% Mizar problem: t46_matrix14,matrix14,3242,5 
fof(t46_matrix14, conjecture,  (! [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) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, k4_ordinal1) =>  (! [C] :  (m1_subset_1(C, k4_ordinal1) =>  (! [D] :  ( (v1_matrix_0(D) &  (v2_matrix_0(D, u1_struct_0(A), B, B) & m2_finseq_1(D, k3_finseq_2(u1_struct_0(A)))) )  =>  ( (C=1 &  (! [E] :  (v7_ordinal1(E) =>  (! [F] :  (v7_ordinal1(F) =>  ( (r1_xxreal_0(1, E) &  (r1_xxreal_0(E, B) &  (r1_xxreal_0(1, F) & r1_xxreal_0(F, B)) ) )  =>  ( (E=F => k3_matrix_0(u1_struct_0(A), D, E, F)=k5_struct_0(A))  &  ( ~ (E=F)  => k3_matrix_0(u1_struct_0(A), D, E, F)=k4_struct_0(A)) ) ) ) ) ) ) )  => D=k4_matrix14(A, B, C)) ) ) ) ) ) ) ) ) ).
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(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(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(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(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(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
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(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(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_card_1, axiom,  (! [A] :  (v1_card_1(A) => v3_ordinal1(A)) ) ).
fof(cc1_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc1_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_matrix_0, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, k3_finseq_2(A)) =>  (v1_matrix_0(B) =>  (v1_funcop_1(B) & v1_matrix_0(B)) ) ) ) ) ).
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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_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(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
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_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_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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_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_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
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_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_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_struct_0, axiom,  (! [A] :  (l4_struct_0(A) =>  ( ~ (v6_struct_0(A))  =>  ~ (v7_struct_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(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_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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_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(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_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_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(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_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_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(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_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(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_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(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_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(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(d2_xboole_0, axiom, k1_xboole_0=o_0_0_xboole_0).
fof(d3_matrix14, axiom,  (! [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) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, k4_ordinal1) =>  (! [C] :  (v7_ordinal1(C) => k4_matrix14(A, B, C)=k2_finseq_7(k3_finseq_2(u1_struct_0(A)), k3_matrix_1(A, B), 1, C)) ) ) ) ) ) ).
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(dt_k13_finseq_1, axiom, $true).
fof(dt_k1_card_1, axiom,  (! [A] : v1_card_1(k1_card_1(A))) ).
fof(dt_k1_finseq_1, axiom, $true).
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_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
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_finseq_7, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  (m1_finseq_1(B, A) &  (v7_ordinal1(C) & v7_ordinal1(D)) ) )  => m2_finseq_1(k2_finseq_7(A, B, C, D), A)) ) ).
fof(dt_k2_matrix_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_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_matrix_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l4_struct_0(A))  & v7_ordinal1(B))  =>  (v1_matrix_0(k3_matrix_1(A, B)) &  (v2_matrix_0(k3_matrix_1(A, B), u1_struct_0(A), B, B) & m2_finseq_1(k3_matrix_1(A, B), k3_finseq_2(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_matrix14, axiom,  (! [A, B, C] :  ( ( ( ~ (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) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  (m1_subset_1(B, k4_ordinal1) & v7_ordinal1(C)) )  =>  (v1_matrix_0(k4_matrix14(A, B, C)) &  (v2_matrix_0(k4_matrix14(A, B, C), u1_struct_0(A), B, B) & m2_finseq_1(k4_matrix14(A, B, C), k3_finseq_2(u1_struct_0(A)))) ) ) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => m1_subset_1(k4_struct_0(A), u1_struct_0(A))) ) ).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_struct_0, axiom,  (! [A] :  (l3_struct_0(A) => m1_subset_1(k5_struct_0(A), u1_struct_0(A))) ) ).
fof(dt_k9_funct_7, axiom, $true).
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_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_subset_1, axiom, $true).
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_o_0_0_xboole_0, axiom, v1_xboole_0(o_0_0_xboole_0)).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_algstr_0, axiom,  (? [A] : l1_algstr_0(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_algstr_0, axiom,  (? [A] : l2_algstr_0(A)) ).
fof(existence_l2_struct_0, axiom,  (? [A] : l2_struct_0(A)) ).
fof(existence_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_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m2_finseq_1, axiom,  (! [A] :  (? [B] : m2_finseq_1(B, A)) ) ).
fof(fc10_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ( ~ (v1_finset_1(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc10_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc10_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => v9_struct_0(k4_struct_0(A), A)) ) ).
fof(fc11_struct_0, axiom,  (! [A] :  ( ( ~ (v6_struct_0(A))  & l4_struct_0(A))  =>  ~ (v9_struct_0(k5_struct_0(A), A)) ) ) ).
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(fc13_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(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(fc15_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_finseq_1(k1_finseq_1(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(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(fc19_struct_0, axiom,  (! [A, B] :  ( (v1_card_1(A) &  (v13_struct_0(B, A) & l1_struct_0(B)) )  => v3_card_1(u1_struct_0(B), A)) ) ).
fof(fc1_card_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v1_xboole_0(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc1_finseq_1, axiom,  (! [A] :  ( (v7_ordinal1(A) & v8_ordinal1(A))  => v1_xboole_0(k1_finseq_1(A))) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc24_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k9_xtuple_0(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_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc31_finseq_1, axiom,  (! [A] : v4_funct_1(k13_finseq_1(A))) ).
fof(fc37_finseq_1, axiom,  (! [A] : v4_finseq_1(k13_finseq_1(A))) ).
