% Mizar problem: t34_polynom8,polynom8,2083,5 
fof(t34_polynom8, conjecture,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  (v13_algstr_0(B) &  (v33_algstr_0(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v5_group_1(B) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, u1_struct_0(B)) &  (v1_polynom1(C, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(B))))) ) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k4_ordinal1, u1_struct_0(B)) &  (v1_polynom1(D, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(B))))) ) )  =>  (! [E] :  (m1_subset_1(E, u1_struct_0(B)) => r2_funct_2(k4_ordinal1, u1_struct_0(B), k4_lopban_3(B, k5_polynom8(A, B, C, E), k5_polynom8(A, B, D, E)), k5_polynom8(A, B, k11_polynom3(B, C, D), E))) ) ) ) ) ) ) ) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(cc10_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A))  => v3_card_1(A, 1)) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc11_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_card_1(A))  =>  (! [B] :  (v3_card_1(B, A) =>  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(cc11_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_algstr_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_algstr_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v5_algstr_0(A) &  (v6_algstr_0(A) &  (v2_algstr_1(A) & v3_algstr_1(A)) ) ) ) ) ) ) ).
fof(cc1_card_1, axiom,  (! [A] :  (v1_card_1(A) => v3_ordinal1(A)) ) ).
fof(cc1_gcd_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & v5_group_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v6_vectsp_1(A)) ) ) ) ).
fof(cc1_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v3_ordinal1(A) & v7_ordinal1(A)) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc1_polynom8, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v1_vectsp_1(A) &  (v4_vectsp_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & v3_group_1(A)) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v1_vectsp_1(A) &  (v4_vectsp_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & v1_vectsp_2(A)) ) ) ) ) ) ) ) ) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc1_vectsp_1, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v5_vectsp_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v1_vectsp_1(A) & v2_vectsp_1(A)) ) ) ) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_algstr_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v5_algstr_0(A) &  (v6_algstr_0(A) &  (v2_algstr_1(A) & v3_algstr_1(A)) ) ) )  =>  ( ~ (v2_struct_0(A))  & v4_algstr_1(A)) ) ) ) ).
fof(cc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_card_1(A)) ) ).
fof(cc2_gcd_1, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v1_vectsp_1(A) & v5_group_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v5_vectsp_1(A)) ) ) ) ).
fof(cc2_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_int_1(A)) ) ).
fof(cc2_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc2_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_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(cc2_xxreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xxreal_0(A)) ) ).
fof(cc3_algstr_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_algstr_1(A))  =>  ( ~ (v2_struct_0(A))  & v2_algstr_1(A)) ) ) ) ).
fof(cc3_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_card_1(A)) ) ).
fof(cc3_gcd_1, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v2_vectsp_1(A) & v5_group_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v5_vectsp_1(A)) ) ) ) ).
fof(cc3_int_1, axiom,  (! [A] :  (v1_int_1(A) => v1_xreal_0(A)) ) ).
fof(cc3_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc3_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_xboole_0(C)) ) ) ) ).
fof(cc3_struct_0, axiom,  (! [A] :  (l4_struct_0(A) =>  ( ~ (v6_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc3_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_vectsp_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & v6_vectsp_1(A)) ) ) ) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc3_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v2_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc4_algstr_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) & v4_rlvect_1(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v1_algstr_1(A) & v4_algstr_1(A)) ) ) ) ) ).
fof(cc4_card_1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v1_finset_1(A)) ) ).
fof(cc4_gcd_1, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & v3_group_1(A)) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & v3_group_1(A)) ) ) ) ) ) ) ) ) ) ).
fof(cc4_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v2_int_1(A)) ) ).
fof(cc4_nat_1, axiom,  (! [A] :  ( (v7_ordinal1(A) & v8_ordinal1(A))  =>  (v7_ordinal1(A) &  ~ (v2_xxreal_0(A)) ) ) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(A)) ) ).
fof(cc4_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => v1_xboole_0(C)) ) ) ) ).
fof(cc4_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc4_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & v6_vectsp_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v1_group_1(A)) ) ) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc4_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ) ).
fof(cc5_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_finset_1(A)) ) ).
fof(cc5_gcd_1, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v1_vectsp_1(A) &  (v2_vectsp_1(A) &  (v4_vectsp_1(A) &  (v6_vectsp_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & v5_group_1(A)) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v1_vectsp_1(A) &  (v2_vectsp_1(A) &  (v4_vectsp_1(A) &  (v6_vectsp_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_group_1(A) & v3_gcd_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc5_int_1, axiom,  (! [A] :  (v2_int_1(A) => v1_int_1(A)) ) ).
