% Mizar problem: t37_projpl_1,projpl_1,1033,5 
fof(t37_projpl_1, conjecture,  (! [A] :  ( (v6_incsp_1(A) &  (v1_incproj(A) &  (v2_incproj(A) &  (v3_incproj(A) &  (v4_incproj(A) &  (v5_incproj(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, u1_incsp_1(A)) =>  (! [G] :  (m1_subset_1(G, u2_incsp_1(A)) =>  (! [H] :  (m1_subset_1(H, u2_incsp_1(A)) =>  ~ ( (r1_incsp_1(A, C, H) &  (r1_incsp_1(A, D, H) &  ( ~ (r1_incsp_1(A, B, H))  &  ( ~ (C=D)  &  ( ~ (E=B)  &  ( ~ (F=B)  &  (r1_incsp_1(A, E, k1_projpl_1(A, B, C)) &  (r1_incsp_1(A, F, k1_projpl_1(A, B, D)) &  (! [I] :  (m1_subset_1(I, u1_incsp_1(A)) =>  ~ ( (r1_incsp_1(A, I, k1_projpl_1(A, E, F)) &  (r1_incsp_1(A, I, G) &  ~ (I=B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_incproj, axiom,  (! [A] :  (l1_incsp_1(A) =>  (v1_incproj(A) <=>  (! [B] :  (m1_subset_1(B, u1_incsp_1(A)) =>  (! [C] :  (m1_subset_1(C, u1_incsp_1(A)) =>  (! [D] :  (m1_subset_1(D, u2_incsp_1(A)) =>  (! [E] :  (m1_subset_1(E, u2_incsp_1(A)) =>  ~ ( (r1_incsp_1(A, B, D) &  (r1_incsp_1(A, C, D) &  (r1_incsp_1(A, B, E) &  (r1_incsp_1(A, C, E) &  ( ~ (B=C)  &  ~ (D=E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d9_incproj, axiom,  (! [A] :  ( (v6_incsp_1(A) &  (v1_incproj(A) &  (v2_incproj(A) &  (v3_incproj(A) &  (v4_incproj(A) & l1_incsp_1(A)) ) ) ) )  =>  (v5_incproj(A) <=>  (! [B] :  (m1_subset_1(B, u2_incsp_1(A)) =>  (! [C] :  (m1_subset_1(C, u2_incsp_1(A)) =>  (? [D] :  (m1_subset_1(D, u1_incsp_1(A)) &  (r1_incsp_1(A, D, B) & r1_incsp_1(A, D, C)) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_projpl_1, axiom,  (! [A, B, C] :  ( ( (v6_incsp_1(A) &  (v1_incproj(A) &  (v2_incproj(A) &  (v3_incproj(A) &  (v4_incproj(A) & l1_incsp_1(A)) ) ) ) )  &  (m1_subset_1(B, u1_incsp_1(A)) & m1_subset_1(C, u1_incsp_1(A))) )  => m1_subset_1(k1_projpl_1(A, B, C), u2_incsp_1(A))) ) ).
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)) ) ).
fof(t16_projpl_1, axiom,  (! [A] :  ( (v6_incsp_1(A) &  (v1_incproj(A) &  (v2_incproj(A) &  (v3_incproj(A) &  (v4_incproj(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, u2_incsp_1(A)) =>  ( ~ (B=C)  =>  (r1_incsp_1(A, B, k1_projpl_1(A, B, C)) &  (r1_incsp_1(A, C, k1_projpl_1(A, B, C)) &  (k1_projpl_1(A, B, C)=k1_projpl_1(A, C, B) &  ( (r1_incsp_1(A, B, D) & r1_incsp_1(A, C, D))  => D=k1_projpl_1(A, B, C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