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(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_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  => v3_ordinal1(k9_xtuple_0(A))) ) ).
fof(fc5_matrix_6, 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)) ) ) ) ) ) ) )  & v7_ordinal1(B))  =>  (v1_matrix_0(k3_matrix_1(A, B)) &  (v2_matrix_0(k3_matrix_1(A, B), u1_struct_0(A), B, B) & v1_matrix_6(k3_matrix_1(A, B), B, A)) ) ) ) ).
fof(fc6_card_1, axiom, v1_card_1(k4_ordinal1)).
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(fc7_card_1, axiom, v2_card_1(k4_ordinal1)).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
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_matrix_6, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) & l6_algstr_0(B)) ) ) ) ) ) ) ) )  =>  (v1_matrix_0(k3_matrix_1(B, A)) &  (v2_matrix_0(k3_matrix_1(B, A), u1_struct_0(B), A, A) & v2_matrix_6(k3_matrix_1(B, A), A, B)) ) ) ) ).
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_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_card_1, axiom,  ~ (v1_finset_1(k4_ordinal1)) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(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_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(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_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ).
fof(rc1_matrix_6, 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)) ) ) ) ) ) ) )  & v7_ordinal1(B))  =>  (? [C] :  (m1_finseq_1(C, k3_finseq_2(u1_struct_0(A))) &  (v1_relat_1(C) &  (v4_relat_1(C, k4_ordinal1) &  (v5_relat_1(C, 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) &  (v1_matrix_0(C) &  (v2_matrix_0(C, u1_struct_0(A), B, B) & v1_matrix_6(C, 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_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc20_struct_0, axiom,  (? [A] :  (l2_struct_0(A) &  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ).
fof(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(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_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) & v8_ordinal1(A)) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_vectsp_1, axiom,  (? [A] :  (l5_algstr_0(A) &  ( ~ (v2_struct_0(A))  & v4_vectsp_1(A)) ) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_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_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_vectsp_1, axiom,  (? [A] :  (l3_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v3_group_1(A) & v5_group_1(A)) ) ) ) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_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_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_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_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_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(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_ordinal1, axiom,  (? [A] : v7_ordinal1(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_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(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_ordinal1, axiom,  (? [A] : v8_ordinal1(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_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rd1_card_1, axiom,  (! [A] :  (v1_card_1(A) => k1_card_1(A)=A) ) ).
fof(redefinition_k2_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => k2_finseq_1(A)=k1_finseq_1(A)) ) ).
fof(redefinition_k2_finseq_7, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  (m1_finseq_1(B, A) &  (v7_ordinal1(C) & v7_ordinal1(D)) ) )  => k2_finseq_7(A, B, C, D)=k9_funct_7(B, C, D)) ) ).
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_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_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) <=> m1_finseq_1(B, A)) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(reflexivity_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => r1_xxreal_0(A, A)) ) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_r1, axiom, r1_xxreal_0(1, 1)).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(t1_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (v7_ordinal1(B) =>  (r2_hidden(A, k1_finseq_1(B)) <=>  (r1_xxreal_0(1, A) & r1_xxreal_0(A, B)) ) ) ) ) ) ).
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(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(t27_matrix_0, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (v7_ordinal1(B) =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  ( (v1_matrix_0(D) &  (v2_matrix_0(D, C, A, B) & m2_finseq_1(D, k3_finseq_2(C))) )  =>  (! [E] :  ( (v1_matrix_0(E) &  (v2_matrix_0(E, C, A, B) & m2_finseq_1(E, k3_finseq_2(C))) )  =>  ( (! [F] :  (v7_ordinal1(F) =>  (! [G] :  (v7_ordinal1(G) =>  (r2_hidden(k4_tarski(F, G), k2_matrix_0(D)) => k3_matrix_0(C, D, F, G)=k3_matrix_0(C, E, F, G)) ) ) ) )  => D=E) ) ) ) ) ) ) ) ) ) ) ).
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(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(t44_matrix14, axiom,  (! [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) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, k4_ordinal1) =>  (! [C] :  ( (v1_matrix_0(C) &  (v2_matrix_0(C, u1_struct_0(A), B, B) & m2_finseq_1(C, k3_finseq_2(u1_struct_0(A)))) )  =>  (! [D] :  (v7_ordinal1(D) =>  ( (r1_xxreal_0(1, D) & r1_xxreal_0(D, B))  => k3_matrix_0(u1_struct_0(A), k4_matrix14(A, B, 1), D, D)=k5_struct_0(A)) ) ) ) ) ) ) ) ) ).
fof(t45_matrix14, axiom,  (! [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) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, k4_ordinal1) =>  (! [C] :  ( (v1_matrix_0(C) &  (v2_matrix_0(C, u1_struct_0(A), B, B) & m2_finseq_1(C, k3_finseq_2(u1_struct_0(A)))) )  =>  (! [D] :  (v7_ordinal1(D) =>  (! [E] :  (v7_ordinal1(E) =>  ( (r1_xxreal_0(1, D) &  (r1_xxreal_0(D, B) &  (r1_xxreal_0(1, E) & r1_xxreal_0(E, B)) ) )  =>  (D=E | k3_matrix_0(u1_struct_0(A), k4_matrix14(A, B, 1), D, E)=k4_struct_0(A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t4_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v2_xxreal_0(B))  & v2_xxreal_0(A)) ) ) ) ) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(B) |  (v3_xxreal_0(A) | v2_xxreal_0(B)) ) ) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t6_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(A) |  (v2_xxreal_0(B) | v3_xxreal_0(A)) ) ) ) ) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(B)) ) ) ) ) ) ) ) ).
fof(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_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)) ) ) ) ) ) ) ) ).
