% Mizar problem: t48_yellow12,yellow12,1318,5 
fof(t48_yellow12, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v2_pre_topc(B) & l1_pre_topc(B)) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  &  (v2_pre_topc(C) & l1_pre_topc(C)) )  =>  (! [D] :  ( ( ~ (v2_struct_0(D))  &  (v2_pre_topc(D) & l1_pre_topc(D)) )  =>  (! [E] :  (m3_yellow_9(E, k2_borsuk_1(A, C), k2_borsuk_1(B, D)) =>  ( (u1_struct_0(A)=u1_struct_0(B) & u1_struct_0(C)=u1_struct_0(D))  =>  (v1_tops_2(a_4_2_yellow12(A, B, C, D), E) &  (v1_cantor_1(a_4_2_yellow12(A, B, C, D), E) & m1_subset_1(a_4_2_yellow12(A, B, C, D), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(E))))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(abstractness_v1_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) =>  (v1_pre_topc(A) => A=g1_pre_topc(u1_struct_0(A), u1_pre_topc(A))) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc1_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc1_tops_1, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_xboole_0(B) => v3_pre_topc(B, A)) ) ) ) ) ).
fof(cc1_yellow12, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) =>  ( (v1_tops_2(B, A) & v1_cantor_1(B, A))  =>  ( ~ (v1_xboole_0(B))  &  (v1_tops_2(B, A) & v1_cantor_1(B, A)) ) ) ) ) ) ) ).
fof(cc2_pre_topc, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_xboole_0(B) => v4_pre_topc(B, A)) ) ) ) ) ).
fof(cc2_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc2_tops_1, axiom,  (! [A] :  (l1_pre_topc(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_xboole_0(B) => v2_tops_1(B, A)) ) ) ) ) ).
fof(cc3_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_xboole_0(C)) ) ) ) ).
fof(cc3_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc3_tops_1, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_xboole_0(B) => v3_tops_1(B, A)) ) ) ) ) ).
fof(cc4_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => v1_xboole_0(C)) ) ) ) ).
fof(cc4_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc5_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
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(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc6_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) & v3_tops_1(B, A))  => v1_xboole_0(B)) ) ) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc7_yellow_9, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  & l1_pre_topc(B))  =>  (! [C] :  (m3_yellow_9(C, A, B) =>  ~ (v2_struct_0(C)) ) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc8_yellow_9, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  & l1_pre_topc(B))  =>  (! [C] :  (m3_yellow_9(C, B, A) =>  ~ (v2_struct_0(C)) ) ) ) ) ).
fof(cc9_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) =>  (v2_struct_0(A) => v6_pre_topc(A)) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(commutativity_k3_setfam_1, axiom,  (! [A, B] : k3_setfam_1(A, B)=k3_setfam_1(B, A)) ).
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(d2_borsuk_1, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (! [B] :  ( (v2_pre_topc(B) & l1_pre_topc(B))  =>  (! [C] :  ( (v1_pre_topc(C) &  (v2_pre_topc(C) & l1_pre_topc(C)) )  =>  (C=k2_borsuk_1(A, B) <=>  (u1_struct_0(C)=k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)) & u1_pre_topc(C)=a_3_0_borsuk_1(A, B, C)) ) ) ) ) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d4_tarski, axiom,  (! [A] :  (! [B] :  (B=k3_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=>  (? [D] :  (r2_hidden(C, D) & r2_hidden(D, A)) ) ) ) ) ) ) ).
fof(d4_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k3_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) & r2_hidden(D, B)) ) ) ) ) ) ) ).
fof(d5_setfam_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k3_setfam_1(A, B) <=>  (! [D] :  (r2_tarski(D, C) <=>  (? [E] :  (? [F] :  (r2_tarski(E, A) &  (r2_tarski(F, B) & D=k3_xboole_0(E, F)) ) ) ) ) ) ) ) ) ) ).
fof(d6_yellow_9, axiom,  (! [A] :  (l1_pre_topc(A) =>  (! [B] :  (l1_pre_topc(B) =>  (! [C] :  ( (v2_pre_topc(C) & l1_pre_topc(C))  =>  (m3_yellow_9(C, A, B) <=>  (u1_struct_0(C)=k2_xboole_0(u1_struct_0(A), u1_struct_0(B)) &  (v1_tops_2(k2_xboole_0(u1_pre_topc(A), u1_pre_topc(B)), C) &  (v2_cantor_1(k2_xboole_0(u1_pre_topc(A), u1_pre_topc(B)), C) & m1_subset_1(k2_xboole_0(u1_pre_topc(A), u1_pre_topc(B)), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C))))) ) ) ) ) ) ) ) ) ) ).
