% Mizar problem: t31_matrixj2,matrixj2,3890,5 
fof(t31_matrixj2, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v2_polynom5(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v13_algstr_0(B) &  (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) &  (v1_matrlin(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(B)) &  (v13_vectsp_1(C, B, B) &  (v1_mod_2(C, A, B, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(B))))) ) ) )  =>  (? [D] :  ( (v2_relat_1(D) &  (v1_matrixj2(D, A) & m2_finseq_1(D, k3_finseq_2(k3_finseq_2(u1_struct_0(A))))) )  &  (? [E] :  (m1_matrlin(E, A, B) &  (k1_matrlin2(A, B, B, C, E, E)=k20_matrixj1(u1_struct_0(A), k4_struct_0(A), D) &  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (m1_vectsp11(F, A, B, C) <=>  (? [G] :  (v7_ordinal1(G) &  (r2_tarski(G, k4_finseq_1(D)) & k14_matrixj1(u1_struct_0(A), D, G)=k2_matrixj2(A, F, k3_finseq_1(k14_matrixj1(u1_struct_0(A), D, G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_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_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_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_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_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_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_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_finseq_1, axiom,  (! [A] :  (m1_finseq_1(A, k4_ordinal1) => v6_valued_0(A)) ) ).
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_finseq_1, axiom,  (! [A] :  (m1_finseq_1(A, k4_numbers) => v5_valued_0(A)) ) ).
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_finseq_1, axiom,  (! [A] :  (m1_finseq_1(A, k3_numbers) => v4_valued_0(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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc1_finseq_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & v7_ordinal1(B))  =>  (! [C] :  (m1_subset_1(C, k4_finseq_2(B, A)) => v3_card_1(C, B)) ) ) ) ).
fof(cc1_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_finset_1(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_matrix13, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(k4_ordinal1)) =>  ( (v1_finset_1(A) & v1_setfam_1(A))  => v3_finseq_1(A)) ) ) ).
fof(cc1_matrixj1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_finseq_1(B, k3_finseq_2(k3_finseq_2(A))) =>  (v2_matrixj1(B, A) => v1_matrixj1(B, A)) ) ) ) ) ).
fof(cc1_matrixj2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_finseq_1(B, k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) =>  (v1_matrixj2(B, A) => v2_matrixj1(B, u1_struct_0(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_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_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_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_finseq_1, axiom,  (! [A] :  (m1_finseq_1(A, k1_numbers) => v3_valued_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_finseq_1, axiom,  (! [A] :  (m1_finseq_1(A, k2_numbers) => v1_valued_0(A)) ) ).
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_finseq_1, axiom,  (! [A] :  (m1_finseq_1(A, k6_numbers) => v2_valued_0(A)) ) ).
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_finseq_2, axiom,  (! [A] :  (! [B] :  (m1_finseq_2(B, A) => v4_funct_1(B)) ) ) ).
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_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_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_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_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_vectsp_9, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) &  (v1_matrlin(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) ) )  =>  (! [C] :  (m1_vectsp_4(C, A, B) => v1_matrlin(C, 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(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_finseq_1, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, A) => v5_relat_1(B, A)) ) ) ).
fof(cc3_finseq_2, axiom,  (! [A] :  (! [B] :  (m1_finseq_2(B, A) => v4_finseq_1(B)) ) ) ).
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_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_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_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_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(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_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_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_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_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_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_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(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_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(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_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_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_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_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(commutativity_k1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_subset_1(B, k4_ordinal1))  => k1_nat_1(A, B)=k1_nat_1(B, A)) ) ).
fof(commutativity_k2_vectsp_5, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  &  (m1_vectsp_4(C, A, B) & m1_vectsp_4(D, A, B)) ) )  => k2_vectsp_5(A, B, C, D)=k2_vectsp_5(A, B, D, C)) ) ).
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(d16_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) )  => k16_finseq_1(A, B)=k5_relat_1(B, k2_finseq_1(A))) ) ) ) ).
fof(d1_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => k1_finseq_1(A)=a_1_0_finseq_1(A)) ) ).
fof(d1_matrixj2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (v7_ordinal1(C) =>  (! [D] :  ( (v1_matrix_0(D) & m2_finseq_1(D, k3_finseq_2(u1_struct_0(A))))  =>  (D=k1_matrixj2(A, B, C) <=>  (k3_finseq_1(D)=C &  (k1_matrix_0(D)=C &  (! [E] :  (v7_ordinal1(E) =>  (! [F] :  (v7_ordinal1(F) =>  (r2_hidden(k4_tarski(E, F), k2_matrix_0(D)) =>  ( (E=F => k3_matrix_0(u1_struct_0(A), D, E, F)=B)  &  ( (k1_nat_1(E, 1)=F => k3_matrix_0(u1_struct_0(A), D, E, F)=k1_group_1(A))  &  ~ ( ( ~ (E=F)  &  ( ~ (k1_nat_1(E, 1)=F)  &  ~ (k3_matrix_0(u1_struct_0(A), D, E, F)=k4_struct_0(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_matrlin2, axiom,  (! [A] :  (l1_struct_0(A) =>  (! [B] :  (v1_relat_1(B) => k2_matrlin2(A, B)=k5_relat_1(B, u1_struct_0(A))) ) ) ) ).
fof(d1_vectsp11, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A))  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(B))))) )  =>  (v1_vectsp11(C, A, B) <=>  (? [D] :  (m1_subset_1(D, u1_struct_0(B)) &  (? [E] :  (m1_subset_1(E, u1_struct_0(A)) &  ( ~ (D=k4_struct_0(B))  & k3_funct_2(u1_struct_0(B), u1_struct_0(B), C, D)=k3_vectsp_1(A, B, E, D)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_matrix_0, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (v7_ordinal1(B) =>  (! [C] :  (v7_ordinal1(C) =>  (! [D] :  ( (v1_matrix_0(D) & m2_finseq_1(D, k3_finseq_2(A)))  =>  (v2_matrix_0(D, A, B, C) <=>  (k3_finseq_1(D)=B &  (! [E] :  (m2_finseq_1(E, A) =>  (r2_tarski(E, k10_xtuple_0(D)) => k3_finseq_1(E)=C) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_vectsp11, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A))  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(B))))) )  =>  (v1_vectsp11(C, A, B) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (m1_vectsp11(D, A, B, C) <=>  (? [E] :  (m1_subset_1(E, u1_struct_0(B)) &  ( ~ (E=k4_struct_0(B))  & k3_funct_2(u1_struct_0(B), u1_struct_0(B), C, E)=k3_vectsp_1(A, B, D, E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (! [B] :  (m1_subset_1(B, k4_ordinal1) =>  (B=k3_finseq_1(A) <=> k2_finseq_1(B)=k9_xtuple_0(A)) ) ) ) ) ).
fof(d3_matrixj2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  ( (v1_matrixj2(C, A) & m2_finseq_1(C, k3_finseq_2(k3_finseq_2(u1_struct_0(A)))))  =>  (m1_matrixj2(C, A, B) <=>  (! [D] :  (v7_ordinal1(D) =>  ~ ( (r2_tarski(D, k4_finseq_1(C)) &  (! [E] :  (v7_ordinal1(E) =>  ~ (k14_matrixj1(u1_struct_0(A), C, D)=k2_matrixj2(A, B, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d4_matrix_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finseq_1(A) & v1_matrix_0(A)) ) )  => k2_matrix_0(A)=k2_zfmisc_1(k4_finseq_1(A), k2_finseq_1(k1_matrix_0(A)))) ) ).
fof(d4_struct_0, axiom,  (! [A] :  (l1_struct_0(A) => k3_struct_0(A)=k6_partfun1(u1_struct_0(A))) ) ).
fof(d4_vectsp_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  => k2_vectsp_4(A, B)=g1_vectsp_1(A, u1_struct_0(B), u1_algstr_0(B), u2_struct_0(B), u1_vectsp_1(A, B))) ) ) ) ).
fof(d4_vectsp_5, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  =>  (! [C] :  (m1_vectsp_4(C, A, B) =>  (! [D] :  (m1_vectsp_4(D, A, B) =>  (r1_vectsp_5(A, B, C, D) <=>  (g1_vectsp_1(A, u1_struct_0(B), u1_algstr_0(B), u2_struct_0(B), u1_vectsp_1(A, B))=k1_vectsp_5(A, B, C, D) & k2_vectsp_5(A, B, C, D)=k1_vectsp_4(A, B)) ) ) ) ) ) ) ) ) ) ).
fof(d5_finseq_1, axiom,  (! [A] : k5_finseq_1(A)=k1_tarski(k4_tarski(1, A))) ).
fof(d5_matrixj1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, A) =>  (! [C] :  ( (v1_matrixj1(C, A) & m2_finseq_1(C, k3_finseq_2(k3_finseq_2(A))))  =>  (! [D] :  ( (v1_matrix_0(D) & m2_finseq_1(D, k3_finseq_2(A)))  =>  (D=k12_matrixj1(A, B, C) <=>  (k3_finseq_1(D)=k1_wsierp_1(k10_matrixj1(A, C)) &  (k1_matrix_0(D)=k1_wsierp_1(k11_matrixj1(A, C)) &  (! [E] :  (v7_ordinal1(E) =>  (! [F] :  (v7_ordinal1(F) =>  (r2_hidden(k4_tarski(E, F), k2_matrix_0(D)) =>  ( ( ~ ( ( ~ (r1_xxreal_0(F, k1_wsierp_1(k17_finseq_1(k4_ordinal1, k7_nat_d(k1_matrixj1(k10_matrixj1(A, C), E), 1), k11_matrixj1(A, C)))))  & r1_xxreal_0(F, k1_wsierp_1(k17_finseq_1(k4_ordinal1, k1_matrixj1(k10_matrixj1(A, C), E), k11_matrixj1(A, C))))) )  => k3_matrix_0(A, D, E, F)=B)  &  (r1_xxreal_0(F, k1_wsierp_1(k17_finseq_1(k4_ordinal1, k1_matrixj1(k10_matrixj1(A, C), E), k11_matrixj1(A, C)))) =>  (r1_xxreal_0(F, k1_wsierp_1(k17_finseq_1(k4_ordinal1, k7_nat_d(k1_matrixj1(k10_matrixj1(A, C), E), 1), k11_matrixj1(A, C)))) | k3_matrix_0(A, D, E, F)=k3_matrix_0(A, k2_matrixj1(A, C, k1_matrixj1(k10_matrixj1(A, C), E)), k7_nat_d(E, k1_wsierp_1(k17_finseq_1(k4_ordinal1, k7_nat_d(k1_matrixj1(k10_matrixj1(A, C), E), 1), k10_matrixj1(A, C)))), k7_nat_d(F, k1_wsierp_1(k17_finseq_1(k4_ordinal1, k7_nat_d(k1_matrixj1(k10_matrixj1(A, C), E), 1), k11_matrixj1(A, C)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_finseq_1, axiom,  (! [A] : k6_finseq_1(A)=k1_xboole_0) ).
fof(d6_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => k4_struct_0(A)=u2_struct_0(A)) ) ).
fof(d7_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) )  =>  (! [C] :  ( (v1_relat_1(C) &  (v1_funct_1(C) & v1_finseq_1(C)) )  =>  (C=k7_finseq_1(A, B) <=>  (k4_finseq_1(C)=k2_finseq_1(k1_nat_1(k3_finseq_1(A), k3_finseq_1(B))) &  ( (! [D] :  (v7_ordinal1(D) =>  (r2_tarski(D, k4_finseq_1(A)) => k1_funct_1(C, D)=k1_funct_1(A, D)) ) )  &  (! [D] :  (v7_ordinal1(D) =>  (r2_tarski(D, k4_finseq_1(B)) => k1_funct_1(C, k2_xcmplx_0(k3_finseq_1(A), D))=k1_funct_1(B, D)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_struct_0, axiom,  (! [A] :  (l3_struct_0(A) => k5_struct_0(A)=u3_struct_0(A)) ) ).
fof(d9_finseq_1, axiom,  (! [A] :  (! [B] : k10_finseq_1(A, B)=k7_finseq_1(k9_finseq_1(A), k9_finseq_1(B))) ) ).
fof(d9_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v2_relat_1(A) <=>  (! [B] :  ~ ( (r2_hidden(B, k9_xtuple_0(A)) & v1_xboole_0(k1_funct_1(A, B))) ) ) ) ) ) ).
