Solving ../../benchmarks/false/mult_leq.smt2...

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


Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(leq, P:
{() -> leq([z, s(nn2)])
() -> leq([z, z])
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)])
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2])
(leq([s(nn1), z])) -> BOT}
)
(plus, F:
{() -> plus([n, z, n])
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)])}
(plus([_xga, _yga, _aha]) /\ plus([_xga, _yga, _zga])) -> eq_nat([_zga, _aha])
)
(mult, F:
{() -> mult([n, z, z])
(mult([n, mm, _bha]) /\ plus([n, _bha, _cha])) -> mult([n, s(mm), _cha])}
(mult([_dha, _eha, _fha]) /\ mult([_dha, _eha, _gha])) -> eq_nat([_fha, _gha])
)
}

properties:
{(mult([n, m, _hha])) -> leq([n, _hha])}


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

Clause system for inference is:

{
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 0
() -> mult([n, z, z]) -> 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
(mult([n, m, _hha])) -> leq([n, _hha]) -> 0
(mult([n, mm, _bha]) /\ plus([n, _bha, _cha])) -> mult([n, s(mm), _cha]) -> 0
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 0
}


Solving took 0.354548 seconds.
Disproved
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.017395 s (model generation: 0.014463,  model checking: 0.002932):

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

}

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

}

Datatype: <nat, 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:
{
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 0
() -> mult([n, z, z]) -> 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
(mult([n, m, _hha])) -> leq([n, _hha]) -> 1
(mult([n, mm, _bha]) /\ plus([n, _bha, _cha])) -> mult([n, s(mm), _cha]) -> 1
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 1
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> z
})

-------------------------------------------
Step 1, which took 0.014615 s (model generation: 0.014444,  model checking: 0.000171):

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

}

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

}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_8641},
Q_f={q_gen_8641},
Delta=
{
<z, z, z>() -> q_gen_8641
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 0
() -> mult([n, z, z]) -> 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
(mult([n, m, _hha])) -> leq([n, _hha]) -> 1
(mult([n, mm, _bha]) /\ plus([n, _bha, _cha])) -> mult([n, s(mm), _cha]) -> 1
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 1
}
Sat witness: Found: (() -> mult([n, z, z]), {
n -> z
})

-------------------------------------------
Step 2, which took 0.015885 s (model generation: 0.015797,  model checking: 0.000088):

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

}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  mult -> 
{{{
Q={q_gen_8642},
Q_f={q_gen_8642},
Delta=
{
<z, z, z>() -> q_gen_8642
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_8641},
Q_f={q_gen_8641},
Delta=
{
<z, z, z>() -> q_gen_8641
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 3
() -> mult([n, z, z]) -> 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
(mult([n, m, _hha])) -> leq([n, _hha]) -> 1
(mult([n, mm, _bha]) /\ plus([n, _bha, _cha])) -> mult([n, s(mm), _cha]) -> 1
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 1
}
Sat witness: Found: (() -> leq([z, z]), {

})

-------------------------------------------
Step 3, which took 0.015112 s (model generation: 0.014983,  model checking: 0.000129):

Model:
|_
{
leq -> 
{{{
Q={q_gen_8643},
Q_f={q_gen_8643},
Delta=
{
<z, z>() -> q_gen_8643
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  mult -> 
{{{
Q={q_gen_8642},
Q_f={q_gen_8642},
Delta=
{
<z, z, z>() -> q_gen_8642
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_8641},
Q_f={q_gen_8641},
Delta=
{
<z, z, z>() -> q_gen_8641
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> mult([n, z, z]) -> 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
(mult([n, m, _hha])) -> leq([n, _hha]) -> 1
(mult([n, mm, _bha]) /\ plus([n, _bha, _cha])) -> mult([n, s(mm), _cha]) -> 1
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 1
}
Sat witness: Found: (() -> leq([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 4, which took 0.075955 s (model generation: 0.017198,  model checking: 0.058757):