fof(dt_g1_pre_topc, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) =>  (v1_pre_topc(g1_pre_topc(A, B)) & l1_pre_topc(g1_pre_topc(A, B))) ) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_borsuk_1, axiom,  (! [A, B] :  ( ( (v2_pre_topc(A) & l1_pre_topc(A))  &  (v2_pre_topc(B) & l1_pre_topc(B)) )  =>  (v1_pre_topc(k2_borsuk_1(A, B)) &  (v2_pre_topc(k2_borsuk_1(A, B)) & l1_pre_topc(k2_borsuk_1(A, B))) ) ) ) ).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_borsuk_1, axiom,  (! [A, B, C, D] :  ( ( (v2_pre_topc(A) & l1_pre_topc(A))  &  ( (v2_pre_topc(B) & l1_pre_topc(B))  &  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) ) )  => m1_subset_1(k3_borsuk_1(A, B, C, D), k1_zfmisc_1(u1_struct_0(k2_borsuk_1(A, B))))) ) ).
fof(dt_k3_setfam_1, axiom, $true).
fof(dt_k3_tarski, axiom, $true).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_setfam_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k5_setfam_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k8_mcart_1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(B)))  => m1_subset_1(k8_mcart_1(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ).
fof(dt_k9_setfam_1, axiom,  (! [A] : m1_subset_1(k9_setfam_1(A), k1_zfmisc_1(k1_zfmisc_1(A)))) ).
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_subset_1, axiom, $true).
fof(dt_m3_yellow_9, axiom,  (! [A, B] :  ( (l1_pre_topc(A) & l1_pre_topc(B))  =>  (! [C] :  (m3_yellow_9(C, A, B) =>  (v2_pre_topc(C) & l1_pre_topc(C)) ) ) ) ) ).
fof(dt_u1_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) => m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) ) ).
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(existence_m3_yellow_9, axiom,  (! [A, B] :  ( (l1_pre_topc(A) & l1_pre_topc(B))  =>  (? [C] : m3_yellow_9(C, A, B)) ) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc1_pre_topc, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  ~ (v1_xboole_0(u1_pre_topc(A))) ) ) ).
fof(fc1_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  &  (v1_relat_1(C) & v4_relat_1(C, A)) )  => v4_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc1_yellow12, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k3_tarski(A))) ) ).
fof(fc2_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  => v4_relat_1(k3_xboole_0(B, C), A)) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc3_borsuk_1, axiom,  (! [A, B] :  ( ( (v2_pre_topc(A) & l1_pre_topc(A))  &  (v2_struct_0(B) &  (v2_pre_topc(B) & l1_pre_topc(B)) ) )  =>  (v2_struct_0(k2_borsuk_1(A, B)) &  (v1_pre_topc(k2_borsuk_1(A, B)) & v2_pre_topc(k2_borsuk_1(A, B))) ) ) ) ).
fof(fc4_borsuk_1, axiom,  (! [A, B] :  ( ( (v2_pre_topc(A) & l1_pre_topc(A))  &  (v2_struct_0(B) &  (v2_pre_topc(B) & l1_pre_topc(B)) ) )  =>  (v2_struct_0(k2_borsuk_1(B, A)) &  (v1_pre_topc(k2_borsuk_1(B, A)) & v2_pre_topc(k2_borsuk_1(B, A))) ) ) ) ).
fof(fc4_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  &  (v1_relat_1(C) & v5_relat_1(C, A)) )  => v5_relat_1(k2_xboole_0(B, C), 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(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc5_borsuk_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  &  ( ~ (v2_struct_0(B))  &  (v2_pre_topc(B) & l1_pre_topc(B)) ) )  =>  ( ~ (v2_struct_0(k2_borsuk_1(A, B)))  &  (v1_pre_topc(k2_borsuk_1(A, B)) & v2_pre_topc(k2_borsuk_1(A, B))) ) ) ) ).
fof(fc5_borsuk_2, axiom,  (! [A, B] :  ( ( (v2_pre_topc(A) &  (v6_pre_topc(A) & l1_pre_topc(A)) )  &  (v2_pre_topc(B) &  (v6_pre_topc(B) & l1_pre_topc(B)) ) )  =>  (v1_pre_topc(k2_borsuk_1(A, B)) &  (v2_pre_topc(k2_borsuk_1(A, B)) & v6_pre_topc(k2_borsuk_1(A, B))) ) ) ) ).
fof(fc5_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  => v5_relat_1(k3_xboole_0(B, C), A)) ) ).
