% Mizar problem: t63_ec_pf_2,ec_pf_2,3814,7 
fof(t63_ec_pf_2, conjecture,  (! [A] :  ( (v7_ordinal1(A) &  (v1_int_2(A) & v1_ec_pf_2(A, 5)) )  =>  (! [B] :  (m2_subset_1(B, k2_zfmisc_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A))), k1_ec_pf_2(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k9_int_3(A))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k9_int_3(A))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(k9_int_3(A))) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(k9_int_3(A))) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(k9_int_3(A))) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(k9_int_3(A))) =>  (! [I] :  (m1_subset_1(I, u1_struct_0(k9_int_3(A))) =>  (! [J] :  (m1_subset_1(J, u1_struct_0(k9_int_3(A))) =>  (! [K] :  (m2_subset_1(K, k3_ec_pf_1(k9_int_3(A)), k6_ec_pf_1(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B))) =>  (! [L] :  (m1_subset_1(L, k3_zfmisc_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)))) =>  ( (C=k5_int_1(2, A) &  (D=k5_int_1(3, A) &  (E=k5_int_1(4, A) &  (F=k5_int_1(8, A) &  (G=k3_rlvect_1(k9_int_3(A), k8_group_1(k9_int_3(A), k2_ec_pf_2(A, B), k2_binom(k9_int_3(A), k6_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), 2)), k8_group_1(k9_int_3(A), D, k2_binom(k9_int_3(A), k4_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), 2))) &  (H=k8_group_1(k9_int_3(A), k5_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), k6_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K)) &  (I=k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), k4_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), k5_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K)), H) &  (J=k5_algstr_0(k9_int_3(A), k2_binom(k9_int_3(A), G, 2), k8_group_1(k9_int_3(A), F, I)) & L=k4_domain_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), C, J), H), k5_algstr_0(k9_int_3(A), k8_group_1(k9_int_3(A), G, k5_algstr_0(k9_int_3(A), k8_group_1(k9_int_3(A), E, I), J)), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), F, k2_binom(k9_int_3(A), k5_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), 2)), k2_binom(k9_int_3(A), H, 2))), k8_group_1(k9_int_3(A), F, k2_binom(k9_int_3(A), H, 3)))) ) ) ) ) ) ) )  => k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), E, k2_binom(k9_int_3(A), H, 2)), k2_binom(k9_int_3(A), k6_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), 2)), k5_algstr_0(k9_int_3(A), k8_group_1(k9_int_3(A), k2_binom(k9_int_3(A), k2_mcart_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), L), 2), k3_mcart_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), L)), k3_rlvect_1(k9_int_3(A), k3_rlvect_1(k9_int_3(A), k2_binom(k9_int_3(A), k1_mcart_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), L), 3), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), k2_ec_pf_2(A, B), k1_mcart_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), L)), k2_binom(k9_int_3(A), k3_mcart_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), L), 2))), k8_group_1(k9_int_3(A), k3_ec_pf_2(A, B), k2_binom(k9_int_3(A), k3_mcart_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), L), 3)))))=k4_struct_0(k9_int_3(A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(abstractness_v36_algstr_0, axiom,  (! [A] :  (l6_algstr_0(A) =>  (v36_algstr_0(A) => A=g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A))) ) ) ).
fof(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_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_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_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
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_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(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_mcart_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k2_zfmisc_1(A, B)) => v1_xtuple_0(C)) ) ) ) ).
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_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
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_xtuple_0, axiom,  (! [A] :  (v2_xtuple_0(A) => v1_xtuple_0(A)) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_int_1(A)) ) ).
fof(cc2_int_3, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_rlvect_1(A) & v4_vectsp_1(A)) ) ) ) )  =>  ( ~ (v2_struct_0(A))  & v1_int_3(A)) ) ) ) ).
fof(cc2_mcart_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ~ (v1_xboole_0(C)) ) )  =>  (! [D] :  (m1_subset_1(D, k3_zfmisc_1(A, B, C)) => v2_xtuple_0(D)) ) ) ) ).
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_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc2_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_int_1, axiom,  (! [A] :  (v1_int_1(A) => v1_xreal_0(A)) ) ).
fof(cc3_int_3, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_int_2(A))  =>  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  & v1_int_2(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_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc3_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_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v2_int_1(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_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, 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_int_1, axiom,  (! [A] :  (v2_int_1(A) => v1_int_1(A)) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc5_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
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_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc6_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_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(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(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_nat_1, axiom,  (! [A, B] :  ( (m1_subset_1(A, k4_ordinal1) & m1_subset_1(B, k4_ordinal1))  => k2_nat_1(A, B)=k2_nat_1(B, A)) ) ).
fof(commutativity_k2_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(A, B)=k2_xcmplx_0(B, A)) ) ).
fof(commutativity_k3_rlvect_1, axiom,  (! [A, B, C] :  ( ( (v2_rlvect_1(A) & l1_algstr_0(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k3_rlvect_1(A, B, C)=k3_rlvect_1(A, C, B)) ) ).
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(commutativity_k8_group_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v5_group_1(A) & l3_algstr_0(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k8_group_1(A, B, C)=k8_group_1(A, C, B)) ) ).
fof(d14_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k5_algstr_0(A, B, C)=k1_algstr_0(A, B, k4_algstr_0(A, C))) ) ) ) ) ) ).
fof(d18_algstr_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k6_algstr_0(A, B, C)=k4_binop_1(u1_struct_0(A), u2_algstr_0(A), B, C)) ) ) ) ) ) ).
fof(d1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k1_algstr_0(A, B, C)=k4_binop_1(u1_struct_0(A), u1_algstr_0(A), B, C)) ) ) ) ) ) ).
fof(d2_binom, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_group_1(A) & l3_algstr_0(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (v7_ordinal1(C) => k2_binom(A, B, C)=k9_nat_1(u1_struct_0(A), k4_group_1(A), B, C)) ) ) ) ) ) ).
fof(d2_ec_pf_2, axiom,  (! [A] :  ( (v7_ordinal1(A) &  (v1_int_2(A) & v1_ec_pf_2(A, 5)) )  => k1_ec_pf_2(A)=a_1_0_ec_pf_2(A)) ) ).
fof(d3_group_1, axiom,  (! [A] :  (l3_algstr_0(A) =>  (v3_group_1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) => k6_algstr_0(A, k6_algstr_0(A, B, C), D)=k6_algstr_0(A, B, k6_algstr_0(A, C, D))) ) ) ) ) ) ) ) ) ).