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_k10_finseq_1, axiom, $true).
fof(dt_k10_matrixj1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  (v1_matrixj1(B, A) & m1_finseq_1(B, k3_finseq_2(k3_finseq_2(A)))) )  => m2_finseq_2(k10_matrixj1(A, B), k4_ordinal1, k4_finseq_2(k3_finseq_1(B), k4_ordinal1))) ) ).
fof(dt_k10_matrlin, axiom,  (! [A, B, C, D, E, F] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) &  (v1_matrlin(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v8_vectsp_1(C, A) &  (v9_vectsp_1(C, A) &  (v10_vectsp_1(C, A) &  (v11_vectsp_1(C, A) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v1_matrlin(C, A) & l1_vectsp_1(C, A)) ) ) ) ) ) ) ) ) )  &  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  &  (m1_finseq_1(E, u1_struct_0(B)) & m1_matrlin(F, A, C)) ) ) ) )  =>  (v1_matrix_0(k10_matrlin(A, B, C, D, E, F)) & m2_finseq_1(k10_matrlin(A, B, C, D, E, F), k3_finseq_2(u1_struct_0(A)))) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k11_matrixj1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  (v1_matrixj1(B, A) & m1_finseq_1(B, k3_finseq_2(k3_finseq_2(A)))) )  => m2_finseq_2(k11_matrixj1(A, B), k4_ordinal1, k4_finseq_2(k3_finseq_1(B), k4_ordinal1))) ) ).
fof(dt_k12_matrixj1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) &  (v1_matrixj1(C, A) & m1_finseq_1(C, k3_finseq_2(k3_finseq_2(A)))) ) )  =>  (v1_matrix_0(k12_matrixj1(A, B, C)) & m2_finseq_1(k12_matrixj1(A, B, C), k3_finseq_2(A))) ) ) ).
fof(dt_k13_finseq_1, axiom, $true).
fof(dt_k13_matrixj1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) &  (v1_matrixj1(C, A) & m1_finseq_1(C, k3_finseq_2(k3_finseq_2(A)))) ) )  =>  (v1_matrix_0(k13_matrixj1(A, B, C)) &  (v2_matrix_0(k13_matrixj1(A, B, C), A, k1_wsierp_1(k10_matrixj1(A, C)), k1_wsierp_1(k11_matrixj1(A, C))) & m2_finseq_1(k13_matrixj1(A, B, C), k3_finseq_2(A))) ) ) ) ).
fof(dt_k14_matrixj1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (v2_matrixj1(B, A) & m1_finseq_1(B, k3_finseq_2(k3_finseq_2(A)))) )  =>  (v1_matrix_0(k14_matrixj1(A, B, C)) &  (v2_matrix_0(k14_matrixj1(A, B, C), A, k3_finseq_1(k2_matrixj1(A, B, C)), k3_finseq_1(k2_matrixj1(A, B, C))) & m2_finseq_1(k14_matrixj1(A, B, C), k3_finseq_2(A))) ) ) ) ).
fof(dt_k15_matrixj1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v2_matrixj1(B, A) & m1_finseq_1(B, k3_finseq_2(k3_finseq_2(A))))  &  (v2_matrixj1(C, A) & m1_finseq_1(C, k3_finseq_2(k3_finseq_2(A)))) ) )  =>  (v2_matrixj1(k15_matrixj1(A, B, C), A) & m2_finseq_1(k15_matrixj1(A, B, C), k3_finseq_2(k3_finseq_2(A)))) ) ) ).
fof(dt_k16_finseq_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) )  =>  (v1_relat_1(k16_finseq_1(A, B)) &  (v1_funct_1(k16_finseq_1(A, B)) & v1_finseq_1(k16_finseq_1(A, B))) ) ) ) ).
fof(dt_k16_matrixj1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (v7_ordinal1(B) &  (v1_matrix_0(C) &  (v2_matrix_0(C, A, B, B) & m1_finseq_1(C, k3_finseq_2(A))) ) ) )  =>  (v2_matrixj1(k16_matrixj1(A, B, C), A) & m2_finseq_1(k16_matrixj1(A, B, C), k3_finseq_2(k3_finseq_2(A)))) ) ) ).
fof(dt_k16_rvsum_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_valued_0(A) & v1_finseq_1(A)) ) )  => v1_xcmplx_0(k16_rvsum_1(A))) ) ).
fof(dt_k17_finseq_1, axiom,  (! [A, B, C] :  ( (v7_ordinal1(B) & m1_finseq_1(C, A))  => m2_finseq_1(k17_finseq_1(A, B, C), A)) ) ).
fof(dt_k17_matrixj1, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  (v7_ordinal1(B) &  (v7_ordinal1(C) &  ( (v1_matrix_0(D) &  (v2_matrix_0(D, A, B, B) & m1_finseq_1(D, k3_finseq_2(A))) )  &  (v1_matrix_0(E) &  (v2_matrix_0(E, A, C, C) & m1_finseq_1(E, k3_finseq_2(A))) ) ) ) ) )  =>  (v2_matrixj1(k17_matrixj1(A, B, C, D, E), A) & m2_finseq_1(k17_matrixj1(A, B, C, D, E), k3_finseq_2(k3_finseq_2(A)))) ) ) ).
fof(dt_k18_rvsum_1, axiom,  (! [A] :  (m1_finseq_1(A, k1_numbers) => v1_xreal_0(k18_rvsum_1(A))) ) ).
fof(dt_k1_card_1, axiom,  (! [A] : v1_card_1(k1_card_1(A))) ).
fof(dt_k1_domain_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, A) & m1_subset_1(D, B)) ) )  => m1_subset_1(k1_domain_1(A, B, C, D), k2_zfmisc_1(A, B))) ) ).
fof(dt_k1_finseq_1, axiom, $true).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_group_1, axiom,  (! [A] :  (l3_algstr_0(A) => m1_subset_1(k1_group_1(A), u1_struct_0(A))) ) ).
fof(dt_k1_matrix_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finseq_1(A) & v1_matrix_0(A)) ) )  => v7_ordinal1(k1_matrix_0(A))) ) ).
fof(dt_k1_matrixj1, axiom,  (! [A, B] :  ( (m1_finseq_1(A, k4_ordinal1) & v7_ordinal1(B))  => m1_subset_1(k1_matrixj1(A, B), k4_ordinal1)) ) ).
fof(dt_k1_matrixj2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & v7_ordinal1(C)) )  =>  (v1_matrix_0(k1_matrixj2(A, B, C)) & m2_finseq_1(k1_matrixj2(A, B, C), k3_finseq_2(u1_struct_0(A)))) ) ) ).
fof(dt_k1_matrlin2, axiom,  (! [A, B, C, D, E, F] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) &  (v1_matrlin(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v8_vectsp_1(C, A) &  (v9_vectsp_1(C, A) &  (v10_vectsp_1(C, A) &  (v11_vectsp_1(C, A) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v1_matrlin(C, A) & l1_vectsp_1(C, A)) ) ) ) ) ) ) ) ) )  &  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  &  (m1_finseq_1(E, u1_struct_0(B)) & m1_matrlin(F, A, C)) ) ) ) )  =>  (v1_matrix_0(k1_matrlin2(A, B, C, D, E, F)) &  (v2_matrix_0(k1_matrlin2(A, B, C, D, E, F), u1_struct_0(A), k3_finseq_1(E), k3_finseq_1(F)) & m2_finseq_1(k1_matrlin2(A, B, C, D, E, F), k3_finseq_2(u1_struct_0(A)))) ) ) ) ).
fof(dt_k1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_subset_1(B, k4_ordinal1))  => m1_subset_1(k1_nat_1(A, B), k4_ordinal1)) ) ).
fof(dt_k1_numbers, axiom, $true).
fof(dt_k1_ranknull, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v8_vectsp_1(C, A) &  (v9_vectsp_1(C, A) &  (v10_vectsp_1(C, A) &  (v11_vectsp_1(C, A) & l1_vectsp_1(C, A)) ) ) ) ) ) ) ) )  &  (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(B), u1_struct_0(C)) &  (v13_vectsp_1(D, B, C) &  (v1_mod_2(D, A, B, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) ) ) ) ) ) )  =>  (v7_vectsp_1(k1_ranknull(A, B, C, D), A) & m1_vectsp_4(k1_ranknull(A, B, C, D), A, B)) ) ) ).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_vectsp11, axiom,  (! [A, B, C] :  ( (l1_struct_0(A) &  ( (v1_funct_1(B) &  (v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) )  & v7_ordinal1(C)) )  =>  (v1_funct_1(k1_vectsp11(A, B, C)) &  (v1_funct_2(k1_vectsp11(A, B, C), u1_struct_0(A), u1_struct_0(A)) & m1_subset_1(k1_vectsp11(A, B, C), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) ) ) ) ).
fof(dt_k1_vectsp_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  =>  (v7_vectsp_1(k1_vectsp_4(A, B), A) & m1_vectsp_4(k1_vectsp_4(A, B), A, B)) ) ) ).
fof(dt_k1_vectsp_5, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  &  (m1_vectsp_4(C, A, B) & m1_vectsp_4(D, A, B)) ) )  =>  (v7_vectsp_1(k1_vectsp_5(A, B, C, D), A) & m1_vectsp_4(k1_vectsp_5(A, B, C, D), A, B)) ) ) ).
fof(dt_k1_vectsp_9, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  => v7_ordinal1(k1_vectsp_9(A, B))) ) ).
fof(dt_k1_wsierp_1, axiom,  (! [A] :  (m1_finseq_1(A, k4_ordinal1) => m1_subset_1(k1_wsierp_1(A), k4_ordinal1)) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_xreal_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k20_matrixj1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) &  (v2_matrixj1(C, A) & m1_finseq_1(C, k3_finseq_2(k3_finseq_2(A)))) ) )  =>  (v1_matrix_0(k20_matrixj1(A, B, C)) &  (v2_matrix_0(k20_matrixj1(A, B, C), A, k1_wsierp_1(k10_matrixj1(A, C)), k1_wsierp_1(k10_matrixj1(A, C))) & m2_finseq_1(k20_matrixj1(A, B, C), k3_finseq_2(A))) ) ) ) ).
fof(dt_k2_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => m1_subset_1(k2_finseq_1(A), k1_zfmisc_1(k4_ordinal1))) ) ).
fof(dt_k2_matrix_0, axiom, $true).
fof(dt_k2_matrixj1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (v1_matrixj1(B, A) & m1_finseq_1(B, k3_finseq_2(k3_finseq_2(A)))) )  =>  (v1_matrix_0(k2_matrixj1(A, B, C)) & m2_finseq_1(k2_matrixj1(A, B, C), k3_finseq_2(A))) ) ) ).
fof(dt_k2_matrixj2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & v7_ordinal1(C)) )  =>  (v1_matrix_0(k2_matrixj2(A, B, C)) &  (v2_matrix_0(k2_matrixj2(A, B, C), u1_struct_0(A), C, C) &  (v2_matrix_1(k2_matrixj2(A, B, C), C, A) & m2_finseq_1(k2_matrixj2(A, B, C), k3_finseq_2(u1_struct_0(A)))) ) ) ) ) ).
fof(dt_k2_matrlin2, axiom, $true).
fof(dt_k2_numbers, axiom, $true).
fof(dt_k2_vectsp11, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  &  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(B)) &  (v13_vectsp_1(C, B, B) &  (v1_mod_2(C, A, B, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(B))))) ) ) ) ) )  =>  (v7_vectsp_1(k2_vectsp11(A, B, C), A) & m1_vectsp_4(k2_vectsp11(A, B, C), A, B)) ) ) ).
fof(dt_k2_vectsp_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  =>  (v7_vectsp_1(k2_vectsp_4(A, B), A) & m1_vectsp_4(k2_vectsp_4(A, B), A, B)) ) ) ).
fof(dt_k2_vectsp_5, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  &  (m1_vectsp_4(C, A, B) & m1_vectsp_4(D, A, B)) ) )  =>  (v7_vectsp_1(k2_vectsp_5(A, B, C, D), A) & m1_vectsp_4(k2_vectsp_5(A, B, C, D), A, B)) ) ) ).
fof(dt_k2_xcmplx_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => m1_subset_1(k3_finseq_1(A), k4_ordinal1)) ) ).
fof(dt_k3_finseq_2, axiom,  (! [A] : m1_finseq_2(k3_finseq_2(A), 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_matrix_0, axiom,  (! [A, B, C, D] :  ( ( (v1_matrix_0(B) & m1_finseq_1(B, k3_finseq_2(A)))  &  (v7_ordinal1(C) & v7_ordinal1(D)) )  => m1_subset_1(k3_matrix_0(A, B, C, D), A)) ) ).
fof(dt_k3_matrixj1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_matrixj1(B, A) & m1_finseq_1(B, k3_finseq_2(k3_finseq_2(A))))  &  (v1_matrixj1(C, A) & m1_finseq_1(C, k3_finseq_2(k3_finseq_2(A)))) ) )  =>  (v1_matrixj1(k3_matrixj1(A, B, C), A) & m2_finseq_1(k3_matrixj1(A, B, C), k3_finseq_2(k3_finseq_2(A)))) ) ) ).
fof(dt_k3_matrixj2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( (v1_matrixj2(B, A) & m1_finseq_1(B, k3_finseq_2(k3_finseq_2(u1_struct_0(A)))))  &  (v1_matrixj2(C, A) & m1_finseq_1(C, k3_finseq_2(k3_finseq_2(u1_struct_0(A))))) ) )  =>  (v1_matrixj2(k3_matrixj2(A, B, C), A) & m2_finseq_1(k3_matrixj2(A, B, C), k3_finseq_2(k3_finseq_2(u1_struct_0(A))))) ) ) ).
fof(dt_k3_matrlin, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  &  ( ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A))  &  ( ( ~ (v2_struct_0(C))  & l1_vectsp_1(C, A))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  &  (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) ) ) ) ) )  =>  (v1_funct_1(k3_matrlin(A, B, C, D, E)) &  (v1_funct_2(k3_matrlin(A, B, C, D, E), u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(k3_matrlin(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) ) ) ) ).
fof(dt_k3_numbers, axiom, $true).
fof(dt_k3_ranknull, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v8_vectsp_1(C, A) &  (v9_vectsp_1(C, A) &  (v10_vectsp_1(C, A) &  (v11_vectsp_1(C, A) & l1_vectsp_1(C, A)) ) ) ) ) ) ) ) )  &  (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(B), u1_struct_0(C)) &  (v13_vectsp_1(D, B, C) &  (v1_mod_2(D, A, B, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) ) ) ) ) ) )  =>  (v7_vectsp_1(k3_ranknull(A, B, C, D), A) & m1_vectsp_4(k3_ranknull(A, B, C, D), A, C)) ) ) ).
fof(dt_k3_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v1_funct_1(k3_struct_0(A)) &  (v1_funct_2(k3_struct_0(A), u1_struct_0(A), u1_struct_0(A)) & m1_subset_1(k3_struct_0(A), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) ) ) ) ).
fof(dt_k3_vectsp_1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  &  ( ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A))  &  (m1_subset_1(C, u1_struct_0(A)) & m1_subset_1(D, u1_struct_0(B))) ) )  => m1_subset_1(k3_vectsp_1(A, B, C, D), u1_struct_0(B))) ) ).
