=======================================================
                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                 
=======================================================
Enter an informal description  between '[' and ']':
qError INPUTRD: '[' was expected.
Enter an informal description  between '[' and ']':
[Using the implicit EC]Enter a variable list:
(x,y,z)Enter the number of free variables:
3
Enter a prenex formula:
[ [x^2 + y^2 + z^2 - 1 = 0 /\ x y z - 1/4 < 0] \/ [(x-4)^2 + (y-1)^2 + (z-2)^2 - 1 = 0 /\ (x-4) (y-1) (z-2) - 1/4 < 0] ].

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Before Normalization >
prop-eqn-const

Before Normalization >
go

Before Projection (z) >
d-proj-factors


A_3,1  = input
       = z^2 + y^2 + x^2 - 1

A_3,2  = input
       = 4 x y z - 1

A_3,3  = input
       = z^2 - 4 z + y^2 - 2 y + x^2 - 8 x + 20

A_3,4  = input
       = 4 x y z - 16 y z - 4 x z + 16 z - 8 x y + 32 y + 8 x - 33



Before Projection (z) >
eqn-const-list (A_3,1, A_3,3)
Before Projection (z) >
go

Before Choice >
go

Before Solution >
d-fpc-stat
          propagation    trial-eval     total
true          0            116            116
false         0            623            623
total         0            739            739

Length of the projection-based formula :5220

Before Solution >
go 
An equivalent quantifier-free formula:

z^2 + y^2 + x^2 - 1 >= 0 /\ z^2 - 4 z + y^2 - 2 y + x^2 - 8 x + 20 >= 0 /\ [ z^2 - 4 z + y^2 - 2 y + x^2 - 8 x + 20 = 0 \/ z^2 + y^2 + x^2 - 1 = 0 ]


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

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26 Garbage collections, 11867391 Cells and 0 Arrays reclaimed, in 133 milliseconds.
430035 Cells in AVAIL, 500000 Cells in SPACE.

System time: 728 milliseconds.
System time after the initialization: 723 milliseconds.
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