% Mizar problem: t23_cfuncdom,cfuncdom,704,5 
fof(t23_cfuncdom, conjecture,  (? [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_clvect_1(A) &  (v2_clvect_1(A) &  (v3_clvect_1(A) &  (v4_clvect_1(A) &  (v5_clvect_1(A) & l1_clvect_1(A)) ) ) ) ) ) ) ) ) )  &  (? [B] :  (m1_subset_1(B, u1_struct_0(A)) &  (? [C] :  (m1_subset_1(C, u1_struct_0(A)) &  ( (! [D] :  (v1_xcmplx_0(D) =>  (! [E] :  (v1_xcmplx_0(E) =>  (k3_rlvect_1(A, k1_clvect_1(A, B, D), k1_clvect_1(A, C, E))=k4_struct_0(A) =>  (D=k5_numbers & E=k5_numbers) ) ) ) ) )  &  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (? [E] :  (v1_xcmplx_0(E) &  (? [F] :  (v1_xcmplx_0(F) & D=k3_rlvect_1(A, k1_clvect_1(A, B, E), k1_clvect_1(A, C, F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(abstractness_v1_clvect_1, axiom,  (! [A] :  (l1_clvect_1(A) =>  (v1_clvect_1(A) => A=g1_clvect_1(u1_struct_0(A), u2_struct_0(A), u1_algstr_0(A), u1_clvect_1(A))) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(cc10_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_int_1(B)) ) ) ) ).
fof(cc10_valued_2, axiom,  (! [A] :  (v2_valued_2(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_valued_2(B)) ) ) ) ).
fof(cc11_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v7_ordinal1(B)) ) ) ) ).
fof(cc11_valued_2, axiom,  (! [A] :  (v3_valued_2(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_valued_2(B)) ) ) ) ).
fof(cc12_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v6_membered(A)) ) ).
fof(cc12_valued_2, axiom,  (! [A] :  (v4_valued_2(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_valued_2(B)) ) ) ) ).
fof(cc13_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_membered(B)) ) ) ) ).
fof(cc13_valued_2, axiom,  (! [A] :  (v5_valued_2(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_valued_2(B)) ) ) ) ).
fof(cc14_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_membered(B)) ) ) ) ).
fof(cc14_valued_2, axiom,  (! [A] :  (v6_valued_2(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_valued_2(B)) ) ) ) ).
fof(cc15_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_membered(B)) ) ) ) ).
fof(cc15_valued_2, axiom,  (! [A] :  (v1_valued_2(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_valued_0(B)) ) ) ) ).
fof(cc16_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_membered(B)) ) ) ) ).
fof(cc16_valued_2, axiom,  (! [A] :  (v2_valued_2(A) =>  (! [B] :  (m1_subset_1(B, A) => v2_valued_0(B)) ) ) ) ).
fof(cc17_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_membered(B)) ) ) ) ).
fof(cc17_valued_2, axiom,  (! [A] :  (v3_valued_2(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_valued_0(B)) ) ) ) ).
fof(cc18_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_membered(B)) ) ) ) ).
fof(cc18_valued_2, axiom,  (! [A] :  (v4_valued_2(A) =>  (! [B] :  (m1_subset_1(B, A) => v5_relat_1(B, k3_numbers)) ) ) ) ).
fof(cc19_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v7_membered(A)) ) ).
fof(cc19_valued_2, axiom,  (! [A] :  (v5_valued_2(A) =>  (! [B] :  (m1_subset_1(B, A) => v5_relat_1(B, k4_numbers)) ) ) ) ).
fof(cc1_membered, axiom,  (! [A] :  (v6_membered(A) => v5_membered(A)) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc1_valued_2, axiom,  (! [A] :  (v6_valued_2(A) => v5_valued_2(A)) ) ).
fof(cc1_xcmplx_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xcmplx_0(A)) ) ).
fof(cc20_valued_2, axiom,  (! [A] :  (v6_valued_2(A) =>  (! [B] :  (m1_subset_1(B, A) => v6_valued_0(B)) ) ) ) ).
fof(cc21_valued_2, axiom,  (! [A] :  (v1_valued_2(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  =>  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v7_valued_2(B)) ) ) ) ) ) ) ).
fof(cc22_valued_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v12_valued_2(A))  =>  (v1_relat_1(A) & v11_valued_2(A)) ) ) ).