fof(d7_vectsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  =>  (v5_vectsp_1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (k6_algstr_0(A, B, k1_algstr_0(A, C, D))=k1_algstr_0(A, k6_algstr_0(A, B, C), k6_algstr_0(A, B, D)) & k6_algstr_0(A, k1_algstr_0(A, C, D), B)=k1_algstr_0(A, k6_algstr_0(A, C, B), k6_algstr_0(A, D, B))) ) ) ) ) ) ) ) ) ) ).
fof(dt_g6_algstr_0, axiom,  (! [A, B, C, D, E] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (m1_subset_1(D, A) & m1_subset_1(E, A)) ) )  =>  (v36_algstr_0(g6_algstr_0(A, B, C, D, E)) & l6_algstr_0(g6_algstr_0(A, B, C, D, E))) ) ) ).
fof(dt_k1_algstr_0, axiom,  (! [A, B, C] :  ( (l1_algstr_0(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k1_algstr_0(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k1_binop_1, axiom, $true).
fof(dt_k1_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_ec_pf_2, axiom,  (! [A] :  ( (v7_ordinal1(A) &  (v1_int_2(A) & v1_ec_pf_2(A, 5)) )  => m1_subset_1(k1_ec_pf_2(A), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)))))) ) ).
fof(dt_k1_mcart_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(D, k3_zfmisc_1(A, B, C))) ) )  => m1_subset_1(k1_mcart_1(A, B, C, D), 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_xboole_0, axiom, $true).
fof(dt_k1_xtuple_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_binom, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v1_group_1(A) & l3_algstr_0(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & v7_ordinal1(C)) )  => m1_subset_1(k2_binom(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k2_ec_pf_2, axiom,  (! [A, B] :  ( ( (v7_ordinal1(A) &  (v1_int_2(A) & v1_ec_pf_2(A, 5)) )  & m1_subset_1(B, k1_ec_pf_2(A)))  => m1_subset_1(k2_ec_pf_2(A, B), u1_struct_0(k9_int_3(A)))) ) ).
fof(dt_k2_mcart_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(D, k3_zfmisc_1(A, B, C))) ) )  => m1_subset_1(k2_mcart_1(A, B, C, D), B)) ) ).
fof(dt_k2_nat_1, axiom,  (! [A, B] :  ( (m1_subset_1(A, k4_ordinal1) & m1_subset_1(B, k4_ordinal1))  => m1_subset_1(k2_nat_1(A, B), k4_ordinal1)) ) ).
fof(dt_k2_xcmplx_0, axiom, $true).
fof(dt_k2_xtuple_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_ec_pf_1, 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)) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v1_xboole_0(k3_ec_pf_1(A)))  & m1_subset_1(k3_ec_pf_1(A), k1_zfmisc_1(k3_zfmisc_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A))))) ) ) ).
fof(dt_k3_ec_pf_2, axiom,  (! [A, B] :  ( ( (v7_ordinal1(A) &  (v1_int_2(A) & v1_ec_pf_2(A, 5)) )  & m1_subset_1(B, k1_ec_pf_2(A)))  => m1_subset_1(k3_ec_pf_2(A, B), u1_struct_0(k9_int_3(A)))) ) ).
fof(dt_k3_mcart_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(D, k3_zfmisc_1(A, B, C))) ) )  => m1_subset_1(k3_mcart_1(A, B, C, D), C)) ) ).
fof(dt_k3_rlvect_1, axiom,  (! [A, B, C] :  ( ( (v2_rlvect_1(A) & l1_algstr_0(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k3_rlvect_1(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k3_xcmplx_0, axiom, $true).
fof(dt_k3_xtuple_0, axiom, $true).
fof(dt_k3_zfmisc_1, axiom, $true).
fof(dt_k4_algstr_0, axiom,  (! [A, B] :  ( (l2_algstr_0(A) & m1_subset_1(B, u1_struct_0(A)))  => m1_subset_1(k4_algstr_0(A, B), u1_struct_0(A))) ) ).
fof(dt_k4_binop_1, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (m1_subset_1(C, A) & m1_subset_1(D, A)) )  => m1_subset_1(k4_binop_1(A, B, C, D), A)) ) ).
fof(dt_k4_domain_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  (m1_subset_1(D, A) &  (m1_subset_1(E, B) & m1_subset_1(F, C)) ) ) ) )  => m1_subset_1(k4_domain_1(A, B, C, D, E, F), k3_zfmisc_1(A, B, C))) ) ).
fof(dt_k4_ec_pf_1, axiom,  (! [A, B, C] :  ( ( (v7_ordinal1(A) & v1_int_2(A))  &  (m1_subset_1(B, u1_struct_0(k9_int_3(A))) & m1_subset_1(C, u1_struct_0(k9_int_3(A)))) )  => m1_subset_1(k4_ec_pf_1(A, B, C), u1_struct_0(k9_int_3(A)))) ) ).
fof(dt_k4_ec_pf_2, axiom,  (! [A, B, C, D] :  ( ( (v7_ordinal1(A) & v1_int_2(A))  &  (m1_subset_1(B, u1_struct_0(k9_int_3(A))) &  (m1_subset_1(C, u1_struct_0(k9_int_3(A))) & m1_subset_1(D, k6_ec_pf_1(A, B, C))) ) )  => m1_subset_1(k4_ec_pf_2(A, B, C, D), u1_struct_0(k9_int_3(A)))) ) ).
fof(dt_k4_group_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_algstr_0(A))  =>  (v1_funct_1(k4_group_1(A)) &  (v1_funct_2(k4_group_1(A), k2_zfmisc_1(u1_struct_0(A), k4_ordinal1), u1_struct_0(A)) & m1_subset_1(k4_group_1(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), k4_ordinal1), 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_k4_xtuple_0, axiom, $true).
fof(dt_k5_algstr_0, axiom,  (! [A, B, C] :  ( (l2_algstr_0(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k5_algstr_0(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k5_ec_pf_2, axiom,  (! [A, B, C, D] :  ( ( (v7_ordinal1(A) & v1_int_2(A))  &  (m1_subset_1(B, u1_struct_0(k9_int_3(A))) &  (m1_subset_1(C, u1_struct_0(k9_int_3(A))) & m1_subset_1(D, k6_ec_pf_1(A, B, C))) ) )  => m1_subset_1(k5_ec_pf_2(A, B, C, D), u1_struct_0(k9_int_3(A)))) ) ).
fof(dt_k5_int_1, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => v1_int_1(k5_int_1(A, B))) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_xtuple_0, axiom, $true).
