/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:
 and(x,false()) -> false()
 and(x,not(false())) -> x
 not(not(x)) -> x
 implies(false(),y) -> not(false())
 implies(x,false()) -> not(x)
 implies(not(x),not(y)) -> implies(y,and(x,y))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [implies](x0, x1) = 4x0 + 4x1,
   
   [not](x0) = 3x0 + 2,
   
   [and](x0, x1) = 2x0 + 2x1 + 3,
   
   [false] = 2
  orientation:
   and(x,false()) = 2x + 7 >= 2 = false()
   
   and(x,not(false())) = 2x + 19 >= x = x
   
   not(not(x)) = 9x + 8 >= x = x
   
   implies(false(),y) = 4y + 8 >= 8 = not(false())
   
   implies(x,false()) = 4x + 8 >= 3x + 2 = not(x)
   
   implies(not(x),not(y)) = 12x + 12y + 16 >= 8x + 12y + 12 = implies(y,and(x,y))
  problem:
   implies(false(),y) -> not(false())
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                        [1 1 0]     [1 0 0]  
    [implies](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                        [0 0 0]     [0 0 0]  ,
    
                [1 0 0]  
    [not](x0) = [0 0 0]x0
                [0 0 0]  ,
    
              [0]
    [false] = [1]
              [0]
   orientation:
                         [1 0 0]    [1]    [0]               
    implies(false(),y) = [0 0 0]y + [0] >= [0] = not(false())
                         [0 0 0]    [0]    [0]               
   problem:
    
   Qed