fof(cc23_valued_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v11_valued_2(A))  =>  (v1_relat_1(A) & v10_valued_2(A)) ) ) ).
fof(cc24_valued_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v10_valued_2(A))  =>  (v1_relat_1(A) & v9_valued_2(A)) ) ) ).
fof(cc25_valued_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_valued_2(A))  =>  (v1_relat_1(A) & v8_valued_2(A)) ) ) ).
fof(cc26_valued_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_valued_2(A))  =>  (v1_relat_1(A) & v7_valued_2(A)) ) ) ).
fof(cc27_valued_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v12_valued_2(A)) ) ) ).
fof(cc28_valued_2, axiom,  (! [A, B] :  (v1_valued_2(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_1(C) =>  (v1_funct_1(C) & v7_valued_2(C)) ) ) ) ) ) ).
fof(cc29_valued_2, axiom,  (! [A, B] :  (v2_valued_2(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_1(C) =>  (v1_funct_1(C) & v8_valued_2(C)) ) ) ) ) ) ).
fof(cc2_membered, axiom,  (! [A] :  (v5_membered(A) => v4_membered(A)) ) ).
fof(cc2_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(cc2_valued_2, axiom,  (! [A] :  (v5_valued_2(A) => v4_valued_2(A)) ) ).
fof(cc30_valued_2, axiom,  (! [A, B] :  (v3_valued_2(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_1(C) =>  (v1_funct_1(C) & v9_valued_2(C)) ) ) ) ) ) ).
fof(cc31_valued_2, axiom,  (! [A, B] :  (v4_valued_2(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_1(C) =>  (v1_funct_1(C) & v10_valued_2(C)) ) ) ) ) ) ).
fof(cc32_valued_2, axiom,  (! [A, B] :  (v5_valued_2(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_1(C) =>  (v1_funct_1(C) & v11_valued_2(C)) ) ) ) ) ) ).
fof(cc33_valued_2, axiom,  (! [A, B] :  (v6_valued_2(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_1(C) =>  (v1_funct_1(C) & v12_valued_2(C)) ) ) ) ) ) ).
fof(cc34_valued_2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v7_valued_2(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ) ).
fof(cc35_valued_2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v9_valued_2(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ) ).
fof(cc36_valued_2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v8_valued_2(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ) ).
fof(cc3_membered, axiom,  (! [A] :  (v4_membered(A) => v3_membered(A)) ) ).
fof(cc3_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_xboole_0(C)) ) ) ) ).
fof(cc3_valued_2, axiom,  (! [A] :  (v4_valued_2(A) => v3_valued_2(A)) ) ).
fof(cc3_xcmplx_0, axiom,  (! [A] :  (m1_subset_1(A, k2_numbers) => v1_xcmplx_0(A)) ) ).
fof(cc4_membered, axiom,  (! [A] :  (v3_membered(A) => v2_membered(A)) ) ).
fof(cc4_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => v1_xboole_0(C)) ) ) ) ).
fof(cc4_valued_2, axiom,  (! [A] :  (v3_valued_2(A) => v1_valued_2(A)) ) ).
fof(cc5_membered, axiom,  (! [A] :  (v3_membered(A) => v1_membered(A)) ) ).
fof(cc5_valued_2, axiom,  (! [A] :  (v3_valued_2(A) => v2_valued_2(A)) ) ).
fof(cc6_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xcmplx_0(B)) ) ) ) ).
fof(cc6_valued_2, axiom,  (! [A] :  (v1_xboole_0(A) => v6_valued_2(A)) ) ).
fof(cc7_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xxreal_0(B)) ) ) ) ).
fof(cc7_valued_2, axiom,  (! [A] :  (v1_valued_2(A) => v4_funct_1(A)) ) ).
fof(cc8_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xreal_0(B)) ) ) ) ).
fof(cc8_valued_2, axiom,  (! [A] :  (v2_valued_2(A) => v4_funct_1(A)) ) ).
fof(cc9_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_rat_1(B)) ) ) ) ).
fof(cc9_valued_2, axiom,  (! [A] :  (v1_valued_2(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_valued_2(B)) ) ) ) ).
fof(commutativity_k2_tarski, axiom,  (! [A, B] : k2_tarski(A, B)=k2_tarski(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(d1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k1_algstr_0(A, B, C)=k4_binop_1(u1_struct_0(A), u1_algstr_0(A), B, C)) ) ) ) ) ) ).
