% Mizar problem: t43_zmodlat3,zmodlat3,3605,7 
fof(t43_zmodlat3, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  (v1_zmodul03(A) &  (v2_zmodlat1(A) &  (v4_zmodlat1(A) &  (v1_zmodlat2(A) & l1_zmodlat1(A, k1_int_3)) ) ) ) ) ) ) ) ) ) ) ) ) )  => k1_zmodul03(A)=k1_zmodul03(k9_zmodlat3(A))) ) ).
fof(abstractness_v1_zmodlat1, axiom,  (! [A, B] :  ( (l1_struct_0(A) & l1_zmodlat1(B, A))  =>  (v1_zmodlat1(B, A) => B=g1_zmodlat1(A, u1_struct_0(B), u1_algstr_0(B), u2_struct_0(B), u1_vectsp_1(A, B), u1_zmodlat1(A, B))) ) ) ).
fof(abstractness_v36_algstr_0, axiom,  (! [A] :  (l6_algstr_0(A) =>  (v36_algstr_0(A) => A=g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A))) ) ) ).
fof(abstractness_v7_vectsp_1, axiom,  (! [A, B] :  ( (l1_struct_0(A) & l1_vectsp_1(B, A))  =>  (v7_vectsp_1(B, A) => B=g1_vectsp_1(A, u1_struct_0(B), u1_algstr_0(B), u2_struct_0(B), u1_vectsp_1(A, B))) ) ) ).
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_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v6_membered(A)) ) ).
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(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_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_finseq_1(A)) ) ).
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(cc12_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) => v4_funct_1(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(cc13_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finseq_1(B)) ) ) ) ).
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(cc14_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_finseq_1(B)) ) ) ) ).
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(cc15_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v3_valued_0(A) & v7_valued_0(A)) ) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_funct_1(A) & v3_valued_0(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(cc16_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finset_1(A) & v2_finseq_1(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(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(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_binop_2, axiom,  (! [A] :  (m1_subset_1(A, k3_numbers) => v1_rat_1(A)) ) ).
fof(cc1_card_1, axiom,  (! [A] :  (v1_card_1(A) => v3_ordinal1(A)) ) ).
fof(cc1_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc1_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_finset_1(A)) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
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_gaussint, axiom,  (! [A] :  (v1_int_1(A) =>  (v1_int_1(A) & v1_gaussint(A)) ) ) ).
fof(cc1_int_1, axiom,  (! [A] :  (m1_subset_1(A, k4_numbers) => v1_int_1(A)) ) ).
fof(cc1_int_3, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) &  (v4_vectsp_1(A) &  (v1_vectsp_2(A) & v1_int_3(A)) ) ) ) ) ) ) ) ) )  =>  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) &  (v4_vectsp_1(A) &  (v1_vectsp_2(A) & v3_gcd_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_rat_1, axiom,  (! [A] :  (v1_rat_1(A) => v1_xreal_0(A)) ) ).
fof(cc1_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc1_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc1_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v5_valued_0(A)) ) ) ).
fof(cc1_vectsp_1, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v5_vectsp_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v1_vectsp_1(A) & v2_vectsp_1(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(cc1_zmodlat2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) & l1_vectsp_1(A, k1_int_3)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v2_vectsp_7(B, k1_int_3, A) =>  ( ~ (v1_xboole_0(B))  & v2_vectsp_7(B, k1_int_3, A)) ) ) ) ) ) ).
fof(cc1_zmodul03, axiom,  (! [A] :  (l1_vectsp_1(A, k1_int_3) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & v3_vectsp_7(A, k1_int_3)) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) & v1_zmodul01(A, k1_int_3)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc1_zmodul06, axiom,  (! [A] :  (l1_vectsp_1(A, k1_int_3) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & v1_zmodul01(A, k1_int_3)) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_zmodul01(A, k1_int_3) & v3_zmodul06(A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc1_zmodul08, axiom,  (! [A] :  (l1_vectsp_1(A, k1_int_3) =>  ( ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & v2_zmodul08(A)) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  ( ~ (v2_zmodul03(A))  & v2_zmodul08(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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(cc2_finset_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_finset_1(B)) ) ) ) ).
fof(cc2_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_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_gaussint, axiom,  (! [A] :  (v1_rat_1(A) =>  (v1_rat_1(A) & v2_gaussint(A)) ) ) ).
fof(cc2_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_int_1(A)) ) ).
fof(cc2_int_3, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_rlvect_1(A) & v4_vectsp_1(A)) ) ) ) )  =>  ( ~ (v2_struct_0(A))  & v1_int_3(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_rat_1, axiom,  (! [A] :  (v1_int_1(A) => v1_rat_1(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_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc2_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v4_valued_0(A)) ) ) ).
fof(cc2_vectsp_1, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v1_vectsp_1(A) & v2_vectsp_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v5_vectsp_1(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_zmodul03, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  (v1_zmodul03(A) & l1_vectsp_1(A, k1_int_3)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v2_vectsp_7(B, k1_int_3, A) =>  (v1_finset_1(B) & v2_vectsp_7(B, k1_int_3, A)) ) ) ) ) ) ).
fof(cc2_zmodul04, axiom,  (! [A] :  (l1_vectsp_1(A, k1_int_3) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) & v2_zmodul03(A)) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  (v1_zmodul03(A) & v2_zmodul03(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc2_zmodul06, axiom,  (! [A] :  (l1_vectsp_1(A, k1_int_3) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & v3_zmodul06(A)) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_zmodul01(A, k1_int_3) & v3_zmodul06(A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc2_zmodul08, axiom,  (! [A] :  (l1_vectsp_1(A, k1_int_3) =>  ( ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & v3_vectsp_7(A, k1_int_3)) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  ~ (v2_zmodul08(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_finset_1, axiom,  (! [A, B] :  (v1_finset_1(A) =>  (! [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_funct_2(C, A, B) & v1_finset_1(C)) ) ) ) ) ) ) ).
fof(cc3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_funct_1(B)) ) ) ) ).
