% Mizar problem: t22_dualsp06,dualsp06,1309,5 
fof(t22_dualsp06, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  ( ( ~ (v2_struct_0(D))  & m1_rlsub_1(D, A))  =>  (r1_struct_0(D, C) =>  (r1_struct_0(D, B) |  ( (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (r1_struct_0(D, E) => r1_xxreal_0(k2_normsp_0(A, k5_algstr_0(A, B, C)), k2_normsp_0(A, k5_algstr_0(A, B, E)))) ) )  <=>  (? [E] :  (m1_subset_1(E, u1_struct_0(k17_dualsp01(A))) &  (r1_struct_0(k3_dualsp06(A, D), E) &  ( ~ (E=k4_struct_0(k17_dualsp01(A)))  & r2_dualsp06(A, k5_algstr_0(A, B, C), E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(abstractness_v1_normsp_1, axiom,  (! [A] :  (l1_normsp_1(A) =>  (v1_normsp_1(A) => A=g1_normsp_1(u1_struct_0(A), u2_struct_0(A), u1_algstr_0(A), u1_rlvect_1(A), u1_normsp_0(A))) ) ) ).
fof(abstractness_v1_rlvect_1, axiom,  (! [A] :  (l1_rlvect_1(A) =>  (v1_rlvect_1(A) => A=g1_rlvect_1(u1_struct_0(A), u2_struct_0(A), u1_algstr_0(A), u1_rlvect_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_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A))  => v3_card_1(A, 1)) ) ).
fof(cc10_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_int_1(B)) ) ) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(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(cc10_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_valued_0(B)) ) ) ) ).
fof(cc10_xxreal_2, axiom,  (! [A] :  ( (v3_membered(A) & v1_xxreal_2(A))  =>  (v3_membered(A) & v3_xxreal_2(A)) ) ) ).
fof(cc11_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_card_1(A))  =>  (! [B] :  (v3_card_1(B, A) =>  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(cc11_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v7_ordinal1(B)) ) ) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(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_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_valued_0(B)) ) ) ) ).
fof(cc11_xxreal_2, axiom,  (! [A] :  ( (v3_membered(A) & v2_xxreal_2(A))  =>  (v3_membered(A) & v4_xxreal_2(A)) ) ) ).
fof(cc12_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v6_membered(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc12_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_valued_0(B)) ) ) ) ).
fof(cc12_xxreal_2, axiom,  (! [A] :  ( (v5_membered(A) & v5_xxreal_2(A))  =>  (v5_membered(A) & v1_finset_1(A)) ) ) ).
fof(cc13_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_membered(B)) ) ) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc13_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_valued_0(B)) ) ) ) ).
fof(cc13_xxreal_2, axiom,  (! [A] :  ( (v6_membered(A) & v4_xxreal_2(A))  =>  (v6_membered(A) &  (v1_finset_1(A) & v4_xxreal_2(A)) ) ) ) ).
fof(cc14_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_membered(B)) ) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc14_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_valued_0(B)) ) ) ) ).
fof(cc14_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) & v5_xxreal_2(A))  =>  (v2_membered(A) & v3_membered(A)) ) ) ).
fof(cc15_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_membered(B)) ) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc15_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_valued_0(B)) ) ) ) ).
fof(cc15_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) & v1_xboole_0(A))  =>  (v2_membered(A) & v6_xxreal_2(A)) ) ) ).
fof(cc16_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_membered(B)) ) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc16_valued_0, axiom,  (! [A, B] :  (v1_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_valued_0(C)) ) ) ) ).
fof(cc16_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) & v1_xxreal_2(A))  =>  (v2_membered(A) &  ~ (v1_xboole_0(A)) ) ) ) ).
fof(cc17_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_membered(B)) ) ) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc17_valued_0, axiom,  (! [A, B] :  (v2_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v2_valued_0(C)) ) ) ) ).
fof(cc17_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) & v2_xxreal_2(A))  =>  (v2_membered(A) &  ~ (v1_xboole_0(A)) ) ) ) ).
fof(cc18_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_membered(B)) ) ) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc18_valued_0, axiom,  (! [A, B] :  (v3_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v3_valued_0(C)) ) ) ) ).
fof(cc19_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v7_membered(A)) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc19_valued_0, axiom,  (! [A, B] :  (v4_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v4_valued_0(C)) ) ) ) ).
fof(cc1_card_1, axiom,  (! [A] :  (v1_card_1(A) => v3_ordinal1(A)) ) ).
fof(cc1_funcop_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_funcop_1(B)) ) ) ) ) ) ).
fof(cc1_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_partfun1(C, A) => v1_funct_2(C, A, B)) ) ) ) ).
fof(cc1_membered, axiom,  (! [A] :  (v6_membered(A) => v5_membered(A)) ) ).
fof(cc1_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v3_ordinal1(A) & v7_ordinal1(A)) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(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_rlvect_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v9_rlvect_1(A))  =>  ( ~ (v2_struct_0(A))  & v4_rlvect_1(A)) ) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc1_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v5_valued_0(A)) ) ) ).
fof(cc1_xcmplx_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xcmplx_0(A)) ) ).
fof(cc1_xreal_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xreal_0(A)) ) ).
fof(cc1_xxreal_0, axiom,  (! [A] :  (m1_subset_1(A, k6_numbers) => v1_xxreal_0(A)) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc20_valued_0, axiom,  (! [A, B] :  (v5_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v5_valued_0(C)) ) ) ) ).
fof(cc21_valued_0, axiom,  (! [A, B] :  (v6_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v6_valued_0(C)) ) ) ) ).
fof(cc22_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_zfmisc_1(A) & v2_valued_0(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) &  (v7_valued_0(A) & v8_valued_0(A)) ) ) ) ) ) ).
fof(cc23_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v7_valued_0(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v9_valued_0(A)) ) ) ) ) ).
fof(cc24_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v8_valued_0(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v10_valued_0(A)) ) ) ) ) ).
fof(cc28_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k2_numbers))  =>  (v1_relat_1(A) & v1_valued_0(A)) ) ) ).
fof(cc29_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k2_numbers)) ) ) ).
fof(cc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_card_1(A)) ) ).
fof(cc2_dualsp01, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k17_dualsp01(A))) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc2_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funcop_1(A)) ) ) ) ).
fof(cc2_funct_2, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc2_membered, axiom,  (! [A] :  (v5_membered(A) => v4_membered(A)) ) ).
fof(cc2_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(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_rlvect_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v2_rlvect_1(A) & v4_rlvect_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v9_rlvect_1(A)) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v4_valued_0(A)) ) ) ).
fof(cc2_xcmplx_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xcmplx_0(A)) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc2_xxreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xxreal_0(A)) ) ).
fof(cc2_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) &  (v1_finset_1(A) &  ~ (v1_xboole_0(A)) ) )  =>  (v2_membered(A) &  ( ~ (v1_xboole_0(A))  &  (v1_xxreal_2(A) & v2_xxreal_2(A)) ) ) ) ) ).
fof(cc30_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k6_numbers))  =>  (v1_relat_1(A) & v2_valued_0(A)) ) ) ).
fof(cc31_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k6_numbers)) ) ) ).
fof(cc32_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k1_numbers))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc33_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k1_numbers)) ) ) ).
fof(cc34_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k3_numbers))  =>  (v1_relat_1(A) & v4_valued_0(A)) ) ) ).
fof(cc35_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k3_numbers)) ) ) ).
fof(cc36_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k4_numbers))  =>  (v1_relat_1(A) & v5_valued_0(A)) ) ) ).
fof(cc37_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k4_numbers)) ) ) ).
fof(cc38_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k4_ordinal1))  =>  (v1_relat_1(A) & v6_valued_0(A)) ) ) ).
fof(cc39_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k4_ordinal1)) ) ) ).
fof(cc3_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_card_1(A)) ) ).
fof(cc3_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ) ).
fof(cc3_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc3_membered, axiom,  (! [A] :  (v4_membered(A) => v3_membered(A)) ) ).
fof(cc3_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(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_rlvect_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) & v2_rlvect_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v12_algstr_0(A)) ) ) ) ).
fof(cc3_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc3_xcmplx_0, axiom,  (! [A] :  (m1_subset_1(A, k2_numbers) => v1_xcmplx_0(A)) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc3_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v2_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc3_xxreal_2, axiom,  (! [A] :  ( (v6_membered(A) &  ~ (v1_xboole_0(A)) )  =>  (v6_membered(A) &  ( ~ (v1_xboole_0(A))  & v1_xxreal_2(A)) ) ) ) ).
fof(cc40_valued_0, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k2_numbers)) ) ) ) ) ).
fof(cc41_valued_0, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v1_valued_0(B)) ) ) ) ) ).
fof(cc42_valued_0, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k6_numbers)) ) ) ) ) ).
fof(cc43_valued_0, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v2_valued_0(B)) ) ) ) ) ).
fof(cc44_valued_0, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k1_numbers)) ) ) ) ) ).
fof(cc45_valued_0, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v3_valued_0(B)) ) ) ) ) ).
fof(cc46_valued_0, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k3_numbers)) ) ) ) ) ).
fof(cc47_valued_0, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v4_valued_0(B)) ) ) ) ) ).