fof(d1_binop_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (! [C] : k1_binop_1(A, B, C)=k1_funct_1(A, k4_tarski(B, C))) ) ) ) ).
fof(d1_clvect_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_clvect_1(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (v1_xcmplx_0(C) => k1_clvect_1(A, B, C)=k1_funct_1(u1_clvect_1(A), k4_tarski(C, B))) ) ) ) ) ) ).
fof(d4_cfuncdom, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  => k4_cfuncdom(A)=k7_funcop_1(A, k5_numbers)) ) ).
fof(d6_cfuncdom, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  => k6_cfuncdom(A)=g1_clvect_1(k9_funct_2(A, k2_numbers), k4_cfuncdom(A), k1_cfuncdom(A), k3_cfuncdom(A))) ) ).
fof(d6_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => k4_struct_0(A)=u2_struct_0(A)) ) ).
fof(dt_g1_clvect_1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(B, A) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(k2_numbers, A), A) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers, A), A)))) ) ) )  =>  (v1_clvect_1(g1_clvect_1(A, B, C, D)) & l1_clvect_1(g1_clvect_1(A, B, C, D))) ) ) ).
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_cfuncdom, axiom,  (! [A] :  (v1_funct_1(k1_cfuncdom(A)) &  (v1_funct_2(k1_cfuncdom(A), k2_zfmisc_1(k9_funct_2(A, k2_numbers), k9_funct_2(A, k2_numbers)), k9_funct_2(A, k2_numbers)) & m1_subset_1(k1_cfuncdom(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k9_funct_2(A, k2_numbers), k9_funct_2(A, k2_numbers)), k9_funct_2(A, k2_numbers))))) ) ) ).
fof(dt_k1_clvect_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_clvect_1(A))  &  (m1_subset_1(B, u1_struct_0(A)) & v1_xcmplx_0(C)) )  => m1_subset_1(k1_clvect_1(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_funct_2, axiom, $true).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_funcop_1, axiom, $true).
fof(dt_k2_numbers, axiom, $true).
fof(dt_k2_tarski, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_cfuncdom, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (v1_funct_1(k3_cfuncdom(A)) &  (v1_funct_2(k3_cfuncdom(A), k2_zfmisc_1(k2_numbers, k9_funct_2(A, k2_numbers)), k9_funct_2(A, k2_numbers)) & m1_subset_1(k3_cfuncdom(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers, k9_funct_2(A, k2_numbers)), k9_funct_2(A, k2_numbers))))) ) ) ) ).
fof(dt_k3_numbers, axiom, $true).
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_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_cfuncdom, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  => m2_funct_2(k4_cfuncdom(A), A, k2_numbers, k9_funct_2(A, k2_numbers))) ) ).
fof(dt_k4_numbers, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => m1_subset_1(k4_struct_0(A), u1_struct_0(A))) ) ).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k5_complex1, axiom, m1_subset_1(k5_complex1, k2_numbers)).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k6_cfuncdom, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v2_struct_0(k6_cfuncdom(A)))  &  (v1_clvect_1(k6_cfuncdom(A)) & l1_clvect_1(k6_cfuncdom(A))) ) ) ) ).
fof(dt_k7_funcop_1, axiom,  (! [A, B] :  (v1_funct_1(k7_funcop_1(A, B)) &  (v1_funct_2(k7_funcop_1(A, B), A, k1_tarski(B)) & m1_subset_1(k7_funcop_1(A, B), k1_zfmisc_1(k2_zfmisc_1(A, k1_tarski(B))))) ) ) ).
fof(dt_k9_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => m1_funct_2(k9_funct_2(A, B), A, B)) ) ).
fof(dt_l1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l1_clvect_1, axiom,  (! [A] :  (l1_clvect_1(A) => l2_algstr_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (l2_struct_0(A) & l1_algstr_0(A)) ) ) ).
fof(dt_l2_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_m1_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_funct_2(C, A, B) =>  ~ (v1_xboole_0(C)) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m2_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (! [D] :  (m2_funct_2(D, A, B, C) =>  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ) ) ) ).