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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => m1_subset_1(k4_finseq_1(A), k1_zfmisc_1(k4_ordinal1))) ) ).
fof(dt_k4_finseq_2, axiom,  (! [A, B] :  (v7_ordinal1(A) => m1_finseq_2(k4_finseq_2(A, B), B)) ) ).
fof(dt_k4_matrixj1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  (v1_matrix_0(B) & m1_finseq_1(B, k3_finseq_2(A))) )  =>  (v1_matrixj1(k4_matrixj1(A, B), A) & m2_finseq_1(k4_matrixj1(A, B), k3_finseq_2(k3_finseq_2(A)))) ) ) ).
fof(dt_k4_matrlin, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  &  ( ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A))  &  ( ( ~ (v2_struct_0(C))  & l1_vectsp_1(C, A))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  & m1_subset_1(E, u1_struct_0(A))) ) ) )  =>  (v1_funct_1(k4_matrlin(A, B, C, D, E)) &  (v1_funct_2(k4_matrlin(A, B, C, D, E), u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(k4_matrlin(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) ) ) ) ).
fof(dt_k4_numbers, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_relat_1, axiom,  (! [A] : v1_relat_1(k4_relat_1(A))) ).
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_tarski, axiom, $true).
fof(dt_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A))) ) ).
fof(dt_k5_finseq_1, axiom, $true).
fof(dt_k5_matrixj1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_matrix_0(B) & m1_finseq_1(B, k3_finseq_2(A)))  &  (v1_matrix_0(C) & m1_finseq_1(C, k3_finseq_2(A))) ) )  =>  (v1_matrixj1(k5_matrixj1(A, B, C), A) & m2_finseq_1(k5_matrixj1(A, B, C), k3_finseq_2(k3_finseq_2(A)))) ) ) ).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k5_relat_1(A, B))) ) ).
fof(dt_k5_struct_0, axiom,  (! [A] :  (l3_struct_0(A) => m1_subset_1(k5_struct_0(A), u1_struct_0(A))) ) ).
fof(dt_k6_finseq_1, axiom,  (! [A] : m2_finseq_1(k6_finseq_1(A), A)) ).
fof(dt_k6_numbers, axiom, $true).
fof(dt_k6_partfun1, axiom,  (! [A] :  (v1_partfun1(k6_partfun1(A), A) & m1_subset_1(k6_partfun1(A), k1_zfmisc_1(k2_zfmisc_1(A, A)))) ) ).
fof(dt_k6_xcmplx_0, axiom, $true).
fof(dt_k7_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ).
fof(dt_k7_nat_d, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => m1_subset_1(k7_nat_d(A, B), k4_ordinal1)) ) ).
fof(dt_k7_xcmplx_0, axiom, $true).
fof(dt_k8_matrixj1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  (v1_matrixj1(B, A) & m1_finseq_1(B, k3_finseq_2(k3_finseq_2(A)))) )  => m2_finseq_1(k8_matrixj1(A, B), k4_ordinal1)) ) ).
fof(dt_k8_matrlin2, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v8_vectsp_1(C, A) &  (v9_vectsp_1(C, A) &  (v10_vectsp_1(C, A) &  (v11_vectsp_1(C, A) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) & l1_vectsp_1(C, A)) ) ) ) ) ) ) ) )  &  (m1_vectsp_4(D, A, B) &  (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) &  (v13_vectsp_1(E, B, C) &  (v1_mod_2(E, A, B, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) ) ) ) ) ) ) )  =>  (v1_funct_1(k8_matrlin2(A, B, C, D, E)) &  (v1_funct_2(k8_matrlin2(A, B, C, D, E), u1_struct_0(D), u1_struct_0(C)) &  (v13_vectsp_1(k8_matrlin2(A, B, C, D, E), D, C) &  (v1_mod_2(k8_matrlin2(A, B, C, D, E), A, D, C) & m1_subset_1(k8_matrlin2(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(D), u1_struct_0(C))))) ) ) ) ) ) ).
fof(dt_k9_finseq_1, axiom,  (! [A] :  (v1_relat_1(k9_finseq_1(A)) & v1_funct_1(k9_finseq_1(A))) ) ).
fof(dt_k9_matrixj1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  (v1_matrixj1(B, A) & m1_finseq_1(B, k3_finseq_2(k3_finseq_2(A)))) )  => m2_finseq_1(k9_matrixj1(A, B), k4_ordinal1)) ) ).
fof(dt_k9_xtuple_0, axiom, $true).
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_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_finseq_1, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, A) =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ).
fof(dt_m1_finseq_2, axiom, $true).
fof(dt_m1_matrixj2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  & m1_subset_1(B, u1_struct_0(A)))  =>  (! [C] :  (m1_matrixj2(C, A, B) =>  (v1_matrixj2(C, A) & m2_finseq_1(C, k3_finseq_2(k3_finseq_2(u1_struct_0(A))))) ) ) ) ) ).
fof(dt_m1_matrlin, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) &  (v1_matrlin(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) ) )  =>  (! [C] :  (m1_matrlin(C, A, B) => m2_finseq_1(C, u1_struct_0(B))) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m1_vectsp11, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  &  ( ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A))  &  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(B))))) ) ) )  =>  (! [D] :  (m1_vectsp11(D, A, B, C) => m1_subset_1(D, u1_struct_0(A))) ) ) ) ).
fof(dt_m1_vectsp_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  =>  (! [C] :  (m1_vectsp_4(C, A, B) =>  ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v8_vectsp_1(C, A) &  (v9_vectsp_1(C, A) &  (v10_vectsp_1(C, A) &  (v11_vectsp_1(C, A) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) & l1_vectsp_1(C, A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_m1_vectsp_5, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  & m1_vectsp_4(C, A, B)) )  =>  (! [D] :  (m1_vectsp_5(D, A, B, C) => m1_vectsp_4(D, A, B)) ) ) ) ).
fof(dt_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) =>  (v1_funct_1(B) &  (v1_finseq_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A)))) ) ) ) ) ).
fof(dt_m2_finseq_2, axiom,  (! [A, B] :  (m1_finseq_2(B, A) =>  (! [C] :  (m2_finseq_2(C, A, B) => m2_finseq_1(C, A)) ) ) ) ).
fof(dt_o_5_2_matrixj2, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v2_polynom5(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v13_algstr_0(B) &  (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) &  (v1_matrlin(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(B)) &  (v13_vectsp_1(C, B, B) &  (v1_mod_2(C, A, B, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(B))))) ) ) )  &  (m1_subset_1(D, u1_struct_0(A)) & v7_ordinal1(E)) ) ) )  => m1_matrlin(o_5_2_matrixj2(A, B, C, D, E), A, k3_ranknull(A, B, B, k1_vectsp11(B, k3_matrlin(A, B, B, C, k4_matrlin(A, B, B, k3_struct_0(B), k4_algstr_0(A, D))), E)))) ) ).
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_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_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_finseq_1, axiom,  (! [A] :  (? [B] : m1_finseq_1(B, A)) ) ).
fof(existence_m1_finseq_2, axiom,  (! [A] :  (? [B] : m1_finseq_2(B, A)) ) ).
fof(existence_m1_matrixj2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  & m1_subset_1(B, u1_struct_0(A)))  =>  (? [C] : m1_matrixj2(C, A, B)) ) ) ).
fof(existence_m1_matrlin, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) &  (v1_matrlin(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) ) )  =>  (? [C] : m1_matrlin(C, A, B)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m1_vectsp11, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  &  ( ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A))  &  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(B))))) ) ) )  =>  (? [D] : m1_vectsp11(D, A, B, C)) ) ) ).
fof(existence_m1_vectsp_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  =>  (? [C] : m1_vectsp_4(C, A, B)) ) ) ).
fof(existence_m1_vectsp_5, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  & m1_vectsp_4(C, A, B)) )  =>  (? [D] : m1_vectsp_5(D, A, B, C)) ) ) ).
fof(existence_m2_finseq_1, axiom,  (! [A] :  (? [B] : m2_finseq_1(B, A)) ) ).
fof(existence_m2_finseq_2, axiom,  (! [A, B] :  (m1_finseq_2(B, A) =>  (? [C] : m2_finseq_2(C, A, B)) ) ) ).
fof(fc100_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v7_valued_0(A)) ) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v7_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc101_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v10_valued_0(A)) ) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v10_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc102_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v8_valued_0(A)) ) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v8_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc103_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v9_valued_0(A)) ) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v9_valued_0(k5_relat_1(A, B))) ) ) ).
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_finseq_1, axiom,  (! [A, B] : v1_finseq_1(k10_finseq_1(A, B))) ).
fof(fc10_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_ordinal1(A))  =>  ~ (v10_ordinal1(k10_xtuple_0(A))) ) ) ).
fof(fc10_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc10_relset_1, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(k9_xtuple_0(A)))) )  =>  ( ~ (v1_xboole_0(k5_relat_1(A, B)))  & v1_relat_1(k5_relat_1(A, B))) ) ) ).
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(fc11_funct_2, axiom,  (! [A] :  (v1_relat_1(k4_relat_1(A)) &  (v4_relat_1(k4_relat_1(A), A) &  (v1_funct_1(k4_relat_1(A)) & v1_partfun1(k4_relat_1(A), A)) ) ) ) ).
fof(fc11_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  => v1_setfam_1(k1_tarski(A))) ) ).
fof(fc11_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  ~ (v9_ordinal1(A)) )  => v10_ordinal1(k10_xtuple_0(A))) ) ).
fof(fc11_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc11_struct_0, axiom,  (! [A] :  ( ( ~ (v6_struct_0(A))  & l4_struct_0(A))  =>  ~ (v9_struct_0(k5_struct_0(A), 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(fc12_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k1_zfmisc_1(A))) ) ) ).
fof(fc12_finseq_1, axiom,  (! [A] :  ~ (v1_xboole_0(k13_finseq_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(fc13_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(A, B))) ) ) ).
fof(fc13_finseq_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v2_finseq_1(k5_relat_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_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v1_finset_1(k2_zfmisc_1(A, B))) ) ).
fof(fc14_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_funcop_1(k5_relat_1(A, B))) ) ) ).
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_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_finseq_1(k1_finseq_1(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_card_1, axiom,  (! [A] : v3_card_1(k1_tarski(A), 1)) ).
fof(fc16_finseq_1, axiom,  (! [A] :  ( (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) )  => v3_finseq_1(k1_tarski(A))) ) ).
fof(fc16_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_xboole_0(B))  =>  (v1_xboole_0(k5_relat_1(A, B)) & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(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_card_1, axiom,  (! [A, B] :  ( (v1_card_1(A) &  (v1_relat_1(B) &  (v1_funct_1(B) & v3_card_1(B, A)) ) )  => v3_card_1(k9_xtuple_0(B), A)) ) ).
fof(fc17_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => v3_finseq_1(k9_xtuple_0(A))) ) ).
fof(fc17_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v1_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc17_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_xboole_0(k5_relat_1(A, B)) & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(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(fc18_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  => v3_finseq_1(k9_xtuple_0(A))) ) ).
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_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_finset_1(A))  => v1_finset_1(k9_xtuple_0(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_card_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v1_xboole_0(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc1_finseq_1, axiom,  (! [A] :  ( (v7_ordinal1(A) & v8_ordinal1(A))  => v1_xboole_0(k1_finseq_1(A))) ) ).
fof(fc1_finset_1, axiom,  (! [A] : v1_finset_1(k1_tarski(A))) ).
fof(fc1_matrix13, axiom,  (! [A] :  (v7_ordinal1(A) => v1_setfam_1(k1_finseq_1(A))) ) ).
fof(fc1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v7_ordinal1(k2_xcmplx_0(A, B))) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_valued_0(A))  => v1_membered(k10_xtuple_0(A))) ) ).
fof(fc1_vectsp11, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(B)) &  (v13_vectsp_1(C, B, B) &  (v1_mod_2(C, A, B, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(B))))) ) ) )  & v7_ordinal1(D)) ) )  =>  (v1_funct_1(k1_vectsp11(B, C, D)) &  (v1_funct_2(k1_vectsp11(B, C, D), u1_struct_0(B), u1_struct_0(B)) &  (v13_vectsp_1(k1_vectsp11(B, C, D), B, B) & v1_mod_2(k1_vectsp11(B, C, D), A, B, B)) ) ) ) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
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_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_finset_1(A))  => v1_finset_1(k10_xtuple_0(A))) ) ).