fof(dt_k6_algstr_0, axiom,  (! [A, B, C] :  ( (l3_algstr_0(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k6_algstr_0(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k6_ec_pf_1, axiom,  (! [A, B, C] :  ( ( (v7_ordinal1(A) & v1_int_2(A))  &  (m1_subset_1(B, u1_struct_0(k9_int_3(A))) & m1_subset_1(C, u1_struct_0(k9_int_3(A)))) )  =>  ( ~ (v1_xboole_0(k6_ec_pf_1(A, B, C)))  & m1_subset_1(k6_ec_pf_1(A, B, C), k1_zfmisc_1(k3_ec_pf_1(k9_int_3(A))))) ) ) ).
fof(dt_k6_ec_pf_2, axiom,  (! [A, B, C, D] :  ( ( (v7_ordinal1(A) & v1_int_2(A))  &  (m1_subset_1(B, u1_struct_0(k9_int_3(A))) &  (m1_subset_1(C, u1_struct_0(k9_int_3(A))) & m1_subset_1(D, k6_ec_pf_1(A, B, C))) ) )  => m1_subset_1(k6_ec_pf_2(A, B, C, D), u1_struct_0(k9_int_3(A)))) ) ).
fof(dt_k8_group_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v5_group_1(A) & l3_algstr_0(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k8_group_1(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k9_int_3, axiom,  (! [A] :  (v7_ordinal1(A) => l6_algstr_0(k9_int_3(A))) ) ).
fof(dt_k9_nat_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, k4_ordinal1), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, k4_ordinal1), A)))) )  &  (m1_subset_1(C, A) & v7_ordinal1(D)) ) )  => m1_subset_1(k9_nat_1(A, B, C, D), A)) ) ).
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_subset_1, axiom, $true).
fof(dt_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) => m1_subset_1(C, A)) ) ) ) ).
fof(dt_u1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  (v1_funct_1(u1_algstr_0(A)) &  (v1_funct_2(u1_algstr_0(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u1_algstr_0(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u2_algstr_0, axiom,  (! [A] :  (l3_algstr_0(A) =>  (v1_funct_1(u2_algstr_0(A)) &  (v1_funct_2(u2_algstr_0(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u2_algstr_0(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(dt_u2_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => m1_subset_1(u2_struct_0(A), u1_struct_0(A))) ) ).
fof(dt_u3_struct_0, axiom,  (! [A] :  (l3_struct_0(A) => m1_subset_1(u3_struct_0(A), u1_struct_0(A))) ) ).
fof(existence_l1_algstr_0, axiom,  (? [A] : l1_algstr_0(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_algstr_0, axiom,  (? [A] : l2_algstr_0(A)) ).
fof(existence_l2_struct_0, axiom,  (? [A] : l2_struct_0(A)) ).
fof(existence_l3_algstr_0, axiom,  (? [A] : l3_algstr_0(A)) ).
fof(existence_l3_struct_0, axiom,  (? [A] : l3_struct_0(A)) ).
fof(existence_l4_algstr_0, axiom,  (? [A] : l4_algstr_0(A)) ).
fof(existence_l4_struct_0, axiom,  (? [A] : l4_struct_0(A)) ).
fof(existence_l5_algstr_0, axiom,  (? [A] : l5_algstr_0(A)) ).
fof(existence_l6_algstr_0, axiom,  (? [A] : l6_algstr_0(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (? [C] : m2_subset_1(C, A, B)) ) ) ).
fof(fc10_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => v9_struct_0(k4_struct_0(A), A)) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(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_subset_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ~ (v1_xboole_0(C)) ) )  =>  ~ (v1_xboole_0(k3_zfmisc_1(A, B, C))) ) ) ).
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_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_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_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(fc1_ec_pf_2, axiom,  (! [A] :  ( (v7_ordinal1(A) &  (v1_int_2(A) & v1_ec_pf_2(A, 5)) )  =>  ~ (v1_xboole_0(k1_ec_pf_2(A))) ) ) ).
fof(fc1_int_1, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => v1_int_1(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_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_xtuple_0, axiom,  (! [A, B] : v1_xtuple_0(k4_tarski(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_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_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k3_xcmplx_0(A, B))) ) ) ).
fof(fc26_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k3_xcmplx_0(A, B))) ) ) ).
fof(fc2_int_1, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => v1_int_1(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_xtuple_0, axiom,  (! [A, B, C] : v2_xtuple_0(k3_xtuple_0(A, B, C))) ).
fof(fc5_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc6_int_3, axiom,  (! [A] :  ( (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) )  =>  ( ~ (v2_struct_0(k9_int_3(A)))  & v36_algstr_0(k9_int_3(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_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k3_xcmplx_0(A, B))) ) ).
fof(fc7_int_1, axiom,  (! [A] :  (v2_int_1(A) => v7_ordinal1(k2_xcmplx_0(A, 1))) ) ).
fof(fc7_int_3, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_int_2(A))  =>  ( ~ (v6_struct_0(k9_int_3(A)))  &  (v13_algstr_0(k9_int_3(A)) &  (v33_algstr_0(k9_int_3(A)) &  (v3_group_1(k9_int_3(A)) &  (v5_group_1(k9_int_3(A)) &  (v2_rlvect_1(k9_int_3(A)) &  (v3_rlvect_1(k9_int_3(A)) &  (v4_rlvect_1(k9_int_3(A)) &  (v4_vectsp_1(k9_int_3(A)) & v5_vectsp_1(k9_int_3(A))) ) ) ) ) ) ) ) ) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_int_1, axiom,  (! [A, B] :  ( (v2_int_1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  => v7_ordinal1(k2_xcmplx_0(A, B))) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(fc9_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k2_xcmplx_0(A, B))) ) ) ).
fof(fraenkel_a_1_0_ec_pf_2, axiom,  (! [A, B] :  ( (v7_ordinal1(B) &  (v1_int_2(B) & v1_ec_pf_2(B, 5)) )  =>  (r2_hidden(A, a_1_0_ec_pf_2(B)) <=>  (? [C, D] :  ( (m1_subset_1(C, u1_struct_0(k9_int_3(B))) & m1_subset_1(D, u1_struct_0(k9_int_3(B))))  &  (A=k1_domain_1(u1_struct_0(k9_int_3(B)), u1_struct_0(k9_int_3(B)), C, D) &  ~ (k4_ec_pf_1(B, C, D)=k4_struct_0(k9_int_3(B))) ) ) ) ) ) ) ).
fof(free_g6_algstr_0, axiom,  (! [A, B, C, D, E] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (m1_subset_1(D, A) & m1_subset_1(E, A)) ) )  =>  (! [F, G, H, I, J] :  (g6_algstr_0(A, B, C, D, E)=g6_algstr_0(F, G, H, I, J) =>  (A=F &  (B=G &  (C=H &  (D=I & E=J) ) ) ) ) ) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(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_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc17_struct_0, axiom,  (! [A] :  (l2_struct_0(A) =>  (? [B] :  (m1_subset_1(B, u1_struct_0(A)) & v9_struct_0(B, A)) ) ) ) ).