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_gaussint, axiom,  (! [A] :  ( (v1_xcmplx_0(A) & v1_gaussint(A))  =>  (v1_xcmplx_0(A) &  (v1_gaussint(A) & v2_gaussint(A)) ) ) ) ).
fof(cc3_int_1, axiom,  (! [A] :  (v1_int_1(A) => v1_xreal_0(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_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(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_struct_0, axiom,  (! [A] :  (l4_struct_0(A) =>  ( ~ (v6_struct_0(A))  =>  ~ (v7_struct_0(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_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc3_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_vectsp_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & v6_vectsp_1(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_zmodul04, axiom,  (! [A] :  (l1_vectsp_1(A, k1_int_3) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) & v1_zmodul03(A)) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  (v1_zmodul03(A) & v2_zmodul03(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc3_zmodul06, axiom,  (! [A] :  (l1_vectsp_1(A, k1_int_3) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & v3_vectsp_7(A, k1_int_3)) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) & v3_zmodul06(A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc3_zmodul08, axiom,  (! [A] :  (l1_vectsp_1(A, k1_int_3) =>  ( ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & v3_zmodul06(A)) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  ( ~ (v8_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & v3_zmodul06(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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc4_finset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) => v1_finset_1(A)) ) ).
fof(cc4_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_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_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v2_int_1(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_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_1(A)) ) ) ).
fof(cc4_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => v1_xboole_0(C)) ) ) ) ).
fof(cc4_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc4_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & v6_vectsp_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v1_group_1(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(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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) ) ) ).
fof(cc5_finset_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_zfmisc_1(A)) ) ) ).
fof(cc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_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_int_1, axiom,  (! [A] :  (v2_int_1(A) => v1_int_1(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_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v4_relat_1(C, A)) ) ) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc5_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc5_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v2_valued_0(A)) ) ) ).
fof(cc5_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_vectsp_1(A))  =>  ( ~ (v2_struct_0(A))  & v1_group_1(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_zmodul06, axiom,  (! [A] :  (l1_vectsp_1(A, k1_int_3) =>  ( ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & v3_zmodul06(A)) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  ( ~ (v2_zmodul06(A))  & v3_zmodul06(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc6_card_1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v1_finset_1(A))  => v7_ordinal1(A)) ) ).
fof(cc6_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ).
fof(cc6_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_finset_1(A)) ) ).
fof(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(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_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v5_relat_1(C, 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_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v5_group_1(A) & v6_vectsp_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v3_vectsp_1(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_zmodul06, axiom,  (! [A] :  (l1_vectsp_1(A, k1_int_3) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v2_zmodul03(A) & v3_zmodul06(A)) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  (v2_zmodul03(A) & v3_zmodul06(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc7_card_1, axiom,  (! [A] :  (v3_card_1(A, k5_ordinal1) => v1_xboole_0(A)) ) ).
fof(cc7_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ) ).
fof(cc7_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finset_1(B)) ) ) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(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_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v4_relat_1(B, 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(cc8_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_card_1(A, k5_ordinal1)) ) ).
fof(cc8_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_finseq_1(A)) ) ).
fof(cc8_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_finset_1(B)) ) ) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
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_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v5_relat_1(B, A)) ) ) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc8_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(cc9_card_1, axiom,  (! [A] :  (v3_card_1(A, 1) =>  ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A)) ) ) ).
fof(cc9_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v1_finset_1(A)) ) ).
fof(cc9_finset_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_finset_1(A)) ) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
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(d3_int_3, axiom, k1_int_3=g6_algstr_0(k4_numbers, k20_binop_2, k22_binop_2, k10_subset_1(1, k4_numbers), k10_subset_1(k5_numbers, k4_numbers))).
fof(d5_vectsp_1, axiom, k2_vectsp_1=g6_algstr_0(k1_numbers, k9_binop_2, k11_binop_2, k10_subset_1(1, k1_numbers), k10_subset_1(k5_numbers, k1_numbers))).
fof(d5_zmodul03, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  (v1_zmodul03(A) & l1_vectsp_1(A, k1_int_3)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (v7_ordinal1(B) =>  (B=k1_zmodul03(A) <=>  (! [C] :  ( (v2_vectsp_7(C, k1_int_3, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))  => B=k4_card_1(C)) ) ) ) ) ) ) ).
fof(dt_g1_vectsp_1, axiom,  (! [A, B, C, D, E] :  ( (l1_struct_0(A) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(B, B), B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B, B), B)))) )  &  (m1_subset_1(D, B) &  (v1_funct_1(E) &  (v1_funct_2(E, k2_zfmisc_1(u1_struct_0(A), B), B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), B), B)))) ) ) ) )  =>  (v7_vectsp_1(g1_vectsp_1(A, B, C, D, E), A) & l1_vectsp_1(g1_vectsp_1(A, B, C, D, E), A)) ) ) ).
fof(dt_g1_zmodlat1, axiom,  (! [A, B, C, D, E, F] :  ( (l1_struct_0(A) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(B, B), B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B, B), B)))) )  &  (m1_subset_1(D, B) &  ( (v1_funct_1(E) &  (v1_funct_2(E, k2_zfmisc_1(u1_struct_0(A), B), B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), B), B)))) )  &  (v1_funct_1(F) &  (v1_funct_2(F, k2_zfmisc_1(B, B), u1_struct_0(k2_vectsp_1)) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B, B), u1_struct_0(k2_vectsp_1))))) ) ) ) ) )  =>  (v1_zmodlat1(g1_zmodlat1(A, B, C, D, E, F), A) & l1_zmodlat1(g1_zmodlat1(A, B, C, D, E, F), A)) ) ) ).
fof(dt_g6_algstr_0, axiom,  (! [A, B, C, D, E] :  ( ( (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)))) )  &  ( (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)))) )  &  (m1_subset_1(D, A) & m1_subset_1(E, A)) ) )  =>  (v36_algstr_0(g6_algstr_0(A, B, C, D, E)) & l6_algstr_0(g6_algstr_0(A, B, C, D, E))) ) ) ).