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_finseq_1, axiom,  (! [A] :  ~ (v1_xboole_0(k5_finseq_1(A))) ) ).
fof(fc23_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v3_relat_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v3_relat_1(k5_relat_1(A, B))) ) ) ).
fof(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_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  ( ~ (v1_xboole_0(k7_finseq_1(A, B)))  & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc24_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k9_xtuple_0(A))) ) ).
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_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(B, A)) &  (v1_funct_1(k7_finseq_1(B, A)) &  ( ~ (v1_xboole_0(k7_finseq_1(B, A)))  & v1_finseq_1(k7_finseq_1(B, A))) ) ) ) ) ).
fof(fc25_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
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_finseq_1, axiom,  (! [A, B] :  ~ (v1_xboole_0(k10_finseq_1(A, B))) ) ).
fof(fc26_finset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v1_finset_1(B))  =>  (v1_relat_1(k5_relat_1(B, A)) & v1_finset_1(k5_relat_1(B, A))) ) ) ).
fof(fc26_relat_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(C) & v5_relat_1(C, B))  =>  (v1_relat_1(k5_relat_1(C, A)) & v5_relat_1(k5_relat_1(C, 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_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k5_relat_1(B, A)) & v1_finset_1(k5_relat_1(B, A))) ) ) ).
fof(fc27_relat_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(C) & v4_relat_1(C, B))  =>  (v1_relat_1(k5_relat_1(C, A)) &  (v4_relat_1(k5_relat_1(C, A), A) & v4_relat_1(k5_relat_1(C, A), B)) ) ) ) ).
fof(fc28_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(k16_finseq_1(k5_numbers, A)) &  (v1_funct_1(k16_finseq_1(k5_numbers, A)) &  (v1_xboole_0(k16_finseq_1(k5_numbers, A)) & v1_finseq_1(k16_finseq_1(k5_numbers, A))) ) ) ) ) ).
fof(fc28_relat_1, axiom,  (! [A] :  (v1_relat_1(k4_relat_1(A)) &  (v4_relat_1(k4_relat_1(A), A) & v5_relat_1(k4_relat_1(A), A)) ) ) ).
fof(fc29_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  & v1_finseq_1(A)) ) )  =>  (v1_relat_1(k16_finseq_1(1, A)) &  (v1_funct_1(k16_finseq_1(1, A)) &  (v3_card_1(k16_finseq_1(1, A), 1) & v1_finseq_1(k16_finseq_1(1, 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_finseq_1, axiom,  (! [A] :  ( (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) )  =>  ~ (v1_xboole_0(k1_finseq_1(A))) ) ) ).
fof(fc2_matrlin2, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v8_vectsp_1(C, A) &  (v9_vectsp_1(C, A) &  (v10_vectsp_1(C, A) &  (v11_vectsp_1(C, A) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) & l1_vectsp_1(C, A)) ) ) ) ) ) ) ) )  &  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(B), u1_struct_0(C)) &  (v13_vectsp_1(D, B, C) &  (v1_mod_2(D, A, B, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) ) ) )  &  (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) &  (v13_vectsp_1(E, B, C) &  (v1_mod_2(E, A, B, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) ) ) ) ) ) ) )  =>  (v1_funct_1(k3_matrlin(A, B, C, D, E)) &  (v1_funct_2(k3_matrlin(A, B, C, D, E), u1_struct_0(B), u1_struct_0(C)) &  (v13_vectsp_1(k3_matrlin(A, B, C, D, E), B, C) & v1_mod_2(k3_matrlin(A, B, C, D, E), A, B, C)) ) ) ) ) ).
fof(fc2_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v7_ordinal1(k3_xcmplx_0(A, B))) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc2_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_valued_0(A))  => v2_membered(k10_xtuple_0(A))) ) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc30_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  & v1_finseq_1(A)) ) )  &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  (v1_relat_1(k16_finseq_1(B, A)) &  (v1_funct_1(k16_finseq_1(B, A)) &  ( ~ (v1_xboole_0(k16_finseq_1(B, A)))  & v1_finseq_1(k16_finseq_1(B, A))) ) ) ) ) ).
fof(fc30_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v5_finset_1(k1_tarski(A))) ) ).
fof(fc31_finseq_1, axiom,  (! [A] : v4_funct_1(k13_finseq_1(A))) ).
fof(fc31_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v5_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc31_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k7_xcmplx_0(A, B))) ) ) ).
fof(fc32_finseq_1, axiom,  (! [A] : v3_card_1(k5_finseq_1(A), 1)) ).
fof(fc32_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k7_xcmplx_0(B, A))) ) ) ).
fof(fc33_finseq_1, axiom,  (! [A, B] : v3_card_1(k10_finseq_1(A, B), 2)) ).
fof(fc33_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v2_relat_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v2_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc33_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k7_xcmplx_0(A, B))) ) ) ).
fof(fc34_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k7_xcmplx_0(A, B))) ) ) ).
fof(fc35_finseq_1, axiom, v4_finseq_1(k1_tarski(k1_xboole_0))).
fof(fc35_finset_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) )  => v1_finset_1(k1_funct_1(A, B))) ) ).
fof(fc36_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_finset_1(A))  => v5_finset_1(k10_xtuple_0(A))) ) ).
fof(fc37_finseq_1, axiom,  (! [A] : v4_finseq_1(k13_finseq_1(A))) ).
fof(fc37_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k1_xreal_0(A, B))) ) ).
fof(fc38_finseq_1, axiom,  (! [A, B, C, D] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ( (v1_relat_1(C) &  (v1_funct_1(C) &  (v3_card_1(C, A) & v1_finseq_1(C)) ) )  &  (v1_relat_1(D) &  (v1_funct_1(D) &  (v3_card_1(D, B) & v1_finseq_1(D)) ) ) ) ) )  =>  (v1_relat_1(k7_finseq_1(C, D)) &  (v1_funct_1(k7_finseq_1(C, D)) &  (v3_card_1(k7_finseq_1(C, D), k2_xcmplx_0(A, B)) & v1_finseq_1(k7_finseq_1(C, D))) ) ) ) ) ).
fof(fc38_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  =>  ( ~ (v3_xxreal_0(k1_xreal_0(A, B)))  & v1_xreal_0(k1_xreal_0(A, B))) ) ) ).
fof(fc39_finseq_1, axiom,  (! [A, B, C] :  ( (v4_finseq_1(A) &  (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) ) )  => v1_finseq_1(k1_funct_1(B, C))) ) ).
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_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_finset_1(k1_finseq_1(A))) ) ).
fof(fc3_matrlin2, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v8_vectsp_1(C, A) &  (v9_vectsp_1(C, A) &  (v10_vectsp_1(C, A) &  (v11_vectsp_1(C, A) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) & l1_vectsp_1(C, A)) ) ) ) ) ) ) ) )  &  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(B), u1_struct_0(C)) &  (v13_vectsp_1(D, B, C) &  (v1_mod_2(D, A, B, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) ) ) )  & m1_subset_1(E, u1_struct_0(A))) ) ) )  =>  (v1_funct_1(k4_matrlin(A, B, C, D, E)) &  (v1_funct_2(k4_matrlin(A, B, C, D, E), u1_struct_0(B), u1_struct_0(C)) &  (v13_vectsp_1(k4_matrlin(A, B, C, D, E), B, C) & v1_mod_2(k4_matrlin(A, B, C, D, E), A, B, C)) ) ) ) ) ).
fof(fc3_mod_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  =>  (v1_funct_1(k3_struct_0(B)) &  (v1_funct_2(k3_struct_0(B), u1_struct_0(B), u1_struct_0(B)) & v1_mod_2(k3_struct_0(B), A, B, B)) ) ) ) ).
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_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  => v3_membered(k10_xtuple_0(A))) ) ).
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(fc42_finseq_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v6_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k16_finseq_1(A, B)) &  (v1_funct_1(k16_finseq_1(A, B)) &  (v6_valued_0(k16_finseq_1(A, B)) & v1_finseq_1(k16_finseq_1(A, B))) ) ) ) ) ).
fof(fc43_finseq_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v1_relat_1(B) &  (v5_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k16_finseq_1(A, B)) &  (v5_relat_1(k16_finseq_1(A, B), k4_ordinal1) &  (v1_funct_1(k16_finseq_1(A, B)) & v1_finseq_1(k16_finseq_1(A, B))) ) ) ) ) ).
fof(fc43_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_valued_0(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc44_finseq_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v5_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k16_finseq_1(A, B)) &  (v1_funct_1(k16_finseq_1(A, B)) &  (v5_valued_0(k16_finseq_1(A, B)) & v1_finseq_1(k16_finseq_1(A, B))) ) ) ) ) ).
fof(fc44_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v2_valued_0(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v2_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc45_finseq_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v1_relat_1(B) &  (v5_relat_1(B, k4_numbers) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k16_finseq_1(A, B)) &  (v5_relat_1(k16_finseq_1(A, B), k4_numbers) &  (v1_funct_1(k16_finseq_1(A, B)) & v1_finseq_1(k16_finseq_1(A, B))) ) ) ) ) ).
fof(fc45_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v3_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc46_finseq_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v4_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k16_finseq_1(A, B)) &  (v1_funct_1(k16_finseq_1(A, B)) &  (v4_valued_0(k16_finseq_1(A, B)) & v1_finseq_1(k16_finseq_1(A, B))) ) ) ) ) ).
fof(fc46_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v4_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc47_finseq_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v1_relat_1(B) &  (v5_relat_1(B, k3_numbers) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k16_finseq_1(A, B)) &  (v5_relat_1(k16_finseq_1(A, B), k3_numbers) &  (v1_funct_1(k16_finseq_1(A, B)) & v1_finseq_1(k16_finseq_1(A, B))) ) ) ) ) ).
fof(fc47_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v5_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc48_finseq_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v3_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k16_finseq_1(A, B)) &  (v1_funct_1(k16_finseq_1(A, B)) &  (v3_valued_0(k16_finseq_1(A, B)) & v1_finseq_1(k16_finseq_1(A, B))) ) ) ) ) ).
fof(fc48_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v6_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc49_finseq_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v1_relat_1(B) &  (v5_relat_1(B, k1_numbers) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k16_finseq_1(A, B)) &  (v5_relat_1(k16_finseq_1(A, B), k1_numbers) &  (v1_funct_1(k16_finseq_1(A, B)) & v1_finseq_1(k16_finseq_1(A, B))) ) ) ) ) ).
fof(fc49_valued_0, axiom,  (! [A] :  (v1_membered(A) =>  (v1_relat_1(k4_relat_1(A)) & v1_valued_0(k4_relat_1(A))) ) ) ).
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_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_card_1(k1_finseq_1(A), A)) ) ).
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_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  => v3_ordinal1(k9_xtuple_0(A))) ) ).
fof(fc4_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  => v4_membered(k10_xtuple_0(A))) ) ).
fof(fc50_finseq_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v1_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k16_finseq_1(A, B)) &  (v1_funct_1(k16_finseq_1(A, B)) &  (v1_valued_0(k16_finseq_1(A, B)) & v1_finseq_1(k16_finseq_1(A, B))) ) ) ) ) ).
fof(fc50_valued_0, axiom,  (! [A] :  (v2_membered(A) =>  (v1_relat_1(k4_relat_1(A)) & v2_valued_0(k4_relat_1(A))) ) ) ).
fof(fc51_finseq_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v1_relat_1(B) &  (v5_relat_1(B, k2_numbers) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k16_finseq_1(A, B)) &  (v5_relat_1(k16_finseq_1(A, B), k2_numbers) &  (v1_funct_1(k16_finseq_1(A, B)) & v1_finseq_1(k16_finseq_1(A, B))) ) ) ) ) ).
fof(fc51_valued_0, axiom,  (! [A] :  (v3_membered(A) =>  (v1_relat_1(k4_relat_1(A)) & v3_valued_0(k4_relat_1(A))) ) ) ).
fof(fc52_finseq_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v2_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k16_finseq_1(A, B)) &  (v1_funct_1(k16_finseq_1(A, B)) &  (v2_valued_0(k16_finseq_1(A, B)) & v1_finseq_1(k16_finseq_1(A, B))) ) ) ) ) ).
fof(fc52_valued_0, axiom,  (! [A] :  (v4_membered(A) =>  (v1_relat_1(k4_relat_1(A)) & v4_valued_0(k4_relat_1(A))) ) ) ).
fof(fc53_finseq_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v1_relat_1(B) &  (v5_relat_1(B, k6_numbers) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k16_finseq_1(A, B)) &  (v5_relat_1(k16_finseq_1(A, B), k6_numbers) &  (v1_funct_1(k16_finseq_1(A, B)) & v1_finseq_1(k16_finseq_1(A, B))) ) ) ) ) ).
fof(fc53_valued_0, axiom,  (! [A] :  (v5_membered(A) =>  (v1_relat_1(k4_relat_1(A)) & v5_valued_0(k4_relat_1(A))) ) ) ).
fof(fc54_finseq_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v1_finseq_1(B)) ) )  &  (v1_relat_1(C) &  (v5_relat_1(C, A) &  (v1_funct_1(C) & v1_finseq_1(C)) ) ) )  =>  (v1_relat_1(k7_finseq_1(B, C)) &  (v5_relat_1(k7_finseq_1(B, C), A) &  (v1_funct_1(k7_finseq_1(B, C)) & v1_finseq_1(k7_finseq_1(B, C))) ) ) ) ) ).
fof(fc54_valued_0, axiom,  (! [A] :  (v6_membered(A) =>  (v1_relat_1(k4_relat_1(A)) & v6_valued_0(k4_relat_1(A))) ) ) ).
fof(fc55_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v6_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v6_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  (v6_valued_0(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc56_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v5_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v5_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  (v5_valued_0(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc57_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v4_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v4_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  (v4_valued_0(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc58_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v3_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  (v3_valued_0(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc59_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v1_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  (v1_valued_0(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc5_finseq_1, axiom,  (! [A] : v1_xboole_0(k6_finseq_1(A))) ).
fof(fc5_finseq_2, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k4_finseq_2(A, B))) ) ) ).
fof(fc5_ordinal1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  & v3_ordinal1(B))  =>  (v1_relat_1(k5_relat_1(A, B)) &  (v5_relat_1(k5_relat_1(A, B), k10_xtuple_0(A)) & v5_ordinal1(k5_relat_1(A, B))) ) ) ) ).
fof(fc5_relat_1, axiom,  (! [A, B] : v1_relat_1(k1_tarski(k4_tarski(A, B)))) ).
fof(fc5_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  => v5_membered(k10_xtuple_0(A))) ) ).
fof(fc5_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc60_finseq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v1_finseq_1(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v2_valued_0(B) & v1_finseq_1(B)) ) ) )  =>  (v1_relat_1(k7_finseq_1(A, B)) &  (v1_funct_1(k7_finseq_1(A, B)) &  (v2_valued_0(k7_finseq_1(A, B)) & v1_finseq_1(k7_finseq_1(A, B))) ) ) ) ) ).
fof(fc61_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => v6_valued_0(k5_finseq_1(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_finseq_1, axiom,  (! [A] :  (v1_int_1(A) => v5_valued_0(k5_finseq_1(A))) ) ).
