dafny_fact_run_custom_7b.txt

Traceback (most recent call last):
  File "/home/namin/llm-verified-with-monte-carlo-tree-search/run.py", line 1, in <module>
    import llm
  File "/home/namin/llm-verified-with-monte-carlo-tree-search/llm.py", line 12, in <module>
    import huggingface_generate
  File "/home/namin/llm-verified-with-monte-carlo-tree-search/huggingface_generate.py", line 6
    <<<<<<< HEAD
    ^^
SyntaxError: invalid syntax
[2023-12-06 22:10:40,137] [INFO] [real_accelerator.py:158:get_accelerator] Setting ds_accelerator to cuda (auto detect)
/home/namin/mambaforge/envs/trl/lib/python3.10/site-packages/trl/trainer/ppo_config.py:141: UserWarning: The `optimize_cuda_cache` arguement will be deprecated soon, please use `optimize_device_cache` instead.
  warnings.warn(
/home/namin/mambaforge/envs/trl/lib/python3.10/site-packages/transformers/models/auto/auto_factory.py:472: FutureWarning: The `use_auth_token` argument is deprecated and will be removed in v5 of Transformers. Please use `token` instead.
  warnings.warn(

Loading checkpoint shards:   0%|          | 0/3 [00:00<?, ?it/s]
Loading checkpoint shards:  33%|███▎      | 1/3 [00:01<00:02,  1.25s/it]
Loading checkpoint shards:  67%|██████▋   | 2/3 [00:02<00:01,  1.22s/it]
Loading checkpoint shards: 100%|██████████| 3/3 [00:03<00:00,  1.09s/it]
Loading checkpoint shards: 100%|██████████| 3/3 [00:03<00:00,  1.13s/it]
/home/namin/mambaforge/envs/trl/lib/python3.10/site-packages/transformers/utils/hub.py:374: FutureWarning: The `use_auth_token` argument is deprecated and will be removed in v5 of Transformers. Please use `token` instead.
  warnings.warn(
Special tokens have been added in the vocabulary, make sure the associated word embeddings are fine-tuned or trained.
/home/namin/mambaforge/envs/trl/lib/python3.10/site-packages/transformers/generation/utils.py:1473: UserWarning: You have modified the pretrained model configuration to control generation. This is a deprecated strategy to control generation and will be removed soon, in a future version. Please use and modify the model generation configuration (see https://huggingface.co/docs/transformers/generation_strategies#default-text-generation-configuration )
  warnings.warn(
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n: nat): nat { if n == 0 then 1 else n * Factorial(n-1) }
lemma {:induction n} FactorialPositive(n: nat)  ensures 1 <= Factorial(n)
{ if n > 0 { FactorialPositive(n-1); } }
method TestFactorial() {
  assert 1 <= Factorial(0);
  assert 1 <= Factorial(1
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n: nat): nat
{
   if n == 0 then 1 else n * fact(n-1)
}

lemma factLemma(n: nat)
   ensures 1 <= fact(n)
{
   if n > 0 {
      factLemma(n-1);
   }
}

method testFact()
{
   assert fact(5) == 120;
   factLemma(5);

File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n: nat): nat { if n == 0 then 1 else n * Factorial(n-1) }

lemma FactorialPositive(n: nat)  ensures 0 < Factorial(n) {}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
    ensures Factorial(n) >= 1
{
    if n == 0 then 1 else n * Factorial(n-1)
}
lemma TestFactorial()
    ensures Factorial(5) >= 1
{}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
    ensures 1 <= Factorial(n)
{
    if n == 0 then 1 else n * Factorial(n-1)
}
lemma TestFactorial()
    ensures forall n:nat :: 1 <= Factorial(n)
{
    forall n:nat { Factorial#[_k](n); }
}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n: nat): nat
{
  if n == 0 then 1 else n * fact(n-1)
}

lemma {:induction false} FactIsPositive(n: nat)
  ensures 1 <= fact(n)
{
  if 0 < n {
    FactIsPositive(n-1);
  }
}

// A simple Fibonacci function and a lemma stating that F
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
    ensures Factorial(n) >= 1
{
    if n == 0 then 1 else n * Factorial(n-1)
}
lemma TestFactorial()
    ensures Factorial(5) >= 1
{}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n: nat): nat
{
  if n == 0 then 1 else n*Fact(n-1)
}

lemma ProveFactPos(n: nat)
  ensures 0 < Fact(n)
{
  if n > 0 {
    ProveFactPos(n-1);
  }
}