fof(rc19_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l2_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, u1_struct_0(A)) &  ~ (v9_struct_0(B, A)) ) ) ) ) ).
fof(rc1_ec_pf_2, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xreal_0(A) &  (v1_int_1(A) &  (v2_int_1(A) &  (v1_int_2(A) &  (v1_xxreal_0(A) & v1_ec_pf_2(A, 5)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_int_1, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v1_xcmplx_0(A) &  (v1_xreal_0(A) & v1_int_1(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_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_0(A)) ).
fof(rc20_struct_0, axiom,  (? [A] :  (l2_struct_0(A) &  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ).
fof(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc2_int_1, axiom,  (? [A] : v1_int_1(A)) ).
fof(rc2_int_3, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v6_struct_0(A) &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v36_algstr_0(A) &  (v1_group_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) &  (v2_vectsp_1(A) &  (v3_vectsp_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & v6_vectsp_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_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(rc2_xtuple_0, axiom,  (? [A] : v2_xtuple_0(A)) ).
fof(rc3_int_1, axiom,  (? [A] : v2_int_1(A)) ).
fof(rc3_int_3, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v8_struct_0(A))  &  (v13_algstr_0(A) &  (v36_algstr_0(A) &  (v1_group_1(A) &  (v3_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) &  (v2_vectsp_1(A) &  (v3_vectsp_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & v6_vectsp_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, 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_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc4_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
fof(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_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc5_vectsp_1, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v36_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v3_vectsp_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & v6_vectsp_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rd1_xtuple_0, axiom,  (! [A, B] : k1_xtuple_0(k4_tarski(A, B))=A) ).
fof(rd2_xtuple_0, axiom,  (! [A, B] : k2_xtuple_0(k4_tarski(A, B))=B) ).
fof(rd3_vectsp_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) & l6_algstr_0(A)) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) &  (v9_struct_0(C, A) & m1_subset_1(C, u1_struct_0(A))) ) )  => k6_algstr_0(A, B, C)=C) ) ).
fof(rd3_xtuple_0, axiom,  (! [A] :  (v1_xtuple_0(A) => k4_tarski(k1_xtuple_0(A), k2_xtuple_0(A))=A) ) ).
fof(rd4_vectsp_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v2_vectsp_1(A) & l6_algstr_0(A)) ) ) ) )  &  ( (v9_struct_0(B, A) & m1_subset_1(B, u1_struct_0(A)))  & m1_subset_1(C, u1_struct_0(A))) )  => k6_algstr_0(A, B, C)=B) ) ).
fof(rd4_xtuple_0, axiom,  (! [A, B, C] : k4_xtuple_0(k3_xtuple_0(A, B, C))=A) ).
fof(rd5_xtuple_0, axiom,  (! [A, B, C] : k5_xtuple_0(k3_xtuple_0(A, B, C))=B) ).
fof(rd6_xtuple_0, axiom,  (! [A, B, C] : k2_xtuple_0(k3_xtuple_0(A, B, C))=C) ).
fof(rd7_xtuple_0, axiom,  (! [A] :  (v2_xtuple_0(A) => k3_xtuple_0(k4_xtuple_0(A), k5_xtuple_0(A), k2_xtuple_0(A))=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_mcart_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(D, k3_zfmisc_1(A, B, C))) ) )  => k1_mcart_1(A, B, C, D)=k4_xtuple_0(D)) ) ).
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_k2_ec_pf_2, axiom,  (! [A, B] :  ( ( (v7_ordinal1(A) &  (v1_int_2(A) & v1_ec_pf_2(A, 5)) )  & m1_subset_1(B, k1_ec_pf_2(A)))  => k2_ec_pf_2(A, B)=k1_xtuple_0(B)) ) ).
fof(redefinition_k2_mcart_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(D, k3_zfmisc_1(A, B, C))) ) )  => k2_mcart_1(A, B, C, D)=k5_xtuple_0(D)) ) ).
fof(redefinition_k2_nat_1, axiom,  (! [A, B] :  ( (m1_subset_1(A, k4_ordinal1) & m1_subset_1(B, k4_ordinal1))  => k2_nat_1(A, B)=k3_xcmplx_0(A, B)) ) ).
fof(redefinition_k3_ec_pf_2, axiom,  (! [A, B] :  ( ( (v7_ordinal1(A) &  (v1_int_2(A) & v1_ec_pf_2(A, 5)) )  & m1_subset_1(B, k1_ec_pf_2(A)))  => k3_ec_pf_2(A, B)=k2_xtuple_0(B)) ) ).
fof(redefinition_k3_mcart_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(D, k3_zfmisc_1(A, B, C))) ) )  => k3_mcart_1(A, B, C, D)=k2_xtuple_0(D)) ) ).
fof(redefinition_k3_rlvect_1, axiom,  (! [A, B, C] :  ( ( (v2_rlvect_1(A) & l1_algstr_0(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k3_rlvect_1(A, B, C)=k1_algstr_0(A, B, C)) ) ).
fof(redefinition_k4_binop_1, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (m1_subset_1(C, A) & m1_subset_1(D, A)) )  => k4_binop_1(A, B, C, D)=k1_binop_1(B, C, D)) ) ).
fof(redefinition_k4_domain_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  (m1_subset_1(D, A) &  (m1_subset_1(E, B) & m1_subset_1(F, C)) ) ) ) )  => k4_domain_1(A, B, C, D, E, F)=k3_xtuple_0(D, E, F)) ) ).
fof(redefinition_k8_group_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v5_group_1(A) & l3_algstr_0(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k8_group_1(A, B, C)=k6_algstr_0(A, B, C)) ) ).
fof(redefinition_k9_nat_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, k4_ordinal1), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, k4_ordinal1), A)))) )  &  (m1_subset_1(C, A) & v7_ordinal1(D)) ) )  => k9_nat_1(A, B, C, D)=k1_binop_1(B, C, D)) ) ).
fof(redefinition_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) ) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(rqRealAdd__k2_xcmplx_0__r1_r1_r2, axiom, k2_xcmplx_0(1, 1)=2).
fof(rqRealAdd__k2_xcmplx_0__r1_r2_r3, axiom, k2_xcmplx_0(1, 2)=3).
fof(rqRealAdd__k2_xcmplx_0__r1_r3_r4, axiom, k2_xcmplx_0(1, 3)=4).
