z
})

-------------------------------------------
Step 1, which took 0.005119 s (model generation: 0.005022,  model checking: 0.000097):

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

}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_1328},
Q_f={q_gen_1328},
Delta=
{
<z, z, z>() -> q_gen_1328
}

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

}
--
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([i, m, _jba])) -> le([i, s(_jba)]) -> 1  ;  (plus([n, mm, _eba])) -> plus([n, s(mm), s(_eba)]) -> 1
}
Sat witness: Yes: (() -> le([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 2, which took 0.004289 s (model generation: 0.004210,  model checking: 0.000079):

Model:
|_
{
le -> 
{{{
Q={q_gen_1329, q_gen_1330},
Q_f={q_gen_1329},
Delta=
{
<z>() -> q_gen_1330
<z, s>(q_gen_1330) -> q_gen_1329
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_1328},
Q_f={q_gen_1328},
Delta=
{
<z, z, z>() -> q_gen_1328
}

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

}
--
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([i, m, _jba])) -> le([i, s(_jba)]) -> 1  ;  (plus([n, mm, _eba])) -> plus([n, s(mm), s(_eba)]) -> 4
}
Sat witness: Yes: ((plus([n, mm, _eba])) -> plus([n, s(mm), s(_eba)]), {
_eba -> z  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 3, which took 0.003829 s (model generation: 0.003735,  model checking: 0.000094):

Model:
|_
{
le -> 
{{{
Q={q_gen_1329, q_gen_1330},
Q_f={q_gen_1329},
Delta=
{
<z>() -> q_gen_1330
<z, s>(q_gen_1330) -> q_gen_1329
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_1328, q_gen_1332},
Q_f={q_gen_1328},
Delta=
{
<z, z>() -> q_gen_1332
<z, s, s>(q_gen_1332) -> q_gen_1328
<z, z, z>() -> q_gen_1328
}

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

}
--
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([i, m, _jba])) -> le([i, s(_jba)]) -> 4  ;  (plus([n, mm, _eba])) -> plus([n, s(mm), s(_eba)]) -> 4
}
Sat witness: Yes: ((plus([i, m, _jba])) -> le([i, s(_jba)]), {
_jba -> s(z)  ;  i -> z  ;  m -> s(z)
})

-------------------------------------------
Step 4, which took 0.004346 s (model generation: 0.003887,  model checking: 0.000459):

Model:
|_
{
le -> 
{{{
Q={q_gen_1329, q_gen_1330},
Q_f={q_gen_1329},
Delta=
{
<s>(q_gen_1330) -> q_gen_1330
<z>() -> q_gen_1330
<z, s>(q_gen_1330) -> q_gen_1329
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_1328, q_gen_1332},
Q_f={q_gen_1328},
Delta=
{
<z, z>() -> q_gen_1332
<z, s, s>(q_gen_1332) -> q_gen_1328
<z, z, z>() -> q_gen_1328
}

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

}
--
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)]) -> 4  ;  (le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 2  ;  (le([s(nn1), z])) -> BOT -> 2  ;  (le([z, z])) -> BOT -> 2  ;  (plus([i, m, _jba])) -> le([i, s(_jba)]) -> 4  ;  (plus([n, mm, _eba])) -> plus([n, s(mm), s(_eba)]) -> 4
}
Sat witness: Yes: ((le([nn1, nn2])) -> le([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> s(z)
})

-------------------------------------------
Step 5, which took 0.005790 s (model generation: 0.005581,  model checking: 0.000209):

Model:
|_
{
le -> 
{{{
Q={q_gen_1329, q_gen_1330},
Q_f={q_gen_1329},
Delta=
{
<s>(q_gen_1330) -> q_gen_1330
<z>() -> q_gen_1330
<s, s>(q_gen_1329) -> q_gen_1329
<z, s>(q_gen_1330) -> q_gen_1329
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_1328, q_gen_1332},
Q_f={q_gen_1328},
Delta=
{
<z, z>() -> q_gen_1332
<z, s, s>(q_gen_1332) -> q_gen_1328
<z, z, z>() -> q_gen_1328
}

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

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

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

-------------------------------------------
Step 6, which took 0.004724 s (model generation: 0.004515,  model checking: 0.000209):

Model:
|_
{
le -> 
{{{
Q={q_gen_1329, q_gen_1330},
Q_f={q_gen_1329},
Delta=
{
<s>(q_gen_1330) -> q_gen_1330
<z>() -> q_gen_1330
<s, s>(q_gen_1329) -> q_gen_1329
<z, s>(q_gen_1330) -> q_gen_1329
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_1328, q_gen_1332},
Q_f={q_gen_1328},
Delta=
{
<z, z>() -> q_gen_1332
<s, z, s>(q_gen_1332) -> q_gen_1328
<z, s, s>(q_gen_1332) -> q_gen_1328
<z, z, z>() -> q_gen_1328
}

