/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


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=3
  
  interpretation:
                   [1 0 0]     [1 0 0]     [1]
   [and](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [0]
                   [1 1 1]     [0 0 0]     [0],
   
                       [1 1 1]     [1 0 1]     [0]
   [implies](x0, x1) = [0 1 0]x0 + [0 1 0]x1 + [1]
                       [1 1 1]     [0 0 1]     [0],
   
             [1]
   [false] = [0]
             [0],
   
               [1 0 1]     [0]
   [not](x0) = [0 1 0]x0 + [1]
               [1 1 1]     [0]
  orientation:
                    [1 0 0]    [2]    [1]          
   and(x,false()) = [0 1 0]x + [0] >= [0] = false()
                    [1 1 1]    [0]    [0]          
   
                         [1 0 0]    [2]         
   and(x,not(false())) = [0 1 0]x + [0] >= x = x
                         [1 1 1]    [0]         
   
                 [2 1 2]    [0]         
   not(not(x)) = [0 1 0]x + [2] >= x = x
                 [2 2 2]    [1]         
   
                        [1 0 1]    [1]    [1]               
   implies(false(),y) = [0 1 0]y + [1] >= [1] = not(false())
                        [0 0 1]    [1]    [1]               
   
                        [1 1 1]    [1]    [1 0 1]    [0]         
   implies(x,false()) = [0 1 0]x + [1] >= [0 1 0]x + [1] = not(x)
                        [1 1 1]    [0]    [1 1 1]    [0]         
   
                            [2 2 2]    [2 1 2]    [1]    [2 1 1]    [2 1 1]    [1]                      
   implies(not(x),not(y)) = [0 1 0]x + [0 1 0]y + [3] >= [0 1 0]x + [0 1 0]y + [1] = implies(y,and(x,y))
                            [2 2 2]    [1 1 1]    [1]    [1 1 1]    [1 1 1]    [0]                      
  problem:
   not(not(x)) -> x
   implies(false(),y) -> not(false())
   implies(not(x),not(y)) -> implies(y,and(x,y))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [and](x0, x1) = 2x0 + 2x1,
    
    [implies](x0, x1) = 6x0 + 4x1 + 6,
    
    [false] = 0,
    
    [not](x0) = 4x0 + 1
   orientation:
    not(not(x)) = 16x + 5 >= x = x
    
    implies(false(),y) = 4y + 6 >= 1 = not(false())
    
    implies(not(x),not(y)) = 24x + 16y + 16 >= 8x + 14y + 6 = implies(y,and(x,y))
   problem:
    
   Qed