fof(th_mg_1a_1, axiom, (! [L,A] : ((line(L) & point(A) & ninc_po_l(A,L)) => (? [B,C] : (point(B) & point(C) & B!=C & inc_po_l(B,L) & inc_po_l(C,L)))))).

fof(th_mg_1a_2, axiom, (! [L,A,B,C] : ((line(L) & point(A) & ninc_po_l(A,L) & point(B) & point(C) & B!=C & inc_po_l(B,L) & inc_po_l(C,L)) => (ncol(A,B,C))))).

fof(th_mg_1a_3, axiom, (! [L,A,B,C] : ((line(L) & point(A) & ninc_po_l(A,L) & point(B) & point(C) & B!=C & inc_po_l(B,L) & inc_po_l(C,L) & ncol(A,B,C)) => (? [P] : (plane(P) & inc_po_pl(A,P) & inc_po_pl(B,P) & inc_po_pl(C,P)))))).

fof(th_mg_1a_4, axiom, (! [L,A,B,C,P] : ((line(L) & point(A) & ninc_po_l(A,L) & point(B) & point(C) & B!=C & inc_po_l(B,L) & inc_po_l(C,L) & ncol(A,B,C) & plane(P) & inc_po_pl(A,P) & inc_po_pl(B,P) & inc_po_pl(C,P)) => (inc_l_pl(L,P))))).