fof(cc5_nat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v8_ordinal1(A)) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc5_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_vectsp_1(A))  =>  ( ~ (v2_struct_0(A))  & v1_group_1(A)) ) ) ) ).
fof(cc5_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v3_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) ) ) ) ).
fof(cc6_card_1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v1_finset_1(A))  => v7_ordinal1(A)) ) ).
fof(cc6_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  =>  ~ (v1_xboole_0(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(cc6_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ) ).
fof(cc7_algstr_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  (v13_struct_0(A, 1) =>  (v13_struct_0(A, 1) &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) & v4_rlvect_1(A)) ) ) ) ) ) ) ).
fof(cc7_card_1, axiom,  (! [A] :  (v3_card_1(A, k5_ordinal1) => v1_xboole_0(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(cc7_xxreal_0, axiom,  (! [A] :  ( (v8_ordinal1(A) & v1_xxreal_0(A))  =>  (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc8_algstr_1, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  (v1_vectsp_1(A) & v4_vectsp_1(A)) ) ) ) ) ).
fof(cc8_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_card_1(A, k5_ordinal1)) ) ).
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(cc8_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) )  =>  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ) ).
fof(cc9_algstr_1, axiom,  (! [A] :  (l3_algstr_0(A) =>  (v13_struct_0(A, 1) =>  (v13_struct_0(A, 1) &  (v2_group_1(A) &  (v3_group_1(A) & v5_group_1(A)) ) ) ) ) ) ).
fof(cc9_card_1, axiom,  (! [A] :  (v3_card_1(A, 1) =>  ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A)) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(commutativity_k11_polynom3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) )  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, u1_struct_0(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) )  &  (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, u1_struct_0(A)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) ) ) )  => k11_polynom3(A, B, C)=k11_polynom3(A, C, B)) ) ).
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(connectedness_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  =>  (r1_xxreal_0(A, B) | r1_xxreal_0(B, A)) ) ) ).
fof(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_funct_2, axiom,  (! [A] :  (! [B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( ( ~ (B=k1_xboole_0)  =>  (v1_funct_2(C, A, B) <=> A=k1_relset_1(A, C)) )  &  (B=k1_xboole_0 =>  (v1_funct_2(C, A, B) <=> C=k1_xboole_0) ) ) ) ) ) ) ).
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(d7_lopban_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_algstr_0(A))  =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, u1_struct_0(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, u1_struct_0(A)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k4_ordinal1, u1_struct_0(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) )  =>  (D=k4_lopban_3(A, B, C) <=>  (! [E] :  (v7_ordinal1(E) => k1_normsp_0(A, D, E)=k6_algstr_0(A, k1_normsp_0(A, B, E), k1_normsp_0(A, C, E))) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_polynom8, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v4_vectsp_1(B) & l6_algstr_0(B)) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, u1_struct_0(B)) &  (v1_polynom1(C, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(B))))) ) )  =>  (! [D] :  (m1_subset_1(D, u1_struct_0(B)) =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, k4_ordinal1, u1_struct_0(B)) &  (v1_polynom1(E, B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(B))))) ) )  =>  (E=k5_polynom8(A, B, C, D) <=>  ( (! [F] :  (v7_ordinal1(F) =>  ( ~ (r1_xxreal_0(A, F))  => k8_nat_1(u1_struct_0(B), E, F)=k2_polynom4(B, C, k2_binom(B, D, F))) ) )  &  (! [F] :  (v7_ordinal1(F) =>  (r1_xxreal_0(A, F) => k8_nat_1(u1_struct_0(B), E, F)=k4_struct_0(B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k10_polynom3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, u1_struct_0(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) )  &  (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, u1_struct_0(A)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) ) ) )  =>  (v1_funct_1(k10_polynom3(A, B, C)) &  (v1_funct_2(k10_polynom3(A, B, C), k4_ordinal1, u1_struct_0(A)) & m1_subset_1(k10_polynom3(A, B, C), k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) ) ) ) ).
fof(dt_k11_polynom3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) )  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, u1_struct_0(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) )  &  (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, u1_struct_0(A)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) ) ) )  =>  (v1_funct_1(k11_polynom3(A, B, C)) &  (v1_funct_2(k11_polynom3(A, B, C), k4_ordinal1, u1_struct_0(A)) & m1_subset_1(k11_polynom3(A, B, C), k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) ) ) ) ).