fof(dt_k10_subset_1, axiom,  (! [A, B] : m1_subset_1(k10_subset_1(A, B), B)) ).
fof(dt_k11_binop_2, axiom,  (v1_funct_1(k11_binop_2) &  (v1_funct_2(k11_binop_2, k2_zfmisc_1(k1_numbers, k1_numbers), k1_numbers) & m1_subset_1(k11_binop_2, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_numbers, k1_numbers), k1_numbers)))) ) ).
fof(dt_k1_card_1, axiom,  (! [A] : v1_card_1(k1_card_1(A))) ).
fof(dt_k1_int_3, axiom, l6_algstr_0(k1_int_3)).
fof(dt_k1_numbers, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k1_zmodul03, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  (v1_zmodul03(A) & l1_vectsp_1(A, k1_int_3)) ) ) ) ) ) ) ) ) ) )  => v7_ordinal1(k1_zmodul03(A))) ) ).
fof(dt_k20_binop_2, axiom,  (v1_funct_1(k20_binop_2) &  (v1_funct_2(k20_binop_2, k2_zfmisc_1(k4_numbers, k4_numbers), k4_numbers) & m1_subset_1(k20_binop_2, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_numbers, k4_numbers), k4_numbers)))) ) ).
fof(dt_k22_binop_2, axiom,  (v1_funct_1(k22_binop_2) &  (v1_funct_2(k22_binop_2, k2_zfmisc_1(k4_numbers, k4_numbers), k4_numbers) & m1_subset_1(k22_binop_2, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_numbers, k4_numbers), k4_numbers)))) ) ).
fof(dt_k2_numbers, axiom, $true).
fof(dt_k2_vectsp_1, axiom,  (v36_algstr_0(k2_vectsp_1) & l6_algstr_0(k2_vectsp_1)) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k2_zmodul08, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_zmodul06(A) & l1_vectsp_1(A, k1_int_3)) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k2_zmodul08(A)))  &  (v13_algstr_0(k2_zmodul08(A)) &  (v7_vectsp_1(k2_zmodul08(A), k1_int_3) &  (v8_vectsp_1(k2_zmodul08(A), k1_int_3) &  (v9_vectsp_1(k2_zmodul08(A), k1_int_3) &  (v10_vectsp_1(k2_zmodul08(A), k1_int_3) &  (v11_vectsp_1(k2_zmodul08(A), k1_int_3) &  (v2_rlvect_1(k2_zmodul08(A)) &  (v3_rlvect_1(k2_zmodul08(A)) &  (v4_rlvect_1(k2_zmodul08(A)) & l1_vectsp_1(k2_zmodul08(A), k1_int_3)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k3_numbers, axiom, $true).
fof(dt_k3_zmodlat2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  (v1_zmodul03(A) &  (v2_zmodlat1(A) & l1_zmodlat1(A, k1_int_3)) ) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k3_zmodlat2(A)))  &  (v13_algstr_0(k3_zmodlat2(A)) &  (v8_vectsp_1(k3_zmodlat2(A), k1_int_3) &  (v9_vectsp_1(k3_zmodlat2(A), k1_int_3) &  (v10_vectsp_1(k3_zmodlat2(A), k1_int_3) &  (v11_vectsp_1(k3_zmodlat2(A), k1_int_3) &  (v2_rlvect_1(k3_zmodlat2(A)) &  (v3_rlvect_1(k3_zmodlat2(A)) &  (v4_rlvect_1(k3_zmodlat2(A)) &  (v3_vectsp_7(k3_zmodlat2(A), k1_int_3) &  (v1_zmodul03(k3_zmodlat2(A)) &  (v1_zmodlat1(k3_zmodlat2(A), k1_int_3) &  (v2_zmodlat1(k3_zmodlat2(A)) & l1_zmodlat1(k3_zmodlat2(A), k1_int_3)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k4_card_1, axiom,  (! [A] :  (v1_finset_1(A) => m1_subset_1(k4_card_1(A), k4_ordinal1)) ) ).
fof(dt_k4_numbers, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k6_numbers, axiom, $true).
fof(dt_k7_zmodlat3, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  (v1_zmodul03(A) &  (v2_zmodlat1(A) &  (v4_zmodlat1(A) &  (v1_zmodlat2(A) & l1_zmodlat1(A, k1_int_3)) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (v2_vectsp_7(B, k1_int_3, k3_zmodlat2(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k3_zmodlat2(A))))) )  => m1_subset_1(k7_zmodlat3(A, B), k1_zfmisc_1(u1_struct_0(k2_zmodul08(A))))) ) ).
fof(dt_k9_binop_2, axiom,  (v1_funct_1(k9_binop_2) &  (v1_funct_2(k9_binop_2, k2_zfmisc_1(k1_numbers, k1_numbers), k1_numbers) & m1_subset_1(k9_binop_2, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_numbers, k1_numbers), k1_numbers)))) ) ).
fof(dt_k9_zmodlat3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  (v1_zmodul03(A) &  (v2_zmodlat1(A) &  (v4_zmodlat1(A) &  (v1_zmodlat2(A) & l1_zmodlat1(A, k1_int_3)) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k9_zmodlat3(A)))  &  (v13_algstr_0(k9_zmodlat3(A)) &  (v8_vectsp_1(k9_zmodlat3(A), k1_int_3) &  (v9_vectsp_1(k9_zmodlat3(A), k1_int_3) &  (v10_vectsp_1(k9_zmodlat3(A), k1_int_3) &  (v11_vectsp_1(k9_zmodlat3(A), k1_int_3) &  (v2_rlvect_1(k9_zmodlat3(A)) &  (v3_rlvect_1(k9_zmodlat3(A)) &  (v4_rlvect_1(k9_zmodlat3(A)) &  (v3_vectsp_7(k9_zmodlat3(A), k1_int_3) &  (v1_zmodul03(k9_zmodlat3(A)) &  (v1_zmodlat1(k9_zmodlat3(A), k1_int_3) &  (v2_zmodlat1(k9_zmodlat3(A)) & l1_zmodlat1(k9_zmodlat3(A), k1_int_3)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_l1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l1_vectsp_1, axiom,  (! [A] :  (l1_struct_0(A) =>  (! [B] :  (l1_vectsp_1(B, A) => l2_algstr_0(B)) ) ) ) ).
fof(dt_l1_zmodlat1, axiom,  (! [A] :  (l1_struct_0(A) =>  (! [B] :  (l1_zmodlat1(B, A) => l1_vectsp_1(B, A)) ) ) ) ).