fof(cc48_valued_0, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k4_numbers)) ) ) ) ) ).
fof(cc49_valued_0, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_valued_0(B)) ) ) ) ) ).
fof(cc4_card_1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v1_finset_1(A)) ) ).
fof(cc4_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  (v1_funct_2(B, A, A) => v1_partfun1(B, A)) ) ) ) ).
fof(cc4_membered, axiom,  (! [A] :  (v3_membered(A) => v2_membered(A)) ) ).
fof(cc4_nat_1, axiom,  (! [A] :  ( (v7_ordinal1(A) & v8_ordinal1(A))  =>  (v7_ordinal1(A) &  ~ (v2_xxreal_0(A)) ) ) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(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_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc4_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ) ).
fof(cc4_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) & v5_xxreal_2(A))  =>  (v2_membered(A) &  (v3_xxreal_2(A) & v4_xxreal_2(A)) ) ) ) ).
fof(cc50_valued_0, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k4_ordinal1)) ) ) ) ) ).
fof(cc51_valued_0, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v6_valued_0(B)) ) ) ) ) ).
fof(cc5_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_finset_1(A)) ) ).
fof(cc5_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A))) =>  (v1_funct_2(B, k2_zfmisc_1(A, A), A) => v1_partfun1(B, k2_zfmisc_1(A, A))) ) ) ) ).
fof(cc5_membered, axiom,  (! [A] :  (v3_membered(A) => v1_membered(A)) ) ).
fof(cc5_nat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v8_ordinal1(A)) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc5_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v2_valued_0(A)) ) ) ).
fof(cc5_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v3_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) ) ) ) ).
fof(cc5_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) &  (v3_xxreal_2(A) & v4_xxreal_2(A)) )  =>  (v2_membered(A) & v5_xxreal_2(A)) ) ) ).
fof(cc6_card_1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v1_finset_1(A))  => v7_ordinal1(A)) ) ).
fof(cc6_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xcmplx_0(B)) ) ) ) ).
fof(cc6_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc6_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v1_valued_0(A)) ) ) ).
fof(cc6_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ) ).
fof(cc6_xxreal_2, axiom,  (! [A] :  ( (v3_membered(A) & v1_finset_1(A))  =>  (v3_membered(A) & v5_xxreal_2(A)) ) ) ).
fof(cc7_card_1, axiom,  (! [A] :  (v3_card_1(A, k5_ordinal1) => v1_xboole_0(A)) ) ).
fof(cc7_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xxreal_0(B)) ) ) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc7_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v4_valued_0(A)) ) ) ).
fof(cc7_xxreal_0, axiom,  (! [A] :  ( (v8_ordinal1(A) & v1_xxreal_0(A))  =>  (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc7_xxreal_2, axiom,  (! [A] :  ( (v5_membered(A) &  ( ~ (v1_xboole_0(A))  & v4_xxreal_2(A)) )  =>  (v5_membered(A) &  ( ~ (v1_xboole_0(A))  & v2_xxreal_2(A)) ) ) ) ).
fof(cc8_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_card_1(A, k5_ordinal1)) ) ).
fof(cc8_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xreal_0(B)) ) ) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc8_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc8_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) )  =>  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ) ).
fof(cc8_xxreal_2, axiom,  (! [A] :  ( (v5_membered(A) &  ( ~ (v1_xboole_0(A))  & v3_xxreal_2(A)) )  =>  (v5_membered(A) &  ( ~ (v1_xboole_0(A))  & v1_xxreal_2(A)) ) ) ) ).
fof(cc9_card_1, axiom,  (! [A] :  (v3_card_1(A, 1) =>  ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A)) ) ) ).
fof(cc9_funct_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(cc9_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_rat_1(B)) ) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(cc9_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v6_valued_0(A)) ) ) ).
fof(cc9_xxreal_2, axiom,  (! [A] :  (v6_membered(A) =>  (v6_membered(A) & v3_xxreal_2(A)) ) ) ).
fof(commutativity_k2_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(A, B)=k2_xcmplx_0(B, A)) ) ).
fof(commutativity_k3_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k3_xcmplx_0(A, B)=k3_xcmplx_0(B, A)) ) ).
fof(connectedness_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  =>  (r1_xxreal_0(A, B) | r1_xxreal_0(B, A)) ) ) ).
fof(d14_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k5_algstr_0(A, B, C)=k1_algstr_0(A, B, k4_algstr_0(A, C))) ) ) ) ) ) ).
fof(d15_dualsp01, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  => k17_dualsp01(A)=g1_normsp_1(k11_dualsp01(A), k7_rsspace(k8_dualsp01(A), k11_dualsp01(A)), k5_rsspace(k8_dualsp01(A), k11_dualsp01(A)), k6_rsspace(k8_dualsp01(A), k11_dualsp01(A)), k16_dualsp01(A))) ) ).
fof(d1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k1_algstr_0(A, B, C)=k4_binop_1(u1_struct_0(A), u1_algstr_0(A), B, C)) ) ) ) ) ) ).
fof(d1_normsp_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_normsp_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k2_normsp_0(A, B)=k3_funct_2(u1_struct_0(A), k1_numbers, u1_normsp_0(A), B)) ) ) ) ).
fof(d1_normsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_normsp_1(A))  =>  (v2_normsp_1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (v1_xreal_0(D) =>  (k2_normsp_0(A, k1_rlvect_1(A, B, D))=k3_xcmplx_0(k9_complex1(D), k2_normsp_0(A, B)) & r1_xxreal_0(k2_normsp_0(A, k1_algstr_0(A, B, C)), k2_xcmplx_0(k2_normsp_0(A, B), k2_normsp_0(A, C)))) ) ) ) ) ) ) ) ) ) ).
fof(d2_dualsp06, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k17_dualsp01(A))) => k2_dualsp06(A, B, C)=k18_dualsp01(A, C, B)) ) ) ) ) ) ).
fof(d2_seq_4, axiom,  (! [A] :  (v3_membered(A) =>  (v3_xxreal_2(A) =>  (v1_xboole_0(A) |  (! [B] :  (v1_xreal_0(B) =>  (B=k3_seq_4(A) <=>  ( (! [C] :  (v1_xreal_0(C) =>  (r2_hidden(C, A) => r1_xxreal_0(B, C)) ) )  &  (! [C] :  (v1_xreal_0(C) =>  ~ ( ( ~ (r1_xxreal_0(C, k5_numbers))  &  (! [D] :  (v1_xreal_0(D) =>  ~ ( (r2_hidden(D, A) &  ~ (r1_xxreal_0(k2_xcmplx_0(B, C), D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_dualsp06, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k17_dualsp01(A))) =>  (r1_dualsp06(A, B, C) <=> k2_dualsp06(A, B, C)=k5_numbers) ) ) ) ) ) ) ).
fof(d4_dualsp06, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k17_dualsp01(A))) =>  (r2_dualsp06(A, B, C) <=> k2_dualsp06(A, B, C)=k3_xcmplx_0(k2_normsp_0(A, B), k2_normsp_0(k17_dualsp01(A), C))) ) ) ) ) ) ) ).
fof(d5_dualsp06, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_rlsub_1(B, A) =>  (! [C] :  ( (v1_rlvect_1(C) & m1_rlsub_1(C, k17_dualsp01(A)))  =>  (C=k3_dualsp06(A, B) <=> u1_struct_0(C)=a_2_0_dualsp06(A, B)) ) ) ) ) ) ) ).
fof(d5_normsp_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_normsp_0(A))  =>  (v3_normsp_0(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (k2_normsp_0(A, B)=k5_numbers => B=k4_struct_0(A)) ) ) ) ) ) ).
fof(d5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (! [B] :  (r1_struct_0(A, B) <=> r2_hidden(B, u1_struct_0(A))) ) ) ) ).
fof(d6_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => k4_struct_0(A)=u2_struct_0(A)) ) ).
fof(d7_dualsp01, 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) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  => k8_dualsp01(A)=g1_rlvect_1(k7_dualsp01(A), k7_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)), k5_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)), k6_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)))) ) ).
fof(d7_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) =>  (! [B] :  (v1_xcmplx_0(B) => k6_xcmplx_0(A, B)=k2_xcmplx_0(A, k4_xcmplx_0(B))) ) ) ) ).
fof(dt_g1_normsp_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, A, k1_numbers) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) ) ) )  =>  (v1_normsp_1(g1_normsp_1(A, B, C, D, E)) & l1_normsp_1(g1_normsp_1(A, B, C, D, E))) ) ) ).
fof(dt_g1_rlvect_1, axiom,  (! [A, B, C, D] :  ( (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_rlvect_1(g1_rlvect_1(A, B, C, D)) & l1_rlvect_1(g1_rlvect_1(A, B, C, D))) ) ) ).
