% Mizar problem: t17_rusub_2,rusub_2,445,5 
fof(t17_rusub_2, 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) &  (v2_bhsp_1(A) & l1_bhsp_1(A)) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_rusub_1(B, A) =>  (! [C] :  ( (v1_bhsp_1(C) & m1_rusub_1(C, A))  =>  (m1_rusub_1(C, B) <=> k2_rusub_2(A, C, B)=C) ) ) ) ) ) ) ).
fof(abstractness_v1_bhsp_1, axiom,  (! [A] :  (l1_bhsp_1(A) =>  (v1_bhsp_1(A) => A=g1_bhsp_1(u1_struct_0(A), u2_struct_0(A), u1_algstr_0(A), u1_rlvect_1(A), u1_bhsp_1(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_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_int_1(B)) ) ) ) ).
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_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v7_ordinal1(B)) ) ) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc12_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v6_membered(A)) ) ).
fof(cc13_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_membered(B)) ) ) ) ).
fof(cc14_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_membered(B)) ) ) ) ).
fof(cc15_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_membered(B)) ) ) ) ).
fof(cc16_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_membered(B)) ) ) ) ).
fof(cc17_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_membered(B)) ) ) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc18_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_membered(B)) ) ) ) ).
fof(cc19_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v7_membered(A)) ) ).
fof(cc1_membered, axiom,  (! [A] :  (v6_membered(A) => v5_membered(A)) ) ).
fof(cc1_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
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_xreal_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xreal_0(A)) ) ).
fof(cc2_membered, axiom,  (! [A] :  (v5_membered(A) => v4_membered(A)) ) ).
fof(cc2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(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_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc3_membered, axiom,  (! [A] :  (v4_membered(A) => v3_membered(A)) ) ).
fof(cc3_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(A)) ) ) ).
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_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc4_membered, axiom,  (! [A] :  (v3_membered(A) => v2_membered(A)) ) ).
fof(cc4_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_1(A)) ) ) ).
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_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc5_membered, axiom,  (! [A] :  (v3_membered(A) => v1_membered(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(cc6_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xcmplx_0(B)) ) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xxreal_0(B)) ) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xreal_0(B)) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc9_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_rat_1(B)) ) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_0(B, A)) ).
fof(d1_rusub_1, 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) &  (v2_bhsp_1(A) & l1_bhsp_1(A)) ) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v5_rlvect_1(B) &  (v6_rlvect_1(B) &  (v7_rlvect_1(B) &  (v8_rlvect_1(B) &  (v2_bhsp_1(B) & l1_bhsp_1(B)) ) ) ) ) ) ) ) ) )  =>  (m1_rusub_1(B, A) <=>  (r1_tarski(u1_struct_0(B), u1_struct_0(A)) &  (k4_struct_0(B)=k4_struct_0(A) &  (u1_algstr_0(B)=k1_realset1(u1_algstr_0(A), u1_struct_0(B)) &  (u1_rlvect_1(B)=k5_relat_1(u1_rlvect_1(A), k2_zfmisc_1(k1_numbers, u1_struct_0(B))) & u1_bhsp_1(B)=k1_realset1(u1_bhsp_1(A), u1_struct_0(B))) ) ) ) ) ) ) ) ) ).
fof(d2_rusub_2, 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) &  (v2_bhsp_1(A) & l1_bhsp_1(A)) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_rusub_1(B, A) =>  (! [C] :  (m1_rusub_1(C, A) =>  (! [D] :  ( (v1_bhsp_1(D) & m1_rusub_1(D, A))  =>  (D=k2_rusub_2(A, B, C) <=> u1_struct_0(D)=k3_xboole_0(u1_struct_0(B), u1_struct_0(C))) ) ) ) ) ) ) ) ) ).
fof(d2_xboole_0, axiom, k1_xboole_0=o_0_0_xboole_0).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(dt_g1_bhsp_1, axiom,  (! [A, B, C, D, E] :  ( (m1_subset_1(B, A) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(k1_numbers, A), A) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_numbers, A), A)))) )  &  (v1_funct_1(E) &  (v1_funct_2(E, k2_zfmisc_1(A, A), k1_numbers) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), k1_numbers)))) ) ) ) )  =>  (v1_bhsp_1(g1_bhsp_1(A, B, C, D, E)) & l1_bhsp_1(g1_bhsp_1(A, B, C, D, E))) ) ) ).
