(a)
Composed relations of {WE} and {WE,V,WW} WE(c,b ) V(c,b ) WW(c,b ) NTPPx (c ,WE(b )) TPPx (c ,WE(b )) ∧ ECx (c ,V(b )) TPPx (c ,V(b )) ∧ ECx (c ,WE(b )) TPPx (c ,V(b )) ∧ ECx (c ,WW(b )) NTPPx (c ,V(b )) EQx (c ,V(b )) NTPPx (c ,WW(b )) TPPx (c ,WW(b )) ∧ ECx (c ,V(b )) WE(b,a ) NTPPx (b ,WE(a )) NTPPx (c ,WE(a )) NTPPx (c ,WE(a )) NTPPx (c ,WE(a )) NTPPx (c ,WE(a )) NTPPx (c ,WE(a )) NTPPx (c ,WE(a )) U-13 relations
NTPPx (c ,WE(a ))
∨
TPPx (c ,WE(a )) ∧ ECx (c ,V(a ))
∨
POx (c ,WE(a )) ∧ POx (c ,V(a )) ∧ DCy(c ,WW(a ))
∨
POx (c ,WE(a )) ∧ POx (c ,V(a )) ∧ ECx (c ,WW(a ))
∨
POx (c ,WE(a )) ∧ POx (c ,WW(a )) ∧ NTPPix (c ,V(a ))
TPPx (b ,WE(a )) ∧ ECx (b ,V(a )) NTPPx (c ,WE(a )) NTPPx (c ,WE(a )) NTPPx (c ,WE(a )) TPPx (c ,WE(a )) ∧ ECx (c ,V(a ))NTPPx (c ,WE(a )) TPPx (c ,WE(a )) ∧ ECx (c ,V(a ))
NTPPx (c ,V(a ))
∨
TPPx (c ,V(a )) ∧ ECx (c ,WW(a ))
∨
TPPx (c ,WW(a )) ∧ ECx (c ,V(a ))
∨
NTPPx (c ,WW(a ))
∨
POx (c ,WW(a )) ∧ POx (c,V(a )) ∧ DCy(c ,WE(a ))
TPPx (c ,V(a )) ∧ ECx (c ,WE(a ))
∨
EQx (c ,V(a ))
∨
POx (c ,WW(a )) ∧ POx (c,V(a )) ∧ ECx (c ,WE(a ))
WE(b,a ) NTPPx (c ,WE(a )) WE(c,a ) WE(c,a ) ∨ V(c,a ) ∨ WW(c,a )
Note: the data in bold are the results of the composition of relations. (b)
Part 1 of composed relations of {V} and {WE,V,WW} WE(c,b ) V(c,b ) WW(c,b ) NTPPx (c ,WE(b )) TPPx (c ,WE(b )) ∧ ECx (c ,V(b )) TPPx (c ,V(b )) ∧ ECx (c ,WE(b )) TPPx (c ,V(b )) ∧ ECx (c ,WW(b )) NTPPx (c ,V(b )) EQx (c ,V(b )) NTPPx (c ,WW(b )) TPPx (c ,WW(b )) ∧ ECx (c ,V(b )) V(b,a ) TPPx (b ,V(a )) ∧ ECx (b ,WE(a )) NTPPx (c ,WE(a )) TPPx (c ,WE(a )) ∧ ECx (c ,V(a )) TPPx (c ,V(a )) ∧ ECx (c ,WE(a )) NTPPx (c ,V(a )) NTPPx (c ,V(a )) TPPx (c ,V(a )) ∧ ECx (c ,WE(a ))
NTPPx (c ,V(a ))
∨
TPPx (c ,V(a )) ∧ ECx (c ,WW(a ))
∨
TPPx (c ,WW(a )) ∧ ECx (c ,V(a ))
∨
NTPPx (c ,WW(a ))
∨
POx (c ,WW(a )) ∧ POx (c ,V(a )) ∧ DCy(c ,WE(a ))
NTPPx (c ,V(a ))
∨
TPPx (c ,V(a )) ∧ ECx (c ,WW(a ))
∨
POx (c ,WW(a )) ∧ POx (c ,V(a )) ∧ DCy(c ,WE(a ))
TPPx (b ,V(a )) ∧ ECx (b ,WW(a ))
NTPPx (c ,V(a ))
∨
TPPx (c ,V(a )) ∧ ECx (c ,WE(a ))
∨
TPPx (c ,WE(a )) ∧ ECx (c ,V(a ))
∨
NTPPx (c ,WE(a ))
∨
POx (c ,WE(a )) ∧ POx (c ,V(a )) ∧ DCy(c ,WW(a ))
NTPPx (c ,V(a ))
∨
TPPx (c ,V(a )) ∧ ECx (c ,WE(a ))
∨
POx (c ,WE(a )) ∧ POx (c,V(a )) ∧ DCy(c ,WW(a ))
NTPPx (c ,V(a )) TPPx (c ,V(a )) ∧ ECx (c ,WE(a )) NTPPx (c ,V(a )) TPPx (c ,V(a )) ∧ ECx (c ,WE(a )) NTPPx (c ,WW(a )) TPPx (c ,WW(a )) ∧ ECx (c ,V(a ))
Note: the data in bold are the results of the composition of relations. (c)
