% Mizar problem: l37_tsp_2,tsp_2,1470,5 
fof(l37_tsp_2, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v2_tsp_2(B, A) & m1_pre_topc(B, A)) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) &  (v5_pre_topc(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) )  =>  (v3_borsuk_1(C, A, B) =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) =>  (! [E] :  (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(B))) =>  (E=D => k8_relset_1(u1_struct_0(A), u1_struct_0(B), C, E)=k3_tex_4(A, D)) ) ) ) ) ) ) ) ) ) ) ) ).
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(cc10_tsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  (v6_pre_topc(A) & l1_pre_topc(A)) ) )  =>  (! [B] :  (m1_pre_topc(B, A) =>  ( ~ (v2_struct_0(B))  =>  ( ~ (v2_struct_0(B))  & v6_pre_topc(B)) ) ) ) ) ) ).
fof(cc10_tsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (! [B] :  (m1_pre_topc(B, A) =>  ( (v1_tex_2(B, A) & v2_tsp_2(B, A))  =>  ~ (v1_borsuk_1(B, A)) ) ) ) ) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc11_tsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  ( ~ (v6_pre_topc(A))  & l1_pre_topc(A)) ) )  =>  (! [B] :  (m1_pre_topc(B, A) =>  ( ( ~ (v2_struct_0(B))  &  ~ (v1_tex_2(B, A)) )  =>  ( ~ (v2_struct_0(B))  &  ~ (v6_pre_topc(B)) ) ) ) ) ) ) ).
fof(cc12_tsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  ( ~ (v6_pre_topc(A))  & l1_pre_topc(A)) ) )  =>  (! [B] :  (m1_pre_topc(B, A) =>  ( ( ~ (v2_struct_0(B))  & v6_pre_topc(B))  =>  ( ~ (v2_struct_0(B))  & v1_tex_2(B, A)) ) ) ) ) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(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(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_tsp_1, axiom,  (! [A] :  (l1_pre_topc(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  =>  ( ~ (v2_struct_0(A))  & v6_pre_topc(A)) ) ) ) ).
fof(cc1_tsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  =>  (! [B] :  (m1_pre_topc(B, A) =>  ( ( ~ (v2_struct_0(B))  & v2_tsp_2(B, A))  =>  ( ~ (v2_struct_0(B))  & v6_pre_topc(B)) ) ) ) ) ) ).
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(cc2_tsp_1, axiom,  (! [A] :  (l1_pre_topc(A) =>  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & v1_tdlat_3(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & v6_pre_topc(A)) ) ) ) ) ).
fof(cc2_tsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  =>  (! [B] :  (m1_pre_topc(B, A) =>  ( ( ~ (v2_struct_0(B))  &  ~ (v6_pre_topc(B)) )  =>  ( ~ (v2_struct_0(B))  &  ~ (v2_tsp_2(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(cc3_tsp_1, axiom,  (! [A] :  (l1_pre_topc(A) =>  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  ~ (v6_pre_topc(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  ~ (v1_tdlat_3(A)) ) ) ) ) ) ).
fof(cc3_tsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (! [B] :  (m1_pre_topc(B, A) =>  (v2_tsp_2(B, A) => v1_tex_3(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(cc4_tsp_1, axiom,  (! [A] :  (l1_pre_topc(A) =>  ( ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v2_pre_topc(A) & v2_tdlat_3(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  ~ (v6_pre_topc(A)) ) ) ) ) ) ).
fof(cc4_tsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (! [B] :  (m1_pre_topc(B, A) =>  ( ~ (v1_tex_3(B, A))  =>  ~ (v2_tsp_2(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(cc5_tsp_1, axiom,  (! [A] :  (l1_pre_topc(A) =>  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  (v6_pre_topc(A) & v2_tdlat_3(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v7_struct_0(A) & v2_pre_topc(A)) ) ) ) ) ).
fof(cc5_tsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (! [B] :  (m1_pre_topc(B, A) =>  ( (v1_tsep_1(B, A) & v2_tsp_2(B, A))  =>  ~ (v1_tex_2(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(cc6_tsp_1, axiom,  (! [A] :  (l1_pre_topc(A) =>  ( ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v2_pre_topc(A) & v6_pre_topc(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  ~ (v2_tdlat_3(A)) ) ) ) ) ) ).
fof(cc6_tsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (! [B] :  (m1_pre_topc(B, A) =>  ( (v1_tsep_1(B, A) & v1_tex_2(B, A))  =>  ~ (v2_tsp_2(B, A)) ) ) ) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc7_tsp_1, axiom,  (! [A] :  (l1_pre_topc(A) =>  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  (v6_pre_topc(A) & v3_tdlat_3(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & v1_tdlat_3(A)) ) ) ) ) ).
fof(cc7_tsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (! [B] :  (m1_pre_topc(B, A) =>  ( (v1_tex_2(B, A) & v2_tsp_2(B, A))  =>  ~ (v1_tsep_1(B, A)) ) ) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc8_tsp_1, axiom,  (! [A] :  (l1_pre_topc(A) =>  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  ( ~ (v1_tdlat_3(A))  & v3_tdlat_3(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  ~ (v6_pre_topc(A)) ) ) ) ) ) ).
fof(cc8_tsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (! [B] :  (m1_pre_topc(B, A) =>  ( (v1_borsuk_1(B, A) & v2_tsp_2(B, A))  =>  ~ (v1_tex_2(B, A)) ) ) ) ) ) ).