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_l3_algstr_0, axiom,  (! [A] :  (l3_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l3_struct_0, axiom,  (! [A] :  (l3_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_l4_algstr_0, axiom,  (! [A] :  (l4_algstr_0(A) =>  (l3_struct_0(A) & l3_algstr_0(A)) ) ) ).
fof(dt_l4_struct_0, axiom,  (! [A] :  (l4_struct_0(A) =>  (l2_struct_0(A) & l3_struct_0(A)) ) ) ).
fof(dt_l5_algstr_0, axiom,  (! [A] :  (l5_algstr_0(A) =>  (l4_algstr_0(A) & l4_struct_0(A)) ) ) ).
fof(dt_l6_algstr_0, axiom,  (! [A] :  (l6_algstr_0(A) =>  (l2_algstr_0(A) & l5_algstr_0(A)) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_o_1_1_zmodlat3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  (v1_zmodul03(A) &  (v2_zmodlat1(A) &  (v4_zmodlat1(A) &  (v1_zmodlat2(A) & l1_zmodlat1(A, k1_int_3)) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (v2_vectsp_7(o_1_1_zmodlat3(A), k1_int_3, k3_zmodlat2(A)) & m1_subset_1(o_1_1_zmodlat3(A), k1_zfmisc_1(u1_struct_0(k3_zmodlat2(A))))) ) ) ).
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_struct_0, axiom, $true).
fof(dt_u1_vectsp_1, axiom,  (! [A, B] :  ( (l1_struct_0(A) & l1_vectsp_1(B, A))  =>  (v1_funct_1(u1_vectsp_1(A, B)) &  (v1_funct_2(u1_vectsp_1(A, B), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)), u1_struct_0(B)) & m1_subset_1(u1_vectsp_1(A, B), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)), u1_struct_0(B))))) ) ) ) ).
fof(dt_u1_zmodlat1, axiom,  (! [A, B] :  ( (l1_struct_0(A) & l1_zmodlat1(B, A))  =>  (v1_funct_1(u1_zmodlat1(A, B)) &  (v1_funct_2(u1_zmodlat1(A, B), k2_zfmisc_1(u1_struct_0(B), u1_struct_0(B)), u1_struct_0(k2_vectsp_1)) & m1_subset_1(u1_zmodlat1(A, B), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(B)), u1_struct_0(k2_vectsp_1))))) ) ) ) ).
fof(dt_u2_algstr_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  (v1_funct_1(u2_algstr_0(A)) &  (v1_funct_2(u2_algstr_0(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u2_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_u2_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => m1_subset_1(u2_struct_0(A), u1_struct_0(A))) ) ).
fof(dt_u3_struct_0, axiom,  (! [A] :  (l3_struct_0(A) => m1_subset_1(u3_struct_0(A), u1_struct_0(A))) ) ).
fof(existence_l1_algstr_0, axiom,  (? [A] : l1_algstr_0(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l1_vectsp_1, axiom,  (! [A] :  (l1_struct_0(A) =>  (? [B] : l1_vectsp_1(B, A)) ) ) ).
fof(existence_l1_zmodlat1, axiom,  (! [A] :  (l1_struct_0(A) =>  (? [B] : l1_zmodlat1(B, 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_l3_algstr_0, axiom,  (? [A] : l3_algstr_0(A)) ).
fof(existence_l3_struct_0, axiom,  (? [A] : l3_struct_0(A)) ).
fof(existence_l4_algstr_0, axiom,  (? [A] : l4_algstr_0(A)) ).
fof(existence_l4_struct_0, axiom,  (? [A] : l4_struct_0(A)) ).
fof(existence_l5_algstr_0, axiom,  (? [A] : l5_algstr_0(A)) ).
fof(existence_l6_algstr_0, axiom,  (? [A] : l6_algstr_0(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc10_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ( ~ (v1_finset_1(k1_card_1(A)))  & v1_card_1(k1_card_1(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(fc12_binop_2, axiom,  (v1_funct_1(k9_binop_2) &  (v1_funct_2(k9_binop_2, k2_zfmisc_1(k1_numbers, k1_numbers), k1_numbers) & v1_setwiseo(k9_binop_2, k1_numbers)) ) ).
fof(fc12_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k1_zfmisc_1(A))) ) ) ).
fof(fc13_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(A, B))) ) ) ).
fof(fc14_binop_2, axiom,  (v1_funct_1(k20_binop_2) &  (v1_funct_2(k20_binop_2, k2_zfmisc_1(k4_numbers, k4_numbers), k4_numbers) & v1_setwiseo(k20_binop_2, k4_numbers)) ) ).
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_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v1_finset_1(k2_zfmisc_1(A, B))) ) ).
fof(fc17_binop_2, axiom,  (v1_funct_1(k11_binop_2) &  (v1_funct_2(k11_binop_2, k2_zfmisc_1(k1_numbers, k1_numbers), k1_numbers) & v1_setwiseo(k11_binop_2, k1_numbers)) ) ).
fof(fc17_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v1_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc17_gaussint, axiom, v5_card_3(k4_numbers)).
fof(fc19_binop_2, axiom,  (v1_funct_1(k22_binop_2) &  (v1_funct_2(k22_binop_2, k2_zfmisc_1(k4_numbers, k4_numbers), k4_numbers) & v1_setwiseo(k22_binop_2, k4_numbers)) ) ).