Part 2 of composed relations of {V} and {WE,V,WW} WE(c,b ) V(c,b ) WW(c,b ) NTPPx (c ,WE(b )) TPPx (c ,WE(b )) ∧ ECx (c ,V(b )) TPPx (c ,V(b )) ∧ ECx (c ,WE(b )) TPPx (c ,V(b )) ∧ ECx (c ,WW(b )) NTPPx (c ,V(b )) EQx (c ,V(b )) NTPPx (c ,WW(b )) TPPx (c ,WW(b )) ∧ ECx (c ,V(b )) V(b,a ) NTPPx (b ,V(a ))
NTPPx (c ,V(a ))
∨
TPPx (c ,V(a )) ∧ ECx (c ,WE(a ))
∨
TPPx (c ,WE(a )) ∧ ECx (c ,V(a ))
∨
NTPPx (c ,WE(a ))
∨
POx (c ,WE(a )) ∧ POx (c ,V(a )) ∧ DCy(c ,WW(a ))
NTPPx (c ,V(a ))
∨
TPPx (c ,V(a )) ∧ ECx (c ,WE(a ))
∨
POx (c ,WE(a )) ∧ POx (c ,V(a )) ∧ DCy(c ,WW(a ))
NTPPx (c ,V(a )) NTPPx (c ,V(a )) NTPPx (c ,V(a )) NTPPx (c ,V(a ))
NTPPx (c ,V(a ))
∨
TPPx (c ,V(a )) ∧ ECx (c ,WW(a ))
∨
TPPx (c ,WW(a )) ∧ ECx (c ,V(a ))
∨
NTPPx (c ,WW(a ))
∨
POx (c ,WW(a )) ∧ POx (c ,V(a )) ∧ DCy(c ,WE(a ))
NTPPx (c ,V(a ))
∨
TPPx (c ,V(a )) ∧ ECx (c ,WW(a ))
∨
POx (c ,WW(a )) ∧ POx (c ,V(a )) ∧ DCy(c ,WE(a ))
EQx (b ,V(a )) NTPPx (c ,WE(a )) TPPx (c ,WE(a )) ∧ ECx (c ,V(a )) TPPx (c ,V(a )) ∧ ECx (c ,WE(a )) TPPx (c ,V(a )) ∧ ECx (c ,WW(a )) NTPPx (c ,V(a )) EQx (c ,V(a )) NTPPx (c ,WW(a )) TPPx (c ,WW(a )) ∧ ECx (c ,V(a )) V(b,a ) WE(c,a ) ∨ V(c,a ) V(c,a ) V(c,a ) ∨ WW(c,a )
Note: the data in bold are the results of the composition of relations. (d)
Composed relations of {WW} and {WE,V,WW} WE
V
WW
NTPPx (c ,WE(b )) TPPx (c ,WE(b )) ∧ ECx (c ,V(b )) TPPx (c ,V(b )) ∧ ECx (c ,WE(b )) TPPx (c ,V(b )) ∧ ECx (c ,WW(b )) NTPPx (c ,V(b )) EQx (c ,V(b )) NTPPx (c ,WW(b )) TPPx (c ,WW(b )) ∧ ECx (c ,V(b )) WW(b,a ) NTPPx (b ,WW(a )) U-13 relations
NTPPx (c ,WW(a ))
∨
TPPx (c ,WW(a )) ∧ ECx (c ,V(a ))
∨
POx (c ,WW(a )) ∧ POx (c ,V(a )) ∧ DCy(c ,WE(a ))
∨
POx (c ,WW(a )) ∧ POx (c ,V(a )) ∧ ECx (c ,WE(a ))
∨
POx (c ,WW(a )) ∧ POx (c ,WE(a )) ∧ NTPPix (c ,V(a ))
NTPPx (c , WW(a )) NTPPx (c , WW(a )) NTPPx (c , WW(a )) NTPPx (c , WW(a )) NTPPx (c , WW(a )) NTPPx (c , WW(a )) TPPx (b ,WW(a )) ∧ ECx (b ,V(a ))
NTPPx (c ,V(a ))
∨
TPPx (c ,V(a )) ∧ ECx (c ,WE(a ))
∨
TPPx (c ,WE(a )) ∧ ECx (c ,V(a ))
∨
NTPPx (c ,WE(a ))
∨
POx (c ,WE(a )) ∧ POx (c ,V(a )) ∧ DCy(c ,WW(a ))
TPPx (c ,V(a )) ∧ ECx (c ,WW(a ))
∨
EQx (c ,V(a ))
∨
POx (c ,WE(a )) ∧ POx (c ,V(a )) ∧ ECx (c ,WW(a ))
TPPx (c ,WW(a )) ∧ ECx (c ,V(a )) NTPPx (c , WW(a )) NTPPx (c , WW(a )) TPPx (c ,WW(a )) ∧ ECx (c ,V(a )) NTPPx (c , WW(a )) NTPPx (c , WW(a )) WW(b,a ) WE(c,a ) ∨ V(c,a ) ∨ WW(c,a ) WW(c,a ) NTPPx (c ,WW(a ))
Note: the data in bold are the results of the composition of relations.