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(cc9_tsp_1, axiom,  (! [A] :  (l1_pre_topc(A) =>  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  (v6_pre_topc(A) &  ~ (v1_tdlat_3(A)) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) &  ~ (v3_tdlat_3(A)) ) ) ) ) ) ).
fof(cc9_tsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (! [B] :  (m1_pre_topc(B, A) =>  ( (v1_borsuk_1(B, A) & v1_tex_2(B, A))  =>  ~ (v2_tsp_2(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(d10_xboole_0, axiom,  (! [A] :  (! [B] :  (A=B <=>  (r1_tarski(A, B) & r1_tarski(B, A)) ) ) ) ).
fof(d11_tex_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => k3_tex_4(A, B)=k3_tarski(a_2_5_tex_4(A, B))) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
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(dt_k1_funct_1, axiom, $true).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_tex_4, axiom,  (! [A, B] :  ( (l1_pre_topc(A) & m1_subset_1(B, u1_struct_0(A)))  => m1_subset_1(k2_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => m1_subset_1(k3_funct_2(A, B, C, D), B)) ) ).
fof(dt_k3_tarski, axiom, $true).
fof(dt_k3_tex_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))  => m1_subset_1(k3_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k4_tex_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  & m1_subset_1(B, u1_struct_0(A)))  =>  ( ~ (v1_xboole_0(k4_tex_4(A, B)))  & m1_subset_1(k4_tex_4(A, B), k1_zfmisc_1(u1_struct_0(A)))) ) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k6_domain_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k8_relat_1, axiom, $true).
fof(dt_k8_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => m1_subset_1(k8_relset_1(A, B, C, D), 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_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_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
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(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(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(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(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(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_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
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_tsp_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  &  (v2_pre_topc(B) & l1_pre_topc(B)) )  & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))  =>  (r2_hidden(A, a_2_0_tsp_2(B, C)) <=>  (? [D] :  (m1_subset_1(D, u1_struct_0(B)) &  (A=k4_tex_4(B, D) & r2_tarski(D, C)) ) ) ) ) ) ).
fof(fraenkel_a_2_5_tex_4, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  & l1_pre_topc(B))  & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))  =>  (r2_hidden(A, a_2_5_tex_4(B, C)) <=>  (? [D] :  (m1_subset_1(D, u1_struct_0(B)) &  (A=k2_tex_4(B, D) & r2_tarski(D, C)) ) ) ) ) ) ).
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(l34_tsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v2_tsp_2(B, A) & m1_pre_topc(B, A)) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) &  (v5_pre_topc(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) )  =>  (v3_borsuk_1(C, A, B) =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) =>  (D=u1_struct_0(B) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) => k9_subset_1(u1_struct_0(A), D, k4_tex_4(A, E))=k6_domain_1(u1_struct_0(B), k3_funct_2(u1_struct_0(A), u1_struct_0(B), C, E))) ) ) ) ) ) ) ) ) ) ) ) ).
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_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(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_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(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(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(rc8_pre_topc, axiom,  (! [A, B] :  ( ( (v2_pre_topc(A) & l1_pre_topc(A))  &  ( ~ (v2_struct_0(B))  &  (v2_pre_topc(B) & l1_pre_topc(B)) ) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) &  (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(A)) &  (v5_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_pre_topc(C, A, B)) ) ) ) ) ) ) ) ) ).
fof(redefinition_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => k3_funct_2(A, B, C, D)=k1_funct_1(C, D)) ) ).
fof(redefinition_k4_tex_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  & m1_subset_1(B, u1_struct_0(A)))  => k4_tex_4(A, B)=k2_tex_4(A, B)) ) ).
fof(redefinition_k6_domain_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => k6_domain_1(A, B)=k1_tarski(B)) ) ).
fof(redefinition_k8_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => k8_relset_1(A, B, C, D)=k8_relat_1(C, D)) ) ).
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(t11_tsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  =>  (! [B] :  (m1_pre_topc(B, A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) =>  (C=u1_struct_0(B) =>  (v1_tsp_2(C, A) <=> v2_tsp_2(B, A)) ) ) ) ) ) ) ) ).
fof(t18_tex_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => r1_tarski(k6_domain_1(u1_struct_0(A), B), k2_tex_4(A, B))) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t1_tsep_1, axiom,  (! [A] :  (l1_pre_topc(A) =>  (! [B] :  (m1_pre_topc(B, A) => m1_subset_1(u1_struct_0(B), k1_zfmisc_1(u1_struct_0(A)))) ) ) ) ).
fof(t21_tex_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r2_tarski(C, k2_tex_4(A, B)) <=> k2_tex_4(A, C)=k2_tex_4(A, B)) ) ) ) ) ) ) ).
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_zfmisc_1, axiom,  (! [A] :  (! [B] :  (r1_tarski(k1_tarski(A), B) <=> r2_hidden(A, B)) ) ) ).
fof(t38_funct_2, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, B, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B, C)))) )  =>  ( ~ (C=k1_xboole_0)  =>  (! [E] :  (r2_hidden(E, k8_relset_1(B, C, D, A)) <=>  (r2_hidden(E, B) & r2_tarski(k1_funct_1(D, E), A)) ) ) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t3_zfmisc_1, axiom,  (! [A] :  (! [B] :  (r1_tarski(k1_tarski(A), k1_tarski(B)) => 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(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t74_zfmisc_1, axiom,  (! [A] :  (! [B] :  (r2_tarski(B, A) => r1_tarski(B, k3_tarski(A))) ) ) ).
fof(t76_zfmisc_1, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_tarski(C, A) => r1_tarski(C, B)) )  => r1_tarski(k3_tarski(A), B)) ) ) ).
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)) ) ) ) ) ).
