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_I1_a

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

conclusions

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

premises
#ax_I1

line(3)

conclusions

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


premises
#ax_I2

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

conclusions

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


premises
#ax_I3

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_I4_a

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

conclusions

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


premises
#ax_I4_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_I4

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_I5

point(1)
point(2)
point(3)

conclusions

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


premises
#ax_I6

point(3)
point(4)
point(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_I7

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_I8

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_I9_a

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

conclusions

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

premises
#ax_I9_b

point(1)
point(2)

conclusions

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

premises
#ax_I9_c

point(1)

conclusions

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

premises
#ax_I9

conclusions

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


premises
#ax_O1

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_O2

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

conclusions
bet(3,2,1)


premises
#ax_O3

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

conclusions
~bet(1,3,2)


premises
#ax_O4

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_O5

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

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

premises
#ax_O6

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

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


premises
#ax_O7

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

conclusions 
bet(1,2,4)


premises
#ax_O8

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

conclusions
bet(1,2,3)


premises 
#ax_O9

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_C1

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

conclusions
eq_point(2,3)


premises
#ax_C2

point(1)
point(2)

conclusions
cong(1,2,2,1)

premises
#ax_C3

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_C4

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_C5

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_C5_1

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

conclusions 

eq_point(5,6)


premises
#ax_C6

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

conclusions
cong(6,5,10,9)


premises
#ax_C7

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

conclusions

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

premises
#ax_C7_1

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

conclusions 

eq_point(7,9)


premises
#ax_E1

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_E2

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)


 