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(fc1_card_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v1_xboole_0(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc1_int_3, axiom,  ( ~ (v2_struct_0(k1_int_3))  & v36_algstr_0(k1_int_3)) ).
fof(fc1_membered, axiom, v1_membered(k2_numbers)).
fof(fc1_numbers, axiom,  ~ (v1_xboole_0(k1_numbers)) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc1_zmodlat1, axiom,  (! [A, B, C, D, E, F] :  ( (l1_struct_0(A) &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, B) &  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(B, B), B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B, B), B)))) )  &  ( (v1_funct_1(E) &  (v1_funct_2(E, k2_zfmisc_1(u1_struct_0(A), B), B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), B), B)))) )  &  (v1_funct_1(F) &  (v1_funct_2(F, k2_zfmisc_1(B, B), u1_struct_0(k2_vectsp_1)) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B, B), u1_struct_0(k2_vectsp_1))))) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(g1_zmodlat1(A, B, D, C, E, F)))  & v1_zmodlat1(g1_zmodlat1(A, B, D, C, E, F), A)) ) ) ).
fof(fc1_zmodlat3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  (v1_zmodul03(A) &  (v2_zmodlat1(A) &  (v1_zmodlat2(A) & l1_zmodlat1(A, k1_int_3)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k3_zmodlat2(A)))  &  (v13_algstr_0(k3_zmodlat2(A)) &  (v8_vectsp_1(k3_zmodlat2(A), k1_int_3) &  (v9_vectsp_1(k3_zmodlat2(A), k1_int_3) &  (v10_vectsp_1(k3_zmodlat2(A), k1_int_3) &  (v11_vectsp_1(k3_zmodlat2(A), k1_int_3) &  (v2_rlvect_1(k3_zmodlat2(A)) &  (v3_rlvect_1(k3_zmodlat2(A)) &  (v4_rlvect_1(k3_zmodlat2(A)) &  (v3_vectsp_7(k3_zmodlat2(A), k1_int_3) &  (v1_zmodul03(k3_zmodlat2(A)) &  (v1_zmodlat1(k3_zmodlat2(A), k1_int_3) &  (v2_zmodlat1(k3_zmodlat2(A)) & v1_zmodlat2(k3_zmodlat2(A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(fc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v8_ordinal1(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc2_int_3, axiom, v5_membered(u1_struct_0(k1_int_3))).
fof(fc2_membered, axiom, v2_membered(k6_numbers)).
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_zmodlat2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  (v1_zmodul03(A) &  (v2_zmodlat1(A) & l1_zmodlat1(A, k1_int_3)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k3_zmodlat2(A)))  &  ( ~ (v7_struct_0(k3_zmodlat2(A)))  &  (v13_algstr_0(k3_zmodlat2(A)) &  (v8_vectsp_1(k3_zmodlat2(A), k1_int_3) &  (v9_vectsp_1(k3_zmodlat2(A), k1_int_3) &  (v10_vectsp_1(k3_zmodlat2(A), k1_int_3) &  (v11_vectsp_1(k3_zmodlat2(A), k1_int_3) &  (v2_rlvect_1(k3_zmodlat2(A)) &  (v3_rlvect_1(k3_zmodlat2(A)) &  (v4_rlvect_1(k3_zmodlat2(A)) &  (v3_vectsp_7(k3_zmodlat2(A), k1_int_3) &  (v1_zmodul03(k3_zmodlat2(A)) &  (v1_zmodlat1(k3_zmodlat2(A), k1_int_3) & v2_zmodlat1(k3_zmodlat2(A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(fc31_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v5_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc3_binop_2, axiom,  (v1_funct_1(k9_binop_2) &  (v1_funct_2(k9_binop_2, k2_zfmisc_1(k1_numbers, k1_numbers), k1_numbers) &  (v1_binop_1(k9_binop_2, k1_numbers) & v2_binop_1(k9_binop_2, k1_numbers)) ) ) ).
fof(fc3_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v1_xboole_0(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc3_int_3, axiom, v4_vectsp_1(k1_int_3)).
fof(fc3_membered, axiom, v3_membered(k1_numbers)).
fof(fc3_numbers, axiom,  ~ (v1_xboole_0(k3_numbers)) ).
fof(fc4_binop_2, axiom,  (v1_funct_1(k11_binop_2) &  (v1_funct_2(k11_binop_2, k2_zfmisc_1(k1_numbers, k1_numbers), k1_numbers) &  (v1_binop_1(k11_binop_2, k1_numbers) & v2_binop_1(k11_binop_2, k1_numbers)) ) ) ).
fof(fc4_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v8_ordinal1(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc4_int_3, axiom,  ( ~ (v6_struct_0(k1_int_3))  &  (v13_algstr_0(k1_int_3) &  (v3_group_1(k1_int_3) &  (v5_group_1(k1_int_3) &  (v2_rlvect_1(k1_int_3) &  (v3_rlvect_1(k1_int_3) &  (v4_rlvect_1(k1_int_3) &  (v5_vectsp_1(k1_int_3) & v1_vectsp_2(k1_int_3)) ) ) ) ) ) ) ) ).
fof(fc4_membered, axiom, v4_membered(k3_numbers)).
fof(fc4_numbers, axiom,  ~ (v1_xboole_0(k4_numbers)) ).
fof(fc4_vectsp_1, axiom,  ( ~ (v2_struct_0(k2_vectsp_1))  & v36_algstr_0(k2_vectsp_1)) ).