fof(dt_k1_numbers, axiom, $true).
fof(dt_k1_realset1, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_rusub_2, 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) &  (v2_bhsp_1(A) & l1_bhsp_1(A)) ) ) ) ) ) ) ) ) )  &  (m1_rusub_1(B, A) & m1_rusub_1(C, A)) )  =>  (v1_bhsp_1(k2_rusub_2(A, B, C)) & m1_rusub_1(k2_rusub_2(A, B, C), A)) ) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => m1_subset_1(k4_struct_0(A), u1_struct_0(A))) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k5_relat_1(A, B))) ) ).
fof(dt_l1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l1_bhsp_1, axiom,  (! [A] :  (l1_bhsp_1(A) => l1_rlvect_1(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_rusub_1, 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) &  (v2_bhsp_1(A) & l1_bhsp_1(A)) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_rusub_1(B, A) =>  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v5_rlvect_1(B) &  (v6_rlvect_1(B) &  (v7_rlvect_1(B) &  (v8_rlvect_1(B) &  (v2_bhsp_1(B) & l1_bhsp_1(B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_o_0_0_xboole_0, axiom, v1_xboole_0(o_0_0_xboole_0)).
fof(dt_u1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  (v1_funct_1(u1_algstr_0(A)) &  (v1_funct_2(u1_algstr_0(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u1_algstr_0(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(dt_u1_bhsp_1, axiom,  (! [A] :  (l1_bhsp_1(A) =>  (v1_funct_1(u1_bhsp_1(A)) &  (v1_funct_2(u1_bhsp_1(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), k1_numbers) & m1_subset_1(u1_bhsp_1(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), k1_numbers)))) ) ) ) ).
fof(dt_u1_rlvect_1, axiom,  (! [A] :  (l1_rlvect_1(A) =>  (v1_funct_1(u1_rlvect_1(A)) &  (v1_funct_2(u1_rlvect_1(A), k2_zfmisc_1(k1_numbers, u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u1_rlvect_1(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_numbers, u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u2_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => m1_subset_1(u2_struct_0(A), u1_struct_0(A))) ) ).
fof(existence_l1_algstr_0, axiom,  (? [A] : l1_algstr_0(A)) ).
fof(existence_l1_bhsp_1, axiom,  (? [A] : l1_bhsp_1(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_rusub_1, 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) &  (v2_bhsp_1(A) & l1_bhsp_1(A)) ) ) ) ) ) ) ) ) )  =>  (? [B] : m1_rusub_1(B, A)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc10_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => v9_struct_0(k4_struct_0(A), 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(fc16_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_xboole_0(B))  =>  (v1_xboole_0(k5_relat_1(A, B)) & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc17_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_xboole_0(k5_relat_1(A, B)) & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc1_bhsp_1, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(k1_numbers, A), A) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_numbers, A), A)))) )  &  (v1_funct_1(E) &  (v1_funct_2(E, k2_zfmisc_1(A, A), k1_numbers) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), k1_numbers)))) ) ) ) ) )  =>  ( ~ (v2_struct_0(g1_bhsp_1(A, B, C, D, E)))  & v1_bhsp_1(g1_bhsp_1(A, B, C, D, E))) ) ) ).
fof(fc1_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k3_xboole_0(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(fc23_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v3_relat_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v3_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc31_membered, axiom,  (! [A, B] :  (v1_membered(A) => v1_membered(k3_xboole_0(A, B))) ) ).
fof(fc32_membered, axiom,  (! [A, B] :  (v1_membered(A) => v1_membered(k3_xboole_0(B, A))) ) ).
fof(fc33_membered, axiom,  (! [A, B] :  (v2_membered(A) => v2_membered(k3_xboole_0(A, B))) ) ).
fof(fc33_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v2_relat_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v2_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc34_membered, axiom,  (! [A, B] :  (v2_membered(A) => v2_membered(k3_xboole_0(B, A))) ) ).
fof(fc35_membered, axiom,  (! [A, B] :  (v3_membered(A) => v3_membered(k3_xboole_0(A, B))) ) ).
fof(fc36_membered, axiom,  (! [A, B] :  (v3_membered(A) => v3_membered(k3_xboole_0(B, A))) ) ).
fof(fc37_membered, axiom,  (! [A, B] :  (v4_membered(A) => v4_membered(k3_xboole_0(A, B))) ) ).
