premises
#ax_D1

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_D3

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

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_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_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_D9

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

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_D11

point(1)
point(2)
point(3)
point(4)
point(5)
point(6)
~eq_point(1,2)
~eq_point(1,3)
~eq_point(4,5)
~eq_point(4,6)
point(7)
col(4,5,7)
~bet(7,4,5)
point(8)
col(4,6,8)
~bet(8,4,6)
cong(1,2,4,7)
cong(1,3,4,8)
cong(2,3,7,8)

conclusions

cong_angle(1,2,3,4,5,6)

premises
#ax_D12

point(1)
point(2)
point(3)
point(4)
point(5)
point(6)
cong_angle(1,2,3,4,5,6)

conclusions

point(7)
point(8)
~eq_point(1,2)
~eq_point(1,3)
~eq_point(4,5)
~eq_point(4,6)
col(4,5,7)
~bet(7,4,5)
col(4,6,8)
~bet(8,4,6)
cong(1,2,4,7)
cong(1,3,4,8)
cong(2,3,7,8)

premises
#ax_I1

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

conclusions

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

premises
#ax_I2

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(1)
point(1)
inc_po_l(1,1)

conclusions

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

premises
#ax_I3a

line(3)

conclusions

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

premises
#ax_I3b

conclusions

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

premises
#ax_I4a

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

plane(1)

conclusions

point(2)
inc_po_pl(2,1)

premises
#ax_I5

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

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

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)

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)

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

conclusions

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

premises
#ax_II1

point(1)
point(2)
point(3)
bet(1,2,3)

conclusions

~eq_point(1,2)
~eq_point(1,3)
~eq_point(2,3)
col(1,2,3)
bet(3,2,1)

premises
#ax_II2

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

conclusions
point(3)
bet(1,2,3)

premises
#ax_II3

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

conclusions

bet(1,2,3)
|
bet(2,3,1)
|
bet(3,1,2)

premises 
#ax_II4

point(1)
point(2)
point(3)
~eq_point(1,2)
~eq_point(1,3)
~eq_point(2,3)
~col(1,2,3)
plane(4)
inc_po_pl(1,4)
inc_po_pl(2,4)
inc_po_pl(3,4)
line(5)
inc_l_pl(5,4)
~inc_po_l(1,5)
~inc_po_l(2,5)
~inc_po_l(3,5)
point(6)
inc_po_l(6,5)
bet(2,6,3)

conclusions

point(7)
inc_po_l(7,5)
bet(3,7,1)
|
point(7)
inc_po_l(7,5)
bet(1,7,2)

premises
#ax_III1

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

conclusions
point(5)
bet(2,1,5)
cong(1,5,3,4)

premises
#ax_III2

point(1)
point(2)
point(3)
point(4)
cong(1,2,3,4)
point(5)
point(6)
cong(1,2,5,6)

conclusions
cong(3,4,5,6)

premises
#ax_III3

point(1)
point(2)
point(3)
bet(1,2,3)
point(4)
point(5)
point(6)
bet(4,5,6)
cong(1,2,4,5)
cong(2,3,5,6)

conclusions
cong(1,3,4,6)

premises
#ax_III4_a

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

conclusions
cong_angle(1,2,3,1,2,3)

premises
#ax_III4_b1

point(1)
point(2)
point(3)
point(4)
point(5)
point(6)
~eq_point(1,2)
~eq_point(1,3)
~eq_point(4,5)
~col(4,5,6)

conclusions

point(7)
point(8)
cong_angle(1,2,3,4,5,7)
cong_angle(1,2,3,4,5,8)
point(9)
point(10)
line(11)
inc_po_l(4,11)
inc_po_l(5,11)
bet(6,9,7)
inc_po_l(9,11)
bet(8,10,7)
inc_po_l(10,11)

premises
#ax_III4_b2

point(1)
point(2)
point(3)
point(4)
point(5)
point(6)
~eq_point(1,2)
~eq_point(1,3)
~eq_point(4,5)
~col(4,5,6)
point(7)
point(8)
cong_angle(1,2,3,4,5,7)
cong_angle(1,2,3,4,5,8)
point(9)
point(10)
line(11)
inc_po_l(4,11)
inc_po_l(5,11)
bet(6,9,7)
inc_po_l(9,11)
bet(6,10,8)
inc_po_l(10,11)

conclusions

bet(4,7,8)
|
bet(4,8,7)
|
eq_point(7,8)

premises
#ax_III5

point(1)
point(2)
point(3)
point(4)
point(5)
point(6)
cong(1,2,4,5)
cong(1,3,4,6)
cong_angle(1,2,3,4,5,6)

conclusions

cong_angle(2,1,3,5,4,6)


premises
#ax_IV_a

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

conclusions

line(3)
inc_po_l(1,3)
inc_l_pl(3,4)
~int_l_l(3,2)

premises
#ax_IV_b

point(1)
line(2)
plane(3)
~inc_po_l(1,2)
inc_po_pl(1,3)
inc_l_pl(2,3)
line(4)
inc_po_l(1,4)
inc_l_pl(4,3)
~int_l_l(2,4)
line(5)
inc_po_l(1,5)
inc_l_pl(5,3)
~int_l_l(2,5)

conclusions

eq_line(4,5)