// A palindrome predicate and a proof that the empty string is a palindrome.
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n: nat): nat { if n == 0 then 1 else n * Factorial(n-1) }
lemma     Lemma_Factorial_Positive(n: nat)  ensures 0 < Factorial(n) }
{ if n == 0 { } else { Lemma_Factorial_Positive(n-1); } }
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n: nat): nat
{
  if n == 0 then 1 else n * fact(n-1)
}

lemma factLemma(n: nat)
  ensures 1 <= fact(n)
{
  if n > 0 {
    factLemma(n-1);
  }
}

method factCheck() {
  assert 1 <= fact(0);
  assert 1 <= fact(1);

File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n:nat):nat
{if n == 0 then 1 else n*fact(n-1)}

lemma fact_pos(n:nat)
  ensures 1 <= fact(n)
{if n != 0 {fact_pos(n-1);}}

method fact_pos_test(n:nat)
  ensures 1 <= fact(n)
{
  assume false;
  fact_pos(n
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
    ensures Factorial(n) >= 1
{
    if n == 0 then 1 else n * Factorial(n-1)
}
lemma TestFactorial()
    ensures Factorial(3) >= 1
{}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
    ensures Factorial(n) > 0
{
    if n == 0 then 1 else n * Factorial(n-1)
}
lemma TestFactorial()
    ensures Factorial(3) > 0
{}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n: nat): nat { if n == 0 then 1 else n * Factorial(n-1) }
lemma {:induction n} FactorialPositive(n: nat)  ensures 0 < Factorial(n) {}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n: nat): nat
{
  if n == 0 then 1 else n * Fact(n-1)
}

lemma {:induction n} FactPositive(n: nat)
  ensures 0 < Fact(n)
{
  if n == 0 {
  } else {
    FactPositive(n-1);
  }
}


datatype Option<T> = None | Some(
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n:nat):nat
{if n == 0 then 1 else n*fact(n-1)}

lemma fact_positive(n:nat)
  ensures 1 <= fact(n)
{if n != 0 {fact_positive(n-1);}}

// A natural number N with property that all numbers smaller than N
// are not prime.
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
    ensures Fact(n) >= 1
{ if n == 0 then 1 else n * Fact(n-1) }

method Test()
{
    var x := Fact(5);
    assert x >= 1; // this is known from the function's postcondition
    x := -x;
    assert x >= -1; // error: should fail because x is negative
}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n: nat): nat
{
   if n == 0 then 1 else n*fact(n-1)
}