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_int_3, axiom, v1_int_3(k1_int_3)).
fof(fc5_membered, axiom, v5_membered(k4_numbers)).
fof(fc5_numbers, axiom,  ~ (v1_xboole_0(k6_numbers)) ).
fof(fc5_vectsp_1, axiom, v3_membered(u1_struct_0(k2_vectsp_1))).
fof(fc5_zmodlat2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  (v1_zmodul03(A) &  (v2_zmodlat1(A) &  (v4_zmodlat1(A) & l1_zmodlat1(A, k1_int_3)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k3_zmodlat2(A)))  &  (v13_algstr_0(k3_zmodlat2(A)) &  (v8_vectsp_1(k3_zmodlat2(A), k1_int_3) &  (v9_vectsp_1(k3_zmodlat2(A), k1_int_3) &  (v10_vectsp_1(k3_zmodlat2(A), k1_int_3) &  (v11_vectsp_1(k3_zmodlat2(A), k1_int_3) &  (v2_rlvect_1(k3_zmodlat2(A)) &  (v3_rlvect_1(k3_zmodlat2(A)) &  (v4_rlvect_1(k3_zmodlat2(A)) &  (v3_vectsp_7(k3_zmodlat2(A), k1_int_3) &  (v1_zmodul03(k3_zmodlat2(A)) &  (v1_zmodlat1(k3_zmodlat2(A), k1_int_3) &  (v2_zmodlat1(k3_zmodlat2(A)) & v4_zmodlat1(k3_zmodlat2(A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(fc5_zmodlat3, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  (v1_zmodul03(A) &  (v2_zmodlat1(A) &  (v4_zmodlat1(A) &  (v1_zmodlat2(A) & l1_zmodlat1(A, k1_int_3)) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (v2_vectsp_7(B, k1_int_3, k3_zmodlat2(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k3_zmodlat2(A))))) )  => v1_finset_1(k7_zmodlat3(A, B))) ) ).
fof(fc5_zmodul08, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  (v1_zmodul03(A) & l1_vectsp_1(A, k1_int_3)) ) ) ) ) ) ) ) ) ) ) )  =>  (v7_ordinal1(k1_zmodul03(A)) &  ~ (v8_ordinal1(k1_zmodul03(A))) ) ) ) ).
fof(fc6_card_1, axiom, v1_card_1(k4_ordinal1)).
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_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(fc6_vectsp_1, axiom,  (v36_algstr_0(k2_vectsp_1) & v4_vectsp_1(k2_vectsp_1)) ).
fof(fc6_zmodlat3, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  (v1_zmodul03(A) &  (v2_zmodlat1(A) &  (v4_zmodlat1(A) &  (v1_zmodlat2(A) & l1_zmodlat1(A, k1_int_3)) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (v2_vectsp_7(B, k1_int_3, k3_zmodlat2(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k3_zmodlat2(A))))) )  =>  ~ (v1_xboole_0(k7_zmodlat3(A, B))) ) ) ).
fof(fc6_zmodul08, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_zmodul06(A) & l1_vectsp_1(A, k1_int_3)) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k2_zmodul08(A)))  &  (v13_algstr_0(k2_zmodul08(A)) &  (v7_vectsp_1(k2_zmodul08(A), k1_int_3) &  (v8_vectsp_1(k2_zmodul08(A), k1_int_3) &  (v9_vectsp_1(k2_zmodul08(A), k1_int_3) &  (v10_vectsp_1(k2_zmodul08(A), k1_int_3) &  (v11_vectsp_1(k2_zmodul08(A), k1_int_3) &  (v2_rlvect_1(k2_zmodul08(A)) &  (v3_rlvect_1(k2_zmodul08(A)) &  (v4_rlvect_1(k2_zmodul08(A)) & v2_zmodul08(k2_zmodul08(A))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(fc7_binop_2, axiom,  (v1_funct_1(k20_binop_2) &  (v1_funct_2(k20_binop_2, k2_zfmisc_1(k4_numbers, k4_numbers), k4_numbers) &  (v1_binop_1(k20_binop_2, k4_numbers) & v2_binop_1(k20_binop_2, k4_numbers)) ) ) ).
fof(fc7_card_1, axiom, v2_card_1(k4_ordinal1)).
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_vectsp_1, axiom,  (v36_algstr_0(k2_vectsp_1) & v1_group_1(k2_vectsp_1)) ).
fof(fc7_zmodlat3, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  (v1_zmodul03(A) &  (v2_zmodlat1(A) &  (v4_zmodlat1(A) &  (v1_zmodlat2(A) & l1_zmodlat1(A, k1_int_3)) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (v2_vectsp_7(B, k1_int_3, k3_zmodlat2(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k3_zmodlat2(A))))) )  => v1_vectsp_7(k7_zmodlat3(A, B), k1_int_3, k2_zmodul08(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_binop_2, axiom,  (v1_funct_1(k22_binop_2) &  (v1_funct_2(k22_binop_2, k2_zfmisc_1(k4_numbers, k4_numbers), k4_numbers) &  (v1_binop_1(k22_binop_2, k4_numbers) & v2_binop_1(k22_binop_2, k4_numbers)) ) ) ).
fof(fc8_card_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc8_int_3, axiom,  ~ (v8_struct_0(k1_int_3)) ).
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_vectsp_1, axiom,  ( ~ (v6_struct_0(k2_vectsp_1))  &  (v13_algstr_0(k2_vectsp_1) &  (v33_algstr_0(k2_vectsp_1) &  (v36_algstr_0(k2_vectsp_1) &  (v2_rlvect_1(k2_vectsp_1) &  (v3_rlvect_1(k2_vectsp_1) &  (v4_rlvect_1(k2_vectsp_1) &  (v3_group_1(k2_vectsp_1) &  (v5_group_1(k2_vectsp_1) &  (v3_vectsp_1(k2_vectsp_1) &  (v5_vectsp_1(k2_vectsp_1) & v6_vectsp_1(k2_vectsp_1)) ) ) ) ) ) ) ) ) ) ) ).