fof(rqRealAdd__k2_xcmplx_0__r1_r4_r5, axiom, k2_xcmplx_0(1, 4)=5).
fof(rqRealAdd__k2_xcmplx_0__r2_r1_r3, axiom, k2_xcmplx_0(2, 1)=3).
fof(rqRealAdd__k2_xcmplx_0__r2_r2_r4, axiom, k2_xcmplx_0(2, 2)=4).
fof(rqRealAdd__k2_xcmplx_0__r2_r3_r5, axiom, k2_xcmplx_0(2, 3)=5).
fof(rqRealAdd__k2_xcmplx_0__r3_r1_r4, axiom, k2_xcmplx_0(3, 1)=4).
fof(rqRealAdd__k2_xcmplx_0__r3_r2_r5, axiom, k2_xcmplx_0(3, 2)=5).
fof(rqRealAdd__k2_xcmplx_0__r3_r5_r8, axiom, k2_xcmplx_0(3, 5)=8).
fof(rqRealAdd__k2_xcmplx_0__r4_r1_r5, axiom, k2_xcmplx_0(4, 1)=5).
fof(rqRealAdd__k2_xcmplx_0__r4_r4_r8, axiom, k2_xcmplx_0(4, 4)=8).
fof(rqRealAdd__k2_xcmplx_0__r5_r3_r8, axiom, k2_xcmplx_0(5, 3)=8).
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_r3_r3, axiom, k3_xcmplx_0(1, 3)=3).
fof(rqRealMult__k3_xcmplx_0__r1_r4_r4, axiom, k3_xcmplx_0(1, 4)=4).
fof(rqRealMult__k3_xcmplx_0__r1_r5_r5, axiom, k3_xcmplx_0(1, 5)=5).
fof(rqRealMult__k3_xcmplx_0__r1_r8_r8, axiom, k3_xcmplx_0(1, 8)=8).
fof(rqRealMult__k3_xcmplx_0__r2_r1_r2, axiom, k3_xcmplx_0(2, 1)=2).
fof(rqRealMult__k3_xcmplx_0__r2_r2_r4, axiom, k3_xcmplx_0(2, 2)=4).
fof(rqRealMult__k3_xcmplx_0__r2_r4_r8, axiom, k3_xcmplx_0(2, 4)=8).
fof(rqRealMult__k3_xcmplx_0__r3_r1_r3, axiom, k3_xcmplx_0(3, 1)=3).
fof(rqRealMult__k3_xcmplx_0__r4_r1_r4, axiom, k3_xcmplx_0(4, 1)=4).
fof(rqRealMult__k3_xcmplx_0__r4_r2_r8, axiom, k3_xcmplx_0(4, 2)=8).
fof(rqRealMult__k3_xcmplx_0__r5_r1_r5, axiom, k3_xcmplx_0(5, 1)=5).
fof(rqRealMult__k3_xcmplx_0__r8_r1_r8, axiom, k3_xcmplx_0(8, 1)=8).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(spc2_boole, axiom,  ~ (v1_xboole_0(2)) ).
fof(spc2_numerals, axiom,  (v2_xxreal_0(2) & m1_subset_1(2, k4_ordinal1)) ).
fof(spc3_boole, axiom,  ~ (v1_xboole_0(3)) ).
fof(spc3_numerals, axiom,  (v2_xxreal_0(3) & m1_subset_1(3, k4_ordinal1)) ).
fof(spc4_boole, axiom,  ~ (v1_xboole_0(4)) ).
fof(spc4_numerals, axiom,  (v2_xxreal_0(4) & m1_subset_1(4, k4_ordinal1)) ).
fof(spc5_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k3_xcmplx_0(k2_xcmplx_0(A, B), C)=k2_xcmplx_0(k3_xcmplx_0(A, C), k3_xcmplx_0(B, C))) ) ).
fof(spc5_boole, axiom,  ~ (v1_xboole_0(5)) ).
fof(spc5_numerals, axiom,  (v2_xxreal_0(5) & m1_subset_1(5, k4_ordinal1)) ).
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_boole, axiom,  ~ (v1_xboole_0(8)) ).
fof(spc8_numerals, axiom,  (v2_xxreal_0(8) & m1_subset_1(8, k4_ordinal1)) ).
fof(t11_ec_pf_2, 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] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (k6_algstr_0(A, k6_algstr_0(A, k6_algstr_0(A, B, C), D), E)=k6_algstr_0(A, B, k6_algstr_0(A, k6_algstr_0(A, C, D), E)) & k6_algstr_0(A, k6_algstr_0(A, k6_algstr_0(A, k6_algstr_0(A, B, C), D), E), F)=k6_algstr_0(A, B, k6_algstr_0(A, k6_algstr_0(A, k6_algstr_0(A, C, D), E), F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t11_vectsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) & l6_algstr_0(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) => k6_algstr_0(A, B, k5_algstr_0(A, C, D))=k5_algstr_0(A, k6_algstr_0(A, B, C), k6_algstr_0(A, B, D))) ) ) ) ) ) ) ) ).
fof(t13_ec_pf_2, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) & l6_algstr_0(B)) ) ) ) ) ) ) )  =>  (! [C] :  (m1_subset_1(C, u1_struct_0(B)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(B)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(B)) =>  (v5_group_1(B) => k2_binom(B, k6_algstr_0(B, k6_algstr_0(B, C, D), E), A)=k6_algstr_0(B, k6_algstr_0(B, k2_binom(B, C, A), k2_binom(B, D, A)), k2_binom(B, E, A))) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_vectsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v2_vectsp_1(A) & l6_algstr_0(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) => k6_algstr_0(A, k5_algstr_0(A, B, C), D)=k5_algstr_0(A, k6_algstr_0(A, B, D), k6_algstr_0(A, C, D))) ) ) ) ) ) ) ) ).