fof(dt_k10_funcsdom, axiom,  (! [A] :  ( ~ (v2_struct_0(k10_funcsdom(A)))  &  (v13_algstr_0(k10_funcsdom(A)) &  (v1_rlvect_1(k10_funcsdom(A)) &  (v2_rlvect_1(k10_funcsdom(A)) &  (v3_rlvect_1(k10_funcsdom(A)) &  (v4_rlvect_1(k10_funcsdom(A)) &  (v5_rlvect_1(k10_funcsdom(A)) &  (v6_rlvect_1(k10_funcsdom(A)) &  (v7_rlvect_1(k10_funcsdom(A)) &  (v8_rlvect_1(k10_funcsdom(A)) & l1_rlvect_1(k10_funcsdom(A))) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k11_dualsp01, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  => m1_subset_1(k11_dualsp01(A), k1_zfmisc_1(u1_struct_0(k8_dualsp01(A))))) ) ).
fof(dt_k16_dualsp01, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (v1_funct_1(k16_dualsp01(A)) &  (v1_funct_2(k16_dualsp01(A), k11_dualsp01(A), k1_numbers) & m1_subset_1(k16_dualsp01(A), k1_zfmisc_1(k2_zfmisc_1(k11_dualsp01(A), k1_numbers)))) ) ) ) ).
fof(dt_k17_dualsp01, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k17_dualsp01(A)))  & l1_normsp_1(k17_dualsp01(A))) ) ) ).
fof(dt_k18_dualsp01, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(k17_dualsp01(A))) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k18_dualsp01(A, B, C), k1_numbers)) ) ).
fof(dt_k1_algstr_0, axiom,  (! [A, B, C] :  ( (l1_algstr_0(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k1_algstr_0(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k1_binop_1, axiom, $true).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_numbers, axiom, $true).
fof(dt_k1_rlvect_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_rlvect_1(A))  &  (m1_subset_1(B, u1_struct_0(A)) & v1_xreal_0(C)) )  => m1_subset_1(k1_rlvect_1(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_xxreal_2, axiom,  (! [A] :  (v2_membered(A) => v1_xxreal_0(k1_xxreal_2(A))) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_dualsp06, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(k17_dualsp01(A)))) )  => v1_xreal_0(k2_dualsp06(A, B, C))) ) ).
fof(dt_k2_normsp_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_normsp_0(A))  & m1_subset_1(B, u1_struct_0(A)))  => v1_xreal_0(k2_normsp_0(A, B))) ) ).
fof(dt_k2_numbers, axiom, $true).
fof(dt_k2_xcmplx_0, axiom, $true).
fof(dt_k2_xxreal_2, axiom,  (! [A] :  (v2_membered(A) => v1_xxreal_0(k2_xxreal_2(A))) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_dualsp06, axiom,  (! [A, B] :  ( ( ( ~ (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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  & m1_rlsub_1(B, A))  =>  (v1_rlvect_1(k3_dualsp06(A, B)) & m1_rlsub_1(k3_dualsp06(A, B), k17_dualsp01(A))) ) ) ).
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_numbers, axiom, $true).
fof(dt_k3_seq_4, axiom,  (! [A] :  (v3_membered(A) => v1_xreal_0(k3_seq_4(A))) ) ).
fof(dt_k3_xcmplx_0, axiom, $true).
fof(dt_k4_algstr_0, axiom,  (! [A, B] :  ( (l2_algstr_0(A) & m1_subset_1(B, u1_struct_0(A)))  => m1_subset_1(k4_algstr_0(A, B), u1_struct_0(A))) ) ).
fof(dt_k4_binop_1, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (m1_subset_1(C, A) & m1_subset_1(D, A)) )  => m1_subset_1(k4_binop_1(A, B, C, D), A)) ) ).
fof(dt_k4_numbers, 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_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A))) ) ).
fof(dt_k5_algstr_0, axiom,  (! [A, B, C] :  ( (l2_algstr_0(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k5_algstr_0(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_rsspace, axiom,  (! [A, B] :  ( ( ( ~ (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) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))  =>  (v1_funct_1(k5_rsspace(A, B)) &  (v1_funct_2(k5_rsspace(A, B), k2_zfmisc_1(B, B), B) & m1_subset_1(k5_rsspace(A, B), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B, B), B)))) ) ) ) ).
fof(dt_k5_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k5_xcmplx_0(A))) ) ).
fof(dt_k6_numbers, axiom, $true).
fof(dt_k6_rsspace, axiom,  (! [A, B] :  ( ( ( ~ (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) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))  =>  (v1_funct_1(k6_rsspace(A, B)) &  (v1_funct_2(k6_rsspace(A, B), k2_zfmisc_1(k1_numbers, B), B) & m1_subset_1(k6_rsspace(A, B), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_numbers, B), B)))) ) ) ) ).
fof(dt_k6_xcmplx_0, axiom, $true).
fof(dt_k7_dualsp01, 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) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  => m1_subset_1(k7_dualsp01(A), k1_zfmisc_1(u1_struct_0(k10_funcsdom(u1_struct_0(A)))))) ) ).
fof(dt_k7_rsspace, axiom,  (! [A, B] :  ( ( ( ~ (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) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))  => m1_subset_1(k7_rsspace(A, B), B)) ) ).
fof(dt_k8_dualsp01, 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) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k8_dualsp01(A)))  &  (v13_algstr_0(k8_dualsp01(A)) &  (v1_rlvect_1(k8_dualsp01(A)) &  (v2_rlvect_1(k8_dualsp01(A)) &  (v3_rlvect_1(k8_dualsp01(A)) &  (v4_rlvect_1(k8_dualsp01(A)) &  (v5_rlvect_1(k8_dualsp01(A)) &  (v6_rlvect_1(k8_dualsp01(A)) &  (v7_rlvect_1(k8_dualsp01(A)) &  (v8_rlvect_1(k8_dualsp01(A)) & l1_rlvect_1(k8_dualsp01(A))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k9_complex1, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xreal_0(k9_complex1(A))) ) ).
fof(dt_l1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l1_normsp_0, axiom,  (! [A] :  (l1_normsp_0(A) => l1_struct_0(A)) ) ).
fof(dt_l1_normsp_1, axiom,  (! [A] :  (l1_normsp_1(A) =>  (l1_rlvect_1(A) & l2_normsp_0(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_normsp_0, axiom,  (! [A] :  (l2_normsp_0(A) =>  (l1_normsp_0(A) & l2_struct_0(A)) ) ) ).
fof(dt_l2_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_m1_rlsub_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) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_rlsub_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) & l1_rlvect_1(B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
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_normsp_0, axiom,  (! [A] :  (l1_normsp_0(A) =>  (v1_funct_1(u1_normsp_0(A)) &  (v1_funct_2(u1_normsp_0(A), u1_struct_0(A), k1_numbers) & m1_subset_1(u1_normsp_0(A), k1_zfmisc_1(k2_zfmisc_1(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_normsp_0, axiom,  (? [A] : l1_normsp_0(A)) ).
fof(existence_l1_normsp_1, axiom,  (? [A] : l1_normsp_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_normsp_0, axiom,  (? [A] : l2_normsp_0(A)) ).
fof(existence_l2_struct_0, axiom,  (? [A] : l2_struct_0(A)) ).
fof(existence_m1_rlsub_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) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  (? [B] : m1_rlsub_1(B, A)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc10_dualsp01, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k17_dualsp01(A)))  &  (v13_algstr_0(k17_dualsp01(A)) &  (v2_rlvect_1(k17_dualsp01(A)) &  (v3_rlvect_1(k17_dualsp01(A)) &  (v4_rlvect_1(k17_dualsp01(A)) &  (v5_rlvect_1(k17_dualsp01(A)) &  (v6_rlvect_1(k17_dualsp01(A)) &  (v7_rlvect_1(k17_dualsp01(A)) &  (v8_rlvect_1(k17_dualsp01(A)) &  (v3_normsp_0(k17_dualsp01(A)) &  (v4_normsp_0(k17_dualsp01(A)) & v2_normsp_1(k17_dualsp01(A))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(fc10_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => v9_struct_0(k4_struct_0(A), A)) ) ).
fof(fc10_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k2_xcmplx_0(A, B))) ) ) ).
fof(fc10_xxreal_2, axiom,  (! [A] :  ( (v6_membered(A) & v2_xxreal_2(A))  =>  (v1_xxreal_0(k1_xxreal_2(A)) & v7_ordinal1(k1_xxreal_2(A))) ) ) ).
fof(fc11_dualsp01, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k17_dualsp01(A)))  & v3_lopban_1(k17_dualsp01(A))) ) ) ).
fof(fc11_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc11_xxreal_2, axiom,  ( ~ (v3_xxreal_2(k1_numbers))  &  ~ (v4_xxreal_2(k1_numbers)) ) ).
fof(fc12_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k1_zfmisc_1(A))) ) ) ).
fof(fc12_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k2_xcmplx_0(B, A))) ) ).
fof(fc12_xxreal_2, axiom, v6_xxreal_2(k6_numbers)).
fof(fc13_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(A, B))) ) ) ).
fof(fc13_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc14_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(B, A))) ) ) ).
fof(fc14_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k2_xcmplx_0(B, A))) ) ).
fof(fc15_xreal_0, axiom,  (! [A] :  ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k4_xcmplx_0(A)) &  ~ (v3_xxreal_0(k4_xcmplx_0(A))) ) ) ) ).
