% Mizar problem: t26_tops_3,tops_3,335,5 
fof(t26_tops_3, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) =>  ( (v3_tops_1(C, A) & r1_tarski(B, C))  => v3_tops_1(B, A)) ) ) ) ) ) ) ).
fof(cc4_tops_1, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v3_tops_1(B, A) => v2_tops_1(B, A)) ) ) ) ) ).
fof(cc5_tops_1, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  ( (v4_pre_topc(B, A) & v2_tops_1(B, A))  => v3_tops_1(B, A)) ) ) ) ) ).
fof(cc9_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) =>  (v2_struct_0(A) => v6_pre_topc(A)) ) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_pre_topc, axiom,  (! [A, B] :  ( (l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))  => m1_subset_1(k2_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_l1_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_pre_topc, axiom,  (? [A] : l1_pre_topc(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc1_tops_1, axiom,  (! [A, B] :  ( ( (v2_pre_topc(A) & l1_pre_topc(A))  & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))  => v4_pre_topc(k2_pre_topc(A, B), A)) ) ).
fof(projectivity_k2_pre_topc, axiom,  (! [A, B] :  ( (l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))  => k2_pre_topc(A, k2_pre_topc(A, B))=k2_pre_topc(A, B)) ) ).
fof(rc5_tops_1, axiom,  (! [A] :  (l1_pre_topc(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v2_tops_1(B, A)) ) ) ) ).
fof(rc6_pre_topc, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(B, A)) ) ) ) ).
fof(rc7_tops_1, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v3_tops_1(B, A)) ) ) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(t11_tops_3, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) =>  ( (v2_tops_1(C, A) & r1_tarski(B, C))  => v2_tops_1(B, A)) ) ) ) ) ) ) ).
fof(t19_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) =>  (r1_tarski(B, C) => r1_tarski(k2_pre_topc(A, B), k2_pre_topc(A, C))) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
