% Mizar problem: t21_projpl_1,projpl_1,540,5 
fof(t21_projpl_1, conjecture,  (! [A] :  (l1_incsp_1(A) =>  (! [B] :  (m1_subset_1(B, u1_incsp_1(A)) =>  (! [C] :  (m1_subset_1(C, u1_incsp_1(A)) =>  (! [D] :  (m1_subset_1(D, u1_incsp_1(A)) =>  (! [E] :  (m1_subset_1(E, u1_incsp_1(A)) =>  (! [F] :  (m1_subset_1(F, u2_incsp_1(A)) =>  (! [G] :  (m1_subset_1(G, u2_incsp_1(A)) =>  (! [H] :  (m1_subset_1(H, u2_incsp_1(A)) =>  (! [I] :  (m1_subset_1(I, u2_incsp_1(A)) =>  ( (v1_projpl_1(A) &  (r3_projpl_1(A, B, G, H, I) &  (r1_zfmisc_1(G, H, I) &  (r2_projpl_1(A, C, F, G) &  (r2_projpl_1(A, D, F, H) & r2_projpl_1(A, E, F, I)) ) ) ) )  =>  (r1_incsp_1(A, B, F) | r1_zfmisc_1(C, D, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_projpl_1, axiom,  (! [A] :  (l1_incsp_1(A) =>  (! [B] :  (m1_subset_1(B, u1_incsp_1(A)) =>  (! [C] :  (m1_subset_1(C, u2_incsp_1(A)) =>  (! [D] :  (m1_subset_1(D, u2_incsp_1(A)) =>  (r2_projpl_1(A, B, C, D) <=>  (r1_incsp_1(A, B, C) & r1_incsp_1(A, B, D)) ) ) ) ) ) ) ) ) ) ).
fof(d3_projpl_1, axiom,  (! [A] :  (l1_incsp_1(A) =>  (! [B] :  (m1_subset_1(B, u1_incsp_1(A)) =>  (! [C] :  (m1_subset_1(C, u2_incsp_1(A)) =>  (! [D] :  (m1_subset_1(D, u2_incsp_1(A)) =>  (! [E] :  (m1_subset_1(E, u2_incsp_1(A)) =>  (r3_projpl_1(A, B, C, D, E) <=>  (r1_incsp_1(A, B, C) &  (r1_incsp_1(A, B, D) & r1_incsp_1(A, B, E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_zfmisc_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (r1_zfmisc_1(A, B, C) <=>  ( ~ (A=B)  &  ( ~ (A=C)  &  ~ (B=C) ) ) ) ) ) ) ).
fof(dt_l1_incsp_1, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_incsp_1, axiom,  (! [A] :  (l1_incsp_1(A) =>  ~ (v1_xboole_0(u1_incsp_1(A))) ) ) ).
fof(dt_u2_incsp_1, axiom,  (! [A] :  (l1_incsp_1(A) =>  ~ (v1_xboole_0(u2_incsp_1(A))) ) ) ).
fof(existence_l1_incsp_1, axiom,  (? [A] : l1_incsp_1(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
