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                Quantifier Elimination                 
                          in                           
            Elementary Algebra and Geometry            
                          by                           
      Partial Cylindrical Algebraic Decomposition      
                                                       
               Version B 1.69, 16 Mar 2012
                                                       
                          by                           
                       Hoon Hong                       
                  (hhong@math.ncsu.edu)                
                                                       
With contributions by: Christopher W. Brown, George E. 
Collins, Mark J. Encarnacion, Jeremy R. Johnson        
Werner Krandick, Richard Liska, Scott McCallum,        
Nicolas Robidoux, and Stanly Steinberg                 
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Enter an informal description  between '[' and ']':
[Testing Psi5]Enter a variable list:
(x,y)Enter the number of free variables:
2
Enter a prenex formula:
[ [x^2 + y^2 - 1 = 0 /\ x y - 1/4 < 0] \/ [(x - 4)^2 + (y - 1)^2 - 1 = 0 /\ (x - 4) (y - 1) - 1/4 < 0] \/ [(x - 8)^2 + (y - 2)^2 - 1 = 0 /\ (x - 8) (y - 2) - 1/4 < 0] \/ [(x - 12)^2 + (y - 3)^2 - 1 = 0 /\ (x - 12) (y - 3) - 1/4 < 0] \/ [(x - 16)^2 + (y - 4)^2 - 1 < 0 /\ (x - 16) (y - 4) - 1/4 < 0] ].

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Before Normalization >
go

Before Projection (y) >
go

Before Choice >
go

Before Solution >
d-fpc-stat
          propagation    trial-eval     total
true          0            199            199
false         0           1780           1780
total         0           1979           1979

Length of the projection-based formula :13930

Before Solution >
go 
An equivalent quantifier-free formula:

y^2 + x^2 - 1 >= 0 /\ y^2 - 2 y + x^2 - 8 x + 16 >= 0 /\ y^2 - 4 y + x^2 - 16 x + 67 >= 0 /\ y^2 - 6 y + x^2 - 24 x + 152 >= 0 /\ y^2 - 8 y + x^2 - 32 x + 271 /= 0 /\ [ [ y^2 - 6 y + x^2 - 24 x + 152 = 0 /\ 4 x y - 48 y - 12 x + 143 < 0 ] \/ [ y^2 - 4 y + x^2 - 16 x + 67 = 0 /\ 4 x y - 32 y - 8 x + 63 < 0 ] \/ [ y^2 - 2 y + x^2 - 8 x + 16 = 0 /\ 4 x y - 16 y - 4 x + 15 < 0 ] \/ [ y^2 + x^2 - 1 = 0 /\ 4 x y - 1 < 0 ] \/ [ y^2 - 8 y + x^2 - 32 x + 271 < 0 /\ 4 x y - 64 y - 16 x + 255 < 0 ] ]


=====================  The End  =======================

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3 Garbage collections, 1131955 Cells and 0 Arrays reclaimed, in 20 milliseconds.
81426 Cells in AVAIL, 500000 Cells in SPACE.

System time: 1576 milliseconds.
System time after the initialization: 1574 milliseconds.
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