lemma factLemma(n: nat)
   ensures 1 <= fact(n)
{
   if n > 0 {
      factLemma(n-1);
   }
}

```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n: nat): nat
{
    if n == 0 then 1 else n * Fact(n-1)
}

lemma {:induction n} FactPositive(n: nat)
    ensures 1 <= Fact(n)
{
    if 0 < n {
        FactPositive(n-1);
    }
}

// A simple Fibonacci function and a proof that it is always positive
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
    ensures  Factorial(n) > 0
{
    if n == 0 then 1 else n * Factorial(n-1)
}
lemma FactorialStrictlyPositive(n:nat)
    ensures  Factorial(n) > 0
{}
// A Fibonacci function and a proof that the Fibonacci numbers are always positive.
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n: nat): nat { if n == 0 then 1 else n * Factorial(n-1) }

lemma {:induction n} FactorialPositive(n: nat)
  ensures 1 <= Factorial(n)
{
  if 0 < n {
    FactorialPositive(n-1);
  }
}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
{ if n == 0 then 1 else n*Fact(n-1) }

lemma ProveFactPositive(n:nat)
  ensures 1 <= Fact(n)
{
  if 0 < n {
    ProveFactPositive(n-1);
  }
}

// A simple Fibonacci function and a proof that it is strictly positive.
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n: nat): nat
{
  if n == 0 then 1 else n * fact(n-1)
}

lemma {:induction n} FactLemma(n: nat)
  ensures 0 < fact(n)
{
  if n == 0 {
  } else {
    FactLemma(n-1);
  }
}

method Test()
{
  assert 0 < fact(5);
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n: nat): nat
{
  if n == 0 then 1 else n * Fact(n-1)
}

lemma ProveFactPos(n: nat)
  ensures 0 < Fact(n)
{
  if n == 0 {
  } else {
    ProveFactPos(n-1);
  }
}

// A palindrome predicate and a proof that the empty string is a palind
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n: nat): nat
{
   if n == 0 then 1 else n * fact(n-1)
}

lemma factLemma(n: nat)
   ensures 1 <= fact(n)
{
   if n > 0 {
      factLemma(n-1);
   }
}

method testFact()
{
   assert fact(5) == 120;
   factLemma(5);

File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n: nat): nat
{
  if n == 0 then 1 else n * Fact(n-1)
}

lemma ProveFactPos(n: nat)
  ensures 0 < Fact(n)
{
  if n > 0 {
    ProveFactPos(n-1);
  }
}

// A palindrome predicate and a proof that the empty string is a palindrome.
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
    ensures 0 < Factorial(n)
{
    if n == 0 then 1 else n * Factorial(n-1)
}
lemma TestFactorial()
    ensures 0 < Factorial(4)
{}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
{ if n == 0 then 1 else n*Fact(n-1) }

lemma ProveFactPositive(n:nat)
    ensures 1 <= Fact(n)
{
    if n > 0 {
        ProveFactPositive(n-1);
    }
}

// A Fibonacci function and a proof that the Fibonacci numbers are always positive.
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
    ensures  Factorial(n) >= 1
{
    if n == 0 then 1 else n * Factorial(n-1)
}
lemma FactorialStrictlyPositive(n:nat)
    ensures  Factorial(n) >= 1
{}
// A Fibonacci function and a proof that the Fibonacci numbers are always strictly positive.
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
    ensures 0 < Factorial(n)
{
    if n == 0 then 1 else n * Factorial(n-1)
}
lemma TestFactorial()
    ensures 0 < Factorial(5)
{}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
    ensures Fact(n) >= 1
{ if n == 0 then 1 else n*Fact(n-1) }

method Test()
{
    var x := Fact(5);
    assert x == 5*4*3*2*1;
}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
{
  if n == 0 then 1 else n*Factorial(n-1)
}

lemma {:induction n} FactorialPositive(n:nat)
  ensures 0 < Factorial(n)
{
  if n == 0 {
  } else {
    FactorialPositive(n-1);
  }
}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n: nat): nat
{
  if n == 0 then 1 else n * Fact(n-1)
}

lemma {:induction n} FactPositive(n: nat)
  ensures 0 < Fact(n)
{
  if 0 < n {
    FactPositive(n-1);
  }
}

// A Fibonacci function and a proof that the Fibonac
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n: nat): nat
{
  if n == 0 then 1 else n*fact(n-1)
}

lemma {:induction false} FactPositive(n: nat)
  ensures 1 <= fact(n)
{
  if 0 < n {
    FactPositive(n-1);
  }
}

method Test()
{
  var x := fact(5);
 
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
    ensures  Factorial(n) > 0
{
    if n == 0 then 1 else n * Factorial(n-1)
}
lemma TestFactorial()
    ensures  Factorial(3) == 6
{
    assert Factorial(3) == 6;
}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n: nat): nat { if n == 0 then 1 else n * Factorial(n-1) }
lemma     Lemma_Factorial_Positive(n: nat)  ensures 0 < Factorial(n) }
{ if n == 0 { } else { Lemma_Factorial_Positive(n-1); } }
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
{
  if n == 0 then 1 else n*Fact(n-1)
}

lemma FactLemma(n:nat)
  ensures 1 <= Fact(n)
{
  if n != 0 {
    FactLemma(n-1);
  }
}

method TestFact()
{
  assert Fact(5) == 5*4*3*2*1;

File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n:nat):nat
{if n == 0 then 1 else n*fact(n-1)}