Model:
|_
{
leq -> 
{{{
Q={q_gen_8643, q_gen_8645},
Q_f={q_gen_8643},
Delta=
{
<z>() -> q_gen_8645
<z, s>(q_gen_8645) -> q_gen_8643
<z, z>() -> q_gen_8643
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  mult -> 
{{{
Q={q_gen_8642},
Q_f={q_gen_8642},
Delta=
{
<z, z, z>() -> q_gen_8642
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_8641},
Q_f={q_gen_8641},
Delta=
{
<z, z, z>() -> q_gen_8641
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> mult([n, z, z]) -> 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
(mult([n, m, _hha])) -> leq([n, _hha]) -> 1
(mult([n, mm, _bha]) /\ plus([n, _bha, _cha])) -> mult([n, s(mm), _cha]) -> 1
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 4
}
Sat witness: Found: ((plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]), {
_wga -> z  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 5, which took 0.016469 s (model generation: 0.016262,  model checking: 0.000207):

Model:
|_
{
leq -> 
{{{
Q={q_gen_8643, q_gen_8645},
Q_f={q_gen_8643},
Delta=
{
<z>() -> q_gen_8645
<z, s>(q_gen_8645) -> q_gen_8643
<z, z>() -> q_gen_8643
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  mult -> 
{{{
Q={q_gen_8642},
Q_f={q_gen_8642},
Delta=
{
<z, z, z>() -> q_gen_8642
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_8641, q_gen_8647},
Q_f={q_gen_8641},
Delta=
{
<z, z>() -> q_gen_8647
<z, s, s>(q_gen_8647) -> q_gen_8641
<z, z, z>() -> q_gen_8641
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> mult([n, z, z]) -> 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
(mult([n, m, _hha])) -> leq([n, _hha]) -> 1
(mult([n, mm, _bha]) /\ plus([n, _bha, _cha])) -> mult([n, s(mm), _cha]) -> 4
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 4
}
Sat witness: Found: ((mult([n, mm, _bha]) /\ plus([n, _bha, _cha])) -> mult([n, s(mm), _cha]), {
_bha -> z  ;  _cha -> z  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 6, which took 0.017422 s (model generation: 0.017125,  model checking: 0.000297):

Model:
|_
{
leq -> 
{{{
Q={q_gen_8643, q_gen_8645},
Q_f={q_gen_8643},
Delta=
{
<z>() -> q_gen_8645
<z, s>(q_gen_8645) -> q_gen_8643
<z, z>() -> q_gen_8643
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  mult -> 
{{{
Q={q_gen_8642, q_gen_8649},
Q_f={q_gen_8642},
Delta=
{
<z>() -> q_gen_8649
<z, s, z>(q_gen_8649) -> q_gen_8642
<z, z, z>() -> q_gen_8642
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_8641, q_gen_8647},
Q_f={q_gen_8641},
Delta=
{
<z, z>() -> q_gen_8647
<z, s, s>(q_gen_8647) -> q_gen_8641
<z, z, z>() -> q_gen_8641
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> mult([n, z, z]) -> 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
(mult([n, m, _hha])) -> leq([n, _hha]) -> 2
(mult([n, mm, _bha]) /\ plus([n, _bha, _cha])) -> mult([n, s(mm), _cha]) -> 4
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 4
}
Sat witness: Found: ((leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 7, which took 0.017285 s (model generation: 0.016823,  model checking: 0.000462):

Model:
|_
{
leq -> 
{{{
Q={q_gen_8643, q_gen_8645},
Q_f={q_gen_8643},
Delta=
{
<z>() -> q_gen_8645
<s, s>(q_gen_8643) -> q_gen_8643
<z, s>(q_gen_8645) -> q_gen_8643
<z, z>() -> q_gen_8643
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  mult -> 
{{{
Q={q_gen_8642, q_gen_8649},
Q_f={q_gen_8642},
Delta=
{
<z>() -> q_gen_8649
<z, s, z>(q_gen_8649) -> q_gen_8642
<z, z, z>() -> q_gen_8642
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_8641, q_gen_8647},
Q_f={q_gen_8641},
Delta=
{
<z, z>() -> q_gen_8647
<z, s, s>(q_gen_8647) -> q_gen_8641
<z, z, z>() -> q_gen_8641
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> mult([n, z, z]) -> 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
(mult([n, m, _hha])) -> leq([n, _hha]) -> 3
(mult([n, mm, _bha]) /\ plus([n, _bha, _cha])) -> mult([n, s(mm), _cha]) -> 4
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 4
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> s(s(z))
})

-------------------------------------------
Step 8, which took 0.018205 s (model generation: 0.017731,  model checking: 0.000474):