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_finseq_1, axiom,  (! [A] :  (v1_rat_1(A) => v4_valued_0(k5_finseq_1(A))) ) ).
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_finseq_1, axiom,  (! [A] :  (v1_xreal_0(A) => v3_valued_0(k5_finseq_1(A))) ) ).
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_finseq_1, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_valued_0(k5_finseq_1(A))) ) ).
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_finseq_1, axiom,  (! [A] :  (v1_xxreal_0(A) => v2_valued_0(k5_finseq_1(A))) ) ).
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_finseq_1, axiom,  (! [A] :  (v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A))) ) ).
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_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  => v6_membered(k10_xtuple_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(fc7_card_1, axiom, v2_card_1(k4_ordinal1)).
fof(fc7_finseq_1, axiom,  (! [A] : v1_finseq_1(k5_finseq_1(A))) ).
fof(fc7_relset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v1_xboole_0(k4_relat_1(A)))  & v1_relat_1(k4_relat_1(A))) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_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(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_card_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc8_finseq_1, axiom,  (! [A, B] :  (v1_relat_1(k10_finseq_1(A, B)) & v1_funct_1(k10_finseq_1(A, B))) ) ).
fof(fc8_grcat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_algstr_0(A))  =>  (v1_funct_1(k3_struct_0(A)) &  (v1_funct_2(k3_struct_0(A), u1_struct_0(A), u1_struct_0(A)) & v13_vectsp_1(k3_struct_0(A), A, A)) ) ) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_relat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  =>  ~ (v1_xboole_0(k9_xtuple_0(A))) ) ) ).
fof(fc8_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C))) => v1_relat_1(k9_xtuple_0(D))) ) ).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc8_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k7_xcmplx_0(A, B))) ) ).
fof(fc90_valued_0, axiom,  (! [A, B] :  (v6_membered(B) => v6_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc99_valued_0, axiom,  (! [A] :  (v2_membered(A) =>  (v1_funct_1(k4_relat_1(A)) &  (v1_funct_2(k4_relat_1(A), A, A) & v7_valued_0(k4_relat_1(A))) ) ) ) ).
fof(fc9_card_1, axiom,  ~ (v1_finset_1(k4_ordinal1)) ).
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_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_relat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  =>  ~ (v1_xboole_0(k10_xtuple_0(A))) ) ) ).
fof(fc9_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k2_zfmisc_1(B, C)))) => v1_relat_1(k10_xtuple_0(D))) ) ).
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_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(fraenkel_a_1_0_finseq_1, axiom,  (! [A, B] :  (v7_ordinal1(B) =>  (r2_hidden(A, a_1_0_finseq_1(B)) <=>  (? [C] :  (v7_ordinal1(C) &  (A=C &  (r1_xxreal_0(1, C) & r1_xxreal_0(C, B)) ) ) ) ) ) ) ).
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(ie10_vectsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_vectsp_1(A) & l4_algstr_0(A)) )  => k1_group_1(A)=k5_struct_0(A)) ) ).
fof(involutiveness_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A))=A) ) ).
fof(projectivity_k1_card_1, axiom,  (! [A] : k1_card_1(k1_card_1(A))=k1_card_1(A)) ).
fof(projectivity_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k3_finseq_1(k3_finseq_1(A))=k3_finseq_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(rc15_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v2_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ).
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(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_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_finseq_2, axiom,  (! [A] :  (? [B] :  (m1_finseq_2(B, A) &  ~ (v1_xboole_0(B)) ) ) ) ).
fof(rc1_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_finset_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_grcat_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_algstr_0(A))  &  ( ~ (v2_struct_0(B))  &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) &  (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(A)) &  (v5_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  &  (v1_partfun1(C, u1_struct_0(A)) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v13_vectsp_1(C, A, B)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_matrix13, axiom,  (? [A] :  (m1_subset_1(A, k1_zfmisc_1(k4_ordinal1)) &  (v1_xboole_0(A) &  (v1_finset_1(A) & v1_setfam_1(A)) ) ) ) ).
fof(rc1_matrixj1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_finseq_1(B, k3_finseq_2(k3_finseq_2(A))) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, k3_finseq_2(k3_finseq_2(A))) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) &  (v2_finseq_1(B) & v1_matrixj1(B, A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_matrixj2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (m1_finseq_1(B, k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) &  (v2_finseq_1(B) &  (v1_funcop_1(B) &  (v2_funcop_1(B) & v1_matrixj2(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_nat_1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(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_valued_0, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v6_valued_0(A)) ) ) ).
fof(rc1_vectsp11, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_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) &  (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) & v1_matrlin(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_vectsp_9, 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(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc20_struct_0, axiom,  (? [A] :  (l2_struct_0(A) &  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ).
fof(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(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_matrix13, axiom,  (? [A] :  (m1_subset_1(A, k1_zfmisc_1(k4_ordinal1)) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) & v1_setfam_1(A)) ) ) ) ).
fof(rc2_matrixj1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_finseq_1(B, k3_finseq_2(k3_finseq_2(A))) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, k3_finseq_2(k3_finseq_2(A))) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) &  (v2_finseq_1(B) & v2_matrixj1(B, A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_matrixj2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  & m1_subset_1(B, u1_struct_0(A)))  =>  (? [C] :  (m1_matrixj2(C, A, B) &  (v1_relat_1(C) &  (v2_relat_1(C) &  (v4_relat_1(C, k4_ordinal1) &  (v5_relat_1(C, k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) &  (v1_funct_1(C) &  (v1_finset_1(C) &  (v1_finseq_1(C) &  (v2_finseq_1(C) &  (v1_funcop_1(C) &  (v2_funcop_1(C) &  (v1_matrixj1(C, u1_struct_0(A)) &  (v2_matrixj1(C, u1_struct_0(A)) & v1_matrixj2(C, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) & v8_ordinal1(A)) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_polynom5, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_vectsp_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v6_vectsp_1(A) &  (v1_group_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & v2_polynom5(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_vectsp11, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) ) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(B)))) &  (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(B)) &  (v5_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  &  (v1_partfun1(C, u1_struct_0(B)) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(B)) &  (v13_vectsp_1(C, B, B) &  (v1_mod_2(C, A, B, B) & v1_vectsp11(C, A, B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc3_card_1, axiom,  (? [A] :  ~ (v1_finset_1(A)) ) ).
fof(rc3_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_xboole_0(B) &  (v1_finset_1(B) & v1_finseq_1(B)) ) ) ) ) ) ) ) ).
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_matrixj2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (m1_finseq_1(B, k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) &  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) &  (v2_finseq_1(B) &  (v1_funcop_1(B) &  (v2_funcop_1(B) &  (v1_matrixj1(B, u1_struct_0(A)) &  (v2_matrixj1(B, u1_struct_0(A)) & v1_matrixj2(B, 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_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_vectsp_9, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  =>  (? [C] :  (m1_vectsp_4(C, A, B) &  ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v7_vectsp_1(C, A) &  (v8_vectsp_1(C, A) &  (v9_vectsp_1(C, A) &  (v10_vectsp_1(C, A) &  (v11_vectsp_1(C, A) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) & v1_matrlin(C, 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(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_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_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_vectsp_9, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) &  (v1_matrlin(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) ) )  =>  (? [C] :  (m1_vectsp_4(C, A, B) &  ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v7_vectsp_1(C, A) &  (v8_vectsp_1(C, A) &  (v9_vectsp_1(C, A) &  (v10_vectsp_1(C, A) &  (v11_vectsp_1(C, A) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) & v1_matrlin(C, 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_funcop_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, 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_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(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_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_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_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(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_finseq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_finseq_1(B, A) &  (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(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_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rd1_card_1, axiom,  (! [A] :  (v1_card_1(A) => k1_card_1(A)=A) ) ).
fof(rd1_finseq_1, axiom,  (! [A] : k1_funct_1(k9_finseq_1(A), 1)=A) ).
fof(rd1_relat_1, axiom,  (! [A] : k9_xtuple_0(k4_relat_1(A))=A) ).
fof(rd2_finseq_1, axiom,  (! [A, B] : k1_funct_1(k10_finseq_1(A, B), 1)=A) ).
fof(rd2_relat_1, axiom,  (! [A] : k10_xtuple_0(k4_relat_1(A))=A) ).
fof(rd3_finseq_1, axiom,  (! [A, B] : k1_funct_1(k10_finseq_1(A, B), 2)=B) ).
fof(rd4_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => k5_relat_1(A, k9_xtuple_0(A))=A) ) ).
fof(rd5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => k5_relat_1(k5_relat_1(A, B), B)=k5_relat_1(A, B)) ) ).
fof(rd5_vectsp_1, axiom,  (! [A, B, C] :  ( ( ( ~ (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)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  & m1_subset_1(C, u1_struct_0(B))) )  => k3_vectsp_1(A, B, k5_struct_0(A), C)=C) ) ).
fof(rd7_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  & v1_finseq_1(A)) ) )  => k3_finseq_1(k16_finseq_1(1, A))=1) ) ).
fof(rd8_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k5_relat_1(B, A)=B) ) ).
fof(redefinition_k10_matrixj1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  (v1_matrixj1(B, A) & m1_finseq_1(B, k3_finseq_2(k3_finseq_2(A)))) )  => k10_matrixj1(A, B)=k8_matrixj1(A, B)) ) ).
fof(redefinition_k11_matrixj1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  (v1_matrixj1(B, A) & m1_finseq_1(B, k3_finseq_2(k3_finseq_2(A)))) )  => k11_matrixj1(A, B)=k9_matrixj1(A, B)) ) ).
fof(redefinition_k13_matrixj1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) &  (v1_matrixj1(C, A) & m1_finseq_1(C, k3_finseq_2(k3_finseq_2(A)))) ) )  => k13_matrixj1(A, B, C)=k12_matrixj1(A, B, C)) ) ).
fof(redefinition_k14_matrixj1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (v2_matrixj1(B, A) & m1_finseq_1(B, k3_finseq_2(k3_finseq_2(A)))) )  => k14_matrixj1(A, B, C)=k1_funct_1(B, C)) ) ).
fof(redefinition_k15_matrixj1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v2_matrixj1(B, A) & m1_finseq_1(B, k3_finseq_2(k3_finseq_2(A))))  &  (v2_matrixj1(C, A) & m1_finseq_1(C, k3_finseq_2(k3_finseq_2(A)))) ) )  => k15_matrixj1(A, B, C)=k7_finseq_1(B, C)) ) ).
fof(redefinition_k16_matrixj1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (v7_ordinal1(B) &  (v1_matrix_0(C) &  (v2_matrix_0(C, A, B, B) & m1_finseq_1(C, k3_finseq_2(A))) ) ) )  => k16_matrixj1(A, B, C)=k5_finseq_1(C)) ) ).
fof(redefinition_k17_finseq_1, axiom,  (! [A, B, C] :  ( (v7_ordinal1(B) & m1_finseq_1(C, A))  => k17_finseq_1(A, B, C)=k16_finseq_1(B, C)) ) ).
fof(redefinition_k17_matrixj1, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  (v7_ordinal1(B) &  (v7_ordinal1(C) &  ( (v1_matrix_0(D) &  (v2_matrix_0(D, A, B, B) & m1_finseq_1(D, k3_finseq_2(A))) )  &  (v1_matrix_0(E) &  (v2_matrix_0(E, A, C, C) & m1_finseq_1(E, k3_finseq_2(A))) ) ) ) ) )  => k17_matrixj1(A, B, C, D, E)=k10_finseq_1(D, E)) ) ).
fof(redefinition_k18_rvsum_1, axiom,  (! [A] :  (m1_finseq_1(A, k1_numbers) => k18_rvsum_1(A)=k16_rvsum_1(A)) ) ).