lemma factLemma(n:nat)
ensures fact(n) > 0
{if n > 0 {factLemma(n-1);}}

method factCheck(n:nat)
ensures fact(n) > 0
{factLemma(n);}

// A palindrome function and a proof that the empty
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n: nat): nat { if n == 0 then 1 else n * Factorial(n-1) }

lemma {:induction n} FactorialPositive(n: nat)
  ensures 1 <= Factorial(n)
{
  if 0 < n {
    FactorialPositive(n-1);
  }
}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n: nat): nat
{
   if n == 0 then 1 else n*fact(n-1)
}

lemma factLemma(n: nat)
   ensures 1 <= fact(n)
{
   if n > 0 {
      factLemma(n-1);
   }
}

method testFact()
{
   assert fact(5) == 5*4*3*2*1;
  
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n: nat): nat
{
  if n == 0 then 1 else n * Fact(n-1)
}

lemma {:induction n} FactPositive(n: nat)
  ensures 0 < Fact(n)
{
  if n == 0 {
  } else {
    FactPositive(n-1);
  }
}

// A simple Fibonacci function and a lemma that
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
    ensures Factorial(n) >= 1
{
    if n == 0 then 1 else n * Factorial(n-1)
}
lemma FactorialStrictlyPositive(n:nat)
    ensures Factorial(n) >= 1
{}
// A proof that n!! (n factored by 2) is always strictly positive.
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n:nat):nat
{if n == 0 then 1 else n*fact(n-1)}

lemma fact_pos(n:nat)
  ensures 1 <= fact(n)
{if 0 < n {fact_pos(n-1);}}

method fact_pos_test(n:nat)
  ensures 1 <= fact(n)
{
  assume false;
  fact_pos(n
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)
}
lemma {:induction n} FactPositive(n:nat)
  ensures 0 < Fact(n)
{
}
method TestFact() {
  assert 5 < Fact(6);
}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n: nat): nat
{
    if n == 0 then 1 else n * Fact(n-1)
}

lemma ProveFactPos(n: nat)
    ensures 1 <= Fact(n)
{
    if n == 0 {
    } else {
        ProveFactPos(n-1);
    }
}

// A simple Fibonacci function and a proof that it is always positive
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n: nat): nat
{
  if n == 0 then 1 else n * Fact(n-1)
}

lemma {:induction n} FactPositive(n: nat)
  ensures 1 <= Fact(n)
{
  if 0 < n {
    FactPositive(n-1);
  }
}

method TestFact()
{
  assert 1 <= Fact(0);

File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n: nat): nat
{
   if n == 0 then 1 else n * fact(n-1)
}

lemma {:induction false} FactLemma(n: nat)
   ensures 1 <= fact(n)
{
   if n == 0 {
   } else {
      FactLemma(n - 1);
   }
}

method TestFact() {
   assert fact(5) == 1
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)
}
lemma TestFact()
  ensures forall n:nat :: 0 < Fact(n)
{
  forall n:nat
    ensures 0 < Fact(n)
  {
    if n != 0 {
      TestFact();
    }
 
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n:nat):nat
{if n == 0 then 1 else n*fact(n-1)}

lemma fact_pos(n:nat)
  ensures 1 <= fact(n)
{if n != 0 {fact_pos(n-1);}}

// A function that computes the nth Fibonacci number
function Fib(n:nat):nat
{if n < 2 then n else F
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
    ensures 0 <= Fact(n)
{
    if n == 0 then 1 else n * Fact(n-1)
}
lemma TestFact()
    ensures forall n:nat :: 0 < Fact(n)
{
    forall n:nat
        ensures 0 < Fact(n)
    {
        if n == 0 { }
        else
        {
            TestFact
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n: nat): nat
{
  if n == 0 then 1 else n * fact(n-1)
}

lemma {:induction false} FactIsPositive(n: nat)
  ensures 1 <= fact(n)
{
  if n != 0 {
    FactIsPositive(n-1);
  }
}

method TestFact() {
  assert fact(5) == 12
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
    ensures Factorial(n) >= 1
{
    if n == 0 then 1 else n * Factorial(n-1)
}
lemma TestFactorial()
    ensures Factorial(5) >= 1
{}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
    ensures 0 < Factorial(n)
{
    if n == 0 then 1 else n * Factorial(n-1)
}
lemma TestFactorial()
    ensures 0 < Factorial(5)
{}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
    ensures Factorial(n) >= 1
{
    if n == 0 then 1 else n * Factorial(n-1)
}
lemma TestFactorial()
    ensures Factorial(3) >= 1
{}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n: nat): nat
{
  if n == 0 then 1 else n * Fact(n-1)
}

lemma {:induction n} FactPositive(n: nat)
  ensures 0 < Fact(n)
{
  if n == 0 {
  } else {
    FactPositive(n-1);
  }
}

// A simple Fibonacci function and a lemma stating
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
{
  if n == 0 then 1 else n*Factorial(n-1)
}

lemma FactorialProof(n:nat)
  ensures 1 <= Factorial(n)
{
  if n == 0 {
  } else {
    FactorialProof(n-1);
  }
}

// A Fibonacci function and a proof that it is always positive
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n: nat): nat
{
   if n == 0 then 1 else n*fact(n-1)
}

lemma {:induction n} PositivityLemma(n: nat)
   ensures 1 <= fact(n)
{
   if n == 0 {
   } else {
      PositivityLemma(n-1);
   }
}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
{
  if n == 0 then 1 else n*Fact(n-1)
}