fof(fc16_xreal_0, axiom,  (! [A] :  ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k4_xcmplx_0(A)) &  ~ (v2_xxreal_0(k4_xcmplx_0(A))) ) ) ) ).
fof(fc17_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k6_xcmplx_0(A, B))) ) ) ).
fof(fc17_xxreal_2, axiom, v6_xxreal_2(k1_numbers)).
fof(fc18_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k6_xcmplx_0(B, A))) ) ) ).
fof(fc19_struct_0, axiom,  (! [A, B] :  ( (v1_card_1(A) &  (v13_struct_0(B, A) & l1_struct_0(B)) )  => v3_card_1(u1_struct_0(B), A)) ) ).
fof(fc19_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k6_xcmplx_0(A, B))) ) ).
fof(fc1_membered, axiom, v1_membered(k2_numbers)).
fof(fc1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v7_ordinal1(k2_xcmplx_0(A, B))) ) ).
fof(fc1_normsp_1, axiom,  (! [A, B] :  ( ( ( ~ (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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  & m1_subset_1(B, u1_struct_0(A)))  =>  ( ~ (v3_xxreal_0(k2_normsp_0(A, B)))  & v1_xreal_0(k2_normsp_0(A, B))) ) ) ).
fof(fc1_numbers, axiom,  ~ (v1_xboole_0(k1_numbers)) ).
fof(fc1_rlvect_1, axiom,  (! [A, B, C, D] :  ( ( ~ (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)))) ) ) ) )  =>  ( ~ (v2_struct_0(g1_rlvect_1(A, B, C, D)))  & v1_rlvect_1(g1_rlvect_1(A, B, C, D))) ) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_valued_1, axiom,  (! [A] :  (v1_rat_1(A) =>  (v1_xreal_0(k9_complex1(A)) & v1_rat_1(k9_complex1(A))) ) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc1_xxreal_2, axiom,  (! [A] :  ( (v3_membered(A) &  ( ~ (v1_xboole_0(A))  & v4_xxreal_2(A)) )  =>  (v1_xxreal_0(k1_xxreal_2(A)) & v1_xreal_0(k1_xxreal_2(A))) ) ) ).
fof(fc20_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k6_xcmplx_0(B, A))) ) ).
fof(fc21_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k6_xcmplx_0(A, B))) ) ).
fof(fc22_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k6_xcmplx_0(B, A))) ) ).
fof(fc23_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k3_xcmplx_0(A, B))) ) ) ).
fof(fc24_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k3_xcmplx_0(B, A))) ) ) ).
fof(fc25_funcop_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_binop_1(A, B, C)) & v1_funct_1(k1_binop_1(A, B, C))) ) ) ).
fof(fc25_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k3_xcmplx_0(A, B))) ) ) ).
fof(fc26_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k3_xcmplx_0(A, B))) ) ) ).
fof(fc27_xreal_0, axiom,  (! [A] :  ( (v2_xxreal_0(A) & v1_xreal_0(A))  =>  (v1_xcmplx_0(k5_xcmplx_0(A)) & v2_xxreal_0(k5_xcmplx_0(A))) ) ) ).
fof(fc28_xreal_0, axiom,  (! [A] :  ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k5_xcmplx_0(A)) &  ~ (v2_xxreal_0(k5_xcmplx_0(A))) ) ) ) ).
fof(fc29_xreal_0, axiom,  (! [A] :  ( (v3_xxreal_0(A) & v1_xreal_0(A))  =>  (v1_xcmplx_0(k5_xcmplx_0(A)) & v3_xxreal_0(k5_xcmplx_0(A))) ) ) ).
fof(fc2_dualsp01, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  ~ (v1_xboole_0(k7_dualsp01(A))) ) ) ).
fof(fc2_membered, axiom, v2_membered(k6_numbers)).
fof(fc2_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v7_ordinal1(k3_xcmplx_0(A, B))) ) ).
fof(fc2_normsp_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_normsp_0(A) & l2_normsp_0(A)) )  &  (v9_struct_0(B, A) & m1_subset_1(B, u1_struct_0(A))) )  =>  (v8_ordinal1(k2_normsp_0(A, B)) & v1_xreal_0(k2_normsp_0(A, B))) ) ) ).
fof(fc2_numbers, axiom,  ~ (v1_xboole_0(k2_numbers)) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc2_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_xcmplx_0(k2_xcmplx_0(A, B))) ) ).
fof(fc2_xxreal_2, axiom,  (! [A] :  ( (v3_membered(A) &  ( ~ (v1_xboole_0(A))  & v3_xxreal_2(A)) )  =>  (v1_xxreal_0(k2_xxreal_2(A)) & v1_xreal_0(k2_xxreal_2(A))) ) ) ).
fof(fc30_xreal_0, axiom,  (! [A] :  ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k5_xcmplx_0(A)) &  ~ (v3_xxreal_0(k5_xcmplx_0(A))) ) ) ) ).
fof(fc3_dualsp01, 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) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  ( ~ (v1_xboole_0(k7_dualsp01(A)))  & v4_funct_1(k7_dualsp01(A))) ) ) ).
fof(fc3_membered, axiom, v3_membered(k1_numbers)).
fof(fc3_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  ~ (v8_ordinal1(k2_xcmplx_0(A, B))) ) ) ).
fof(fc3_numbers, axiom,  ~ (v1_xboole_0(k3_numbers)) ).
fof(fc3_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_xcmplx_0(k3_xcmplx_0(A, B))) ) ).
fof(fc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) =>  (v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A))) ) ) ).
fof(fc3_xxreal_2, axiom,  (! [A] :  ( (v3_membered(A) & v1_xxreal_2(A))  =>  (v1_xxreal_0(k2_xxreal_2(A)) & v1_xreal_0(k2_xxreal_2(A))) ) ) ).
fof(fc4_dualsp01, 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) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  (v13_algstr_0(g1_rlvect_1(k7_dualsp01(A), k7_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)), k5_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)), k6_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)))) &  (v1_rlvect_1(g1_rlvect_1(k7_dualsp01(A), k7_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)), k5_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)), k6_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)))) &  (v2_rlvect_1(g1_rlvect_1(k7_dualsp01(A), k7_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)), k5_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)), k6_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)))) &  (v3_rlvect_1(g1_rlvect_1(k7_dualsp01(A), k7_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)), k5_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)), k6_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)))) &  (v4_rlvect_1(g1_rlvect_1(k7_dualsp01(A), k7_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)), k5_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)), k6_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)))) &  (v5_rlvect_1(g1_rlvect_1(k7_dualsp01(A), k7_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)), k5_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)), k6_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)))) &  (v6_rlvect_1(g1_rlvect_1(k7_dualsp01(A), k7_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)), k5_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)), k6_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)))) &  (v7_rlvect_1(g1_rlvect_1(k7_dualsp01(A), k7_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)), k5_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)), k6_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)))) & v8_rlvect_1(g1_rlvect_1(k7_dualsp01(A), k7_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)), k5_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A)), k6_rsspace(k10_funcsdom(u1_struct_0(A)), k7_dualsp01(A))))) ) ) ) ) ) ) ) ) ) ).
fof(fc4_membered, axiom, v4_membered(k3_numbers)).
fof(fc4_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  ~ (v8_ordinal1(k2_xcmplx_0(B, A))) ) ) ).
fof(fc4_numbers, axiom,  ~ (v1_xboole_0(k4_numbers)) ).
fof(fc4_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_xcmplx_0(k6_xcmplx_0(A, B))) ) ).
fof(fc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) =>  (v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A))) ) ) ).
fof(fc4_xxreal_2, axiom,  (! [A] :  ( (v4_membered(A) & v1_xxreal_2(A))  =>  (v1_xxreal_0(k2_xxreal_2(A)) & v1_rat_1(k2_xxreal_2(A))) ) ) ).
fof(fc55_membered, axiom, v7_membered(k2_numbers)).
fof(fc56_membered, axiom, v7_membered(k1_numbers)).
fof(fc57_membered, axiom, v7_membered(k3_numbers)).
fof(fc58_membered, axiom, v7_membered(k4_numbers)).
fof(fc59_membered, axiom, v7_membered(k4_ordinal1)).
fof(fc5_dualsp01, 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) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k8_dualsp01(A)))  &  (v13_algstr_0(k8_dualsp01(A)) &  (v1_rlvect_1(k8_dualsp01(A)) &  (v2_rlvect_1(k8_dualsp01(A)) &  (v3_rlvect_1(k8_dualsp01(A)) &  (v4_rlvect_1(k8_dualsp01(A)) &  (v5_rlvect_1(k8_dualsp01(A)) &  (v6_rlvect_1(k8_dualsp01(A)) &  (v7_rlvect_1(k8_dualsp01(A)) &  (v8_rlvect_1(k8_dualsp01(A)) & v1_monoid_0(k8_dualsp01(A))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(fc5_membered, axiom, v5_membered(k4_numbers)).
fof(fc5_numbers, axiom,  ~ (v1_xboole_0(k6_numbers)) ).
fof(fc5_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc5_xxreal_2, axiom,  (! [A] :  ( (v5_membered(A) & v1_xxreal_2(A))  =>  (v1_xxreal_0(k2_xxreal_2(A)) & v1_int_1(k2_xxreal_2(A))) ) ) ).
