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


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YES

Problem:
 not(x) -> if(x,false(),true())
 and(x,y) -> if(x,y,false())
 or(x,y) -> if(x,true(),y)
 implies(x,y) -> if(x,y,true())
 =(x,x) -> true()
 =(x,y) -> if(x,y,not(y))
 if(true(),x,y) -> x
 if(false(),x,y) -> y
 if(x,x,if(x,false(),true())) -> true()
 =(x,y) -> if(x,y,if(y,false(),true()))

Proof:
 Polynomial Interpretation Processor:
  dimension: 1
  interpretation:
   [and](x0, x1) = 4x0 + x1 + x1x1 + 2,
   
   [false] = 0,
   
   [if](x0, x1, x2) = 4x0 + x1 + x2 + 1,
   
   [or](x0, x1) = 4x0 + 3x1 + 2x0x0 + x1x1 + 4,
   
   [not](x0) = 6x0 + 5,
   
   [=](x0, x1) = 5x0 + 7x1 + 4x0x0 + 7,
   
   [implies](x0, x1) = 4x0 + 2x1 + x1x1 + 4,
   
   [true] = 2
  orientation:
   not(x) = 6x + 5 >= 4x + 3 = if(x,false(),true())
   
   and(x,y) = 4x + y + y*y + 2 >= 4x + y + 1 = if(x,y,false())
   
   or(x,y) = 4x + 2x*x + 3y + y*y + 4 >= 4x + y + 3 = if(x,true(),y)
   
   implies(x,y) = 4x + 2y + y*y + 4 >= 4x + y + 3 = if(x,y,true())
   
   =(x,x) = 12x + 4x*x + 7 >= 2 = true()
   
   =(x,y) = 5x + 4x*x + 7y + 7 >= 4x + 7y + 6 = if(x,y,not(y))
   
   if(true(),x,y) = x + y + 9 >= x = x
   
   if(false(),x,y) = x + y + 1 >= y = y
   
   if(x,x,if(x,false(),true())) = 9x + 4 >= 2 = true()
   
   =(x,y) = 5x + 4x*x + 7y + 7 >= 4x + 5y + 4 = if(x,y,if(y,false(),true()))
  problem:
   
  Qed