#===================================================
#
#  Examples for RQE based geometrical inequality proving - Mma file [2]
#   Each example is given with their inputs for
#   Mma for easy copy/pasting
#   It meant to be as an input formula for the Mathematica function 
#   Resolve 
#  Version 2.0 - 17/04/20
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#===================================================

#1: Triangle-SymmHomPoly-3-2-1
inputform3201:=Exists[{b,c}, 1+b>c \[And] 1+c>b \[And] b+c>1, 
(1+b+c)^2 == m(1 + b^2 + c^2)]

#2: Triangle-SymmHomPoly-3-2-2
inputform3202:=Exists[{b,c}, 1+b>c \[And] 1+c>b \[And] b+c>1, 
(1+b+c)^2 == m(b + c+ b c)]

#3: Triangle-SymmHomPoly-3-2-3
inputform3203:=Exists[{b,c}, 1+b>c \[And] 1+c>b \[And] b+c>1, 
1+b^2+c^2 == m(b + c+ b c)]


#4: Triangle-SymmHomPoly-3-3-1
inputform3301:=Exists[{b,c}, 1+b>c \[And] 1+c>b \[And] b+c>1, 
(1+b+c)^3 == m(1 + b^3 + c^3)]




#8: SymmHomPoly-3-01-3
inputform3013:=Exists[{b,c}, 1+b>c \[And] 1+c>b \[And] b+c>1, 
1+b^3+c^3 == m(1 + b + c)^3]

#9: SymmHomPoly-3-02-1
inputform3021:=Exists[{b,c}, 1+b>c \[And] 1+c>b \[And] b+c>1, 
(1+b+c)^3 == m(1 b c)]

#10: SymmHomPoly-3-02-3
inputform3023:=Exists[{b,c}, 1+b>c \[And] 1+c>b \[And] b+c>1, 
1 b c == m(1 + b + c)^3]

#11: SymmHomPoly-3-03-1
inputform3031:=Exists[{b,c}, 1+b>c \[And] 1+c>b \[And] b+c>1, 
(1+b+c)^3 == m(b+c+ b^2(1+c)+ c^2(1+b))]

#12: SymmHomPoly-3-03-3
inputform3033:=Exists[{b,c}, 1+b>c \[And] 1+c>b \[And] b+c>1, 
b+c+b^2(1+c)+c^2(1+b) == m(1 + b + c)^3]

#13: SymmHomPoly-3-04-1
inputform3041:=Exists[{b,c}, 1+b>c \[And] 1+c>b \[And] b+c>1, 
1+b^3+c^3 == m(1 b c)]

#14: SymmHomPoly-3-04-3
inputform3043:=Exists[{b,c}, 1+b>c \[And] 1+c>b \[And] b+c>1, 
1 b c == m(1 + b^3 + c^3)]