fof(fc61_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  => v1_xcmplx_0(k1_funct_1(A, B))) ) ).
fof(fc62_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_valued_0(A)) )  => v1_xxreal_0(k1_funct_1(A, B))) ) ).
fof(fc63_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_valued_0(A)) )  => v1_xreal_0(k1_funct_1(A, B))) ) ).
fof(fc64_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v4_valued_0(A)) )  => v1_rat_1(k1_funct_1(A, B))) ) ).
fof(fc65_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_valued_0(A)) )  => v1_int_1(k1_funct_1(A, B))) ) ).
fof(fc66_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v6_valued_0(A)) )  => v7_ordinal1(k1_funct_1(A, B))) ) ).
fof(fc6_card_1, axiom, v1_card_1(k4_ordinal1)).
fof(fc6_dualsp01, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  ~ (v1_xboole_0(k11_dualsp01(A))) ) ) ).
fof(fc6_membered, axiom, v6_membered(k4_ordinal1)).
fof(fc6_numbers, axiom,  ~ (v1_finset_1(k4_numbers)) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc6_xcmplx_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A))  =>  ( ~ (v8_ordinal1(k4_xcmplx_0(A)))  & v1_xcmplx_0(k4_xcmplx_0(A))) ) ) ).
fof(fc6_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k3_xcmplx_0(A, B))) ) ).
fof(fc6_xxreal_2, axiom,  (! [A] :  ( (v6_membered(A) & v1_xxreal_2(A))  =>  (v1_xxreal_0(k2_xxreal_2(A)) & v7_ordinal1(k2_xxreal_2(A))) ) ) ).
fof(fc7_card_1, axiom, v2_card_1(k4_ordinal1)).
fof(fc7_dualsp01, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (v13_algstr_0(g1_rlvect_1(k11_dualsp01(A), k7_rsspace(k8_dualsp01(A), k11_dualsp01(A)), k5_rsspace(k8_dualsp01(A), k11_dualsp01(A)), k6_rsspace(k8_dualsp01(A), k11_dualsp01(A)))) &  (v1_rlvect_1(g1_rlvect_1(k11_dualsp01(A), k7_rsspace(k8_dualsp01(A), k11_dualsp01(A)), k5_rsspace(k8_dualsp01(A), k11_dualsp01(A)), k6_rsspace(k8_dualsp01(A), k11_dualsp01(A)))) &  (v2_rlvect_1(g1_rlvect_1(k11_dualsp01(A), k7_rsspace(k8_dualsp01(A), k11_dualsp01(A)), k5_rsspace(k8_dualsp01(A), k11_dualsp01(A)), k6_rsspace(k8_dualsp01(A), k11_dualsp01(A)))) &  (v3_rlvect_1(g1_rlvect_1(k11_dualsp01(A), k7_rsspace(k8_dualsp01(A), k11_dualsp01(A)), k5_rsspace(k8_dualsp01(A), k11_dualsp01(A)), k6_rsspace(k8_dualsp01(A), k11_dualsp01(A)))) &  (v4_rlvect_1(g1_rlvect_1(k11_dualsp01(A), k7_rsspace(k8_dualsp01(A), k11_dualsp01(A)), k5_rsspace(k8_dualsp01(A), k11_dualsp01(A)), k6_rsspace(k8_dualsp01(A), k11_dualsp01(A)))) &  (v5_rlvect_1(g1_rlvect_1(k11_dualsp01(A), k7_rsspace(k8_dualsp01(A), k11_dualsp01(A)), k5_rsspace(k8_dualsp01(A), k11_dualsp01(A)), k6_rsspace(k8_dualsp01(A), k11_dualsp01(A)))) &  (v6_rlvect_1(g1_rlvect_1(k11_dualsp01(A), k7_rsspace(k8_dualsp01(A), k11_dualsp01(A)), k5_rsspace(k8_dualsp01(A), k11_dualsp01(A)), k6_rsspace(k8_dualsp01(A), k11_dualsp01(A)))) &  (v7_rlvect_1(g1_rlvect_1(k11_dualsp01(A), k7_rsspace(k8_dualsp01(A), k11_dualsp01(A)), k5_rsspace(k8_dualsp01(A), k11_dualsp01(A)), k6_rsspace(k8_dualsp01(A), k11_dualsp01(A)))) & v8_rlvect_1(g1_rlvect_1(k11_dualsp01(A), k7_rsspace(k8_dualsp01(A), k11_dualsp01(A)), k5_rsspace(k8_dualsp01(A), k11_dualsp01(A)), k6_rsspace(k8_dualsp01(A), k11_dualsp01(A))))) ) ) ) ) ) ) ) ) ) ).
fof(fc7_numbers, axiom,  ~ (v1_finset_1(k3_numbers)) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc7_xcmplx_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A))  =>  ( ~ (v8_ordinal1(k5_xcmplx_0(A)))  & v1_xcmplx_0(k5_xcmplx_0(A))) ) ) ).
fof(fc7_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k6_xcmplx_0(A, B))) ) ).
fof(fc7_xxreal_2, axiom,  (! [A] :  ( (v3_membered(A) & v2_xxreal_2(A))  =>  (v1_xxreal_0(k1_xxreal_2(A)) & v1_xreal_0(k1_xxreal_2(A))) ) ) ).
fof(fc85_valued_0, axiom,  (! [A, B] :  (v1_membered(B) => v1_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc86_valued_0, axiom,  (! [A, B] :  (v2_membered(B) => v2_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc87_valued_0, axiom,  (! [A, B] :  (v3_membered(B) => v3_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc88_valued_0, axiom,  (! [A, B] :  (v4_membered(B) => v4_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc89_valued_0, axiom,  (! [A, B] :  (v5_membered(B) => v5_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc8_numbers, axiom,  ~ (v1_finset_1(k1_numbers)) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc8_xcmplx_0, axiom,  (! [A, B] :  ( ( ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A))  &  ( ~ (v8_ordinal1(B))  & v1_xcmplx_0(B)) )  =>  ~ (v8_ordinal1(k3_xcmplx_0(A, B))) ) ) ).
fof(fc8_xxreal_2, axiom,  (! [A] :  ( (v4_membered(A) & v2_xxreal_2(A))  =>  (v1_xxreal_0(k1_xxreal_2(A)) & v1_rat_1(k1_xxreal_2(A))) ) ) ).
fof(fc90_valued_0, axiom,  (! [A, B] :  (v6_membered(B) => v6_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc9_card_1, axiom,  ~ (v1_finset_1(k4_ordinal1)) ).
fof(fc9_dualsp01, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k17_dualsp01(A)))  &  (v3_normsp_0(k17_dualsp01(A)) &  (v4_normsp_0(k17_dualsp01(A)) & v2_normsp_1(k17_dualsp01(A))) ) ) ) ) ).
fof(fc9_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_funct_1(A, B)) & v1_funct_1(k1_funct_1(A, B))) ) ) ).
fof(fc9_numbers, axiom,  ~ (v1_finset_1(k2_numbers)) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(fc9_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k2_xcmplx_0(A, B))) ) ) ).
fof(fc9_xxreal_2, axiom,  (! [A] :  ( (v5_membered(A) & v2_xxreal_2(A))  =>  (v1_xxreal_0(k1_xxreal_2(A)) & v1_int_1(k1_xxreal_2(A))) ) ) ).
fof(fraenkel_a_2_0_dualsp06, axiom,  (! [A, B, C] :  ( ( ( ~ (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) &  (v3_normsp_0(B) &  (v4_normsp_0(B) &  (v2_normsp_1(B) & l1_normsp_1(B)) ) ) ) ) ) ) ) ) ) ) )  & m1_rlsub_1(C, B))  =>  (r2_hidden(A, a_2_0_dualsp06(B, C)) <=>  (? [D] :  (m1_subset_1(D, u1_struct_0(k17_dualsp01(B))) &  (A=D &  (! [E] :  (m1_subset_1(E, u1_struct_0(B)) =>  (r1_struct_0(C, E) => r1_dualsp06(B, E, D)) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_2_2_dualsp06, axiom,  (! [A, B, C] :  ( ( ( ~ (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) &  (v3_normsp_0(B) &  (v4_normsp_0(B) &  (v2_normsp_1(B) & l1_normsp_1(B)) ) ) ) ) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(C))  & m1_rlsub_1(C, B)) )  =>  (r2_hidden(A, a_2_2_dualsp06(B, C)) <=>  (? [D] :  (m1_subset_1(D, u1_struct_0(k17_dualsp01(B))) &  (A=D &  (! [E] :  (m1_subset_1(E, u1_struct_0(B)) =>  (r1_struct_0(C, E) => r1_dualsp06(B, E, D)) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_3_0_dualsp06, axiom,  (! [A, B, C, D] :  ( ( ( ~ (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) &  (v3_normsp_0(B) &  (v4_normsp_0(B) &  (v2_normsp_1(B) & l1_normsp_1(B)) ) ) ) ) ) ) ) ) ) ) )  &  (m1_subset_1(C, u1_struct_0(B)) &  ( ~ (v2_struct_0(D))  & m1_rlsub_1(D, B)) ) )  =>  (r2_hidden(A, a_3_0_dualsp06(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, u1_struct_0(B)) &  (A=k2_normsp_0(B, k5_algstr_0(B, C, E)) & r1_struct_0(D, E)) ) ) ) ) ) ).
