premises
#ax_D1
%po scot-u nema potrebe za razlicitosti tacaka, tj. izgleda da
%i za 2 tacke kaze da su kolinearne
%MORA RAZLICITOST, PRAVI PROBLEMA U KOMBINACIJI SA SLEDECOM DEFINICIJOM!!!
%U STVARI MORA RAZLICITOST U SLEDECOJ DEFINICIJI!!!!!!!!!!!!!

point(1)
point(2)
point(3)
%~eq_point(1,2)
%~eq_point(1,3)
%~eq_point(2,3)
line(4)
inc_po_l(1,4)
inc_po_l(2,4)
inc_po_l(3,4)

conclusions

col(1,2,3)

premises
#ax_D2

point(1)
point(2)
point(3)
col(1,2,3)

conclusions

line(4)
inc_po_l(1,4)
inc_po_l(2,4)
inc_po_l(3,4)

premises
#ax_D1a

point(1) 
point(2)
~eq_point(1,2)
point(3)
line(4)
inc_po_l(1,4)
inc_po_l(2,4)
~inc_po_l(3,4) 

conclusions

~col(1,2,3)

%premises
%#ax_D2a
%
%point(1)
%point(2)
%~eq_point(1,2)
%point(3)
%line(4)
%inc_po_l(1,4)
%inc_po_l(2,4)
%~col(1,2,3) 
%
%conclusions
%
%~inc_po_l(3,4)


premises
#ax_D3
%ok scot - njegov planar

point(1)
point(2)
point(3)
point(4)
%~eq_point(1,2)
%~eq_point(1,3)
%~eq_point(1,4)
%~eq_point(2,3)
%~eq_point(2,4)
%~eq_point(3,4)
plane(5)
inc_po_pl(1,5)
inc_po_pl(2,5)
inc_po_pl(3,5)
inc_po_pl(4,5)

conclusions

comp(1,2,3,4)

premises
#ax_D4
%dodato ~col kao razlicitost za definiciju col
%promenjeno na produktivnu aksiomu

point(1)
point(2)
point(3)
point(4)
comp(1,2,3,4)

conclusions

plane(5)
inc_po_pl(1,5)
inc_po_pl(2,5)
inc_po_pl(3,5)
inc_po_pl(4,5)

premises
#ax_D3a

point(1)
point(2)
point(3)
~col(1,2,3)
point(4)
plane(5)
inc_po_pl(1,5)
inc_po_pl(2,5)
inc_po_pl(3,5)
~inc_po_pl(4,5) 

conclusions

~comp(1,2,3,4)

%premises
%#ax_D4a
%
%point(1)
%point(2)
%point(3)
%~col(1,2,3)
%point(4)
%plane(5)
%inc_po_pl(1,5)
%inc_po_pl(2,5)
%inc_po_pl(3,5)
%~comp(1,2,3,4) 
%
%conclusions
%
%~inc_po_pl(4,5)  

premises
#ax_D5

line(1)
line(2)
~eq_line(1,2)
point(3)
inc_po_l(3,1)
inc_po_l(3,2)

conclusions

int_l_l(1,2)

premises
#ax_D6

line(1)
line(2)
int_l_l(1,2)

conclusions

point(3)
inc_po_l(3,1)
inc_po_l(3,2)
~eq_line(1,2)

%premises
%#ax_D5a
%%a ovde da ubacimo
%
%line(1)
%line(2)
%~eq_line(1,2)
%~int_l_l(1,2)
%point(3)
%inc_po_l(3,1)
%
%conclusions
%
%~inc_po_l(3,2)

premises
#ax_D6a
%pedja kaze da izbacimo razlicitost

line(1)
line(2)
%~eq_line(1,2)

conclusions

int_l_l(1,2)
|
~int_l_l(1,2)

premises
#ax_D7

plane(1)
plane(2)
~eq_plane(1,2)
point(3)
inc_po_pl(3,1)
inc_po_pl(3,2)

conclusions

int_pl_pl(1,2)

premises
#ax_D8

plane(1)
plane(2)
int_pl_pl(1,2)

conclusions

point(3)
inc_po_pl(3,1)
inc_po_pl(3,2)
~eq_plane(1,2)