fof(fc5_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(k2_xboole_0(B, C), A)) ) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc6_pre_topc, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (v1_pre_topc(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A))) & v2_pre_topc(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)))) ) ) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(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(fc7_pre_topc, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  =>  ( ~ (v2_struct_0(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A))))  & v1_pre_topc(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)))) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc7_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(k2_xboole_0(B, C), A)) ) ).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_pre_topc, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))))  =>  ( ~ (v2_struct_0(g1_pre_topc(A, B)))  & v1_pre_topc(g1_pre_topc(A, B))) ) ) ).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(fraenkel_a_2_0_borsuk_1, axiom,  (! [A, B, C] :  ( ( (v2_pre_topc(B) & l1_pre_topc(B))  &  (v2_pre_topc(C) & l1_pre_topc(C)) )  =>  (r2_hidden(A, a_2_0_borsuk_1(B, C)) <=>  (? [D, E] :  ( (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(C))))  &  (A=k8_mcart_1(u1_struct_0(B), u1_struct_0(C), D, E) &  (r2_tarski(D, u1_pre_topc(B)) & r2_tarski(E, u1_pre_topc(C))) ) ) ) ) ) ) ).
fof(fraenkel_a_2_3_yellow12, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  &  (v2_pre_topc(B) & l1_pre_topc(B)) )  &  ( ~ (v2_struct_0(C))  &  (v2_pre_topc(C) & l1_pre_topc(C)) ) )  =>  (r2_hidden(A, a_2_3_yellow12(B, C)) <=>  (? [D] :  (m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k2_borsuk_1(B, C))))) &  (A=k5_setfam_1(u1_struct_0(k2_borsuk_1(B, C)), D) & r1_tarski(D, a_2_4_yellow12(B, C))) ) ) ) ) ) ).
fof(fraenkel_a_2_4_yellow12, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  &  (v2_pre_topc(B) & l1_pre_topc(B)) )  &  ( ~ (v2_struct_0(C))  &  (v2_pre_topc(C) & l1_pre_topc(C)) ) )  =>  (r2_hidden(A, a_2_4_yellow12(B, C)) <=>  (? [D, E] :  ( (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(C))))  &  (A=k3_borsuk_1(B, C, D, E) &  (r2_tarski(D, u1_pre_topc(B)) & r2_tarski(E, u1_pre_topc(C))) ) ) ) ) ) ) ).
fof(fraenkel_a_3_0_borsuk_1, axiom,  (! [A, B, C, D] :  ( ( (v2_pre_topc(B) & l1_pre_topc(B))  &  ( (v2_pre_topc(C) & l1_pre_topc(C))  &  (v1_pre_topc(D) &  (v2_pre_topc(D) & l1_pre_topc(D)) ) ) )  =>  (r2_hidden(A, a_3_0_borsuk_1(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(D)))) &  (A=k5_setfam_1(u1_struct_0(D), E) & r1_tarski(E, a_2_0_borsuk_1(B, C))) ) ) ) ) ) ).
fof(fraenkel_a_4_2_yellow12, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(B))  &  (v2_pre_topc(B) & l1_pre_topc(B)) )  &  ( ( ~ (v2_struct_0(C))  &  (v2_pre_topc(C) & l1_pre_topc(C)) )  &  ( ( ~ (v2_struct_0(D))  &  (v2_pre_topc(D) & l1_pre_topc(D)) )  &  ( ~ (v2_struct_0(E))  &  (v2_pre_topc(E) & l1_pre_topc(E)) ) ) ) )  =>  (r2_hidden(A, a_4_2_yellow12(B, C, D, E)) <=>  (? [F, G, H, I] :  ( (m1_subset_1(F, k1_zfmisc_1(u1_struct_0(B))) &  (m1_subset_1(G, k1_zfmisc_1(u1_struct_0(C))) &  (m1_subset_1(H, k1_zfmisc_1(u1_struct_0(D))) & m1_subset_1(I, k1_zfmisc_1(u1_struct_0(E)))) ) )  &  (A=k9_subset_1(u1_struct_0(k2_borsuk_1(C, E)), k3_borsuk_1(B, D, F, H), k3_borsuk_1(C, E, G, I)) &  (v3_pre_topc(F, B) &  (v3_pre_topc(G, C) &  (v3_pre_topc(H, D) & v3_pre_topc(I, E)) ) ) ) ) ) ) ) ) ).
fof(free_g1_pre_topc, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) =>  (! [C, D] :  (g1_pre_topc(A, B)=g1_pre_topc(C, D) =>  (A=C & B=D) ) ) ) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=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(rc11_pre_topc, axiom,  (? [A] :  (l1_pre_topc(A) &  (v2_struct_0(A) & v1_pre_topc(A)) ) ) ).
fof(rc12_pre_topc, axiom,  (? [A] :  (l1_pre_topc(A) &  (v2_struct_0(A) &  (v1_pre_topc(A) & v2_pre_topc(A)) ) ) ) ).
fof(rc1_pre_topc, axiom,  (? [A] :  (l1_pre_topc(A) & v1_pre_topc(A)) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
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(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_yellow12, axiom,  (! [A, B] :  ( (l1_pre_topc(A) & l1_pre_topc(B))  =>  (? [C] :  (m3_yellow_9(C, A, B) &  (v1_pre_topc(C) & v2_pre_topc(C)) ) ) ) ) ).