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_clvect_1, axiom,  (! [A] :  (l1_clvect_1(A) =>  (v1_funct_1(u1_clvect_1(A)) &  (v1_funct_2(u1_clvect_1(A), k2_zfmisc_1(k2_numbers, u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u1_clvect_1(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers, u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u2_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => m1_subset_1(u2_struct_0(A), u1_struct_0(A))) ) ).
fof(existence_l1_algstr_0, axiom,  (? [A] : l1_algstr_0(A)) ).
fof(existence_l1_clvect_1, axiom,  (? [A] : l1_clvect_1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_algstr_0, axiom,  (? [A] : l2_algstr_0(A)) ).
fof(existence_l2_struct_0, axiom,  (? [A] : l2_struct_0(A)) ).
fof(existence_m1_funct_2, axiom,  (! [A, B] :  (? [C] : m1_funct_2(C, A, B)) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m2_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (? [D] : m2_funct_2(D, A, B, C)) ) ) ).
fof(fc10_membered, axiom,  (! [A] :  (v1_rat_1(A) => v4_membered(k1_tarski(A))) ) ).
fof(fc11_membered, axiom,  (! [A] :  (v1_int_1(A) => v5_membered(k1_tarski(A))) ) ).
fof(fc12_membered, axiom,  (! [A] :  (v7_ordinal1(A) => v6_membered(k1_tarski(A))) ) ).
fof(fc13_membered, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_membered(k2_tarski(A, B))) ) ).
fof(fc14_membered, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => v2_membered(k2_tarski(A, B))) ) ).
fof(fc14_valued_2, axiom,  (! [A, B, C, D] :  ( (v1_valued_2(C) &  (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, C)))) )  =>  (v1_relat_1(k1_funct_1(D, B)) & v1_funct_1(k1_funct_1(D, B))) ) ) ).
fof(fc15_membered, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v3_membered(k2_tarski(A, B))) ) ).
fof(fc15_valued_2, axiom,  (! [A, B, C, D] :  ( (v2_valued_2(C) &  (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, C)))) )  =>  (v1_relat_1(k1_funct_1(D, B)) & v1_funct_1(k1_funct_1(D, B))) ) ) ).
fof(fc16_membered, axiom,  (! [A, B] :  ( (v1_rat_1(A) & v1_rat_1(B))  => v4_membered(k2_tarski(A, B))) ) ).
fof(fc16_valued_2, axiom,  (! [A, B, C, D] :  ( (v1_valued_2(C) &  (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, C)))) )  => v1_valued_0(k1_funct_1(D, B))) ) ).
fof(fc17_membered, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => v5_membered(k2_tarski(A, B))) ) ).
fof(fc17_valued_2, axiom,  (! [A, B, C, D] :  ( (v2_valued_2(C) &  (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, C)))) )  => v2_valued_0(k1_funct_1(D, B))) ) ).
fof(fc18_membered, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v6_membered(k2_tarski(A, B))) ) ).
fof(fc18_valued_2, axiom,  (! [A, B, C, D] :  ( (v3_valued_2(C) &  (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, C)))) )  => v3_valued_0(k1_funct_1(D, B))) ) ).
fof(fc19_valued_2, axiom,  (! [A, B, C, D] :  ( (v4_valued_2(C) &  (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, C)))) )  => v5_relat_1(k1_funct_1(D, B), k3_numbers)) ) ).
fof(fc1_cfuncdom, axiom,  (! [A] :  (v1_funct_1(k1_cfuncdom(A)) &  (v1_funct_2(k1_cfuncdom(A), k2_zfmisc_1(k9_funct_2(A, k2_numbers), k9_funct_2(A, k2_numbers)), k9_funct_2(A, k2_numbers)) & v7_valued_2(k1_cfuncdom(A))) ) ) ).
fof(fc1_clvect_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(k2_numbers, A), A) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers, A), A)))) ) ) ) )  =>  ( ~ (v2_struct_0(g1_clvect_1(A, B, C, D)))  & v1_clvect_1(g1_clvect_1(A, B, C, D))) ) ) ).
fof(fc1_membered, axiom, v1_membered(k2_numbers)).
fof(fc1_valued_2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  => v1_valued_2(k1_tarski(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc20_valued_2, axiom,  (! [A, B, C, D] :  ( (v5_valued_2(C) &  (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, C)))) )  => v5_relat_1(k1_funct_1(D, B), k4_numbers)) ) ).