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_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_vectsp_1, axiom,  (! [A, B, C, D, E] :  ( (l1_struct_0(A) &  ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(B, B), B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B, B), B)))) )  &  (m1_subset_1(D, B) &  (v1_funct_1(E) &  (v1_funct_2(E, k2_zfmisc_1(u1_struct_0(A), B), B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), B), B)))) ) ) ) ) )  =>  ( ~ (v2_struct_0(g1_vectsp_1(A, B, C, D, E)))  & v7_vectsp_1(g1_vectsp_1(A, B, C, D, E), A)) ) ) ).
fof(fc9_zmodul08, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_zmodul06(A) & l1_vectsp_1(A, k1_int_3)) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k2_zmodul08(A)))  &  (v13_algstr_0(k2_zmodul08(A)) &  (v7_vectsp_1(k2_zmodul08(A), k1_int_3) &  (v8_vectsp_1(k2_zmodul08(A), k1_int_3) &  (v9_vectsp_1(k2_zmodul08(A), k1_int_3) &  (v10_vectsp_1(k2_zmodul08(A), k1_int_3) &  (v11_vectsp_1(k2_zmodul08(A), k1_int_3) &  (v2_rlvect_1(k2_zmodul08(A)) &  (v3_rlvect_1(k2_zmodul08(A)) &  (v4_rlvect_1(k2_zmodul08(A)) & v3_zmodul06(k2_zmodul08(A))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(free_g1_vectsp_1, axiom,  (! [A, B, C, D, E] :  ( (l1_struct_0(A) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(B, B), B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B, B), B)))) )  &  (m1_subset_1(D, B) &  (v1_funct_1(E) &  (v1_funct_2(E, k2_zfmisc_1(u1_struct_0(A), B), B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), B), B)))) ) ) ) )  =>  (! [F, G, H, I, J] :  (g1_vectsp_1(A, B, C, D, E)=g1_vectsp_1(F, G, H, I, J) =>  (A=F &  (B=G &  (C=H &  (D=I & E=J) ) ) ) ) ) ) ) ).
fof(free_g1_zmodlat1, axiom,  (! [A, B, C, D, E, F] :  ( (l1_struct_0(A) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(B, B), B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B, B), B)))) )  &  (m1_subset_1(D, B) &  ( (v1_funct_1(E) &  (v1_funct_2(E, k2_zfmisc_1(u1_struct_0(A), B), B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), B), B)))) )  &  (v1_funct_1(F) &  (v1_funct_2(F, k2_zfmisc_1(B, B), u1_struct_0(k2_vectsp_1)) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B, B), u1_struct_0(k2_vectsp_1))))) ) ) ) ) )  =>  (! [G, H, I, J, K, L] :  (g1_zmodlat1(A, B, C, D, E, F)=g1_zmodlat1(G, H, I, J, K, L) =>  (A=G &  (B=H &  (C=I &  (D=J &  (E=K & F=L) ) ) ) ) ) ) ) ) ).
fof(free_g6_algstr_0, axiom,  (! [A, B, C, D, E] :  ( ( (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)))) )  &  ( (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)))) )  &  (m1_subset_1(D, A) & m1_subset_1(E, A)) ) )  =>  (! [F, G, H, I, J] :  (g6_algstr_0(A, B, C, D, E)=g6_algstr_0(F, G, H, I, J) =>  (A=F &  (B=G &  (C=H &  (D=I & E=J) ) ) ) ) ) ) ) ).
fof(projectivity_k1_card_1, axiom,  (! [A] : k1_card_1(k1_card_1(A))=k1_card_1(A)) ).
fof(projectivity_k4_card_1, axiom,  (! [A] :  (v1_finset_1(A) => k4_card_1(k4_card_1(A))=k4_card_1(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_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v3_card_1(B, A) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ).
fof(rc10_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) ) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_finseq_1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc11_vectsp_1, axiom,  (? [A] :  (l4_algstr_0(A) &  ( ~ (v2_struct_0(A))  & v4_vectsp_1(A)) ) ) ).
fof(rc12_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ).
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(rc14_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v2_funct_1(A) &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(rc16_finseq_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) &  (v6_valued_0(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ) ).
fof(rc1_card_1, axiom,  (? [A] : v1_card_1(A)) ).
fof(rc1_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A))) &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ).
fof(rc1_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_finset_1(A)) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_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_int_1, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v1_xcmplx_0(A) &  (v1_xreal_0(A) & v1_int_1(A)) ) ) ) ).
fof(rc1_int_3, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v36_algstr_0(A) &  (v1_group_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) &  (v2_vectsp_1(A) &  (v3_vectsp_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v6_vectsp_1(A) &  (v1_vectsp_2(A) & v1_int_3(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc1_nat_1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_rat_1, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v1_xcmplx_0(A) &  (v1_xreal_0(A) & v1_rat_1(A)) ) ) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_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_zmodlat1, axiom,  (! [A] :  (l1_struct_0(A) =>  (? [B] :  (l1_zmodlat1(B, A) & v1_zmodlat1(B, 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_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) & v1_finseq_1(B)) ) ) ) ) ) ).
fof(rc2_finset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_finset_1(B)) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_int_1, axiom,  (? [A] : v1_int_1(A)) ).
fof(rc2_int_3, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v6_struct_0(A) &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v36_algstr_0(A) &  (v1_group_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) &  (v2_vectsp_1(A) &  (v3_vectsp_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & v6_vectsp_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_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_rat_1, axiom,  (? [A] : v1_rat_1(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_valued_0, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v4_valued_0(A) &  (v5_valued_0(A) & v6_valued_0(A)) ) ) ) ) ) ) ).
fof(rc2_vectsp_1, axiom,  (? [A] :  (l5_algstr_0(A) &  ( ~ (v2_struct_0(A))  & v4_vectsp_1(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_zmodlat1, axiom,  (! [A] :  (l1_struct_0(A) =>  (? [B] :  (l1_zmodlat1(B, A) &  ( ~ (v2_struct_0(B))  & v1_zmodlat1(B, A)) ) ) ) ) ).