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

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

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

-------------------------------------------
Step 7, which took 0.004664 s (model generation: 0.004285,  model checking: 0.000379):

Model:
|_
{
le -> 
{{{
Q={q_gen_1329, q_gen_1330},
Q_f={q_gen_1329},
Delta=
{
<s>(q_gen_1330) -> q_gen_1330
<z>() -> q_gen_1330
<s, s>(q_gen_1329) -> q_gen_1329
<z, s>(q_gen_1330) -> q_gen_1329
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_1328, q_gen_1332, q_gen_1339},
Q_f={q_gen_1328},
Delta=
{
<z>() -> q_gen_1339
<z, z>() -> q_gen_1332
<s, s, s>(q_gen_1328) -> q_gen_1328
<s, z, s>(q_gen_1332) -> q_gen_1328
<z, s, s>(q_gen_1332) -> q_gen_1328
<z, z, s>(q_gen_1339) -> q_gen_1328
<z, z, z>() -> q_gen_1328
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 5  ;  () -> plus([n, z, n]) -> 9  ;  (le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 5  ;  (le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 5  ;  (le([s(nn1), z])) -> BOT -> 5  ;  (le([z, z])) -> BOT -> 5  ;  (plus([i, m, _jba])) -> le([i, s(_jba)]) -> 5  ;  (plus([n, mm, _eba])) -> plus([n, s(mm), s(_eba)]) -> 7
}
Sat witness: Yes: (() -> plus([n, z, n]), {
n -> s(s(z))
})

-------------------------------------------
Step 8, which took 0.006545 s (model generation: 0.006044,  model checking: 0.000501):

Model:
|_
{
le -> 
{{{
Q={q_gen_1329, q_gen_1330},
Q_f={q_gen_1329},
Delta=
{
<s>(q_gen_1330) -> q_gen_1330
<z>() -> q_gen_1330
<s, s>(q_gen_1329) -> q_gen_1329
<z, s>(q_gen_1330) -> q_gen_1329
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_1328, q_gen_1332, q_gen_1339},
Q_f={q_gen_1328},
Delta=
{
<z>() -> q_gen_1339
<s, s>(q_gen_1332) -> q_gen_1332
<z, z>() -> q_gen_1332
<s, s, s>(q_gen_1328) -> q_gen_1328
<s, z, s>(q_gen_1332) -> q_gen_1328
<z, s, s>(q_gen_1332) -> q_gen_1328
<z, z, s>(q_gen_1339) -> q_gen_1328
<z, z, z>() -> q_gen_1328
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 6  ;  () -> plus([n, z, n]) -> 9  ;  (le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 6  ;  (le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 6  ;  (le([s(nn1), z])) -> BOT -> 6  ;  (le([z, z])) -> BOT -> 6  ;  (plus([i, m, _jba])) -> le([i, s(_jba)]) -> 6  ;  (plus([n, mm, _eba])) -> plus([n, s(mm), s(_eba)]) -> 10
}
Sat witness: Yes: ((plus([n, mm, _eba])) -> plus([n, s(mm), s(_eba)]), {
_eba -> s(z)  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 9, which took 0.005442 s (model generation: 0.005070,  model checking: 0.000372):

Model:
|_
{
le -> 
{{{
Q={q_gen_1329, q_gen_1330},
Q_f={q_gen_1329},
Delta=
{
<s>(q_gen_1330) -> q_gen_1330
<z>() -> q_gen_1330
<s, s>(q_gen_1329) -> q_gen_1329
<z, s>(q_gen_1330) -> q_gen_1329
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  plus -> 
{{{
Q={q_gen_1328, q_gen_1332, q_gen_1339},
Q_f={q_gen_1328},
Delta=
{
<z>() -> q_gen_1339
<s, s>(q_gen_1332) -> q_gen_1332
<z, s>(q_gen_1339) -> q_gen_1332
<z, z>() -> q_gen_1332
<s, s, s>(q_gen_1328) -> q_gen_1328
<s, z, s>(q_gen_1332) -> q_gen_1328
<z, s, s>(q_gen_1332) -> q_gen_1328
<z, z, s>(q_gen_1339) -> q_gen_1328
<z, z, z>() -> q_gen_1328
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 7  ;  () -> plus([n, z, n]) -> 10  ;  (le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 7  ;  (le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 7  ;  (le([s(nn1), z])) -> BOT -> 7  ;  (le([z, z])) -> BOT -> 7  ;  (plus([i, m, _jba])) -> le([i, s(_jba)]) -> 7  ;  (plus([n, mm, _eba])) -> plus([n, s(mm), s(_eba)]) -> 13
}
Sat witness: Yes: ((plus([n, mm, _eba])) -> plus([n, s(mm), s(_eba)]), {
_eba -> s(s(z))  ;  mm -> z  ;  n -> s(z)
})

Total time: 0.054337
Reason for stopping: Proved