fof(fc21_valued_2, axiom,  (! [A, B, C, D] :  ( (v6_valued_2(C) &  (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, C)))) )  => v6_valued_0(k1_funct_1(D, B))) ) ).
fof(fc28_valued_2, axiom,  (! [A, B] :  (v1_membered(B) => v1_valued_2(k1_funct_2(A, B))) ) ).
fof(fc29_valued_2, axiom,  (! [A, B] :  (v2_membered(B) => v2_valued_2(k1_funct_2(A, B))) ) ).
fof(fc2_numbers, axiom,  ~ (v1_xboole_0(k2_numbers)) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc30_valued_2, axiom,  (! [A, B] :  (v3_membered(B) => v3_valued_2(k1_funct_2(A, B))) ) ).
fof(fc31_valued_2, axiom,  (! [A, B] :  (v4_membered(B) => v4_valued_2(k1_funct_2(A, B))) ) ).
fof(fc32_valued_2, axiom,  (! [A, B] :  (v5_membered(B) => v5_valued_2(k1_funct_2(A, B))) ) ).
fof(fc33_valued_2, axiom,  (! [A, B] :  (v6_membered(B) => v6_valued_2(k1_funct_2(A, B))) ) ).
fof(fc3_cfuncdom, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (v1_funct_1(k3_cfuncdom(A)) &  (v1_funct_2(k3_cfuncdom(A), k2_zfmisc_1(k2_numbers, k9_funct_2(A, k2_numbers)), k9_funct_2(A, k2_numbers)) & v7_valued_2(k3_cfuncdom(A))) ) ) ) ).
fof(fc3_numbers, axiom,  ~ (v1_xboole_0(k3_numbers)) ).
fof(fc3_xboole_0, axiom,  (! [A, B] :  ~ (v1_xboole_0(k2_tarski(A, B))) ) ).
fof(fc40_valued_2, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v7_valued_2(A)) )  =>  (v1_relat_1(k1_funct_1(A, B)) & v1_funct_1(k1_funct_1(A, B))) ) ) ).
fof(fc41_valued_2, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v8_valued_2(A)) )  =>  (v1_relat_1(k1_funct_1(A, B)) & v1_funct_1(k1_funct_1(A, B))) ) ) ).
fof(fc42_valued_2, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v7_valued_2(A)) )  => v1_valued_0(k1_funct_1(A, B))) ) ).
fof(fc43_valued_2, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v8_valued_2(A)) )  => v2_valued_0(k1_funct_1(A, B))) ) ).
fof(fc44_valued_2, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v9_valued_2(A)) )  => v3_valued_0(k1_funct_1(A, B))) ) ).
fof(fc45_valued_2, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v10_valued_2(A)) )  => v5_relat_1(k1_funct_1(A, B), k3_numbers)) ) ).
fof(fc46_valued_2, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v11_valued_2(A)) )  => v5_relat_1(k1_funct_1(A, B), k4_numbers)) ) ).
fof(fc47_valued_2, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v12_valued_2(A)) )  => v6_valued_0(k1_funct_1(A, B))) ) ).
fof(fc48_valued_2, axiom,  (! [A, B, C] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v9_valued_2(A)) )  =>  (v1_relat_1(k1_binop_1(A, B, C)) &  (v1_funct_1(k1_binop_1(A, B, C)) & v3_valued_0(k1_binop_1(A, B, C))) ) ) ) ).
fof(fc4_cfuncdom, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v2_struct_0(k6_cfuncdom(A)))  &  (v13_algstr_0(k6_cfuncdom(A)) &  (v2_rlvect_1(k6_cfuncdom(A)) &  (v3_rlvect_1(k6_cfuncdom(A)) &  (v4_rlvect_1(k6_cfuncdom(A)) &  (v1_clvect_1(k6_cfuncdom(A)) &  (v2_clvect_1(k6_cfuncdom(A)) &  (v3_clvect_1(k6_cfuncdom(A)) &  (v4_clvect_1(k6_cfuncdom(A)) & v5_clvect_1(k6_cfuncdom(A))) ) ) ) ) ) ) ) ) ) ) ).
fof(fc4_membered, axiom, v4_membered(k3_numbers)).
fof(fc4_numbers, axiom,  ~ (v1_xboole_0(k4_numbers)) ).
fof(fc55_membered, axiom, v7_membered(k2_numbers)).
fof(fc57_membered, axiom, v7_membered(k3_numbers)).