lemma  LFact(n:nat)
  ensures 1 <= Fact(n)
{
  if n != 0 {
    LFact(n-1);
  }
}
method  MFact(n:nat) returns (r:nat)
  ensures r == Fact(n)
{
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n: nat): nat
{
   if n == 0 then 1 else n * fact(n-1)
}

lemma factLemma(n: nat)
   ensures 1 <= fact(n)
{
   if n > 0 {
      factLemma(n-1);
   }
}

method factCheck()
{
   assert 1 <= fact(0);
   assert 1 <= fact(1);
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n: nat): nat { if n == 0 then 1 else n * Factorial(n-1) }
lemma {:induction n} FactorialStrictlyPositive(n: nat)  ensures 0 < Factorial(n) {}

method FactorialTables()
{
  // Print factorial tables for the first 10 positive integers.
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
    ensures Fact(n) >= 1
{ if n == 0 then 1 else n*Fact(n-1) }

method Test()
{
    assert Fact(5) == 5*4*3*2*1;
    assert Fact(0) == 1;
    assert Fact(1) == 1;
    assert Fact(2) == 2;
    assert Fact(3) == 6;
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n:nat):nat
{if n == 0 then 1 else n*fact(n-1)}

lemma fact_positive(n:nat)
  ensures 1 <= fact(n)
{if n != 0 {fact_positive(n-1);}}

method fact_pos(n:nat)
  ensures 1 <= fact(n)
{
  assume  false;
}

method fact_pos
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n: nat): nat { if n == 0 then 1 else n * Factorial(n-1) }
lemma {:induction n} FactorialPositive(n: nat)  ensures 0 < Factorial(n) {}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
    ensures 0 <= Factorial(n)
{
    if n == 0 then 1 else n * Factorial(n-1)
}

lemma FactorialStrictlyPositive(n:nat)
    ensures 0 < Factorial(n)
{
}

// An abstract stack interface that supports an unlimited number of push and
// pop operations.
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
    ensures Factorial(n) >= 1
{
    if n == 0 then 1 else n * Factorial(n-1)
}
lemma TestFactorial()
    ensures Factorial(3) >= 1
{}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n: nat): nat
{
  if n == 0 then 1 else n*Fact(n-1)
}

lemma {:induction n} FactPositive(n: nat)
  ensures 0 < Fact(n)
{
  if n == 0 {
  } else {
    FactPositive(n-1);
  }
}

// A simple Fibonacci function and a proof that
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
    ensures Factorial(n) >= 1
{
    if n == 0 then 1 else n * Factorial(n-1)
}
lemma FactorialStrictlyPositive(n:nat)
    ensures Factorial(n) >= 1
{}
// A positive natural number n satisfies the proposition "at least twice as large as n"
// for all numbers larger than n do not satisfy this proposition.
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n:nat):nat
{ if n == 0 then 1 else n*fact(n-1) }

lemma fact_positive(n:nat)
  ensures 1 <= fact(n)
{ if n > 0 { fact_positive(n-1); } }

// A simple Fibonacci function and a proof that it is monotonic.
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n: nat): nat
{
   if n == 0 then 1 else n * fact(n-1)
}

lemma factLemma(n: nat)
   ensures 1 <= fact(n)
{
   if n > 0 {
      factLemma(n-1);
   }
}

method testFact()
{
   assert fact(5) == 120;
   factLemma(5);

File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n: nat): nat
{
  if n == 0 then 1 else n*fact(n-1)
}

lemma {:induction n} FactPositive(n: nat)
  ensures 0 < fact(n)
{
  if n == 0 {
  } else {
    FactPositive(n-1);
  }
}

// A simple specification and proof of a function that returns the maximum
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
    ensures 0 < Factorial(n)
{
    if n == 0 then 1 else n * Factorial(n-1)
}
lemma TestFactorial()
    ensures 0 < Factorial(5)
{}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n: nat): nat
{
  if n == 0 then 1 else n * Fact(n-1)
}

lemma {:induction false} FactPositive(n: nat)
  ensures 1 <= Fact(n)
{
  if n == 0 {
  } else {
    FactPositive(n-1);
  }
}

// A simple Fibonacci function and a proof that
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
    ensures Factorial(n) >= 1
{
    if n == 0 then 1 else n * Factorial(n-1)
}
lemma TestFactorial()
    ensures Factorial(5) >= 1
{}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
{
  if n == 0 then 1 else n*Fact(n-1)
}

lemma {:induction n} FactPositive(n:nat)
  ensures 1 <= Fact(n)
{
  if n == 0 {
  } else {
    FactPositive(n-1);
  }
}

method TestFact()
{
  assert Fact(5)
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n: nat): nat
{
  if n == 0 then 1 else n * Fact(n-1)
}

lemma FactLemma(n: nat)
  ensures 0 < Fact(n)
{
  if n > 0 {
    FactLemma(n-1);
  }
}

method TestFact()
{
  assert Fact(5) == 5*4*3*2*1;
 
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Factorial(n:nat):nat
    ensures Factorial(n) >= 1
{
    if n == 0 then 1 else n * Factorial(n-1)
}
lemma TestFactorial()
    ensures Factorial(5) >= 1
{}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
    ensures  Fact(n) >= 1
{
    if n == 0 then 1 else n * Fact(n-1)
}
lemma TestFact()
    ensures  Fact(3) >= 1
{}
```
File "./ex.v", line 1, characters 0-5:
Error: Syntax error: illegal begin of vernac.


