% Mizar problem: t13_dirort,dirort,440,5 
fof(t13_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)) =>  (! [D] :  ( ( ~ (v2_struct_0(D))  &  (v1_dirort(D) & l1_analmetr(D)) )  =>  ( (r1_analmetr(A, B, C) & D=k5_analort(A, B, C))  =>  (v5_dirort(D) &  (v4_dirort(D) &  (v3_dirort(D) & v2_dirort(D)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(abstractness_v1_analmetr, axiom,  (! [A] :  (l1_analmetr(A) =>  (v1_analmetr(A) => A=g1_analmetr(u1_struct_0(A), u1_analmetr(A))) ) ) ).
fof(d7_analort, 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)) => k5_analort(A, B, C)=g1_analmetr(u1_struct_0(A), k3_analort(A, B, C))) ) ) ) ) ) ).
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_k3_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))) )  => m1_subset_1(k3_analort(A, B, C), 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_k5_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(k5_analort(A, B, C)) & l1_analmetr(k5_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(fc1_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(k5_analort(A, B, C)))  & v1_analmetr(k5_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(t18_analort, 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)) =>  (! [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)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  ( (r1_analmetr(A, F, G) & r1_analort(A, F, G, B, C, D, E))  => r1_analort(A, F, G, D, E, C, B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t42_analort, 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)) =>  (! [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)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  (! [I] :  (m1_subset_1(I, u1_struct_0(A)) =>  (! [J] :  (m1_subset_1(J, u1_struct_0(A)) =>  (! [K] :  (m1_subset_1(K, u1_struct_0(A)) =>  ~ ( (r1_analmetr(A, J, K) &  (r1_analort(A, J, K, B, C, E, F) &  (r1_analort(A, J, K, H, I, E, F) &  (r1_analort(A, J, K, H, I, D, G) &  ( ~ (H=I)  &  ( ~ (E=F)  &  ~ (r1_analort(A, J, K, B, C, D, G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t44_analort, 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)) =>  (! [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)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  (! [I] :  (m1_subset_1(I, u1_struct_0(A)) =>  (! [J] :  (m1_subset_1(J, u1_struct_0(A)) =>  (! [K] :  (m1_subset_1(K, u1_struct_0(A)) =>  ~ ( (r1_analmetr(A, J, K) &  (r1_analort(A, J, K, B, C, E, F) &  (r1_analort(A, J, K, E, F, H, I) &  (r1_analort(A, J, K, D, G, H, I) &  ( ~ (r1_analort(A, J, K, B, C, D, G))  &  ( ~ (E=F)  &  ~ (H=I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t46_analort, 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)) =>  (! [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)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  (! [I] :  (m1_subset_1(I, u1_struct_0(A)) =>  (! [J] :  (m1_subset_1(J, u1_struct_0(A)) =>  (! [K] :  (m1_subset_1(K, u1_struct_0(A)) =>  ~ ( (r1_analmetr(A, J, K) &  (r1_analort(A, J, K, B, C, E, F) &  (r1_analort(A, J, K, E, F, H, I) &  (r1_analort(A, J, K, B, C, D, G) &  ( ~ (r1_analort(A, J, K, D, G, H, I))  &  ( ~ (E=F)  &  ~ (B=C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t54_analort, 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)) =>  (! [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)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(k5_analort(A, F, G))) =>  (! [I] :  (m1_subset_1(I, u1_struct_0(k5_analort(A, F, G))) =>  (! [J] :  (m1_subset_1(J, u1_struct_0(k5_analort(A, F, G))) =>  (! [K] :  (m1_subset_1(K, u1_struct_0(k5_analort(A, F, G))) =>  ( (B=H &  (D=I &  (C=J & E=K) ) )  =>  (r4_analmetr(k5_analort(A, F, G), H, I, J, K) <=> r1_analort(A, F, G, B, D, C, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
