% Mizar problem: t3_dirort,dirort,212,5 
fof(t3_dirort, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r1_analmetr(A, B, C) =>  ( ~ (v2_struct_0(k6_analort(A, B, C)))  &  (v1_dirort(k6_analort(A, B, C)) & l1_analmetr(k6_analort(A, B, C))) ) ) ) ) ) ) ) ) ).
fof(abstractness_v1_analmetr, axiom,  (! [A] :  (l1_analmetr(A) =>  (v1_analmetr(A) => A=g1_analmetr(u1_struct_0(A), u1_analmetr(A))) ) ) ).
fof(d1_dirort, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_analmetr(A))  =>  (v1_dirort(A) <=>  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (r4_analmetr(A, B, B, D, F) &  (r4_analmetr(A, B, D, F, F) &  ( ~ ( (r4_analmetr(A, B, D, C, E) &  (r4_analmetr(A, B, D, E, C) &  ( ~ (B=D)  &  ~ (C=E) ) ) ) )  &  ( ~ ( (r4_analmetr(A, B, D, C, E) &  (r4_analmetr(A, B, D, C, F) &  ( ~ (r4_analmetr(A, B, D, E, F))  &  ~ (r4_analmetr(A, B, D, F, E)) ) ) ) )  &  ( (r4_analmetr(A, B, D, C, E) => r4_analmetr(A, D, B, E, C))  &  ( ( (r4_analmetr(A, B, D, C, E) & r4_analmetr(A, B, D, E, F))  => r4_analmetr(A, B, D, C, F))  &  ~ ( (r4_analmetr(A, B, C, D, E) &  ( ~ (r4_analmetr(A, D, E, B, C))  &  ~ (r4_analmetr(A, D, E, C, B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (? [E] :  (m1_subset_1(E, u1_struct_0(A)) &  ( ~ (D=E)  & r4_analmetr(A, D, E, B, C)) ) ) ) ) ) ) ) )  &  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (? [E] :  (m1_subset_1(E, u1_struct_0(A)) &  ( ~ (D=E)  & r4_analmetr(A, B, C, D, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_g1_analmetr, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), k2_zfmisc_1(A, A)))) =>  (v1_analmetr(g1_analmetr(A, B)) & l1_analmetr(g1_analmetr(A, B))) ) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k6_analort, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  =>  (v1_analmetr(k6_analort(A, B, C)) & l1_analmetr(k6_analort(A, B, C))) ) ) ).
fof(dt_l1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l1_analmetr, axiom,  (! [A] :  (l1_analmetr(A) => l1_struct_0(A)) ) ).
fof(dt_l1_rlvect_1, axiom,  (! [A] :  (l1_rlvect_1(A) => l2_algstr_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (l2_struct_0(A) & l1_algstr_0(A)) ) ) ).
fof(dt_l2_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_analmetr, axiom,  (! [A] :  (l1_analmetr(A) => m1_subset_1(u1_analmetr(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)))))) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_algstr_0, axiom,  (? [A] : l1_algstr_0(A)) ).
fof(existence_l1_analmetr, axiom,  (? [A] : l1_analmetr(A)) ).
fof(existence_l1_rlvect_1, axiom,  (? [A] : l1_rlvect_1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_algstr_0, axiom,  (? [A] : l2_algstr_0(A)) ).
fof(existence_l2_struct_0, axiom,  (? [A] : l2_struct_0(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc2_analort, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  =>  ( ~ (v2_struct_0(k6_analort(A, B, C)))  & v1_analmetr(k6_analort(A, B, C))) ) ) ).
fof(free_g1_analmetr, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), k2_zfmisc_1(A, A)))) =>  (! [C, D] :  (g1_analmetr(A, B)=g1_analmetr(C, D) =>  (A=C & B=D) ) ) ) ) ).
fof(rc1_analmetr, axiom,  (? [A] :  (l1_analmetr(A) & v1_analmetr(A)) ) ).
fof(rc1_dirort, axiom,  (? [A] :  (l1_analmetr(A) &  ( ~ (v2_struct_0(A))  & v1_dirort(A)) ) ) ).
fof(rc4_analmetr, axiom,  (? [A] :  (l1_analmetr(A) &  ~ (v2_struct_0(A)) ) ) ).
fof(t2_dirort, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r1_analmetr(A, B, C) =>  ( (! [D] :  (m1_subset_1(D, u1_struct_0(k6_analort(A, B, C))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(k6_analort(A, B, C))) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(k6_analort(A, B, C))) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(k6_analort(A, B, C))) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(k6_analort(A, B, C))) =>  (r4_analmetr(k6_analort(A, B, C), D, D, F, H) &  (r4_analmetr(k6_analort(A, B, C), D, F, H, H) &  ( ~ ( (r4_analmetr(k6_analort(A, B, C), D, F, E, G) &  (r4_analmetr(k6_analort(A, B, C), D, F, G, E) &  ( ~ (D=F)  &  ~ (E=G) ) ) ) )  &  ( ~ ( (r4_analmetr(k6_analort(A, B, C), D, F, E, G) &  (r4_analmetr(k6_analort(A, B, C), D, F, E, H) &  ( ~ (r4_analmetr(k6_analort(A, B, C), D, F, G, H))  &  ~ (r4_analmetr(k6_analort(A, B, C), D, F, H, G)) ) ) ) )  &  ( (r4_analmetr(k6_analort(A, B, C), D, F, E, G) => r4_analmetr(k6_analort(A, B, C), F, D, G, E))  &  ( ( (r4_analmetr(k6_analort(A, B, C), D, F, E, G) & r4_analmetr(k6_analort(A, B, C), D, F, G, H))  => r4_analmetr(k6_analort(A, B, C), D, F, E, H))  &  ~ ( (r4_analmetr(k6_analort(A, B, C), D, E, F, G) &  ( ~ (r4_analmetr(k6_analort(A, B, C), F, G, D, E))  &  ~ (r4_analmetr(k6_analort(A, B, C), F, G, E, D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [D] :  (m1_subset_1(D, u1_struct_0(k6_analort(A, B, C))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(k6_analort(A, B, C))) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(k6_analort(A, B, C))) =>  (? [G] :  (m1_subset_1(G, u1_struct_0(k6_analort(A, B, C))) &  ( ~ (F=G)  & r4_analmetr(k6_analort(A, B, C), F, G, D, E)) ) ) ) ) ) ) ) )  &  (! [D] :  (m1_subset_1(D, u1_struct_0(k6_analort(A, B, C))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(k6_analort(A, B, C))) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(k6_analort(A, B, C))) =>  (? [G] :  (m1_subset_1(G, u1_struct_0(k6_analort(A, B, C))) &  ( ~ (F=G)  & r4_analmetr(k6_analort(A, B, C), D, E, F, G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