SCORE
-1.0
TEXT
[2023-12-06 22:18:43,258] [INFO] [real_accelerator.py:158:get_accelerator] Setting ds_accelerator to cuda (auto detect)
/home/namin/mambaforge/envs/trl/lib/python3.10/site-packages/trl/trainer/ppo_config.py:141: UserWarning: The `optimize_cuda_cache` arguement will be deprecated soon, please use `optimize_device_cache` instead.
  warnings.warn(
/home/namin/mambaforge/envs/trl/lib/python3.10/site-packages/transformers/models/auto/auto_factory.py:472: FutureWarning: The `use_auth_token` argument is deprecated and will be removed in v5 of Transformers. Please use `token` instead.
  warnings.warn(

Loading checkpoint shards:   0%|          | 0/3 [00:00<?, ?it/s]
Loading checkpoint shards:  33%|███▎      | 1/3 [00:01<00:02,  1.32s/it]
Loading checkpoint shards:  67%|██████▋   | 2/3 [00:02<00:01,  1.30s/it]
Loading checkpoint shards: 100%|██████████| 3/3 [00:03<00:00,  1.13s/it]
Loading checkpoint shards: 100%|██████████| 3/3 [00:03<00:00,  1.18s/it]
/home/namin/mambaforge/envs/trl/lib/python3.10/site-packages/transformers/utils/hub.py:374: FutureWarning: The `use_auth_token` argument is deprecated and will be removed in v5 of Transformers. Please use `token` instead.
  warnings.warn(
Special tokens have been added in the vocabulary, make sure the associated word embeddings are fine-tuned or trained.
Traceback (most recent call last):
  File "/home/namin/llm-verified-with-monte-carlo-tree-search/run.py", line 8, in <module>
    from prompts import prompt, expansion_count, min_lines, check_func
  File "/home/namin/llm-verified-with-monte-carlo-tree-search/prompts.py", line 333, in <module>
    assert LANG in supported_langs
AssertionError
[2023-12-06 22:20:15,911] [INFO] [real_accelerator.py:158:get_accelerator] Setting ds_accelerator to cuda (auto detect)
/home/namin/mambaforge/envs/trl/lib/python3.10/site-packages/trl/trainer/ppo_config.py:141: UserWarning: The `optimize_cuda_cache` arguement will be deprecated soon, please use `optimize_device_cache` instead.
  warnings.warn(
/home/namin/mambaforge/envs/trl/lib/python3.10/site-packages/transformers/models/auto/auto_factory.py:472: FutureWarning: The `use_auth_token` argument is deprecated and will be removed in v5 of Transformers. Please use `token` instead.
  warnings.warn(