Model:
|_
{
leq -> 
{{{
Q={q_gen_8643, q_gen_8645},
Q_f={q_gen_8643},
Delta=
{
<z>() -> q_gen_8645
<s, s>(q_gen_8643) -> q_gen_8643
<z, s>(q_gen_8645) -> q_gen_8643
<z, z>() -> q_gen_8643
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  mult -> 
{{{
Q={q_gen_8642, q_gen_8649},
Q_f={q_gen_8642},
Delta=
{
<z>() -> q_gen_8649
<z, s, z>(q_gen_8649) -> q_gen_8642
<z, z, z>() -> q_gen_8642
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_8641, q_gen_8647},
Q_f={q_gen_8641},
Delta=
{
<s, s>(q_gen_8647) -> q_gen_8647
<z, z>() -> q_gen_8647
<s, z, s>(q_gen_8647) -> q_gen_8641
<z, s, s>(q_gen_8647) -> q_gen_8641
<z, z, z>() -> q_gen_8641
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> mult([n, z, z]) -> 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
(mult([n, m, _hha])) -> leq([n, _hha]) -> 4
(mult([n, mm, _bha]) /\ plus([n, _bha, _cha])) -> mult([n, s(mm), _cha]) -> 4
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 4
}
Sat witness: Found: (() -> mult([n, z, z]), {
n -> s(s(z))
})

-------------------------------------------
Step 9, which took 0.018772 s (model generation: 0.018576,  model checking: 0.000196):

Model:
|_
{
leq -> 
{{{
Q={q_gen_8643, q_gen_8645},
Q_f={q_gen_8643},
Delta=
{
<z>() -> q_gen_8645
<s, s>(q_gen_8643) -> q_gen_8643
<z, s>(q_gen_8645) -> q_gen_8643
<z, z>() -> q_gen_8643
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  mult -> 
{{{
Q={q_gen_8642, q_gen_8649},
Q_f={q_gen_8642},
Delta=
{
<s>(q_gen_8649) -> q_gen_8649
<z>() -> q_gen_8649
<s, z, z>(q_gen_8649) -> q_gen_8642
<z, s, z>(q_gen_8649) -> q_gen_8642
<z, z, z>() -> q_gen_8642
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_8641, q_gen_8647},
Q_f={q_gen_8641},
Delta=
{
<s, s>(q_gen_8647) -> q_gen_8647
<z, z>() -> q_gen_8647
<s, z, s>(q_gen_8647) -> q_gen_8641
<z, s, s>(q_gen_8647) -> q_gen_8641
<z, z, z>() -> q_gen_8641
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> mult([n, z, z]) -> 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
(mult([n, m, _hha])) -> leq([n, _hha]) -> 4
(mult([n, mm, _bha]) /\ plus([n, _bha, _cha])) -> mult([n, s(mm), _cha]) -> 4
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 4
}
Sat witness: Found: (() -> leq([z, s(nn2)]), {
nn2 -> s(z)
})

-------------------------------------------
Step 10, which took 0.018789 s (model generation: 0.018466,  model checking: 0.000323):

Model:
|_
{
leq -> 
{{{
Q={q_gen_8643, q_gen_8645},
Q_f={q_gen_8643},
Delta=
{
<s>(q_gen_8645) -> q_gen_8645
<z>() -> q_gen_8645
<s, s>(q_gen_8643) -> q_gen_8643
<z, s>(q_gen_8645) -> q_gen_8643
<z, z>() -> q_gen_8643
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  mult -> 
{{{
Q={q_gen_8642, q_gen_8649},
Q_f={q_gen_8642},
Delta=
{
<s>(q_gen_8649) -> q_gen_8649
<z>() -> q_gen_8649
<s, z, z>(q_gen_8649) -> q_gen_8642
<z, s, z>(q_gen_8649) -> q_gen_8642
<z, z, z>() -> q_gen_8642
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_8641, q_gen_8647},
Q_f={q_gen_8641},
Delta=
{
<s, s>(q_gen_8647) -> q_gen_8647
<z, z>() -> q_gen_8647
<s, z, s>(q_gen_8647) -> q_gen_8641
<z, s, s>(q_gen_8647) -> q_gen_8641
<z, z, z>() -> q_gen_8641
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> mult([n, z, z]) -> 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
(mult([n, m, _hha])) -> leq([n, _hha]) -> 4
(mult([n, mm, _bha]) /\ plus([n, _bha, _cha])) -> mult([n, s(mm), _cha]) -> 4
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 7
}
Sat witness: Found: ((plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]), {
_wga -> s(z)  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 11, which took 0.021317 s (model generation: 0.021021,  model checking: 0.000296):