fof(fc38_membered, axiom,  (! [A, B] :  (v4_membered(A) => v4_membered(k3_xboole_0(B, A))) ) ).
fof(fc39_membered, axiom,  (! [A, B] :  (v5_membered(A) => v5_membered(k3_xboole_0(A, B))) ) ).
fof(fc3_membered, axiom, v3_membered(k1_numbers)).
fof(fc40_membered, axiom,  (! [A, B] :  (v5_membered(A) => v5_membered(k3_xboole_0(B, A))) ) ).
fof(fc41_membered, axiom,  (! [A, B] :  (v6_membered(A) => v6_membered(k3_xboole_0(A, B))) ) ).
fof(fc42_membered, axiom,  (! [A, B] :  (v6_membered(A) => v6_membered(k3_xboole_0(B, A))) ) ).
fof(fc56_membered, axiom, v7_membered(k1_numbers)).
fof(fc59_membered, axiom, v7_membered(k4_ordinal1)).
fof(fc6_membered, axiom, v6_membered(k4_ordinal1)).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(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(free_g1_bhsp_1, axiom,  (! [A, B, C, D, E] :  ( (m1_subset_1(B, A) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(k1_numbers, A), A) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_numbers, A), A)))) )  &  (v1_funct_1(E) &  (v1_funct_2(E, k2_zfmisc_1(A, A), k1_numbers) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), k1_numbers)))) ) ) ) )  =>  (! [F, G, H, I, J] :  (g1_bhsp_1(A, B, C, D, E)=g1_bhsp_1(F, G, H, I, J) =>  (A=F &  (B=G &  (C=H &  (D=I & E=J) ) ) ) ) ) ) ) ).
fof(idempotence_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, A)=A) ).
fof(rc17_struct_0, axiom,  (! [A] :  (l2_struct_0(A) =>  (? [B] :  (m1_subset_1(B, u1_struct_0(A)) & v9_struct_0(B, A)) ) ) ) ).
fof(rc19_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l2_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, u1_struct_0(A)) &  ~ (v9_struct_0(B, A)) ) ) ) ) ).
fof(rc1_bhsp_1, axiom,  (? [A] :  (l1_bhsp_1(A) & v1_bhsp_1(A)) ) ).
fof(rc1_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_rusub_1, 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) &  (v2_bhsp_1(A) & l1_bhsp_1(A)) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (m1_rusub_1(B, A) &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v5_rlvect_1(B) &  (v6_rlvect_1(B) &  (v7_rlvect_1(B) &  (v8_rlvect_1(B) &  (v1_bhsp_1(B) & v2_bhsp_1(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_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc20_struct_0, axiom,  (? [A] :  (l2_struct_0(A) &  ( ~ (v2_struct_0(A))  & v7_struct_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_bhsp_1, axiom,  (? [A] :  (l1_bhsp_1(A) &  ( ~ (v2_struct_0(A))  & v1_bhsp_1(A)) ) ) ).
fof(rc2_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc3_bhsp_1, axiom,  (? [A] :  (l1_bhsp_1(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) &  (v1_bhsp_1(A) & v2_bhsp_1(A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v6_membered(A) & v7_membered(A)) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(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(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rd5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => k5_relat_1(k5_relat_1(A, B), B)=k5_relat_1(A, B)) ) ).
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(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(t16_rusub_2, 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) &  (v2_bhsp_1(A) & l1_bhsp_1(A)) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_rusub_1(B, A) =>  (! [C] :  (m1_rusub_1(C, A) =>  (m1_rusub_1(k2_rusub_2(A, B, C), B) & m1_rusub_1(k2_rusub_2(A, B, C), C)) ) ) ) ) ) ) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t24_rusub_1, 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) &  (v2_bhsp_1(A) & l1_bhsp_1(A)) ) ) ) ) ) ) ) ) )  =>  (! [B] :  ( (v1_bhsp_1(B) & m1_rusub_1(B, A))  =>  (! [C] :  ( (v1_bhsp_1(C) & m1_rusub_1(C, A))  =>  (u1_struct_0(B)=u1_struct_0(C) => B=C) ) ) ) ) ) ) ).
fof(t28_xboole_1, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) => k3_xboole_0(A, B)=A) ) ) ).
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(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(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
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)) ) ) ) ) ).