fof(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc2_pre_topc, axiom,  (? [A] :  (l1_pre_topc(A) &  ( ~ (v2_struct_0(A))  &  (v1_pre_topc(A) & v2_pre_topc(A)) ) ) ) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
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(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_yellow12, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  & l1_pre_topc(B))  =>  (? [C] :  (m3_yellow_9(C, A, B) &  ( ~ (v2_struct_0(C))  &  (v1_pre_topc(C) & v2_pre_topc(C)) ) ) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc3_tops_1, axiom,  (! [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))) &  ( ~ (v1_xboole_0(B))  &  (v3_pre_topc(B, A) & v4_pre_topc(B, A)) ) ) ) ) ) ).
fof(rc3_yellow12, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  & l1_pre_topc(B))  =>  (? [C] :  (m3_yellow_9(C, B, A) &  ( ~ (v2_struct_0(C))  &  (v1_pre_topc(C) & v2_pre_topc(C)) ) ) ) ) ) ).
fof(rc4_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc4_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
fof(rc5_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(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(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc6_tops_1, axiom,  (! [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))) &  ( ~ (v1_xboole_0(B))  &  ~ (v2_tops_1(B, A)) ) ) ) ) ) ).
fof(rc7_pre_topc, axiom,  (! [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))) &  ( ~ (v1_xboole_0(B))  & 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(redefinition_k3_borsuk_1, axiom,  (! [A, B, C, D] :  ( ( (v2_pre_topc(A) & l1_pre_topc(A))  &  ( (v2_pre_topc(B) & l1_pre_topc(B))  &  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) ) )  => k3_borsuk_1(A, B, C, D)=k2_zfmisc_1(C, D)) ) ).
fof(redefinition_k5_setfam_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => k5_setfam_1(A, B)=k3_tarski(B)) ) ).
fof(redefinition_k8_mcart_1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, k1_zfmisc_1(B)))  => k8_mcart_1(A, B, C, D)=k2_zfmisc_1(C, D)) ) ).
fof(redefinition_k9_setfam_1, axiom,  (! [A] : k9_setfam_1(A)=k1_zfmisc_1(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(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t27_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  ( (r1_tarski(A, B) & r1_tarski(C, D))  => r1_tarski(k3_xboole_0(A, C), k3_xboole_0(B, D))) ) ) ) ) ).
fof(t2_boole, axiom,  (! [A] : k3_xboole_0(A, k1_xboole_0)=k1_xboole_0) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t2_tarski, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_hidden(C, A) <=> r2_hidden(C, B)) )  => A=B) ) ) ).
fof(t31_yellow_9, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (! [B] :  ( (v1_tops_2(B, A) &  (v1_cantor_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) =>  (v3_pre_topc(C, A) <=>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  ~ ( (r2_tarski(D, C) &  (! [E] :  (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) =>  ~ ( (r2_tarski(E, B) &  (r2_tarski(D, E) & r1_tarski(E, C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t32_yellow_9, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) =>  ( (r1_tarski(B, u1_pre_topc(A)) &  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) =>  (v3_pre_topc(C, A) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  ~ ( (r2_tarski(D, C) &  (! [E] :  (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) =>  ~ ( (r2_tarski(E, B) &  (r2_tarski(D, E) & r1_tarski(E, C)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (v1_tops_2(B, A) &  (v1_cantor_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t60_yellow_9, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v2_pre_topc(B) & l1_pre_topc(B)) )  =>  (u1_struct_0(A)=u1_struct_0(B) =>  (! [C] :  (m3_yellow_9(C, A, B) =>  (v1_tops_2(k3_setfam_1(u1_pre_topc(A), u1_pre_topc(B)), C) &  (v1_cantor_1(k3_setfam_1(u1_pre_topc(A), u1_pre_topc(B)), C) & m1_subset_1(k3_setfam_1(u1_pre_topc(A), u1_pre_topc(B)), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C))))) ) ) ) ) ) ) ) ) ).
fof(t64_tops_2, axiom,  (! [A] :  (l1_pre_topc(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) =>  (v1_tops_2(B, A) <=> r1_tarski(B, u1_pre_topc(A))) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t6_borsuk_1, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (! [B] :  ( (v2_pre_topc(B) & l1_pre_topc(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B))) =>  ( (v3_pre_topc(C, A) & v3_pre_topc(D, B))  => v3_pre_topc(k3_borsuk_1(A, B, C, D), k2_borsuk_1(A, B))) ) ) ) ) ) ) ) ) ).
fof(t74_zfmisc_1, axiom,  (! [A] :  (! [B] :  (r2_tarski(B, A) => r1_tarski(B, k3_tarski(A))) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