Model:
|_
{
leq -> 
{{{
Q={q_gen_8643, q_gen_8645},
Q_f={q_gen_8643},
Delta=
{
<s>(q_gen_8645) -> q_gen_8645
<z>() -> q_gen_8645
<s, s>(q_gen_8643) -> q_gen_8643
<z, s>(q_gen_8645) -> q_gen_8643
<z, z>() -> q_gen_8643
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  mult -> 
{{{
Q={q_gen_8642, q_gen_8649},
Q_f={q_gen_8642},
Delta=
{
<s>(q_gen_8649) -> q_gen_8649
<z>() -> q_gen_8649
<s, z, z>(q_gen_8649) -> q_gen_8642
<z, s, z>(q_gen_8649) -> q_gen_8642
<z, z, z>() -> q_gen_8642
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_8641, q_gen_8647, q_gen_8660},
Q_f={q_gen_8641},
Delta=
{
<z>() -> q_gen_8660
<s, s>(q_gen_8647) -> q_gen_8647
<z, z>() -> q_gen_8647
<s, s, s>(q_gen_8641) -> q_gen_8641
<s, z, s>(q_gen_8647) -> q_gen_8641
<z, s, s>(q_gen_8647) -> q_gen_8641
<z, z, s>(q_gen_8660) -> q_gen_8641
<z, z, z>() -> q_gen_8641
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> mult([n, z, z]) -> 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
(mult([n, m, _hha])) -> leq([n, _hha]) -> 4
(mult([n, mm, _bha]) /\ plus([n, _bha, _cha])) -> mult([n, s(mm), _cha]) -> 7
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 7
}
Sat witness: Found: ((mult([n, mm, _bha]) /\ plus([n, _bha, _cha])) -> mult([n, s(mm), _cha]), {
_bha -> z  ;  _cha -> s(z)  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 12, which took 0.021902 s (model generation: 0.021738,  model checking: 0.000164):

Model:
|_
{
leq -> 
{{{
Q={q_gen_8643, q_gen_8645},
Q_f={q_gen_8643},
Delta=
{
<s>(q_gen_8645) -> q_gen_8645
<z>() -> q_gen_8645
<s, s>(q_gen_8643) -> q_gen_8643
<z, s>(q_gen_8645) -> q_gen_8643
<z, z>() -> q_gen_8643
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  mult -> 
{{{
Q={q_gen_8642, q_gen_8649, q_gen_8662},
Q_f={q_gen_8642},
Delta=
{
<s>(q_gen_8649) -> q_gen_8649
<z>() -> q_gen_8649
<z, z>() -> q_gen_8662
<s, z, z>(q_gen_8649) -> q_gen_8642
<z, s, s>(q_gen_8662) -> q_gen_8642
<z, s, z>(q_gen_8649) -> q_gen_8642
<z, z, z>() -> q_gen_8642
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_8641, q_gen_8647, q_gen_8660},
Q_f={q_gen_8641},
Delta=
{
<z>() -> q_gen_8660
<s, s>(q_gen_8647) -> q_gen_8647
<z, z>() -> q_gen_8647
<s, s, s>(q_gen_8641) -> q_gen_8641
<s, z, s>(q_gen_8647) -> q_gen_8641
<z, s, s>(q_gen_8647) -> q_gen_8641
<z, z, s>(q_gen_8660) -> q_gen_8641
<z, z, z>() -> q_gen_8641
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> mult([n, z, z]) -> 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
(mult([n, m, _hha])) -> leq([n, _hha]) -> 7
(mult([n, mm, _bha]) /\ plus([n, _bha, _cha])) -> mult([n, s(mm), _cha]) -> 7
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 7
}
Sat witness: Found: ((mult([n, m, _hha])) -> leq([n, _hha]), {
_hha -> z  ;  m -> z  ;  n -> s(z)
})

-------------------------------------------
Step 13, which took 0.021564 s (model generation: 0.021503,  model checking: 0.000061):