fof(rc2_zmodul03, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l1_vectsp_1(A, k1_int_3)) ) ) ) ) ) ) ) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  (v1_finset_1(B) & v1_vectsp_7(B, k1_int_3, A)) ) ) ) ) ).
fof(rc3_card_1, axiom,  (? [A] :  ~ (v1_finset_1(A)) ) ).
fof(rc3_finset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc3_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ).
fof(rc3_int_1, axiom,  (? [A] : v2_int_1(A)) ).
fof(rc3_int_3, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v8_struct_0(A))  &  (v13_algstr_0(A) &  (v36_algstr_0(A) &  (v1_group_1(A) &  (v3_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) &  (v2_vectsp_1(A) &  (v3_vectsp_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & v6_vectsp_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_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_relat_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, 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_vectsp_1, axiom,  (? [A] :  (l3_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v3_group_1(A) & v5_group_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_zmodlat1, axiom,  (? [A] :  (l1_zmodlat1(A, k1_int_3) &  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & v1_zmodlat1(A, k1_int_3)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc4_card_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc4_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ).
fof(rc4_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(rc4_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(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_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
fof(rc4_valued_0, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A))) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v3_funct_1(B) & v1_funct_2(B, k4_ordinal1, A)) ) ) ) ) ) ) ) ).
fof(rc4_vectsp_1, axiom,  (? [A] :  (l4_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v1_group_1(A) &  (v3_group_1(A) & v5_group_1(A)) ) ) ) ) ).
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(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_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v3_finseq_1(A)) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_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_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc5_vectsp_1, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v36_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v3_vectsp_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & v6_vectsp_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_zmodul03, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) & l1_vectsp_1(A, k1_int_3)) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v2_vectsp_7(B, k1_int_3, 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_finseq_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) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(rc6_finset_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ).
fof(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc6_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_vectsp_1, axiom,  (! [A] :  (l1_struct_0(A) =>  (? [B] :  (l1_vectsp_1(B, A) & v7_vectsp_1(B, A)) ) ) ) ).
fof(rc7_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] : v3_card_1(B, A)) ) ) ).
fof(rc7_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ) ).
fof(rc7_finset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (? [C] :  ( ~ (v1_xboole_0(C))  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ) ) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc7_vectsp_1, axiom,  (! [A] :  (l1_struct_0(A) =>  (? [B] :  (l1_vectsp_1(B, A) &  ( ~ (v2_struct_0(B))  & v7_vectsp_1(B, A)) ) ) ) ) ).
fof(rc7_zmodlat1, axiom,  (? [A] :  (l1_zmodlat1(A, k1_int_3) &  ( ~ (v2_struct_0(A))  & v2_zmodlat1(A)) ) ) ).
fof(rc7_zmodul06, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v3_group_1(A) &  (v5_vectsp_1(A) &  (v6_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  =>  (? [B] :  (l1_vectsp_1(B, A) &  ( ~ (v2_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v13_algstr_0(B) &  (v7_vectsp_1(B, A) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) & v4_rlvect_1(B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_finset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_zfmisc_1(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc8_vectsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (? [B] :  (l1_vectsp_1(B, A) &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v7_vectsp_1(B, A) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) & v11_vectsp_1(B, 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_finseq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ).
fof(rc9_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) & v5_finset_1(A)) ) ) ).
fof(rc9_funct_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) ) ) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rd1_card_1, axiom,  (! [A] :  (v1_card_1(A) => k1_card_1(A)=A) ) ).
fof(rd1_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) => k10_subset_1(A, k4_ordinal1)=A) ) ).
fof(rd1_rat_1, axiom,  (! [A] :  (v1_rat_1(A) => k10_subset_1(A, k3_numbers)=A) ) ).
fof(rd1_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => k10_subset_1(B, A)=B) ) ).
fof(rd1_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k10_subset_1(A, k2_numbers)=A) ) ).
fof(rd1_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => k10_subset_1(A, k1_numbers)=A) ) ).
fof(rd1_xxreal_0, axiom,  (! [A] :  (v1_xxreal_0(A) => k10_subset_1(A, k6_numbers)=A) ) ).
fof(rd5_int_1, axiom,  (! [A] :  (v1_int_1(A) => k10_subset_1(A, k4_numbers)=A) ) ).
fof(redefinition_k4_card_1, axiom,  (! [A] :  (v1_finset_1(A) => k4_card_1(A)=k1_card_1(A)) ) ).
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(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
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(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t31_zmodlat3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  (v1_zmodul03(A) &  (v2_zmodlat1(A) &  (v4_zmodlat1(A) &  (v1_zmodlat2(A) & l1_zmodlat1(A, k1_int_3)) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  ( (v2_vectsp_7(B, k1_int_3, k3_zmodlat2(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k3_zmodlat2(A)))))  => k4_card_1(B)=k1_card_1(k7_zmodlat3(A, B))) ) ) ) ).
fof(t39_zmodlat3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  (v1_zmodul03(A) &  (v2_zmodlat1(A) &  (v4_zmodlat1(A) &  (v1_zmodlat2(A) & l1_zmodlat1(A, k1_int_3)) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  ( (v2_vectsp_7(B, k1_int_3, k3_zmodlat2(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k3_zmodlat2(A)))))  =>  (v2_vectsp_7(k7_zmodlat3(A, B), k1_int_3, k9_zmodlat3(A)) & m1_subset_1(k7_zmodlat3(A, B), k1_zfmisc_1(u1_struct_0(k9_zmodlat3(A))))) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t42_zmodlat2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v8_vectsp_1(A, k1_int_3) &  (v9_vectsp_1(A, k1_int_3) &  (v10_vectsp_1(A, k1_int_3) &  (v11_vectsp_1(A, k1_int_3) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_7(A, k1_int_3) &  (v1_zmodul03(A) &  (v2_zmodlat1(A) & l1_zmodlat1(A, k1_int_3)) ) ) ) ) ) ) ) ) ) ) )  => k1_zmodul03(A)=k1_zmodul03(k3_zmodlat2(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_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)) ) ) ) ) ).