Loading checkpoint shards:   0%|          | 0/3 [00:00<?, ?it/s]
Loading checkpoint shards:  33%|███▎      | 1/3 [00:01<00:02,  1.29s/it]
Loading checkpoint shards:  67%|██████▋   | 2/3 [00:02<00:01,  1.28s/it]
Loading checkpoint shards: 100%|██████████| 3/3 [00:03<00:00,  1.11s/it]
Loading checkpoint shards: 100%|██████████| 3/3 [00:03<00:00,  1.16s/it]
/home/namin/mambaforge/envs/trl/lib/python3.10/site-packages/transformers/utils/hub.py:374: FutureWarning: The `use_auth_token` argument is deprecated and will be removed in v5 of Transformers. Please use `token` instead.
  warnings.warn(
Special tokens have been added in the vocabulary, make sure the associated word embeddings are fine-tuned or trained.
/home/namin/mambaforge/envs/trl/lib/python3.10/site-packages/transformers/generation/utils.py:1473: UserWarning: You have modified the pretrained model configuration to control generation. This is a deprecated strategy to control generation and will be removed soon, in a future version. Please use and modify the model generation configuration (see https://huggingface.co/docs/transformers/generation_strategies#default-text-generation-configuration )
  warnings.warn(
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat

SCORE
1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)

SCORE
1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{

  |
4 | {
  |  ^

ex.dfy(4,1): Error: invalid UnaryExpression
1 parse errors detected in ex.dfy

SCORE
None
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)

  |
5 |   if n == 0 then 1 else n * Fact(n-1)
  |                                      ^

ex.dfy(5,37): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)
}

SCORE
1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)
}
lemma {:induction n} FactLemma(n:nat)

SCORE
1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)
}
lemma {:induction n} FactLemma(n:nat)
  ensures 0 < Fact(n)

SCORE
1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)
}
lemma {:induction n} FactLemma(n:nat)
  ensures 0 < Fact(n)
{

  |
9 | {
  |  ^

ex.dfy(9,1): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)
}
lemma {:induction n} FactLemma(n:nat)
  ensures 0 < Fact(n)
{
  if n == 0 {

   |
10 |   if n == 0 {
   |              ^

ex.dfy(10,13): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)
}
lemma {:induction n} FactLemma(n:nat)
  ensures 0 < Fact(n)
{
  if n == 0 {
  } else {

   |
11 |   } else {
   |           ^

ex.dfy(11,10): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)
}
lemma {:induction n} FactLemma(n:nat)
  ensures 0 < Fact(n)
{
  if n == 0 {
  } else {
    FactLemma(n-1);

   |
12 |     FactLemma(n-1);
   |                    ^

ex.dfy(12,19): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)
}
lemma {:induction n} FactLemma(n:nat)
  ensures 0 < Fact(n)
{
  if n == 0 {
  } else {
    FactLemma(n-1);
  }

   |
13 |   }
   |    ^

ex.dfy(13,3): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)
}
lemma {:induction n} FactLemma(n:nat)
  ensures 0 < Fact(n)
{
  if n == 0 {
  } else {
    FactLemma(n-1);
  }
}

SCORE
1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)
}
lemma {:induction n} FactLemma(n:nat)
  ensures 0 < Fact(n)
{
  if n == 0 {
  } else {
    FactLemma(n-1);
  }
}
// A simple method that uses the lemma.

