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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 ']':

[f1 only]Enter a variable list:
(v,u,x,y,z)Enter the number of free variables:
5
Enter a prenex formula:
[ [z^2 + x - y = 0] /\ [-u^2 + v^2 + z^2 - 1 = 0] /\ [z^2 + x + y = 0] /\ [u^2 - v^2 + z^2 - 1 = 0] /\ [0 <= x^2 - 1] /\ [0 <= z]].

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Before Normalization >
full-cad

Before Normalization >
go

Before Projection (z) >
go

Before Choice >
go

Before Solution >
d-fpc-stat
          propagation    trial-eval     total
true          0             37             37
false         0          1118168        1118168
total         0          1118205        1118205

Length of the projection-based formula :1443

Before Solution >
go

An equivalent quantifier-free formula:

x + 1 = 0 /\ y - x - u^2 + v^2 - 1 = 0 /\ z > 0 /\ z^2 - y + x = 0 /\ [ u + v = 0 \/ u - v = 0 ]


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

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1 Garbage collections, 198791817 Cells and 15 Arrays reclaimed, in 3039 milliseconds.
144804038 Cells in AVAIL, 250000000 Cells in SPACE.

System time: 183909 milliseconds.
System time after the initialization: 181908 milliseconds.
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