/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:
 not(x) -> xor(x,true())
 implies(x,y) -> xor(and(x,y),xor(x,true()))
 or(x,y) -> xor(and(x,y),xor(x,y))
 =(x,y) -> xor(x,xor(y,true()))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [=](x0, x1) = x0 + x1 + 1,
   
   [or](x0, x1) = 2x0 + 3x1,
   
   [and](x0, x1) = x0 + 2x1,
   
   [implies](x0, x1) = 2x0 + 2x1,
   
   [xor](x0, x1) = x0 + x1,
   
   [true] = 0,
   
   [not](x0) = x0
  orientation:
   not(x) = x >= x = xor(x,true())
   
   implies(x,y) = 2x + 2y >= 2x + 2y = xor(and(x,y),xor(x,true()))
   
   or(x,y) = 2x + 3y >= 2x + 3y = xor(and(x,y),xor(x,y))
   
   =(x,y) = x + y + 1 >= x + y = xor(x,xor(y,true()))
  problem:
   not(x) -> xor(x,true())
   implies(x,y) -> xor(and(x,y),xor(x,true()))
   or(x,y) -> xor(and(x,y),xor(x,y))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [or](x0, x1) = 4x0 + 2x1 + 1,
    
    [and](x0, x1) = 3x0 + x1,
    
    [implies](x0, x1) = 4x0 + x1,
    
    [xor](x0, x1) = x0 + x1,
    
    [true] = 0,
    
    [not](x0) = x0
   orientation:
    not(x) = x >= x = xor(x,true())
    
    implies(x,y) = 4x + y >= 4x + y = xor(and(x,y),xor(x,true()))
    
    or(x,y) = 4x + 2y + 1 >= 4x + 2y = xor(and(x,y),xor(x,y))
   problem:
    not(x) -> xor(x,true())
    implies(x,y) -> xor(and(x,y),xor(x,true()))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [and](x0, x1) = 3x0 + x1,
     
     [implies](x0, x1) = 5x0 + x1 + 7,
     
     [xor](x0, x1) = x0 + x1 + 2,
     
     [true] = 2,
     
     [not](x0) = x0 + 4
    orientation:
     not(x) = x + 4 >= x + 4 = xor(x,true())
     
     implies(x,y) = 5x + y + 7 >= 4x + y + 6 = xor(and(x,y),xor(x,true()))
    problem:
     not(x) -> xor(x,true())
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                      [1 0 0]     [1 0 0]  
      [xor](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                      [0 0 0]     [0 0 0]  ,
      
               [0]
      [true] = [0]
               [0],
      
                  [1 0 0]     [1]
      [not](x0) = [0 0 0]x0 + [0]
                  [0 0 0]     [0]
     orientation:
               [1 0 0]    [1]    [1 0 0]                 
      not(x) = [0 0 0]x + [0] >= [0 0 0]x = xor(x,true())
               [0 0 0]    [0]    [0 0 0]                 
     problem:
      
     Qed