% Mizar problem: t13_tsep_1,tsep_1,335,5 
fof(t13_tsep_1, conjecture,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (! [B] :  ( (v1_borsuk_1(B, A) & m1_pre_topc(B, A))  =>  (! [C] :  ( (v1_borsuk_1(C, B) & m1_pre_topc(C, B))  =>  (v1_borsuk_1(C, A) & m1_pre_topc(C, A)) ) ) ) ) ) ) ).
fof(cc1_pre_topc, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (! [B] :  (m1_pre_topc(B, A) => v2_pre_topc(B)) ) ) ) ).
fof(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_0(B, A)) ).
fof(commutativity_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, C)=k9_subset_1(A, C, B)) ) ).
fof(d11_borsuk_1, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (! [B] :  (m1_pre_topc(B, A) =>  (v1_borsuk_1(B, A) <=>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) =>  (C=u1_struct_0(B) => v4_pre_topc(C, A)) ) ) ) ) ) ) ) ).
fof(d3_struct_0, axiom,  (! [A] :  (l1_struct_0(A) => k2_struct_0(A)=u1_struct_0(A)) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) => m1_subset_1(k2_struct_0(A), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => m1_subset_1(k9_subset_1(A, B, C), k1_zfmisc_1(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_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) =>  (! [B] :  (m1_pre_topc(B, A) => l1_pre_topc(B)) ) ) ) ).
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_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) =>  (? [B] : m1_pre_topc(B, A)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc10_tops_1, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  => v3_pre_topc(k2_struct_0(A), A)) ) ).
fof(fc12_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ~ (v1_subset_1(k2_struct_0(A), u1_struct_0(A))) ) ) ).
fof(fc12_tops_1, axiom,  (! [A] :  (l1_pre_topc(A) => v1_tops_1(k2_struct_0(A), A)) ) ).
fof(fc4_pre_topc, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  => v4_pre_topc(k2_struct_0(A), A)) ) ).
fof(fc4_tops_1, axiom,  (! [A, B, C] :  ( ( (v2_pre_topc(A) & l1_pre_topc(A))  &  ( (v4_pre_topc(B, A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))  &  (v4_pre_topc(C, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) ) )  => v4_pre_topc(k3_xboole_0(B, C), A)) ) ).
fof(fc6_tops_1, axiom,  (! [A, B, C] :  ( ( (v2_pre_topc(A) & l1_pre_topc(A))  &  ( (v3_pre_topc(B, A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))  &  (v3_pre_topc(C, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) ) )  => v3_pre_topc(k3_xboole_0(B, C), A)) ) ).
fof(idempotence_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, A)=A) ).
fof(idempotence_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, B)=B) ) ).
fof(rc10_pre_topc, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B, A)) ) ) ) ).
fof(rc1_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_pre_topc(B, A)) ) ) ) ).
fof(rc2_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_pre_topc(B, A) & v4_pre_topc(B, A)) ) ) ) ) ).
fof(rc4_tops_1, axiom,  (! [A] :  (l1_pre_topc(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_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(redefinition_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, C)=k3_xboole_0(B, C)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(t13_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) =>  (! [B] :  (m1_pre_topc(B, A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) =>  (v4_pre_topc(C, B) <=>  (? [D] :  (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) &  (v4_pre_topc(D, A) & k9_subset_1(u1_struct_0(B), D, k2_struct_0(B))=C) ) ) ) ) ) ) ) ) ) ).
fof(t1_borsuk_1, axiom,  (! [A] :  (l1_pre_topc(A) =>  (! [B] :  (m1_pre_topc(B, A) => r1_tarski(u1_struct_0(B), u1_struct_0(A))) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t7_tsep_1, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (! [B] :  (m1_pre_topc(B, A) =>  (! [C] :  (m1_pre_topc(C, B) => m1_pre_topc(C, A)) ) ) ) ) ) ).