Model:
|_
{
leq -> 
{{{
Q={q_gen_8643, q_gen_8645},
Q_f={q_gen_8643},
Delta=
{
<s>(q_gen_8645) -> q_gen_8645
<z>() -> q_gen_8645
<s, s>(q_gen_8643) -> q_gen_8643
<s, z>(q_gen_8645) -> q_gen_8643
<z, s>(q_gen_8645) -> q_gen_8643
<z, z>() -> q_gen_8643
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  mult -> 
{{{
Q={q_gen_8642, q_gen_8649, q_gen_8662},
Q_f={q_gen_8642},
Delta=
{
<s>(q_gen_8649) -> q_gen_8649
<z>() -> q_gen_8649
<z, z>() -> q_gen_8662
<s, z, z>(q_gen_8649) -> q_gen_8642
<z, s, s>(q_gen_8662) -> q_gen_8642
<z, s, z>(q_gen_8649) -> q_gen_8642
<z, z, z>() -> q_gen_8642
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_8641, q_gen_8647, q_gen_8660},
Q_f={q_gen_8641},
Delta=
{
<z>() -> q_gen_8660
<s, s>(q_gen_8647) -> q_gen_8647
<z, z>() -> q_gen_8647
<s, s, s>(q_gen_8641) -> q_gen_8641
<s, z, s>(q_gen_8647) -> q_gen_8641
<z, s, s>(q_gen_8647) -> q_gen_8641
<z, z, s>(q_gen_8660) -> q_gen_8641
<z, z, z>() -> q_gen_8641
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> mult([n, z, z]) -> 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 -> 7
(mult([n, m, _hha])) -> leq([n, _hha]) -> 7
(mult([n, mm, _bha]) /\ plus([n, _bha, _cha])) -> mult([n, s(mm), _cha]) -> 7
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 7
}
Sat witness: Found: ((leq([s(nn1), z])) -> BOT, {
nn1 -> z
})

-------------------------------------------
Step 14, which took 0.023283 s (model generation: 0.022228,  model checking: 0.001055):

Model:
|_
{
leq -> 
{{{
Q={q_gen_8643, q_gen_8645, q_gen_8664},
Q_f={q_gen_8643},
Delta=
{
<s>(q_gen_8645) -> q_gen_8645
<z>() -> q_gen_8645
<s, s>(q_gen_8643) -> q_gen_8643
<z, s>(q_gen_8645) -> q_gen_8643
<z, z>() -> q_gen_8643
<s, z>(q_gen_8645) -> q_gen_8664
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  mult -> 
{{{
Q={q_gen_8642, q_gen_8649, q_gen_8654, q_gen_8662, q_gen_8663},
Q_f={q_gen_8642},
Delta=
{
<z>() -> q_gen_8649
<s>(q_gen_8649) -> q_gen_8654
<z, z>() -> q_gen_8662
<s, z, z>(q_gen_8654) -> q_gen_8642
<z, s, s>(q_gen_8662) -> q_gen_8642
<z, s, z>(q_gen_8649) -> q_gen_8642
<z, z, z>() -> q_gen_8642
<s, z, z>(q_gen_8649) -> q_gen_8663
}

Datatype: <nat, nat, nat>
Convolution form: left
}}}
  ;  plus -> 
{{{
Q={q_gen_8641, q_gen_8647, q_gen_8660},
Q_f={q_gen_8641},
Delta=
{
<z>() -> q_gen_8660
<s, s>(q_gen_8647) -> q_gen_8647
<z, z>() -> q_gen_8647
<s, s, s>(q_gen_8641) -> q_gen_8641
<s, z, s>(q_gen_8647) -> q_gen_8641
<z, s, s>(q_gen_8647) -> q_gen_8641
<z, z, s>(q_gen_8660) -> q_gen_8641
<z, z, z>() -> q_gen_8641
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 5
() -> mult([n, z, z]) -> 9
() -> plus([n, z, n]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5
(leq([s(nn1), z])) -> BOT -> 7
(mult([n, m, _hha])) -> leq([n, _hha]) -> 7
(mult([n, mm, _bha]) /\ plus([n, _bha, _cha])) -> mult([n, s(mm), _cha]) -> 7
(plus([n, mm, _wga])) -> plus([n, s(mm), s(_wga)]) -> 7
}
Sat witness: Found: (() -> mult([n, z, z]), {
n -> s(z)
})

Total time: 0.354548
Reason for stopping: Disproved