fof(redefinition_k1_domain_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, A) & m1_subset_1(D, B)) ) )  => k1_domain_1(A, B, C, D)=k4_tarski(C, D)) ) ).
fof(redefinition_k1_matrlin2, axiom,  (! [A, B, C, D, E, F] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) &  (v1_matrlin(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v8_vectsp_1(C, A) &  (v9_vectsp_1(C, A) &  (v10_vectsp_1(C, A) &  (v11_vectsp_1(C, A) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v1_matrlin(C, A) & l1_vectsp_1(C, A)) ) ) ) ) ) ) ) ) )  &  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  &  (m1_finseq_1(E, u1_struct_0(B)) & m1_matrlin(F, A, C)) ) ) ) )  => k1_matrlin2(A, B, C, D, E, F)=k10_matrlin(A, B, C, D, E, F)) ) ).
fof(redefinition_k1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_subset_1(B, k4_ordinal1))  => k1_nat_1(A, B)=k2_xcmplx_0(A, B)) ) ).
fof(redefinition_k1_wsierp_1, axiom,  (! [A] :  (m1_finseq_1(A, k4_ordinal1) => k1_wsierp_1(A)=k16_rvsum_1(A)) ) ).
fof(redefinition_k20_matrixj1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) &  (v2_matrixj1(C, A) & m1_finseq_1(C, k3_finseq_2(k3_finseq_2(A)))) ) )  => k20_matrixj1(A, B, C)=k12_matrixj1(A, B, C)) ) ).
fof(redefinition_k2_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => k2_finseq_1(A)=k1_finseq_1(A)) ) ).
fof(redefinition_k2_matrixj1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (v1_matrixj1(B, A) & m1_finseq_1(B, k3_finseq_2(k3_finseq_2(A)))) )  => k2_matrixj1(A, B, C)=k1_funct_1(B, C)) ) ).
fof(redefinition_k2_matrixj2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & v7_ordinal1(C)) )  => k2_matrixj2(A, B, C)=k1_matrixj2(A, B, C)) ) ).
fof(redefinition_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k3_finseq_1(A)=k1_card_1(A)) ) ).
fof(redefinition_k3_finseq_2, axiom,  (! [A] : k3_finseq_2(A)=k13_finseq_1(A)) ).
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_k3_matrixj1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_matrixj1(B, A) & m1_finseq_1(B, k3_finseq_2(k3_finseq_2(A))))  &  (v1_matrixj1(C, A) & m1_finseq_1(C, k3_finseq_2(k3_finseq_2(A)))) ) )  => k3_matrixj1(A, B, C)=k7_finseq_1(B, C)) ) ).
fof(redefinition_k3_matrixj2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( (v1_matrixj2(B, A) & m1_finseq_1(B, k3_finseq_2(k3_finseq_2(u1_struct_0(A)))))  &  (v1_matrixj2(C, A) & m1_finseq_1(C, k3_finseq_2(k3_finseq_2(u1_struct_0(A))))) ) )  => k3_matrixj2(A, B, C)=k7_finseq_1(B, C)) ) ).
fof(redefinition_k4_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k4_finseq_1(A)=k9_xtuple_0(A)) ) ).
fof(redefinition_k4_matrixj1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  (v1_matrix_0(B) & m1_finseq_1(B, k3_finseq_2(A))) )  => k4_matrixj1(A, B)=k5_finseq_1(B)) ) ).
fof(redefinition_k5_matrixj1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_matrix_0(B) & m1_finseq_1(B, k3_finseq_2(A)))  &  (v1_matrix_0(C) & m1_finseq_1(C, k3_finseq_2(A))) ) )  => k5_matrixj1(A, B, C)=k10_finseq_1(B, C)) ) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_k6_partfun1, axiom,  (! [A] : k6_partfun1(A)=k4_relat_1(A)) ).
fof(redefinition_k7_nat_d, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => k7_nat_d(A, B)=k1_xreal_0(A, B)) ) ).
fof(redefinition_k8_matrlin2, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v8_vectsp_1(C, A) &  (v9_vectsp_1(C, A) &  (v10_vectsp_1(C, A) &  (v11_vectsp_1(C, A) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) & l1_vectsp_1(C, A)) ) ) ) ) ) ) ) )  &  (m1_vectsp_4(D, A, B) &  (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) &  (v13_vectsp_1(E, B, C) &  (v1_mod_2(E, A, B, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) ) ) ) ) ) ) )  => k8_matrlin2(A, B, C, D, E)=k2_matrlin2(D, E)) ) ).
fof(redefinition_k9_finseq_1, axiom,  (! [A] : k9_finseq_1(A)=k5_finseq_1(A)) ).
fof(redefinition_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) <=> m1_finseq_1(B, A)) ) ) ).
fof(redefinition_m2_finseq_2, axiom,  (! [A, B] :  (m1_finseq_2(B, A) =>  (! [C] :  (m2_finseq_2(C, A, B) <=> m1_subset_1(C, B)) ) ) ) ).
fof(redefinition_r1_funct_2, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(D))  &  ( (v1_funct_1(E) &  (v1_funct_2(E, A, B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(F) &  (v1_funct_2(F, C, D) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D)))) ) ) ) )  =>  (r1_funct_2(A, B, C, D, E, F) <=> E=F) ) ) ).
fof(redefinition_r2_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (r2_funct_2(A, B, C, D) <=> C=D) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_funct_2, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(D))  &  ( (v1_funct_1(E) &  (v1_funct_2(E, A, B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(F) &  (v1_funct_2(F, C, D) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D)))) ) ) ) )  => r1_funct_2(A, B, C, D, E, E)) ) ).
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(reflexivity_r2_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  => r2_funct_2(A, B, C, C)) ) ).
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__r0_rn1d2, axiom, r1_xxreal_0(0, k7_xcmplx_0(1, 2))).
fof(rqLessOrEqual__r1_xxreal_0__r0_rnm1d2, axiom,  ~ (r1_xxreal_0(0, k7_xcmplx_0(k4_xcmplx_0(1), 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__r1_rn1d2, axiom,  ~ (r1_xxreal_0(1, k7_xcmplx_0(1, 2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_rnm1d2, axiom,  ~ (r1_xxreal_0(1, k7_xcmplx_0(k4_xcmplx_0(1), 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__r2_rn1d2, axiom,  ~ (r1_xxreal_0(2, k7_xcmplx_0(1, 2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_rnm1d2, axiom,  ~ (r1_xxreal_0(2, k7_xcmplx_0(k4_xcmplx_0(1), 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__rm1_rn1d2, axiom, r1_xxreal_0(k4_xcmplx_0(1), k7_xcmplx_0(1, 2))).
fof(rqLessOrEqual__r1_xxreal_0__rm1_rnm1d2, axiom, r1_xxreal_0(k4_xcmplx_0(1), k7_xcmplx_0(k4_xcmplx_0(1), 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(rqLessOrEqual__r1_xxreal_0__rm2_rn1d2, axiom, r1_xxreal_0(k4_xcmplx_0(2), k7_xcmplx_0(1, 2))).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_r0, axiom,  ~ (r1_xxreal_0(k7_xcmplx_0(1, 2), 0)) ).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_r1, axiom, r1_xxreal_0(k7_xcmplx_0(1, 2), 1)).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_r2, axiom, r1_xxreal_0(k7_xcmplx_0(1, 2), 2)).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_rm1, axiom,  ~ (r1_xxreal_0(k7_xcmplx_0(1, 2), k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_rm2, axiom,  ~ (r1_xxreal_0(k7_xcmplx_0(1, 2), k4_xcmplx_0(2))) ).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_rn1d2, axiom, r1_xxreal_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(1, 2))).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_rnm1d2, axiom,  ~ (r1_xxreal_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))) ).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_r0, axiom, r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 0)).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_r1, axiom, r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 1)).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_r2, axiom, r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 2)).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_rm1, axiom,  ~ (r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_rn1d2, axiom, r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(1, 2))).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_rnm1d2, axiom, r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(k4_xcmplx_0(1), 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__r0_rn1d2_rn1d2, axiom, k2_xcmplx_0(0, k7_xcmplx_0(1, 2))=k7_xcmplx_0(1, 2)).
fof(rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, axiom, k2_xcmplx_0(0, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(k4_xcmplx_0(1), 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__r1_rnm1d2_rn1d2, axiom, k2_xcmplx_0(1, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(1, 2)).
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__rm1_rn1d2_rnm1d2, axiom, k2_xcmplx_0(k4_xcmplx_0(1), k7_xcmplx_0(1, 2))=k7_xcmplx_0(k4_xcmplx_0(1), 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(rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, axiom, k2_xcmplx_0(k7_xcmplx_0(1, 2), 0)=k7_xcmplx_0(1, 2)).
fof(rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, axiom, k2_xcmplx_0(k7_xcmplx_0(1, 2), k4_xcmplx_0(1))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, axiom, k2_xcmplx_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(1, 2))=1).
fof(rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, axiom, k2_xcmplx_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))=0).
fof(rqRealAdd__k2_xcmplx_0__rnm1d2_r0_rnm1d2, axiom, k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 0)=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, axiom, k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 1)=k7_xcmplx_0(1, 2)).
fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, axiom, k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(1, 2))=0).
fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, axiom, k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))=k4_xcmplx_0(1)).
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__r0_rn1d2_rnm1d2, axiom, k6_xcmplx_0(0, k7_xcmplx_0(1, 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, axiom, k6_xcmplx_0(0, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(1, 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__r1_rn1d2_rn1d2, axiom, k6_xcmplx_0(1, k7_xcmplx_0(1, 2))=k7_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__rm1_rnm1d2_rnm1d2, axiom, k6_xcmplx_0(k4_xcmplx_0(1), k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
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(rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, axiom, k6_xcmplx_0(k7_xcmplx_0(1, 2), 0)=k7_xcmplx_0(1, 2)).
fof(rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, axiom, k6_xcmplx_0(k7_xcmplx_0(1, 2), 1)=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, axiom, k6_xcmplx_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(1, 2))=0).
fof(rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, axiom, k6_xcmplx_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))=1).
fof(rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, axiom, k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 0)=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, axiom, k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k4_xcmplx_0(1))=k7_xcmplx_0(1, 2)).
fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, axiom, k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(1, 2))=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, axiom, k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))=0).
fof(rqRealDiv__k7_xcmplx_0__r1_r1_r1, axiom, k7_xcmplx_0(1, 1)=1).
fof(rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, axiom, k7_xcmplx_0(1, 2)=k7_xcmplx_0(1, 2)).
fof(rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, axiom, k7_xcmplx_0(1, k4_xcmplx_0(1))=k4_xcmplx_0(1)).
fof(rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, axiom, k7_xcmplx_0(1, k4_xcmplx_0(2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, axiom, k7_xcmplx_0(1, k7_xcmplx_0(1, 2))=2).
fof(rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, axiom, k7_xcmplx_0(1, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k4_xcmplx_0(2)).
fof(rqRealDiv__k7_xcmplx_0__r2_r1_r2, axiom, k7_xcmplx_0(2, 1)=2).
fof(rqRealDiv__k7_xcmplx_0__r2_r2_r1, axiom, k7_xcmplx_0(2, 2)=1).
fof(rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, axiom, k7_xcmplx_0(k4_xcmplx_0(1), 1)=k4_xcmplx_0(1)).
fof(rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, axiom, k7_xcmplx_0(k4_xcmplx_0(1), 2)=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, axiom, k7_xcmplx_0(k4_xcmplx_0(2), 2)=k4_xcmplx_0(1)).
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__r0_rn1d2_r0, axiom, k3_xcmplx_0(0, k7_xcmplx_0(1, 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__r1_rn1d2_rn1d2, axiom, k3_xcmplx_0(1, k7_xcmplx_0(1, 2))=k7_xcmplx_0(1, 2)).
fof(rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, axiom, k3_xcmplx_0(1, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(k4_xcmplx_0(1), 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__r2_rn1d2_r1, axiom, k3_xcmplx_0(2, k7_xcmplx_0(1, 2))=1).
fof(rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, axiom, k3_xcmplx_0(2, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k4_xcmplx_0(1)).
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(rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, axiom, k3_xcmplx_0(k4_xcmplx_0(2), k7_xcmplx_0(1, 2))=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, axiom, k3_xcmplx_0(k4_xcmplx_0(2), k7_xcmplx_0(k4_xcmplx_0(1), 2))=1).
fof(rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 2), 0)=0).
fof(rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 2), 1)=k7_xcmplx_0(1, 2)).
fof(rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 2), 2)=1).
fof(rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 2), k4_xcmplx_0(2))=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 1)=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 2)=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k4_xcmplx_0(2))=1).