fof(fc58_membered, axiom, v7_membered(k4_numbers)).
fof(fc59_membered, axiom, v7_membered(k4_ordinal1)).
fof(fc5_membered, axiom, v5_membered(k4_numbers)).
fof(fc6_membered, axiom, v6_membered(k4_ordinal1)).
fof(fc6_numbers, axiom,  ~ (v1_finset_1(k4_numbers)) ).
fof(fc7_membered, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_membered(k1_tarski(A))) ) ).
fof(fc7_numbers, axiom,  ~ (v1_finset_1(k3_numbers)) ).
fof(fc8_membered, axiom,  (! [A] :  (v1_xxreal_0(A) => v2_membered(k1_tarski(A))) ) ).
fof(fc9_membered, axiom,  (! [A] :  (v1_xreal_0(A) => v3_membered(k1_tarski(A))) ) ).
fof(fc9_numbers, axiom,  ~ (v1_finset_1(k2_numbers)) ).
fof(free_g1_clvect_1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(B, A) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(k2_numbers, A), A) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers, A), A)))) ) ) )  =>  (! [E, F, G, H] :  (g1_clvect_1(A, B, C, D)=g1_clvect_1(E, F, G, H) =>  (A=E &  (B=F &  (C=G & D=H) ) ) ) ) ) ) ).
fof(l31_cfuncdom, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (? [B] :  (? [C] :  (A=k2_tarski(B, C) &  ~ (B=C) ) ) ) ) ) ).
fof(rc1_clvect_1, axiom,  (? [A] :  (l1_clvect_1(A) & v1_clvect_1(A)) ) ).
fof(rc1_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
fof(rc1_valued_2, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_valued_2(A)) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xcmplx_0, axiom,  (? [A] : v1_xcmplx_0(A)) ).
fof(rc2_clvect_1, axiom,  (? [A] :  (l1_clvect_1(A) &  ~ (v2_struct_0(A)) ) ) ).
fof(rc2_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc2_valued_2, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v12_valued_2(A)) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xcmplx_0, axiom,  (? [A] : v1_xcmplx_0(A)) ).
fof(rc3_clvect_1, axiom,  (? [A] :  (l1_clvect_1(A) &  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_clvect_1(A) &  (v2_clvect_1(A) &  (v3_clvect_1(A) &  (v4_clvect_1(A) & v5_clvect_1(A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v6_membered(A) & v7_membered(A)) ) ) ).
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_k5_complex1, axiom, k5_complex1=k5_ordinal1).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_k7_funcop_1, axiom,  (! [A, B] : k7_funcop_1(A, B)=k2_funcop_1(A, B)) ).
fof(redefinition_k9_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => k9_funct_2(A, B)=k1_funct_2(A, B)) ) ).
fof(redefinition_m2_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (! [D] :  (m2_funct_2(D, A, B, C) <=> m1_subset_1(D, C)) ) ) ) ).
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(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(t22_cfuncdom, axiom,  (! [A] :  (! [B] :  (! [C] :  ( ~ (v1_xboole_0(C))  =>  ~ ( (C=k2_tarski(A, B) &  ( ~ (A=B)  &  (! [D] :  (m2_funct_2(D, C, k2_numbers, k9_funct_2(C, k2_numbers)) =>  (! [E] :  (m2_funct_2(E, C, k2_numbers, k9_funct_2(C, k2_numbers)) =>  ~ ( ( (! [F] :  (v1_xcmplx_0(F) =>  (! [G] :  (v1_xcmplx_0(G) =>  (k1_binop_1(k1_cfuncdom(C), k1_funct_1(k3_cfuncdom(C), k4_tarski(F, D)), k1_funct_1(k3_cfuncdom(C), k4_tarski(G, E)))=k4_cfuncdom(C) =>  (F=k5_numbers & G=k5_numbers) ) ) ) ) )  &  (! [F] :  (m2_funct_2(F, C, k2_numbers, k9_funct_2(C, k2_numbers)) =>  (? [G] :  (v1_xcmplx_0(G) &  (? [H] :  (v1_xcmplx_0(H) & F=k1_binop_1(k1_cfuncdom(C), k1_funct_1(k3_cfuncdom(C), k4_tarski(G, D)), k1_funct_1(k3_cfuncdom(C), k4_tarski(H, E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, 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(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
