/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:
 implies(not(x),y) -> or(x,y)
 implies(not(x),or(y,z)) -> implies(y,or(x,z))
 implies(x,or(y,z)) -> or(y,implies(x,z))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                  [1 0 0]     [1 0 0]  
   [or](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                  [0 0 0]     [0 0 0]  ,
   
                       [1 0 0]     [1 0 0]  
   [implies](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                       [0 0 0]     [0 0 0]  ,
   
               [1 0 0]     [1]
   [not](x0) = [0 0 0]x0 + [0]
               [0 0 0]     [0]
  orientation:
                       [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]           
   implies(not(x),y) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y = or(x,y)
                       [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]           
   
                             [1 0 0]    [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]    [1 0 0]                      
   implies(not(x),or(y,z)) = [0 0 0]x + [0 0 0]y + [0 0 0]z + [0] >= [0 0 0]x + [0 0 0]y + [0 0 0]z = implies(y,or(x,z))
                             [0 0 0]    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0 0 0]                      
   
                        [1 0 0]    [1 0 0]    [1 0 0]     [1 0 0]    [1 0 0]    [1 0 0]                      
   implies(x,or(y,z)) = [0 0 0]x + [0 0 0]y + [0 0 0]z >= [0 0 0]x + [0 0 0]y + [0 0 0]z = or(y,implies(x,z))
                        [0 0 0]    [0 0 0]    [0 0 0]     [0 0 0]    [0 0 0]    [0 0 0]                      
  problem:
   implies(x,or(y,z)) -> or(y,implies(x,z))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                   [1 0 0]     [1 0 0]     [0]
    [or](x0, x1) = [0 0 0]x0 + [0 0 1]x1 + [0]
                   [0 0 0]     [0 1 0]     [1],
    
                        [1 0 0]     [1 1 1]     [0]
    [implies](x0, x1) = [0 0 0]x0 + [0 0 1]x1 + [0]
                        [0 0 0]     [0 1 0]     [1]
   orientation:
                         [1 0 0]    [1 0 0]    [1 1 1]    [1]    [1 0 0]    [1 0 0]    [1 1 1]    [0]                     
    implies(x,or(y,z)) = [0 0 0]x + [0 0 0]y + [0 1 0]z + [1] >= [0 0 0]x + [0 0 0]y + [0 1 0]z + [1] = or(y,implies(x,z))
                         [0 0 0]    [0 0 0]    [0 0 1]    [1]    [0 0 0]    [0 0 0]    [0 0 1]    [1]                     
   problem:
    
   Qed