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_N1

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

conclusions
inc_po_pl(1,3)


premises
#ax_N2_1

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_N2_2

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)

premises
#ax_N3

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

conclusions
eq_point(3,4)


premises
#ax_N4

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_N5

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

conclusions

cong(1,2,4,5)


premises
#ax_N6

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

conclusions

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


premises
#ax_N7

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

conclusions
bet(3,2,1)


premises
#ax_N8

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

conclusions
~bet(1,3,2)


premises
#ax_N9

point(1)
point(2)

conclusions
cong(1,2,2,1)



premises
#ax_N10

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

conclusions
eq_line(1,2)


premises
#ax_N11

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

conclusions
eq_plane(1,2)


premises
#ax_N12

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

conclusions
inc_l_pl(2,1)




 
premises
#ax_G1

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_G2

point(1)
point(2)
point(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)
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_P1

point(1)
point(2)
point(3)
~col(1,2,3)
point(4)
point(5)
plane(8)
inc_po_pl(4,8)
inc_po_pl(5,8)
cong(1,2,4,5)

conclusions

point(6)
point(7)
inc_po_pl(6,8)
inc_po_pl(7,8)
cong(1,3,4,6)
cong(1,3,4,7)
cong(2,3,5,6)
cong(2,3,5,7)

premises
#ax_P2

point(1)
point(2)
point(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)
~eq_point(1,2)
line(6)
inc_po_l(1,6)
inc_po_l(2,6)
~eq_point(3,4)
~inc_po_l(3,6)
~inc_po_l(4,6)
cong(1,3,1,4)
cong(2,3,2,4)

conclusions

point(7)
inc_po_l(7,6)
bet(3,7,4)

premises
#ax_P3

point(1)
point(2)
point(3)
point(4)
point(5)
point(6)
~col(1,2,3)
~col(4,5,6)
line(7)
line(8)
inc_po_l(1,7)
inc_po_l(2,7)
inc_po_l(4,8)
inc_po_l(5,8)
point(9)
point(10)
inc_po_l(9,7)
inc_po_l(10,8)
cong(1,2,4,5)
cong(2,3,5,6)
cong(3,1,6,4)
cong(2,9,5,10)

conclusions

cong(1,9,4,10)


premises
#ax_P4

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_P5

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

conclusions

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

premises
#ax_P6

point(1)
point(2)
point(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_P7_a

line(1)
point(2)
inc_po_l(2,1)

conclusions

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

premises
#ax_P7

line(1)

conclusions

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

premises
#ax_P8_a

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

conclusions

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


premises
#ax_P8_b

plane(4)
point(1)
inc_po_pl(1,4)

conclusions

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


premises
#ax_P8

plane(4)

conclusions

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

premises
#ax_P9

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

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

premises
#ax_P10

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

conclusions

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


premises
#ax_SP1_a

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

conclusions

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

premises
#ax_SP1_b

point(1)
point(2)

conclusions

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

premises
#ax_SP1_c

point(1)

conclusions

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

premises
#ax_SP1

conclusions

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