fof(t14_ec_pf_2, 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] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (k6_algstr_0(A, B, k3_rlvect_1(A, k3_rlvect_1(A, C, D), E))=k3_rlvect_1(A, k3_rlvect_1(A, k6_algstr_0(A, B, C), k6_algstr_0(A, B, D)), k6_algstr_0(A, B, E)) &  (k6_algstr_0(A, B, k5_algstr_0(A, k3_rlvect_1(A, C, D), E))=k5_algstr_0(A, k3_rlvect_1(A, k6_algstr_0(A, B, C), k6_algstr_0(A, B, D)), k6_algstr_0(A, B, E)) &  (k6_algstr_0(A, B, k3_rlvect_1(A, k5_algstr_0(A, C, D), E))=k3_rlvect_1(A, k5_algstr_0(A, k6_algstr_0(A, B, C), k6_algstr_0(A, B, D)), k6_algstr_0(A, B, E)) &  (k6_algstr_0(A, B, k5_algstr_0(A, k5_algstr_0(A, C, D), E))=k5_algstr_0(A, k5_algstr_0(A, k6_algstr_0(A, B, C), k6_algstr_0(A, B, D)), k6_algstr_0(A, B, E)) &  (k6_algstr_0(A, B, k3_rlvect_1(A, k3_rlvect_1(A, k4_algstr_0(A, C), D), E))=k3_rlvect_1(A, k3_rlvect_1(A, k4_algstr_0(A, k6_algstr_0(A, B, C)), k6_algstr_0(A, B, D)), k6_algstr_0(A, B, E)) &  (k6_algstr_0(A, B, k5_algstr_0(A, k3_rlvect_1(A, k4_algstr_0(A, C), D), E))=k5_algstr_0(A, k3_rlvect_1(A, k4_algstr_0(A, k6_algstr_0(A, B, C)), k6_algstr_0(A, B, D)), k6_algstr_0(A, B, E)) &  (k6_algstr_0(A, B, k3_rlvect_1(A, k5_algstr_0(A, k4_algstr_0(A, C), D), E))=k3_rlvect_1(A, k5_algstr_0(A, k4_algstr_0(A, k6_algstr_0(A, B, C)), k6_algstr_0(A, B, D)), k6_algstr_0(A, B, E)) & k6_algstr_0(A, B, k5_algstr_0(A, k5_algstr_0(A, k4_algstr_0(A, C), D), E))=k5_algstr_0(A, k5_algstr_0(A, k4_algstr_0(A, k6_algstr_0(A, B, C)), k6_algstr_0(A, B, D)), k6_algstr_0(A, B, E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t15_ec_pf_2, 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) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k8_group_1(A, k3_rlvect_1(A, B, C), k5_algstr_0(A, B, C))=k5_algstr_0(A, k2_binom(A, B, 2), k2_binom(A, C, 2))) ) ) ) ) ) ).
fof(t17_rlvect_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k4_algstr_0(A, k4_algstr_0(A, B))=B) ) ) ) ).
fof(t17_vectsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (k4_algstr_0(A, k1_algstr_0(A, C, D))=k5_algstr_0(A, k4_algstr_0(A, D), C) &  (k4_algstr_0(A, k1_algstr_0(A, D, k4_algstr_0(A, C)))=k5_algstr_0(A, C, D) &  (k4_algstr_0(A, k5_algstr_0(A, C, D))=k1_algstr_0(A, D, k4_algstr_0(A, C)) &  (k4_algstr_0(A, k5_algstr_0(A, k4_algstr_0(A, C), D))=k1_algstr_0(A, D, C) & k5_algstr_0(A, B, k1_algstr_0(A, D, C))=k5_algstr_0(A, k5_algstr_0(A, B, C), D)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t18_ec_pf_1, axiom,  (! [A] :  (v1_int_1(A) =>  (! [B] :  (v1_int_1(B) =>  (! [C] :  ( (v7_ordinal1(C) & v1_int_2(C))  =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k9_int_3(C))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(k9_int_3(C))) =>  ( (D=k5_int_1(A, C) & E=k5_int_1(B, C))  => k8_group_1(k9_int_3(C), D, E)=k5_int_1(k3_xcmplx_0(A, B), C)) ) ) ) ) ) ) ) ) ) ) ).
fof(t19_vectsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  ( (k1_algstr_0(A, B, k4_algstr_0(A, C))=k4_struct_0(A) => B=C)  &  ( (B=C => k1_algstr_0(A, B, k4_algstr_0(A, C))=k4_struct_0(A))  &  ( (k5_algstr_0(A, B, C)=k4_struct_0(A) => B=C)  &  (B=C => k5_algstr_0(A, B, C)=k4_struct_0(A)) ) ) ) ) ) ) ) ) ) ).
fof(t1_ec_pf_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_group_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k2_binom(A, B, 2)=k2_binom(A, k4_algstr_0(A, B), 2)) ) ) ) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t20_ec_pf_2, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_int_2(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k9_int_3(A))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k9_int_3(A))) =>  (B=k5_int_1(2, A) => k3_rlvect_1(k9_int_3(A), C, C)=k8_group_1(k9_int_3(A), B, C)) ) ) ) ) ) ) ).
fof(t22_ec_pf_1, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_int_2(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k9_int_3(A))) => k2_binom(k9_int_3(A), B, 2)=k8_group_1(k9_int_3(A), B, B)) ) ) ) ).
fof(t24_ec_pf_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_group_1(A) &  (v3_group_1(A) & l3_algstr_0(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (v7_ordinal1(C) => k2_binom(A, B, k1_nat_1(C, 1))=k6_algstr_0(A, k2_binom(A, B, C), B)) ) ) ) ) ) ).
fof(t25_ec_pf_2, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_int_2(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k9_int_3(A))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k9_int_3(A))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k9_int_3(A))) =>  (B=k5_int_1(2, A) => k2_binom(k9_int_3(A), k3_rlvect_1(k9_int_3(A), C, D), 2)=k3_rlvect_1(k9_int_3(A), k3_rlvect_1(k9_int_3(A), k2_binom(k9_int_3(A), C, 2), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), B, C), D)), k2_binom(k9_int_3(A), D, 2))) ) ) ) ) ) ) ) ) ).
fof(t26_ec_pf_2, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_int_2(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k9_int_3(A))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k9_int_3(A))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k9_int_3(A))) =>  (B=k5_int_1(2, A) => k2_binom(k9_int_3(A), k5_algstr_0(k9_int_3(A), C, D), 2)=k3_rlvect_1(k9_int_3(A), k5_algstr_0(k9_int_3(A), k2_binom(k9_int_3(A), C, 2), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), B, C), D)), k2_binom(k9_int_3(A), D, 2))) ) ) ) ) ) ) ) ) ).