SCORE
1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)
}
lemma {:induction n} FactLemma(n:nat)
  ensures 0 < Fact(n)
{
  if n == 0 {
  } else {
    FactLemma(n-1);
  }
}
// A simple method that uses the lemma.
method TestFact()

SCORE
1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)
}
lemma {:induction n} FactLemma(n:nat)
  ensures 0 < Fact(n)
{
  if n == 0 {
  } else {
    FactLemma(n-1);
  }
}
// A simple method that uses the lemma.
method TestFact()
{

   |
17 | {
   |  ^

ex.dfy(17,1): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)
}
lemma {:induction n} FactLemma(n:nat)
  ensures 0 < Fact(n)
{
  if n == 0 {
  } else {
    FactLemma(n-1);
  }
}
// A simple method that uses the lemma.
method TestFact()
{
  assert 0 < Fact(5); // this assumes that the lemma is correct

   |
18 |   assert 0 < Fact(5); // this assumes that the lemma is correct
   |                                                                ^

ex.dfy(18,63): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)
}
lemma {:induction n} FactLemma(n:nat)
  ensures 0 < Fact(n)
{
  if n == 0 {
  } else {
    FactLemma(n-1);
  }
}
// A simple method that uses the lemma.
method TestFact()
{
  assert 0 < Fact(5); // this assumes that the lemma is correct
}

SCORE
1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)
}
lemma {:induction n} FactLemma(n:nat)
  ensures 0 < Fact(n)
{
  if n == 0 {
  } else {
    FactLemma(n-1);
  }
}
// A simple method that uses the lemma.
method TestFact()
{
  assert 0 < Fact(5); // this assumes that the lemma is correct
}


SCORE
1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)
}
lemma {:induction n} FactLemma(n:nat)
  ensures 0 < Fact(n)
{
  if n == 0 {
  } else {
    FactLemma(n-1);
  }
}
// A simple method that uses the lemma.
method TestFact()
{
  assert 0 < Fact(5); // this assumes that the lemma is correct
}



SCORE
1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)
}
lemma {:induction n} FactLemma(n:nat)
  ensures 0 < Fact(n)
{
  if n == 0 {
  } else {
    FactLemma(n-1);
  }
}
// A simple method that uses the lemma.
method TestFact()
{
  assert 0 < Fact(5); // this assumes that the lemma is correct
}


// A fibonacci function and a proof that the function is always positive.

SCORE
1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)
}
lemma {:induction n} FactLemma(n:nat)
  ensures 0 < Fact(n)
{
  if n == 0 {
  } else {
    FactLemma(n-1);
  }
}
// A simple method that uses the lemma.
method TestFact()
{
  assert 0 < Fact(5); // this assumes that the lemma is correct
}


// A fibonacci function and a proof that the function is always positive.
// Note that the proof needs the help of a lemma in some cases.

SCORE
1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  Fact(n:nat):nat
  ensures 0 <= Fact(n)
{
  if n == 0 then 1 else n * Fact(n-1)
}
lemma {:induction n} FactLemma(n:nat)
  ensures 0 < Fact(n)
{
  if n == 0 {
  } else {
    FactLemma(n-1);
  }
}
// A simple method that uses the lemma.
method TestFact()
{
  assert 0 < Fact(5); // this assumes that the lemma is correct
}


// A fibonacci function and a proof that the function is always positive.
// Note that the proof needs the help of a lemma in some cases.
function  Fib(n:nat):nat

SCORE
1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n:nat):nat

SCORE
1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n:nat):nat
{if n == 0 then 1 else n*fact(n-1)}

SCORE
1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n:nat):nat
{if n == 0 then 1 else n*fact(n-1)}
lemma fact_pos(n:nat)

SCORE
1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n:nat):nat
{if n == 0 then 1 else n*fact(n-1)}
lemma fact_pos(n:nat)
ensures 1 <= fact(n)

SCORE
1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n:nat):nat
{if n == 0 then 1 else n*fact(n-1)}
lemma fact_pos(n:nat)
ensures 1 <= fact(n)
{if n != 0 {fact_pos(n-1);}}

SCORE
1.0
TEXT
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n:nat):nat
{if n == 0 then 1 else n*fact(n-1)}
lemma fact_pos(n:nat)
ensures 1 <= fact(n)
{if n != 0 {fact_pos(n-1);}}
```
SCORE
1.0
CHOSEN SOLUTION
```dafny
// A factorial function and a proof that the factorial is always strictly positive.
function  fact(n:nat):nat
{if n == 0 then 1 else n*fact(n-1)}
lemma fact_pos(n:nat)
ensures 1 <= fact(n)
{if n != 0 {fact_pos(n-1);}}
```

STATS

number of nodes: 41
number of gen nodes: 21 (including leaves: 2)
number of back nodes: 20 (including leaves: 19)

expansion count: 21 (including failed: 1)