/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) -> 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:
   [=](x0, x1) = 4x0 + 6x1 + 7,
   
   [implies](x0, x1) = 4x0 + 2x1 + 3x0x0 + 4x1x1 + 4,
   
   [or](x0, x1) = 4x0 + 3x1 + 2x0x0 + x1x1 + 4,
   
   [and](x0, x1) = 4x0 + 2x1 + 3,
   
   [if](x0, x1, x2) = 4x0 + x1 + x2,
   
   [true] = 2,
   
   [false] = 2,
   
   [not](x0) = 4x0 + 5
  orientation:
   not(x) = 4x + 5 >= 4x + 4 = if(x,false(),true())
   
   and(x,y) = 4x + 2y + 3 >= 4x + y + 2 = if(x,y,false())
   
   or(x,y) = 4x + 2x*x + 3y + y*y + 4 >= 4x + y + 2 = if(x,true(),y)
   
   implies(x,y) = 4x + 3x*x + 2y + 4y*y + 4 >= 4x + y + 2 = if(x,y,true())
   
   =(x,x) = 10x + 7 >= 2 = true()
   
   =(x,y) = 4x + 6y + 7 >= 4x + 5y + 5 = if(x,y,not(y))
   
   if(true(),x,y) = x + y + 8 >= x = x
   
   if(false(),x,y) = x + y + 8 >= y = y
   
   if(x,x,if(x,false(),true())) = 9x + 4 >= 2 = true()
   
   =(x,y) = 4x + 6y + 7 >= 4x + 5y + 4 = if(x,y,if(y,false(),true()))
  problem:
   
  Qed