fof(fraenkel_a_3_1_dualsp06, axiom,  (! [A, B, C, D] :  ( ( ( ~ (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) &  (v3_normsp_0(B) &  (v4_normsp_0(B) &  (v2_normsp_1(B) & l1_normsp_1(B)) ) ) ) ) ) ) ) ) ) ) )  &  (m1_subset_1(C, u1_struct_0(B)) &  ( ~ (v2_struct_0(D))  & m1_rlsub_1(D, B)) ) )  =>  (r2_hidden(A, a_3_1_dualsp06(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, u1_struct_0(k17_dualsp01(B))) &  (A=k2_dualsp06(B, C, E) &  (r1_struct_0(k3_dualsp06(B, D), E) & r1_xxreal_0(k2_normsp_0(k17_dualsp01(B), E), 1)) ) ) ) ) ) ) ).
fof(free_g1_normsp_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, A, k1_numbers) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, k1_numbers)))) ) ) ) )  =>  (! [F, G, H, I, J] :  (g1_normsp_1(A, B, C, D, E)=g1_normsp_1(F, G, H, I, J) =>  (A=F &  (B=G &  (C=H &  (D=I & E=J) ) ) ) ) ) ) ) ).
fof(free_g1_rlvect_1, axiom,  (! [A, B, C, D] :  ( (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)))) ) ) )  =>  (! [E, F, G, H] :  (g1_rlvect_1(A, B, C, D)=g1_rlvect_1(E, F, G, H) =>  (A=E &  (B=F &  (C=G & D=H) ) ) ) ) ) ) ).
fof(ie1_seq_4, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  (v3_membered(A) & v3_xxreal_2(A)) )  => k3_seq_4(A)=k2_xxreal_2(A)) ) ).
fof(involutiveness_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A))=A) ) ).
fof(involutiveness_k5_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k5_xcmplx_0(k5_xcmplx_0(A))=A) ) ).
fof(projectivity_k9_complex1, axiom,  (! [A] :  (v1_xcmplx_0(A) => k9_complex1(k9_complex1(A))=k9_complex1(A)) ) ).
fof(rc10_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_card_1(B)) ) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(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_card_1, axiom,  (? [A] : v1_card_1(A)) ).
fof(rc1_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ).
fof(rc1_funct_2, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(rc1_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc1_nat_1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc1_normsp_1, axiom,  (? [A] :  (l1_normsp_1(A) & v1_normsp_1(A)) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(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_rlvect_1, axiom,  (? [A] :  (l1_rlvect_1(A) & v1_rlvect_1(A)) ) ).
fof(rc1_seq_4, axiom,  (? [A] :  (m1_subset_1(A, k1_zfmisc_1(k1_numbers)) &  ( ~ (v1_xboole_0(A))  &  (v1_membered(A) &  (v2_membered(A) &  (v3_membered(A) &  (v3_xxreal_2(A) & v4_xxreal_2(A)) ) ) ) ) ) ) ).
fof(rc1_valued_0, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v6_valued_0(A)) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xcmplx_0, axiom,  (? [A] : v1_xcmplx_0(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc1_xxreal_2, axiom,  (? [A] :  (v1_membered(A) &  (v2_membered(A) &  (v3_membered(A) &  (v4_membered(A) &  (v5_membered(A) &  (v6_membered(A) &  ( ~ (v1_xboole_0(A))  &  (v1_xxreal_2(A) & v2_xxreal_2(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(rc23_struct_0, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (l1_struct_0(B) & v13_struct_0(B, A)) ) ) ) ).
fof(rc2_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v1_finset_1(A) & v1_card_1(A)) ) ) ) ) ).
fof(rc2_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc2_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) & v8_ordinal1(A)) ) ).
fof(rc2_normsp_1, axiom,  (? [A] :  (l1_normsp_1(A) &  ( ~ (v2_struct_0(A))  & v1_normsp_1(A)) ) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_rlvect_1, axiom,  (? [A] :  (l1_rlvect_1(A) &  ~ (v2_struct_0(A)) ) ) ).
fof(rc2_valued_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xcmplx_0, axiom,  (? [A] : v1_xcmplx_0(A)) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc2_xxreal_2, axiom,  (? [A] :  (v6_membered(A) &  (v1_finset_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ).
fof(rc3_card_1, axiom,  (? [A] :  ~ (v1_finset_1(A)) ) ).
fof(rc3_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v6_membered(A) & v7_membered(A)) ) ) ).
fof(rc3_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc3_normsp_1, axiom,  (? [A] :  (l1_normsp_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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v1_normsp_1(A) & v2_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_valued_0, axiom,  (? [A] :  (m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k4_ordinal1))) &  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v5_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_partfun1(A, k4_ordinal1) &  (v1_funct_2(A, k4_ordinal1, k4_ordinal1) &  (v1_valued_0(A) &  (v2_valued_0(A) &  (v3_valued_0(A) &  (v4_valued_0(A) &  (v5_valued_0(A) &  (v6_valued_0(A) & v7_valued_0(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_valued_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  & v1_finset_1(A)) ) ) ) ) ).
fof(rc3_xcmplx_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xcmplx_0(A)) ) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc3_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ).
fof(rc3_xxreal_2, axiom,  (? [A] :  (v1_membered(A) &  (v2_membered(A) &  (v3_membered(A) &  (v4_membered(A) &  (v5_membered(A) &  (v6_membered(A) &  ( ~ (v1_xboole_0(A))  &  (v1_xxreal_2(A) & v5_xxreal_2(A)) ) ) ) ) ) ) ) ) ).
fof(rc4_card_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc4_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) ) ) ) ) ).
fof(rc4_nat_1, axiom,  (? [A] :  (m1_subset_1(A, k1_zfmisc_1(k1_numbers)) &  ( ~ (v1_xboole_0(A))  & v3_ordinal1(A)) ) ) ).
fof(rc4_ordinal1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v5_ordinal1(B)) ) ) ) ) ).
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_valued_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v1_finset_1(A) & v3_card_1(A, 1)) ) ) ) ) ).
fof(rc4_xcmplx_0, axiom,  (? [A] :  ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A)) ) ).
fof(rc4_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ).
fof(rc4_xxreal_2, axiom,  (? [A] :  (v2_membered(A) &  ( ~ (v1_xboole_0(A))  & v6_xxreal_2(A)) ) ) ).
fof(rc5_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  & v1_card_1(A)) ) ) ) ) ) ).
fof(rc5_nat_1, axiom,  (? [A] :  (m1_subset_1(A, k4_ordinal1) &  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v1_xreal_0(A) &  (v1_finset_1(A) & v1_card_1(A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_rlvect_1, axiom,  (? [A] :  (l1_rlvect_1(A) &  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v1_rlvect_1(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)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc5_valued_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v1_valued_0(B) &  (v2_valued_0(B) &  (v3_valued_0(B) &  (v4_valued_0(B) &  (v5_valued_0(B) & v6_valued_0(B)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc5_xcmplx_0, axiom,  (? [A] :  ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A)) ) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc5_xxreal_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ).
fof(rc5_xxreal_2, axiom,  (? [A] :  (v2_membered(A) &  (v1_xxreal_2(A) &  (v2_xxreal_2(A) & v6_xxreal_2(A)) ) ) ) ).
fof(rc6_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_finset_1(B)) ) ) ) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_valued_0, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v6_valued_0(B)) ) ) ) ) ) ).
fof(rc6_xxreal_2, axiom,  (? [A] :  (v2_membered(A) &  ( ~ (v1_xxreal_2(A))  &  (v2_xxreal_2(A) & v6_xxreal_2(A)) ) ) ) ).
fof(rc7_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] : v3_card_1(B, A)) ) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc7_xxreal_2, axiom,  (? [A] :  (v2_membered(A) &  (v1_xxreal_2(A) &  ( ~ (v2_xxreal_2(A))  & v6_xxreal_2(A)) ) ) ) ).
fof(rc8_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (v1_relat_1(B) &  (v1_funct_1(B) & v3_card_1(B, A)) ) ) ) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc8_xxreal_2, axiom,  (? [A] :  (v2_membered(A) &  ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xxreal_2(A))  &  ( ~ (v2_xxreal_2(A))  & v6_xxreal_2(A)) ) ) ) ) ).
fof(rc9_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v3_card_1(B, 1)) ) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rd1_absvalue, axiom,  (! [A] :  ( (v1_xreal_0(A) &  ~ (v3_xxreal_0(A)) )  => k9_complex1(A)=A) ) ).
fof(rd1_rlvect_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  &  ( (v9_struct_0(B, A) & m1_subset_1(B, u1_struct_0(A)))  & m1_subset_1(C, u1_struct_0(A))) )  => k1_algstr_0(A, B, C)=C) ) ).
fof(rd2_rlvect_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  &  ( (v9_struct_0(B, A) & m1_subset_1(B, u1_struct_0(A)))  & m1_subset_1(C, u1_struct_0(A))) )  => k1_algstr_0(A, C, B)=C) ) ).
fof(rd3_rlvect_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) )  &  ( (v9_struct_0(B, A) & m1_subset_1(B, u1_struct_0(A)))  & v1_xreal_0(C)) )  => k1_rlvect_1(A, B, C)=B) ) ).
fof(rd4_rlvect_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  &  (v9_struct_0(B, A) & m1_subset_1(B, u1_struct_0(A))) )  => k4_algstr_0(A, B)=B) ) ).
fof(rd5_rlvect_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) &  (v9_struct_0(C, A) & m1_subset_1(C, u1_struct_0(A))) ) )  => k5_algstr_0(A, B, C)=B) ) ).
fof(rd6_rlvect_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  & m1_subset_1(B, u1_struct_0(A)))  => k4_algstr_0(A, k4_algstr_0(A, B))=B) ) ).
fof(redefinition_k18_dualsp01, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(k17_dualsp01(A))) & m1_subset_1(C, u1_struct_0(A))) )  => k18_dualsp01(A, B, C)=k1_funct_1(B, C)) ) ).