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(rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, axiom, k4_xcmplx_0(k7_xcmplx_0(1, 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, axiom, k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(1, 2)).
fof(s2_nat_1__e3_53__matrixj2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v2_polynom5(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( ( (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v13_algstr_0(B) &  (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) &  (v1_matrlin(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) ) )  =>  (r1_xxreal_0(k1_vectsp_9(A, B), k5_numbers) =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(B)) &  (v13_vectsp_1(C, B, B) &  (v1_mod_2(C, A, B, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(B))))) ) ) )  =>  (? [D] :  ( (v2_relat_1(D) &  (v1_matrixj2(D, A) & m2_finseq_1(D, k3_finseq_2(k3_finseq_2(u1_struct_0(A))))) )  &  (? [E] :  (m1_matrlin(E, A, B) &  (k1_matrlin2(A, B, B, C, E, E)=k20_matrixj1(u1_struct_0(A), k4_struct_0(A), D) &  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (m1_vectsp11(F, A, B, C) <=>  (? [G] :  (v7_ordinal1(G) &  (r2_tarski(G, k4_finseq_1(D)) & k14_matrixj1(u1_struct_0(A), D, G)=k2_matrixj2(A, F, k3_finseq_1(k14_matrixj1(u1_struct_0(A), D, G)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [H] :  (v7_ordinal1(H) =>  ( (! [I] :  ( ( ~ (v2_struct_0(I))  &  ( ~ (v7_struct_0(I))  &  (v13_algstr_0(I) &  (v8_vectsp_1(I, A) &  (v9_vectsp_1(I, A) &  (v10_vectsp_1(I, A) &  (v11_vectsp_1(I, A) &  (v2_rlvect_1(I) &  (v3_rlvect_1(I) &  (v4_rlvect_1(I) &  (v1_matrlin(I, A) & l1_vectsp_1(I, A)) ) ) ) ) ) ) ) ) ) )  =>  (r1_xxreal_0(k1_vectsp_9(A, I), H) =>  (! [J] :  ( (v1_funct_1(J) &  (v1_funct_2(J, u1_struct_0(I), u1_struct_0(I)) &  (v13_vectsp_1(J, I, I) &  (v1_mod_2(J, A, I, I) & m1_subset_1(J, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(I), u1_struct_0(I))))) ) ) )  =>  (? [K] :  ( (v2_relat_1(K) &  (v1_matrixj2(K, A) & m2_finseq_1(K, k3_finseq_2(k3_finseq_2(u1_struct_0(A))))) )  &  (? [L] :  (m1_matrlin(L, A, I) &  (k1_matrlin2(A, I, I, J, L, L)=k20_matrixj1(u1_struct_0(A), k4_struct_0(A), K) &  (! [M] :  (m1_subset_1(M, u1_struct_0(A)) =>  (m1_vectsp11(M, A, I, J) <=>  (? [N] :  (v7_ordinal1(N) &  (r2_tarski(N, k4_finseq_1(K)) & k14_matrixj1(u1_struct_0(A), K, N)=k2_matrixj2(A, M, k3_finseq_1(k14_matrixj1(u1_struct_0(A), K, N)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [O] :  ( ( ~ (v2_struct_0(O))  &  ( ~ (v7_struct_0(O))  &  (v13_algstr_0(O) &  (v8_vectsp_1(O, A) &  (v9_vectsp_1(O, A) &  (v10_vectsp_1(O, A) &  (v11_vectsp_1(O, A) &  (v2_rlvect_1(O) &  (v3_rlvect_1(O) &  (v4_rlvect_1(O) &  (v1_matrlin(O, A) & l1_vectsp_1(O, A)) ) ) ) ) ) ) ) ) ) )  =>  (r1_xxreal_0(k1_vectsp_9(A, O), k1_nat_1(H, 1)) =>  (! [P] :  ( (v1_funct_1(P) &  (v1_funct_2(P, u1_struct_0(O), u1_struct_0(O)) &  (v13_vectsp_1(P, O, O) &  (v1_mod_2(P, A, O, O) & m1_subset_1(P, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(O), u1_struct_0(O))))) ) ) )  =>  (? [Q] :  ( (v2_relat_1(Q) &  (v1_matrixj2(Q, A) & m2_finseq_1(Q, k3_finseq_2(k3_finseq_2(u1_struct_0(A))))) )  &  (? [R] :  (m1_matrlin(R, A, O) &  (k1_matrlin2(A, O, O, P, R, R)=k20_matrixj1(u1_struct_0(A), k4_struct_0(A), Q) &  (! [S] :  (m1_subset_1(S, u1_struct_0(A)) =>  (m1_vectsp11(S, A, O, P) <=>  (? [T] :  (v7_ordinal1(T) &  (r2_tarski(T, k4_finseq_1(Q)) & k14_matrixj1(u1_struct_0(A), Q, T)=k2_matrixj2(A, S, k3_finseq_1(k14_matrixj1(u1_struct_0(A), Q, T)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [H] :  (v7_ordinal1(H) =>  (! [U] :  ( ( ~ (v2_struct_0(U))  &  ( ~ (v7_struct_0(U))  &  (v13_algstr_0(U) &  (v8_vectsp_1(U, A) &  (v9_vectsp_1(U, A) &  (v10_vectsp_1(U, A) &  (v11_vectsp_1(U, A) &  (v2_rlvect_1(U) &  (v3_rlvect_1(U) &  (v4_rlvect_1(U) &  (v1_matrlin(U, A) & l1_vectsp_1(U, A)) ) ) ) ) ) ) ) ) ) )  =>  (r1_xxreal_0(k1_vectsp_9(A, U), H) =>  (! [V] :  ( (v1_funct_1(V) &  (v1_funct_2(V, u1_struct_0(U), u1_struct_0(U)) &  (v13_vectsp_1(V, U, U) &  (v1_mod_2(V, A, U, U) & m1_subset_1(V, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(U), u1_struct_0(U))))) ) ) )  =>  (? [W] :  ( (v2_relat_1(W) &  (v1_matrixj2(W, A) & m2_finseq_1(W, k3_finseq_2(k3_finseq_2(u1_struct_0(A))))) )  &  (? [X] :  (m1_matrlin(X, A, U) &  (k1_matrlin2(A, U, U, V, X, X)=k20_matrixj1(u1_struct_0(A), k4_struct_0(A), W) &  (! [Y] :  (m1_subset_1(Y, u1_struct_0(A)) =>  (m1_vectsp11(Y, A, U, V) <=>  (? [Z] :  (v7_ordinal1(Z) &  (r2_tarski(Z, k4_finseq_1(W)) & k14_matrixj1(u1_struct_0(A), W, Z)=k2_matrixj2(A, Y, k3_finseq_1(k14_matrixj1(u1_struct_0(A), W, Z)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(spc0_boole, axiom, v1_xboole_0(0)).
fof(spc0_numerals, axiom, m1_subset_1(0, k4_ordinal1)).
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(spc4_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k3_xcmplx_0(A, k7_xcmplx_0(B, C))=k7_xcmplx_0(k3_xcmplx_0(A, B), C)) ) ).
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(symmetry_r1_funct_2, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(D))  &  ( (v1_funct_1(E) &  (v1_funct_2(E, A, B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(F) &  (v1_funct_2(F, C, D) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D)))) ) ) ) )  =>  (r1_funct_2(A, B, C, D, E, F) => r1_funct_2(A, B, C, D, F, E)) ) ) ).
fof(symmetry_r2_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (r2_funct_2(A, B, C, D) => r2_funct_2(A, B, D, C)) ) ) ).
fof(t10_vectsp_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  =>  (! [C] :  (m1_vectsp_4(C, A, B) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(C)) => m1_subset_1(D, u1_struct_0(B))) ) ) ) ) ) ) ) ).
fof(t11_vectsp_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  =>  (! [C] :  (m1_vectsp_4(C, A, B) => k4_struct_0(C)=k4_struct_0(B)) ) ) ) ) ) ).
fof(t13_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (v7_ordinal1(B) =>  ( ~ (r1_xxreal_0(k1_nat_1(B, 1), A))  <=> r1_xxreal_0(A, B)) ) ) ) ) ).
fof(t14_vectsp11, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(B)) &  (v13_vectsp_1(C, B, B) &  (v1_mod_2(C, A, B, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(B))))) ) ) )  =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  ( (v1_vectsp11(C, A, B) & m1_vectsp11(D, A, B, C))  <=>  ~ (v7_struct_0(k1_ranknull(A, B, B, k3_matrlin(A, B, B, C, k4_matrlin(A, B, B, k3_struct_0(B), k4_algstr_0(A, D)))))) ) ) ) ) ) ) ) ) ) ).
fof(t14_vectsp_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(B)) =>  (! [E] :  (m1_vectsp_4(E, A, B) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(E)) =>  (F=D => k3_vectsp_1(A, E, C, F)=k3_vectsp_1(A, B, C, D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t16_vectsp11, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v2_polynom5(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v13_algstr_0(B) &  (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) &  (v1_matrlin(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(B)) &  (v13_vectsp_1(C, B, B) &  (v1_mod_2(C, A, B, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(B))))) ) ) )  => v1_vectsp11(C, A, B)) ) ) ) ) ) ).
fof(t19_vectsp11, axiom,  (! [A] :  (l1_struct_0(A) =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) )  => r2_funct_2(u1_struct_0(A), u1_struct_0(A), k1_vectsp11(A, B, 1), B)) ) ) ) ).
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(t1_xxreal_0, axiom,  (! [A] :  (v1_xxreal_0(A) =>  (! [B] :  (v1_xxreal_0(B) =>  ( (r1_xxreal_0(A, B) & r1_xxreal_0(B, A))  => A=B) ) ) ) ) ).
fof(t21_matrlin2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) &  (v1_matrlin(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  =>  (! [C] :  (m1_matrlin(C, A, B) => k3_finseq_1(C)=k1_vectsp_9(A, B)) ) ) ) ) ) ).
fof(t24_matrix_0, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  ( (v1_matrix_0(C) &  (v2_matrix_0(C, B, A, A) & m2_finseq_1(C, k3_finseq_2(B))) )  =>  (k3_finseq_1(C)=A &  (k1_matrix_0(C)=A & k2_matrix_0(C)=k2_zfmisc_1(k2_finseq_1(A), k2_finseq_1(A))) ) ) ) ) ) ) ) ).
fof(t25_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) )  =>  (! [C] :  (v7_ordinal1(C) =>  ~ ( (r2_tarski(C, k4_finseq_1(k7_finseq_1(A, B))) &  ( ~ (r2_tarski(C, k4_finseq_1(A)))  &  (! [D] :  (v7_ordinal1(D) =>  ~ ( (r2_tarski(D, k4_finseq_1(B)) & C=k2_xcmplx_0(k3_finseq_1(A), D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t25_vectsp11, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  (v13_algstr_0(B) &  (v33_algstr_0(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v8_vectsp_1(C, B) &  (v9_vectsp_1(C, B) &  (v10_vectsp_1(C, B) &  (v11_vectsp_1(C, B) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) & l1_vectsp_1(C, B)) ) ) ) ) ) ) ) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(C), u1_struct_0(C)) &  (v13_vectsp_1(D, C, C) &  (v1_mod_2(D, B, C, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C), u1_struct_0(C))))) ) ) )  => m1_vectsp_4(k1_ranknull(B, C, C, k1_vectsp11(C, D, A)), B, k2_vectsp11(B, C, D))) ) ) ) ) ) ) ) ).
fof(t25_vectsp_9, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) &  (v1_matrlin(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  =>  (! [C] :  (m1_vectsp_4(C, A, B) => r1_xxreal_0(k1_vectsp_9(A, C), k1_vectsp_9(A, B))) ) ) ) ) ) ).
fof(t26_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) )  => r1_tarski(k4_finseq_1(A), k4_finseq_1(k7_finseq_1(A, B)))) ) ) ) ).
fof(t26_matrlin2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) &  (v1_matrlin(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  =>  (! [C] :  (m1_vectsp_4(C, A, B) =>  (! [D] :  (m1_vectsp_4(D, A, B) =>  (k2_vectsp_5(A, B, C, D)=k1_vectsp_4(A, B) =>  (! [E] :  (m1_matrlin(E, A, C) =>  (! [F] :  (m1_matrlin(F, A, D) => m1_matrlin(k7_finseq_1(E, F), A, k1_vectsp_5(A, B, C, D))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t27_matrlin2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) &  (v1_matrlin(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v8_vectsp_1(C, A) &  (v9_vectsp_1(C, A) &  (v10_vectsp_1(C, A) &  (v11_vectsp_1(C, A) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v1_matrlin(C, A) & l1_vectsp_1(C, A)) ) ) ) ) ) ) ) ) )  =>  (! [D] :  (m1_matrlin(D, A, B) =>  (! [E] :  (m1_matrlin(E, A, C) =>  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, u1_struct_0(B), u1_struct_0(C)) &  (v13_vectsp_1(F, B, C) &  (v1_mod_2(F, A, B, C) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) ) ) )  =>  (! [G] :  (m1_vectsp_4(G, A, B) =>  (! [H] :  (m1_vectsp_4(H, A, B) =>  (! [I] :  (m1_vectsp_4(I, A, C) =>  (! [J] :  (m1_vectsp_4(J, A, C) =>  (r1_vectsp_5(A, C, I, J) =>  ( (k1_vectsp_9(A, G)=k5_numbers &  ~ (k1_vectsp_9(A, I)=k5_numbers) )  |  ( (k1_vectsp_9(A, H)=k5_numbers &  ~ (k1_vectsp_9(A, J)=k5_numbers) )  |  (! [K] :  ( (v1_funct_1(K) &  (v1_funct_2(K, u1_struct_0(G), u1_struct_0(I)) &  (v13_vectsp_1(K, G, I) &  (v1_mod_2(K, A, G, I) & m1_subset_1(K, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(G), u1_struct_0(I))))) ) ) )  =>  (! [L] :  ( (v1_funct_1(L) &  (v1_funct_2(L, u1_struct_0(H), u1_struct_0(J)) &  (v13_vectsp_1(L, H, J) &  (v1_mod_2(L, A, H, J) & m1_subset_1(L, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(H), u1_struct_0(J))))) ) ) )  =>  ( (K=k2_matrlin2(G, F) & L=k2_matrlin2(H, F))  =>  (! [M] :  (m1_matrlin(M, A, G) =>  (! [N] :  (m1_matrlin(N, A, H) =>  (! [O] :  (m1_matrlin(O, A, I) =>  (! [P] :  (m1_matrlin(P, A, J) =>  ( (k7_finseq_1(M, N)=D & k7_finseq_1(O, P)=E)  => k1_matrlin2(A, B, C, F, D, E)=k13_matrixj1(u1_struct_0(A), k4_struct_0(A), k5_matrixj1(u1_struct_0(A), k1_matrlin2(A, G, I, K, M, O), k1_matrlin2(A, H, J, L, N, P)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t27_vectsp11, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) &  (v1_matrlin(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(B)) &  (v13_vectsp_1(C, B, B) &  (v1_mod_2(C, A, B, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(B))))) ) ) )  =>  (? [D] :  (v7_ordinal1(D) & k2_vectsp11(A, B, C)=k1_ranknull(A, B, B, k1_vectsp11(B, C, D))) ) ) ) ) ) ) ) ).