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(t3_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(1, A)=A) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_rlvect_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (k1_algstr_0(A, B, k4_struct_0(A))=B & k1_algstr_0(A, k4_struct_0(A), B)=B) ) ) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t59_ec_pf_2, axiom,  (! [A] :  ( (v7_ordinal1(A) &  (v1_int_2(A) & v1_ec_pf_2(A, 5)) )  =>  (! [B] :  (m2_subset_1(B, k2_zfmisc_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A))), k1_ec_pf_2(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k9_int_3(A))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k9_int_3(A))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(k9_int_3(A))) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(k9_int_3(A))) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(k9_int_3(A))) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(k9_int_3(A))) =>  (! [I] :  (m1_subset_1(I, u1_struct_0(k9_int_3(A))) =>  (! [J] :  (m1_subset_1(J, u1_struct_0(k9_int_3(A))) =>  (! [K] :  (m2_subset_1(K, k3_ec_pf_1(k9_int_3(A)), k6_ec_pf_1(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B))) =>  (! [L] :  (m1_subset_1(L, k3_zfmisc_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)))) =>  ( (C=k5_int_1(2, A) &  (D=k5_int_1(3, A) &  (E=k5_int_1(4, A) &  (F=k5_int_1(8, A) &  (G=k3_rlvect_1(k9_int_3(A), k8_group_1(k9_int_3(A), k2_ec_pf_2(A, B), k2_binom(k9_int_3(A), k6_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), 2)), k8_group_1(k9_int_3(A), D, k2_binom(k9_int_3(A), k4_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), 2))) &  (H=k8_group_1(k9_int_3(A), k5_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), k6_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K)) &  (I=k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), k4_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), k5_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K)), H) &  (J=k5_algstr_0(k9_int_3(A), k2_binom(k9_int_3(A), G, 2), k8_group_1(k9_int_3(A), F, I)) & L=k4_domain_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), C, J), H), k5_algstr_0(k9_int_3(A), k8_group_1(k9_int_3(A), G, k5_algstr_0(k9_int_3(A), k8_group_1(k9_int_3(A), E, I), J)), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), F, k2_binom(k9_int_3(A), k5_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), 2)), k2_binom(k9_int_3(A), H, 2))), k8_group_1(k9_int_3(A), F, k2_binom(k9_int_3(A), H, 3)))) ) ) ) ) ) ) )  => k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), C, H), k6_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K)), k2_mcart_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), L))=k4_algstr_0(k9_int_3(A), k3_rlvect_1(k9_int_3(A), k8_group_1(k9_int_3(A), G, k5_algstr_0(k9_int_3(A), k8_group_1(k9_int_3(A), k6_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), k1_mcart_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), L)), k8_group_1(k9_int_3(A), k4_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), k3_mcart_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), L)))), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), C, H), k5_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K)), k3_mcart_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), L))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t5_rlvect_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (k1_algstr_0(A, B, k4_algstr_0(A, B))=k4_struct_0(A) & k1_algstr_0(A, k4_algstr_0(A, B), B)=k4_struct_0(A)) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t60_ec_pf_2, axiom,  (! [A] :  ( (v7_ordinal1(A) &  (v1_int_2(A) & v1_ec_pf_2(A, 5)) )  =>  (! [B] :  (m2_subset_1(B, k2_zfmisc_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A))), k1_ec_pf_2(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k9_int_3(A))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k9_int_3(A))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(k9_int_3(A))) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(k9_int_3(A))) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(k9_int_3(A))) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(k9_int_3(A))) =>  (! [I] :  (m1_subset_1(I, u1_struct_0(k9_int_3(A))) =>  (! [J] :  (m1_subset_1(J, u1_struct_0(k9_int_3(A))) =>  (! [K] :  (m2_subset_1(K, k3_ec_pf_1(k9_int_3(A)), k6_ec_pf_1(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B))) =>  (! [L] :  (m1_subset_1(L, k3_zfmisc_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)))) =>  ( (C=k5_int_1(2, A) &  (D=k5_int_1(3, A) &  (E=k5_int_1(4, A) &  (F=k5_int_1(8, A) &  (G=k3_rlvect_1(k9_int_3(A), k8_group_1(k9_int_3(A), k2_ec_pf_2(A, B), k2_binom(k9_int_3(A), k6_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), 2)), k8_group_1(k9_int_3(A), D, k2_binom(k9_int_3(A), k4_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), 2))) &  (H=k8_group_1(k9_int_3(A), k5_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), k6_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K)) &  (I=k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), k4_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), k5_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K)), H) &  (J=k5_algstr_0(k9_int_3(A), k2_binom(k9_int_3(A), G, 2), k8_group_1(k9_int_3(A), F, I)) & L=k4_domain_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), C, J), H), k5_algstr_0(k9_int_3(A), k8_group_1(k9_int_3(A), G, k5_algstr_0(k9_int_3(A), k8_group_1(k9_int_3(A), E, I), J)), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), F, k2_binom(k9_int_3(A), k5_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), 2)), k2_binom(k9_int_3(A), H, 2))), k8_group_1(k9_int_3(A), F, k2_binom(k9_int_3(A), H, 3)))) ) ) ) ) ) ) )  => k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), E, k2_binom(k9_int_3(A), H, 2)), k6_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K)), k1_mcart_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), L))=k8_group_1(k9_int_3(A), k3_mcart_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), L), k5_algstr_0(k9_int_3(A), k8_group_1(k9_int_3(A), k2_binom(k9_int_3(A), G, 2), k6_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K)), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), F, k2_binom(k9_int_3(A), H, 2)), k4_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t61_ec_pf_2, axiom,  (! [A] :  ( (v7_ordinal1(A) &  (v1_int_2(A) & v1_ec_pf_2(A, 5)) )  =>  (! [B] :  (m2_subset_1(B, k2_zfmisc_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A))), k1_ec_pf_2(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k9_int_3(A))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k9_int_3(A))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(k9_int_3(A))) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(k9_int_3(A))) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(k9_int_3(A))) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(k9_int_3(A))) =>  (! [I] :  (m1_subset_1(I, u1_struct_0(k9_int_3(A))) =>  (! [J] :  (m1_subset_1(J, u1_struct_0(k9_int_3(A))) =>  (! [K] :  (m2_subset_1(K, k3_ec_pf_1(k9_int_3(A)), k6_ec_pf_1(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B))) =>  (! [L] :  (m1_subset_1(L, k3_zfmisc_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)))) =>  ( (C=k5_int_1(2, A) &  (D=k5_int_1(3, A) &  (E=k5_int_1(4, A) &  (F=k5_int_1(8, A) &  (G=k3_rlvect_1(k9_int_3(A), k8_group_1(k9_int_3(A), k2_ec_pf_2(A, B), k2_binom(k9_int_3(A), k6_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), 2)), k8_group_1(k9_int_3(A), D, k2_binom(k9_int_3(A), k4_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), 2))) &  (H=k8_group_1(k9_int_3(A), k5_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), k6_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K)) &  (I=k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), k4_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), k5_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K)), H) &  (J=k5_algstr_0(k9_int_3(A), k2_binom(k9_int_3(A), G, 2), k8_group_1(k9_int_3(A), F, I)) & L=k4_domain_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), C, J), H), k5_algstr_0(k9_int_3(A), k8_group_1(k9_int_3(A), G, k5_algstr_0(k9_int_3(A), k8_group_1(k9_int_3(A), E, I), J)), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), F, k2_binom(k9_int_3(A), k5_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), 2)), k2_binom(k9_int_3(A), H, 2))), k8_group_1(k9_int_3(A), F, k2_binom(k9_int_3(A), H, 3)))) ) ) ) ) ) ) )  => k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), E, k2_binom(k9_int_3(A), H, 2)), k2_binom(k9_int_3(A), k6_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), 2)), k8_group_1(k9_int_3(A), k3_ec_pf_2(A, B), k3_mcart_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), L)))=k5_algstr_0(k9_int_3(A), k8_group_1(k9_int_3(A), k3_mcart_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), L), k2_binom(k9_int_3(A), k5_algstr_0(k9_int_3(A), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), C, H), k5_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K)), k8_group_1(k9_int_3(A), G, k4_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K))), 2)), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), E, k2_binom(k9_int_3(A), H, 2)), k2_binom(k9_int_3(A), k4_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), 2)), k1_mcart_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), L)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t62_ec_pf_2, axiom,  (! [A] :  ( (v7_ordinal1(A) &  (v1_int_2(A) & v1_ec_pf_2(A, 5)) )  =>  (! [B] :  (m2_subset_1(B, k2_zfmisc_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A))), k1_ec_pf_2(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k9_int_3(A))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k9_int_3(A))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(k9_int_3(A))) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(k9_int_3(A))) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(k9_int_3(A))) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(k9_int_3(A))) =>  (! [I] :  (m1_subset_1(I, u1_struct_0(k9_int_3(A))) =>  (! [J] :  (m1_subset_1(J, u1_struct_0(k9_int_3(A))) =>  (! [K] :  (m2_subset_1(K, k3_ec_pf_1(k9_int_3(A)), k6_ec_pf_1(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B))) =>  (! [L] :  (m1_subset_1(L, k3_zfmisc_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)))) =>  ( (C=k5_int_1(2, A) &  (D=k5_int_1(3, A) &  (E=k5_int_1(4, A) &  (F=k5_int_1(8, A) &  (G=k3_rlvect_1(k9_int_3(A), k8_group_1(k9_int_3(A), k2_ec_pf_2(A, B), k2_binom(k9_int_3(A), k6_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), 2)), k8_group_1(k9_int_3(A), D, k2_binom(k9_int_3(A), k4_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), 2))) &  (H=k8_group_1(k9_int_3(A), k5_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), k6_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K)) &  (I=k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), k4_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), k5_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K)), H) &  (J=k5_algstr_0(k9_int_3(A), k2_binom(k9_int_3(A), G, 2), k8_group_1(k9_int_3(A), F, I)) & L=k4_domain_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), C, J), H), k5_algstr_0(k9_int_3(A), k8_group_1(k9_int_3(A), G, k5_algstr_0(k9_int_3(A), k8_group_1(k9_int_3(A), E, I), J)), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), F, k2_binom(k9_int_3(A), k5_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), 2)), k2_binom(k9_int_3(A), H, 2))), k8_group_1(k9_int_3(A), F, k2_binom(k9_int_3(A), H, 3)))) ) ) ) ) ) ) )  => k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), C, k2_binom(k9_int_3(A), H, 2)), k2_binom(k9_int_3(A), k6_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), 2)), k8_group_1(k9_int_3(A), k2_ec_pf_2(A, B), k3_mcart_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), L)))=k3_rlvect_1(k9_int_3(A), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), G, k6_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K)), k3_mcart_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), L)), k5_algstr_0(k9_int_3(A), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), C, H), k5_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K)), k8_group_1(k9_int_3(A), G, k4_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K)))), k8_group_1(k9_int_3(A), k2_binom(k9_int_3(A), H, 2), k3_rlvect_1(k9_int_3(A), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), E, k4_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K)), k6_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K)), k1_mcart_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), L)), k8_group_1(k9_int_3(A), k8_group_1(k9_int_3(A), C, k2_binom(k9_int_3(A), k4_ec_pf_2(A, k2_ec_pf_2(A, B), k3_ec_pf_2(A, B), K), 2)), k3_mcart_1(u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), u1_struct_0(k9_int_3(A)), L)))))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_algstr_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_algstr_0(A))  =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  <=>  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k1_algstr_0(A, B, k4_struct_0(A))=B) )  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (? [C] :  (m1_subset_1(C, u1_struct_0(A)) & k1_algstr_0(A, B, C)=k4_struct_0(A)) ) ) )  &  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) => k1_algstr_0(A, k1_algstr_0(A, B, C), D)=k1_algstr_0(A, B, k1_algstr_0(A, C, D))) ) ) ) ) ) ) ) ) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_algstr_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_algstr_0(A))  =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) ) )  <=>  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k1_algstr_0(A, B, k4_struct_0(A))=B) )  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (? [C] :  (m1_subset_1(C, u1_struct_0(A)) & k1_algstr_0(A, B, C)=k4_struct_0(A)) ) ) )  &  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) => k1_algstr_0(A, k1_algstr_0(A, B, C), D)=k1_algstr_0(A, B, k1_algstr_0(A, C, D))) ) ) ) ) )  &  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k1_algstr_0(A, B, C)=k1_algstr_0(A, C, B)) ) ) ) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_ec_pf_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (k3_rlvect_1(A, k3_rlvect_1(A, k3_rlvect_1(A, B, C), D), E)=k3_rlvect_1(A, B, k3_rlvect_1(A, k3_rlvect_1(A, C, D), E)) & k3_rlvect_1(A, k3_rlvect_1(A, k3_rlvect_1(A, k3_rlvect_1(A, B, C), D), E), F)=k3_rlvect_1(A, B, k3_rlvect_1(A, k3_rlvect_1(A, k3_rlvect_1(A, C, D), E), F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t8_vectsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) & l6_algstr_0(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k6_algstr_0(A, B, k4_algstr_0(A, C))=k4_algstr_0(A, k6_algstr_0(A, B, C))) ) ) ) ) ) ).
fof(t9_binom, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_group_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l3_algstr_0(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (v7_ordinal1(D) => k2_binom(A, k8_group_1(A, B, C), D)=k8_group_1(A, k2_binom(A, B, D), k2_binom(A, C, D))) ) ) ) ) ) ) ) ).
fof(t9_vectsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v2_vectsp_1(A) & l6_algstr_0(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k6_algstr_0(A, k4_algstr_0(A, B), C)=k4_algstr_0(A, k6_algstr_0(A, B, C))) ) ) ) ) ) ).