%premises
%#ax_D7a
%
%plane(1)
%plane(2)
%~eq_plane(1,2)
%~int_pl_pl(1,2)
%point(3)
%inc_po_pl(3,1)
%
%conclusions
%
%~inc_po_pl(3,2)

premises
#ax_D8a

plane(1)
plane(2)

conclusions

int_pl_pl(1,2)
|
~int_pl_pl(1,2)

premises
#ax_D9
%dodato ~inc

line(1)
plane(2)
~inc_l_pl(1,2)
point(3)
inc_po_l(3,1)
inc_po_pl(3,2)

conclusions

int_l_pl(1,2)

premises
#ax_D10

line(1)
plane(2)
int_l_pl(1,2)

conclusions

point(3)
inc_po_l(3,1)
inc_po_pl(3,2)
~inc_l_pl(1,2)


premises
#ax_D10a

line(1)
plane(2)

conclusions

int_l_pl(1,2)
|
~int_l_pl(1,2)

premises
#ax_D11

point(1)
line(2)
plane(3)
inc_l_pl(2,3)
inc_po_l(1,2)

conclusions

inc_po_pl(1,3)

premises
#ax_D11b

point(1)
line(2)
plane(3)
inc_po_l(1,2)
~inc_po_pl(1,3)

conclusions

~inc_l_pl(2,3)

%AKSIOME VEZE

premises
#ax_I1
%ok i scot

point(1)
point(2)
~eq_point(1,2)

conclusions

line(3)
inc_po_l(1,3)
inc_po_l(2,3)

premises
#ax_I2
%ok i scot

point(3)
point(4)
~eq_point(3,4)
line(1)
inc_po_l(3,1)
inc_po_l(4,1)
line(2)
inc_po_l(3,2)
inc_po_l(4,2)

conclusions

eq_line(1,2)

%premises
%#ax_I3a_1
%
%line(3)
%point(1)
%inc_po_l(1,3)
%
%conclusions
%
%point(2)
%~eq_point(1,2)
%inc_po_l(2,3)

premises
#ax_I3a
%ok i scot

line(3)

conclusions

point(1)
inc_po_l(1,3)
point(2)
~eq_point(1,2)
inc_po_l(2,3)

%minileme
%premises
%#ax_I3b_1
%
%point(1)
%
%conclusions
%
%point(2)
%point(3)
%~col(1,2,3)
%
%premises
%#ax_I3b_2
%
%point(1)
%point(2)
%~eq_point(1,2)
%
%conclusions
%
%point(3)
%~col(1,2,3)

premises
#ax_I3b
%ok i scot

conclusions

point(1)
point(2)
point(3)
~col(1,2,3)

premises
#ax_I4a
%kod scot-a nema razlicitosti

point(1)
point(2)
%~eq_point(1,2)
point(3)
%~eq_point(1,3)
%~eq_point(2,3)
~col(1,2,3)

conclusions

plane(4)
inc_po_pl(1,4)
inc_po_pl(2,4)
inc_po_pl(3,4)

premises
#ax_I4b
%ok i scot

plane(1)

conclusions

point(2)
inc_po_pl(2,1)

premises
#ax_I5
%ok - kod scota nema razlicitosti

point(3)
point(4)
point(5)
%~eq_point(3,4)
%~eq_point(3,5)
%~eq_point(4,5)
~col(3,4,5)
plane(1)
inc_po_pl(3,1)
inc_po_pl(4,1)
inc_po_pl(5,1)
plane(2)
inc_po_pl(3,2)
inc_po_pl(4,2)
inc_po_pl(5,2)

conclusions

eq_plane(1,2)

premises
#ax_I6
%ok i scot

line(2)
point(3)
inc_po_l(3,2)
point(4)
~eq_point(3,4)
inc_po_l(4,2)
plane(1)
inc_po_pl(3,1)
inc_po_pl(4,1)

conclusions

inc_l_pl(2,1)
 
premises
#ax_I7
%ok i scot

plane(1)
plane(2)
~eq_plane(1,2)
point(3)
inc_po_pl(3,1)
inc_po_pl(3,2)

conclusions

point(4)
~eq_point(3,4)
inc_po_pl(4,1)
inc_po_pl(4,2)

%mini leme
%premises
%#ax_I8_1
%
%point(1)
%point(2)
%point(3)
%~col(1,2,3)
%
%conclusions
%
%point(4)
%~comp(1,2,3,4)
%
%premises
%#ax_I8_2
%
%point(1)
%point(2)
%~eq_point(1,2)
%
%conclusions
%
%point(3)
%point(4)
%~comp(1,2,3,4)
%
%premises
%#ax_I8_3
%
%point(1)
%
%conclusions
%
%point(2)
%point(3)
%point(4)
%~comp(1,2,3,4)

premises
#ax_I8
%ok i scot

conclusions

point(1)
point(2)
point(3)
point(4)
~comp(1,2,3,4)