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_binop_1, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (m1_subset_1(C, A) & m1_subset_1(D, A)) )  => k4_binop_1(A, B, C, D)=k1_binop_1(B, C, D)) ) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
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(reflexivity_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => r1_xxreal_0(A, A)) ) ).
fof(rqLessOrEqual__r1_xxreal_0__r0_r0, axiom, r1_xxreal_0(0, 0)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r1, axiom, r1_xxreal_0(0, 1)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r2, axiom, r1_xxreal_0(0, 2)).
fof(rqLessOrEqual__r1_xxreal_0__r0_rm1, axiom,  ~ (r1_xxreal_0(0, k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__r0_rm2, axiom,  ~ (r1_xxreal_0(0, k4_xcmplx_0(2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_r0, axiom,  ~ (r1_xxreal_0(1, 0)) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_r1, axiom, r1_xxreal_0(1, 1)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r2, axiom, r1_xxreal_0(1, 2)).
fof(rqLessOrEqual__r1_xxreal_0__r1_rm1, axiom,  ~ (r1_xxreal_0(1, k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_rm2, axiom,  ~ (r1_xxreal_0(1, k4_xcmplx_0(2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_r0, axiom,  ~ (r1_xxreal_0(2, 0)) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_r1, axiom,  ~ (r1_xxreal_0(2, 1)) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_r2, axiom, r1_xxreal_0(2, 2)).
fof(rqLessOrEqual__r1_xxreal_0__r2_rm1, axiom,  ~ (r1_xxreal_0(2, k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_rm2, axiom,  ~ (r1_xxreal_0(2, k4_xcmplx_0(2))) ).
fof(rqLessOrEqual__r1_xxreal_0__rm1_r0, axiom, r1_xxreal_0(k4_xcmplx_0(1), 0)).
fof(rqLessOrEqual__r1_xxreal_0__rm1_r1, axiom, r1_xxreal_0(k4_xcmplx_0(1), 1)).
fof(rqLessOrEqual__r1_xxreal_0__rm1_r2, axiom, r1_xxreal_0(k4_xcmplx_0(1), 2)).
fof(rqLessOrEqual__r1_xxreal_0__rm1_rm1, axiom, r1_xxreal_0(k4_xcmplx_0(1), k4_xcmplx_0(1))).
fof(rqLessOrEqual__r1_xxreal_0__rm1_rm2, axiom,  ~ (r1_xxreal_0(k4_xcmplx_0(1), k4_xcmplx_0(2))) ).
fof(rqLessOrEqual__r1_xxreal_0__rm2_r0, axiom, r1_xxreal_0(k4_xcmplx_0(2), 0)).
fof(rqLessOrEqual__r1_xxreal_0__rm2_r1, axiom, r1_xxreal_0(k4_xcmplx_0(2), 1)).
fof(rqLessOrEqual__r1_xxreal_0__rm2_r2, axiom, r1_xxreal_0(k4_xcmplx_0(2), 2)).
fof(rqLessOrEqual__r1_xxreal_0__rm2_rm1, axiom, r1_xxreal_0(k4_xcmplx_0(2), k4_xcmplx_0(1))).
fof(rqLessOrEqual__r1_xxreal_0__rm2_rm2, axiom, r1_xxreal_0(k4_xcmplx_0(2), k4_xcmplx_0(2))).
fof(rqRealAdd__k2_xcmplx_0__r0_r0_r0, axiom, k2_xcmplx_0(0, 0)=0).
fof(rqRealAdd__k2_xcmplx_0__r0_r1_r1, axiom, k2_xcmplx_0(0, 1)=1).
fof(rqRealAdd__k2_xcmplx_0__r0_r2_r2, axiom, k2_xcmplx_0(0, 2)=2).
fof(rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, axiom, k2_xcmplx_0(0, k4_xcmplx_0(1))=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, axiom, k2_xcmplx_0(0, k4_xcmplx_0(2))=k4_xcmplx_0(2)).
fof(rqRealAdd__k2_xcmplx_0__r1_r0_r1, axiom, k2_xcmplx_0(1, 0)=1).
fof(rqRealAdd__k2_xcmplx_0__r1_r1_r2, axiom, k2_xcmplx_0(1, 1)=2).
fof(rqRealAdd__k2_xcmplx_0__r1_rm1_r0, axiom, k2_xcmplx_0(1, k4_xcmplx_0(1))=0).
fof(rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, axiom, k2_xcmplx_0(1, k4_xcmplx_0(2))=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__r2_r0_r2, axiom, k2_xcmplx_0(2, 0)=2).
fof(rqRealAdd__k2_xcmplx_0__r2_rm1_r1, axiom, k2_xcmplx_0(2, k4_xcmplx_0(1))=1).
fof(rqRealAdd__k2_xcmplx_0__r2_rm2_r0, axiom, k2_xcmplx_0(2, k4_xcmplx_0(2))=0).
fof(rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, axiom, k2_xcmplx_0(k4_xcmplx_0(1), 0)=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__rm1_r1_r0, axiom, k2_xcmplx_0(k4_xcmplx_0(1), 1)=0).
fof(rqRealAdd__k2_xcmplx_0__rm1_r2_r1, axiom, k2_xcmplx_0(k4_xcmplx_0(1), 2)=1).
fof(rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, axiom, k2_xcmplx_0(k4_xcmplx_0(1), k4_xcmplx_0(1))=k4_xcmplx_0(2)).
fof(rqRealAdd__k2_xcmplx_0__rm2_r0_rm2, axiom, k2_xcmplx_0(k4_xcmplx_0(2), 0)=k4_xcmplx_0(2)).
fof(rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, axiom, k2_xcmplx_0(k4_xcmplx_0(2), 1)=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__rm2_r2_r0, axiom, k2_xcmplx_0(k4_xcmplx_0(2), 2)=0).
fof(rqRealDiff__k6_xcmplx_0__r0_r0_r0, axiom, k6_xcmplx_0(0, 0)=0).
fof(rqRealDiff__k6_xcmplx_0__r0_r1_rm1, axiom, k6_xcmplx_0(0, 1)=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__r0_r2_rm2, axiom, k6_xcmplx_0(0, 2)=k4_xcmplx_0(2)).
fof(rqRealDiff__k6_xcmplx_0__r0_rm1_r1, axiom, k6_xcmplx_0(0, k4_xcmplx_0(1))=1).
fof(rqRealDiff__k6_xcmplx_0__r0_rm2_r2, axiom, k6_xcmplx_0(0, k4_xcmplx_0(2))=2).
fof(rqRealDiff__k6_xcmplx_0__r1_r0_r1, axiom, k6_xcmplx_0(1, 0)=1).
fof(rqRealDiff__k6_xcmplx_0__r1_r1_r0, axiom, k6_xcmplx_0(1, 1)=0).
fof(rqRealDiff__k6_xcmplx_0__r1_r2_rm1, axiom, k6_xcmplx_0(1, 2)=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__r1_rm1_r2, axiom, k6_xcmplx_0(1, k4_xcmplx_0(1))=2).
fof(rqRealDiff__k6_xcmplx_0__r2_r0_r2, axiom, k6_xcmplx_0(2, 0)=2).
fof(rqRealDiff__k6_xcmplx_0__r2_r1_r1, axiom, k6_xcmplx_0(2, 1)=1).
fof(rqRealDiff__k6_xcmplx_0__r2_r2_r0, axiom, k6_xcmplx_0(2, 2)=0).
fof(rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, axiom, k6_xcmplx_0(k4_xcmplx_0(1), 0)=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, axiom, k6_xcmplx_0(k4_xcmplx_0(1), 1)=k4_xcmplx_0(2)).
fof(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, axiom, k6_xcmplx_0(k4_xcmplx_0(1), k4_xcmplx_0(1))=0).
fof(rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, axiom, k6_xcmplx_0(k4_xcmplx_0(1), k4_xcmplx_0(2))=1).
fof(rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, axiom, k6_xcmplx_0(k4_xcmplx_0(2), 0)=k4_xcmplx_0(2)).
