/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 not(true()) -> false()
 not(false()) -> true()
 evenodd(x,0()) -> not(evenodd(x,s(0())))
 evenodd(0(),s(0())) -> false()
 evenodd(s(x),s(0())) -> evenodd(x,0())

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
             [1 0 0]  
   [s](x0) = [0 0 0]x0
             [0 1 1]  ,
   
                       [1 0 0]     [1 0 0]     [1]
   [evenodd](x0, x1) = [0 0 1]x0 + [0 0 0]x1 + [0]
                       [0 0 1]     [0 0 0]     [0],
   
         [0]
   [0] = [0]
         [1],
   
             [0]
   [false] = [0]
             [0],
   
               [1 0 0]  
   [not](x0) = [0 0 0]x0
               [0 0 0]  ,
   
            [0]
   [true] = [0]
            [0]
  orientation:
                 [0]    [0]          
   not(true()) = [0] >= [0] = false()
                 [0]    [0]          
   
                  [0]    [0]         
   not(false()) = [0] >= [0] = true()
                  [0]    [0]         
   
                    [1 0 0]    [1]    [1 0 0]    [1]                         
   evenodd(x,0()) = [0 0 1]x + [0] >= [0 0 0]x + [0] = not(evenodd(x,s(0())))
                    [0 0 1]    [0]    [0 0 0]    [0]                         
   
                         [1]    [0]          
   evenodd(0(),s(0())) = [1] >= [0] = false()
                         [1]    [0]          
   
                          [1 0 0]    [1]    [1 0 0]    [1]                 
   evenodd(s(x),s(0())) = [0 1 1]x + [0] >= [0 0 1]x + [0] = evenodd(x,0())
                          [0 1 1]    [0]    [0 0 1]    [0]                 
  problem:
   not(true()) -> false()
   not(false()) -> true()
   evenodd(x,0()) -> not(evenodd(x,s(0())))
   evenodd(s(x),s(0())) -> evenodd(x,0())
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]     [0]
    [s](x0) = [0 1 0]x0 + [1]
              [0 0 0]     [0],
    
                        [1 1 0]     [1 0 1]  
    [evenodd](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                        [0 0 0]     [0 0 0]  ,
    
          [0]
    [0] = [0]
          [1],
    
              [0]
    [false] = [0]
              [1],
    
                [1 0 1]  
    [not](x0) = [0 0 0]x0
                [0 0 1]  ,
    
             [0]
    [true] = [0]
             [1]
   orientation:
                  [1]    [0]          
    not(true()) = [0] >= [0] = false()
                  [1]    [1]          
    
                   [1]    [0]         
    not(false()) = [0] >= [0] = true()
                   [1]    [1]         
    
                     [1 1 0]    [1]    [1 1 0]                          
    evenodd(x,0()) = [0 0 0]x + [0] >= [0 0 0]x = not(evenodd(x,s(0())))
                     [0 0 0]    [0]    [0 0 0]                          
    
                           [1 1 0]    [1]    [1 1 0]    [1]                 
    evenodd(s(x),s(0())) = [0 0 0]x + [0] >= [0 0 0]x + [0] = evenodd(x,0())
                           [0 0 0]    [0]    [0 0 0]    [0]                 
   problem:
    evenodd(s(x),s(0())) -> evenodd(x,0())
   Matrix Interpretation Processor: dim=3
    
    interpretation:
               [1 0 0]     [0]
     [s](x0) = [0 0 0]x0 + [0]
               [0 0 0]     [1],
     
                         [1 0 0]     [1 0 1]  
     [evenodd](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                         [0 0 0]     [0 0 0]  ,
     
           [0]
     [0] = [0]
           [0]
    orientation:
                            [1 0 0]    [1]    [1 0 0]                  
     evenodd(s(x),s(0())) = [0 0 0]x + [0] >= [0 0 0]x = evenodd(x,0())
                            [0 0 0]    [0]    [0 0 0]                  
    problem:
     
    Qed