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


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YES

Problem:
 or(x,x) -> x
 and(x,x) -> x
 not(not(x)) -> x
 not(and(x,y)) -> or(not(x),not(y))
 not(or(x,y)) -> and(not(x),not(y))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [not](x0) = 4x0 + 5,
   
   [and](x0, x1) = x0 + 2x1 + 4,
   
   [or](x0, x1) = x0 + 2x1 + 6
  orientation:
   or(x,x) = 3x + 6 >= x = x
   
   and(x,x) = 3x + 4 >= x = x
   
   not(not(x)) = 16x + 25 >= x = x
   
   not(and(x,y)) = 4x + 8y + 21 >= 4x + 8y + 21 = or(not(x),not(y))
   
   not(or(x,y)) = 4x + 8y + 29 >= 4x + 8y + 19 = and(not(x),not(y))
  problem:
   not(and(x,y)) -> or(not(x),not(y))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                [1 0 1]  
    [not](x0) = [0 1 0]x0
                [0 0 0]  ,
    
                    [1 0 0]     [1 0 0]     [1]
    [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                    [0 1 1]     [0 0 1]     [0],
    
                   [1 1 0]     [1 0 0]  
    [or](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                   [0 0 0]     [0 0 0]  
   orientation:
                    [1 1 1]    [1 0 1]    [1]    [1 1 1]    [1 0 1]                     
    not(and(x,y)) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y = or(not(x),not(y))
                    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]                     
   problem:
    
   Qed