reserve IPP for IncProjSp;
reserve a,b,c,d,p,q,o,r,s,t,u,v,w,x,y for POINT of IPP;
reserve A,B,C,D,L,P,Q,S for LINE of IPP;
reserve IPP for Fanoian IncProjSp;
reserve a,b,c,d,p,q,r,s for POINT of IPP;
reserve A,B,C,D,L,Q,R,S for LINE of IPP;

theorem
  ex p,q,r,s,a,b,c,A,B,C,Q,L,R,S,D st not q on L & not r on L & not p on
Q & not s on Q & not p on R & not r on R & not q on S & not s on S & {a,p,s} on
L & {a,q,r} on Q & {b,q,s} on R & {b,p,r} on S & {c,p,q} on A & {c,r,s} on B &
  {a,b} on C & not c on C
proof
  ex p,q,r,s,a,b,c,A,B,C,Q,L,R,S,D,d st not q on L & not r on L & not p on
Q & not s on Q & not p on R & not r on R & not q on S & not s on S & {a,p,s} on
L & {a,q,r} on Q & {b,q,s} on R & {b,p,r} on S & {c,p,q} on A & {c,r,s} on B &
{a,b} on C & not c on C & b on D & c on D & C,D,R,S are_mutually_distinct & d
  on A & c,d,p,q are_mutually_distinct by Lm2;
  hence thesis;
end;