fof(rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, axiom, k6_xcmplx_0(k4_xcmplx_0(2), k4_xcmplx_0(1))=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, axiom, k6_xcmplx_0(k4_xcmplx_0(2), k4_xcmplx_0(2))=0).
fof(rqRealMult__k3_xcmplx_0__r0_r0_r0, axiom, k3_xcmplx_0(0, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r0_r1_r0, axiom, k3_xcmplx_0(0, 1)=0).
fof(rqRealMult__k3_xcmplx_0__r0_r2_r0, axiom, k3_xcmplx_0(0, 2)=0).
fof(rqRealMult__k3_xcmplx_0__r0_rm2_r0, axiom, k3_xcmplx_0(0, k4_xcmplx_0(2))=0).
fof(rqRealMult__k3_xcmplx_0__r1_r0_r0, axiom, k3_xcmplx_0(1, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r1_r1_r1, axiom, k3_xcmplx_0(1, 1)=1).
fof(rqRealMult__k3_xcmplx_0__r1_r2_r2, axiom, k3_xcmplx_0(1, 2)=2).
fof(rqRealMult__k3_xcmplx_0__r1_rm2_rm2, axiom, k3_xcmplx_0(1, k4_xcmplx_0(2))=k4_xcmplx_0(2)).
fof(rqRealMult__k3_xcmplx_0__r2_r0_r0, axiom, k3_xcmplx_0(2, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r2_r1_r2, axiom, k3_xcmplx_0(2, 1)=2).
fof(rqRealMult__k3_xcmplx_0__rm2_r0_r0, axiom, k3_xcmplx_0(k4_xcmplx_0(2), 0)=0).
fof(rqRealMult__k3_xcmplx_0__rm2_r1_rm2, axiom, k3_xcmplx_0(k4_xcmplx_0(2), 1)=k4_xcmplx_0(2)).
fof(rqRealNeg__k4_xcmplx_0__r0_r0, axiom, k4_xcmplx_0(0)=0).
fof(rqRealNeg__k4_xcmplx_0__r1_rm1, axiom, k4_xcmplx_0(1)=k4_xcmplx_0(1)).
fof(rqRealNeg__k4_xcmplx_0__r2_rm2, axiom, k4_xcmplx_0(2)=k4_xcmplx_0(2)).
fof(rqRealNeg__k4_xcmplx_0__rm1_r1, axiom, k4_xcmplx_0(k4_xcmplx_0(1))=1).
fof(rqRealNeg__k4_xcmplx_0__rm2_r2, axiom, k4_xcmplx_0(k4_xcmplx_0(2))=2).
fof(spc0_boole, axiom, v1_xboole_0(0)).
fof(spc0_numerals, axiom, m1_subset_1(0, k4_ordinal1)).
fof(spc10_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k3_xcmplx_0(k5_xcmplx_0(A), k5_xcmplx_0(B))=k5_xcmplx_0(k3_xcmplx_0(A, B))) ) ).
fof(spc1_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(A, k4_xcmplx_0(B))=k6_xcmplx_0(A, B)) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(spc2_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(A, k4_xcmplx_0(1))=k4_xcmplx_0(A)) ) ).
fof(spc2_boole, axiom,  ~ (v1_xboole_0(2)) ).
fof(spc2_numerals, axiom,  (v2_xxreal_0(2) & m1_subset_1(2, k4_ordinal1)) ).
fof(spc5_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k3_xcmplx_0(k2_xcmplx_0(A, B), C)=k2_xcmplx_0(k3_xcmplx_0(A, C), k3_xcmplx_0(B, C))) ) ).
fof(spc6_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k2_xcmplx_0(k2_xcmplx_0(A, B), C)=k2_xcmplx_0(A, k2_xcmplx_0(B, C))) ) ).
fof(spc7_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k3_xcmplx_0(k3_xcmplx_0(A, B), C)=k3_xcmplx_0(A, k3_xcmplx_0(B, C))) ) ).
fof(spc8_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(k4_xcmplx_0(A), k4_xcmplx_0(B))=k4_xcmplx_0(k2_xcmplx_0(A, B))) ) ).
fof(spc9_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k6_xcmplx_0(k4_xcmplx_0(A), k4_xcmplx_0(B))=k6_xcmplx_0(B, A)) ) ).
fof(t13_dualsp06, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k17_dualsp01(A))) => k2_dualsp06(A, k5_algstr_0(A, B, C), D)=k6_xcmplx_0(k2_dualsp06(A, B, D), k2_dualsp06(A, C, D))) ) ) ) ) ) ) ) ).
fof(t16_dualsp06, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_rlsub_1(B, A) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k17_dualsp01(A))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  ( (r1_struct_0(k3_dualsp06(A, B), C) & r1_struct_0(B, D))  => k2_dualsp06(A, D, C)=k5_numbers) ) ) ) ) ) ) ) ) ).
fof(t1_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k2_xcmplx_0(A, k5_numbers)=A) ) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v2_xxreal_0(A))  => v2_xxreal_0(B)) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t21_dualsp06, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  ( ( ~ (v2_struct_0(C))  & m1_rlsub_1(C, A))  =>  ~ ( ( ~ (r1_struct_0(C, B))  &  (! [D] :  ( ( ~ (v1_xboole_0(D))  &  (v3_membered(D) & v3_xxreal_2(D)) )  =>  (! [E] :  ( ( ~ (v1_xboole_0(E))  &  (v3_membered(E) & v4_xxreal_2(E)) )  =>  ~ ( (D=a_3_0_dualsp06(A, B, C) &  (E=a_3_1_dualsp06(A, B, C) &  (k2_xxreal_2(D)=k1_xxreal_2(E) &  (r2_hidden(k1_xxreal_2(E), E) &  ( ~ ( ( ~ (r1_xxreal_0(k2_xxreal_2(D), k5_numbers))  &  (! [F] :  (m1_subset_1(F, u1_struct_0(k17_dualsp01(A))) =>  ~ ( (k2_normsp_0(k17_dualsp01(A), F)=1 &  (r1_struct_0(k3_dualsp06(A, C), F) & k2_dualsp06(A, B, F)=k2_xxreal_2(D)) ) ) ) ) ) )  &  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  ( (r1_struct_0(C, F) & k2_normsp_0(A, k5_algstr_0(A, B, F))=k2_xxreal_2(D))  =>  (! [G] :  (m1_subset_1(G, u1_struct_0(k17_dualsp01(A))) =>  ( (k2_normsp_0(k17_dualsp01(A), G)=1 &  (r1_struct_0(k3_dualsp06(A, C), G) & k2_dualsp06(A, B, G)=k2_xxreal_2(D)) )  => r2_dualsp06(A, k5_algstr_0(A, B, F), G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t21_rlsub_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) & l1_rlvect_1(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (v1_xreal_0(C) =>  (! [D] :  (m1_rlsub_1(D, A) =>  (r1_struct_0(D, B) => r1_struct_0(D, k1_rlvect_1(A, B, C))) ) ) ) ) ) ) ) ) ).
fof(t2_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(A, k5_numbers)=k5_numbers) ) ).
fof(t2_dualsp06, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k17_dualsp01(A))) => r1_xxreal_0(k9_complex1(k2_dualsp06(A, B, C)), k3_xcmplx_0(k2_normsp_0(k17_dualsp01(A), C), k2_normsp_0(A, B)))) ) ) ) ) ) ).
fof(t2_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v3_xxreal_0(B))  => v3_xxreal_0(A)) ) ) ) ) ).
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(t30_dualsp01, 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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k17_dualsp01(A))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k17_dualsp01(A))) =>  (! [D] :  (v1_xreal_0(D) =>  (C=k1_rlvect_1(k17_dualsp01(A), B, D) <=>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) => k18_dualsp01(A, C, E)=k3_xcmplx_0(D, k18_dualsp01(A, B, E))) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(1, A)=A) ) ).
fof(t3_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v3_xxreal_0(A))  & v3_xxreal_0(B)) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k6_xcmplx_0(A, k5_numbers)=A) ) ).
fof(t4_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v2_xxreal_0(B))  & v2_xxreal_0(A)) ) ) ) ) ) ) ).
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_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(B) |  (v3_xxreal_0(A) | v2_xxreal_0(B)) ) ) ) ) ) ) ).
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(t6_normsp_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) &  (v3_normsp_0(A) &  (v4_normsp_0(A) &  (v2_normsp_1(A) & l1_normsp_1(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (k2_normsp_0(A, k5_algstr_0(A, B, C))=k5_numbers <=> B=C) ) ) ) ) ) ) ).
fof(t6_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(A) |  (v2_xxreal_0(B) | v3_xxreal_0(A)) ) ) ) ) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(B)) ) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v3_xxreal_0(B))  &  ~ (v2_xxreal_0(A)) ) ) ) ) ) ) ) ).
fof(t8_xreal_1, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (! [C] :  (v1_xreal_0(C) =>  (! [D] :  (v1_xreal_0(D) =>  ~ ( ( ~ (r1_xxreal_0(B, A))  &  (r1_xxreal_0(C, D) & r1_xxreal_0(k2_xcmplx_0(B, D), k2_xcmplx_0(A, C))) ) ) ) ) ) ) ) ) ) ) ).