fof(t28_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) )  =>  (! [C] :  ( (v1_relat_1(C) &  (v1_funct_1(C) & v1_finseq_1(C)) )  =>  (r2_tarski(A, k4_finseq_1(C)) => r2_tarski(k2_xcmplx_0(k3_finseq_1(B), A), k4_finseq_1(k7_finseq_1(B, C)))) ) ) ) ) ) ) ).
fof(t29_vectsp11, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  (v13_algstr_0(B) &  (v33_algstr_0(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v8_vectsp_1(C, B) &  (v9_vectsp_1(C, B) &  (v10_vectsp_1(C, B) &  (v11_vectsp_1(C, B) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) & l1_vectsp_1(C, B)) ) ) ) ) ) ) ) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(C), u1_struct_0(C)) &  (v13_vectsp_1(D, C, C) &  (v1_mod_2(D, B, C, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C), u1_struct_0(C))))) ) ) )  =>  (! [E] :  (m1_subset_1(E, u1_struct_0(B)) =>  (v1_funct_1(k8_matrlin2(B, C, C, k1_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A)), D)) &  (v1_funct_2(k8_matrlin2(B, C, C, k1_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A)), D), u1_struct_0(k1_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A))), u1_struct_0(k1_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A)))) &  (v13_vectsp_1(k8_matrlin2(B, C, C, k1_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A)), D), k1_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A)), k1_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A))) &  (v1_mod_2(k8_matrlin2(B, C, C, k1_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A)), D), B, k1_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A)), k1_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A))) & m1_subset_1(k8_matrlin2(B, C, C, k1_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A)), D), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A))), u1_struct_0(k1_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(A, k5_numbers)=k5_numbers) ) ).
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_matrixj2, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  (v13_algstr_0(B) &  (v33_algstr_0(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C] :  (m1_subset_1(C, u1_struct_0(B)) =>  (! [D] :  ( ( ~ (v2_struct_0(D))  &  (v13_algstr_0(D) &  (v8_vectsp_1(D, B) &  (v9_vectsp_1(D, B) &  (v10_vectsp_1(D, B) &  (v11_vectsp_1(D, B) &  (v2_rlvect_1(D) &  (v3_rlvect_1(D) &  (v4_rlvect_1(D) & l1_vectsp_1(D, B)) ) ) ) ) ) ) ) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(D), u1_struct_0(D)) &  (v13_vectsp_1(E, D, D) &  (v1_mod_2(E, B, D, D) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(D), u1_struct_0(D))))) ) ) )  =>  (! [F] :  ( (v1_matrlin(F, B) & m1_vectsp_4(F, B, D))  =>  (! [G] :  ( (v1_funct_1(G) &  (v1_funct_2(G, u1_struct_0(F), u1_struct_0(F)) &  (v13_vectsp_1(G, F, F) &  (v1_mod_2(G, B, F, F) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(F), u1_struct_0(F))))) ) ) )  =>  ~ ( (F=k1_ranknull(B, D, D, k1_vectsp11(D, k3_matrlin(B, D, D, E, k4_matrlin(B, D, D, k3_struct_0(D), k4_algstr_0(B, C))), A)) &  (r1_funct_2(u1_struct_0(F), u1_struct_0(D), u1_struct_0(F), u1_struct_0(F), k8_matrlin2(B, D, D, F, E), G) &  (! [H] :  ( (v2_relat_1(H) & m1_matrixj2(H, B, C))  =>  (! [I] :  (m1_matrlin(I, B, F) =>  ~ (k1_matrlin2(B, F, F, G, I, I)=k20_matrixj1(u1_struct_0(B), k4_struct_0(B), H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t33_vectsp11, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  (v13_algstr_0(B) &  (v33_algstr_0(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v8_vectsp_1(C, B) &  (v9_vectsp_1(C, B) &  (v10_vectsp_1(C, B) &  (v11_vectsp_1(C, B) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) & l1_vectsp_1(C, B)) ) ) ) ) ) ) ) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(C), u1_struct_0(C)) &  (v13_vectsp_1(D, C, C) &  (v1_mod_2(D, B, C, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C), u1_struct_0(C))))) ) ) )  =>  (! [E] :  (m1_subset_1(E, u1_struct_0(B)) =>  (v1_funct_1(k8_matrlin2(B, C, C, k3_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A)), D)) &  (v1_funct_2(k8_matrlin2(B, C, C, k3_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A)), D), u1_struct_0(k3_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A))), u1_struct_0(k3_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A)))) &  (v13_vectsp_1(k8_matrlin2(B, C, C, k3_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A)), D), k3_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A)), k3_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A))) &  (v1_mod_2(k8_matrlin2(B, C, C, k3_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A)), D), B, k3_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A)), k3_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A))) & m1_subset_1(k8_matrlin2(B, C, C, k3_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A)), D), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k3_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A))), u1_struct_0(k3_ranknull(B, C, C, k1_vectsp11(C, k3_matrlin(B, C, C, D, k4_matrlin(B, C, C, k3_struct_0(C), E)), A))))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t34_matrixj1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, A) =>  (! [C] :  ( (v1_matrix_0(C) & m2_finseq_1(C, k3_finseq_2(A)))  => k13_matrixj1(A, B, k4_matrixj1(A, C))=C) ) ) ) ) ) ).
fof(t34_vectsp11, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  (v13_algstr_0(B) &  (v33_algstr_0(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v8_vectsp_1(C, B) &  (v9_vectsp_1(C, B) &  (v10_vectsp_1(C, B) &  (v11_vectsp_1(C, B) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) & l1_vectsp_1(C, B)) ) ) ) ) ) ) ) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(C), u1_struct_0(C)) &  (v13_vectsp_1(D, C, C) &  (v1_mod_2(D, B, C, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C), u1_struct_0(C))))) ) ) )  =>  (k2_vectsp11(B, C, D)=k1_ranknull(B, C, C, k1_vectsp11(C, D, A)) => k2_vectsp_5(B, C, k1_ranknull(B, C, C, k1_vectsp11(C, D, A)), k3_ranknull(B, C, C, k1_vectsp11(C, D, A)))=k1_vectsp_4(B, C)) ) ) ) ) ) ) ) ) ).
fof(t34_vectsp_9, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) &  (v1_matrlin(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  =>  (! [C] :  (m1_vectsp_4(C, A, B) =>  (! [D] :  (m1_vectsp_4(D, A, B) =>  (r1_vectsp_5(A, B, C, D) => k1_vectsp_9(A, B)=k2_xcmplx_0(k1_vectsp_9(A, C), k1_vectsp_9(A, D))) ) ) ) ) ) ) ) ) ).
fof(t35_matrixj1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, A) =>  (! [C] :  ( (v1_matrixj1(C, A) & m2_finseq_1(C, k3_finseq_2(k3_finseq_2(A))))  =>  (! [D] :  ( (v1_matrixj1(D, A) & m2_finseq_1(D, k3_finseq_2(k3_finseq_2(A))))  => k13_matrixj1(A, B, k3_matrixj1(A, C, D))=k13_matrixj1(A, B, k3_matrixj1(A, k4_matrixj1(A, k13_matrixj1(A, B, C)), D))) ) ) ) ) ) ) ) ).
fof(t35_vectsp11, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) &  (v1_matrlin(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(B)) &  (v13_vectsp_1(C, B, B) &  (v1_mod_2(C, A, B, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(B))))) ) ) )  =>  (! [D] :  (v7_ordinal1(D) =>  (k2_vectsp11(A, B, C)=k1_ranknull(A, B, B, k1_vectsp11(B, C, D)) => r1_vectsp_5(A, B, k1_ranknull(A, B, B, k1_vectsp11(B, C, D)), k3_ranknull(A, B, B, k1_vectsp11(B, C, D)))) ) ) ) ) ) ) ) ) ).
fof(t36_matrixj1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, A) =>  (! [C] :  ( (v1_matrixj1(C, A) & m2_finseq_1(C, k3_finseq_2(k3_finseq_2(A))))  =>  (! [D] :  ( (v1_matrixj1(D, A) & m2_finseq_1(D, k3_finseq_2(k3_finseq_2(A))))  => k13_matrixj1(A, B, k3_matrixj1(A, C, D))=k13_matrixj1(A, B, k3_matrixj1(A, C, k4_matrixj1(A, k13_matrixj1(A, B, D))))) ) ) ) ) ) ) ) ).
fof(t37_vectsp_5, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  =>  (! [C] :  (m1_vectsp_4(C, A, B) =>  (! [D] :  (m1_vectsp_4(D, A, B) =>  (r1_vectsp_5(A, B, C, D) => m1_vectsp_5(D, A, B, C)) ) ) ) ) ) ) ) ) ).
fof(t39_vectsp11, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(B)) &  (v13_vectsp_1(C, B, B) &  (v1_mod_2(C, A, B, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(B))))) ) ) )  =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  ( (v1_vectsp11(C, A, B) & m1_vectsp11(E, A, B, C))  =>  (D=E |  (! [F] :  (m1_vectsp_5(F, A, B, k2_vectsp11(A, B, k3_matrlin(A, B, B, C, k4_matrlin(A, B, B, k3_struct_0(B), k4_algstr_0(A, D))))) =>  (! [G] :  ( (v1_funct_1(G) &  (v1_funct_2(G, u1_struct_0(F), u1_struct_0(F)) &  (v13_vectsp_1(G, F, F) &  (v1_mod_2(G, A, F, F) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(F), u1_struct_0(F))))) ) ) )  =>  (r1_funct_2(u1_struct_0(F), u1_struct_0(F), u1_struct_0(F), u1_struct_0(B), G, k8_matrlin2(A, B, B, F, C)) =>  (v1_vectsp11(G, A, F) &  ( ~ (m1_vectsp11(D, A, F, G))  &  (m1_vectsp11(E, A, F, G) & m1_vectsp_4(k2_vectsp11(A, B, k3_matrlin(A, B, B, C, k4_matrlin(A, B, B, k3_struct_0(B), k4_algstr_0(A, E)))), A, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(1, A)=A) ) ).
fof(t3_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (A=k5_numbers | r2_hidden(A, k1_finseq_1(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(t40_matrixj1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, A) =>  (! [C] :  ( (v1_matrix_0(C) & m2_finseq_1(C, k3_finseq_2(A)))  =>  (! [D] :  ( (v1_matrixj1(D, A) & m2_finseq_1(D, k3_finseq_2(k3_finseq_2(A))))  =>  (C=k1_xboole_0 =>  (k13_matrixj1(A, B, k3_matrixj1(A, D, k4_matrixj1(A, C)))=k13_matrixj1(A, B, D) & k13_matrixj1(A, B, k3_matrixj1(A, k4_matrixj1(A, C), D))=k13_matrixj1(A, B, D)) ) ) ) ) ) ) ) ) ) ).
fof(t42_matrlin2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) &  (v1_matrlin(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  =>  (v7_struct_0(B) <=> k1_vectsp_9(A, B)=k5_numbers) ) ) ) ) ).
fof(t49_funct_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_hidden(B, A) => k1_funct_1(k5_relat_1(C, A), B)=k1_funct_1(C, B)) ) ) ) ) ).
fof(t4_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k6_xcmplx_0(A, k5_numbers)=A) ) ).
fof(t4_matrlin2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (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) &  (v1_matrlin(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  =>  (! [C] :  (m1_matrlin(C, A, k2_vectsp_4(A, B)) => m1_matrlin(C, A, B)) ) ) ) ) ) ).
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_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k7_xcmplx_0(k5_numbers, A)=k5_numbers) ) ).
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_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k7_xcmplx_0(A, 1)=A) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
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(t72_rvsum_1, axiom, k18_rvsum_1(k6_finseq_1(k1_numbers))=k5_numbers).
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(t87_zfmisc_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (r2_hidden(k4_tarski(C, D), k2_zfmisc_1(A, B)) <=>  (r2_hidden(C, A) & r2_hidden(D, B)) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (v7_ordinal1(B) =>  ~ ( (r1_xxreal_0(A, k1_nat_1(B, 1)) &  ( ~ (r1_xxreal_0(A, B))  &  ~ (A=k1_nat_1(B, 1)) ) ) ) ) ) ) ) ).
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)) ) ) ) ) ) ) ) ).
