premises
# ax_def_col_1

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

conclusions

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


premises
# ax_def_col_2

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

conclusions

col(1,2,3)


premises
# ax_def_col_3

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

conclusions

col(1,2,3)


premises
# ax_def_col_4

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

conclusions

col(1,2,3)


premises 
# ax_bet_identity

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

conclusions

eq_point(1,2)


premises
# ax_cong_sym

point(1)
point(2)
 
conclusions 

cong(1,2,2,1)

premises
# ax_cong_ident

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

conclusions 

eq_point(1,2)

premises
# ax_cong_pseudotr

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_pasch

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

conclusions 

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

premises
# ax_euclid

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

conclusions 

point(6)
point(7)
bet(1,4,6)
bet(1,5,7)
bet(6,3,7)


premises
# ax_five_segments

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

conclusions

cong(5,7,6,8)


premises
# ax_segment_constr

point(1)
point(2)
point(3)
point(4)

conclusions

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


premises
# ax_lower_dim

conclusions

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


premises
# ax_upper_dim_3 

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

conclusions

bet(1,4,5)
|
bet(4,5,1)
|
bet(5,1,4)