fof(dt_k1_binop_1, axiom, $true).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_normsp_0, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, u1_struct_0(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) )  & v7_ordinal1(C)) )  => m1_subset_1(k1_normsp_0(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => m1_subset_1(k1_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k1_xboole_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_polynom4, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v1_group_1(A) & l6_algstr_0(A)) )  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, u1_struct_0(A)) &  (v1_polynom1(B, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) ) )  & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k2_polynom4(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
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_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_lopban_3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l3_algstr_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, u1_struct_0(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) )  &  (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, u1_struct_0(A)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) ) ) )  =>  (v1_funct_1(k4_lopban_3(A, B, C)) &  (v1_funct_2(k4_lopban_3(A, B, C), k4_ordinal1, u1_struct_0(A)) & m1_subset_1(k4_lopban_3(A, B, C), k1_zfmisc_1(k2_zfmisc_1(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_k5_ordinal1, axiom, $true).
fof(dt_k5_polynom8, axiom,  (! [A, B, C, D] :  ( (v7_ordinal1(A) &  ( ( ~ (v2_struct_0(B))  &  (v4_vectsp_1(B) & l6_algstr_0(B)) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, u1_struct_0(B)) &  (v1_polynom1(C, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(B))))) ) )  & m1_subset_1(D, u1_struct_0(B))) ) )  =>  (v1_funct_1(k5_polynom8(A, B, C, D)) &  (v1_funct_2(k5_polynom8(A, B, C, D), k4_ordinal1, u1_struct_0(B)) &  (v1_polynom1(k5_polynom8(A, B, C, D), B) & m1_subset_1(k5_polynom8(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(B))))) ) ) ) ) ).
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_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_k8_nat_1, axiom,  (! [A, B, C] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A)))) )  & v7_ordinal1(C))  => m1_subset_1(k8_nat_1(A, B, C), 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_k9_xtuple_0, axiom, $true).
fof(dt_l1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (l2_struct_0(A) & l1_algstr_0(A)) ) ) ).
fof(dt_l2_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_l3_algstr_0, axiom,  (! [A] :  (l3_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l3_struct_0, axiom,  (! [A] :  (l3_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_l4_algstr_0, axiom,  (! [A] :  (l4_algstr_0(A) =>  (l3_struct_0(A) & l3_algstr_0(A)) ) ) ).
fof(dt_l4_struct_0, axiom,  (! [A] :  (l4_struct_0(A) =>  (l2_struct_0(A) & l3_struct_0(A)) ) ) ).
fof(dt_l5_algstr_0, axiom,  (! [A] :  (l5_algstr_0(A) =>  (l4_algstr_0(A) & l4_struct_0(A)) ) ) ).
fof(dt_l6_algstr_0, axiom,  (! [A] :  (l6_algstr_0(A) =>  (l2_algstr_0(A) & l5_algstr_0(A)) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
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(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(fc10_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => v9_struct_0(k4_struct_0(A), A)) ) ).
fof(fc12_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k1_zfmisc_1(A))) ) ) ).
fof(fc13_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(A, B))) ) ) ).
fof(fc14_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(B, A))) ) ) ).
fof(fc17_card_1, axiom,  (! [A, B] :  ( (v1_card_1(A) &  (v1_relat_1(B) &  (v1_funct_1(B) & v3_card_1(B, A)) ) )  => v3_card_1(k9_xtuple_0(B), A)) ) ).
fof(fc19_struct_0, axiom,  (! [A, B] :  ( (v1_card_1(A) &  (v13_struct_0(B, A) & l1_struct_0(B)) )  => v3_card_1(u1_struct_0(B), A)) ) ).
fof(fc1_polynom8, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_vectsp_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) )  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, u1_struct_0(A)) &  (v1_polynom1(B, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) ) )  &  (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, u1_struct_0(A)) &  (v1_polynom1(C, A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) ) ) ) )  =>  (v1_funct_1(k4_lopban_3(A, B, C)) &  (v1_funct_2(k4_lopban_3(A, B, C), k4_ordinal1, u1_struct_0(A)) & v1_polynom1(k4_lopban_3(A, B, C), A)) ) ) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc4_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  => v3_ordinal1(k9_xtuple_0(A))) ) ).
fof(fc4_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc6_card_1, axiom, v1_card_1(k4_ordinal1)).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc7_card_1, axiom, v2_card_1(k4_ordinal1)).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_polynom3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) )  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, u1_struct_0(A)) &  (v1_polynom1(B, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) ) )  &  (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, u1_struct_0(A)) &  (v1_polynom1(C, A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) ) ) ) )  =>  (v1_funct_1(k10_polynom3(A, B, C)) &  (v1_funct_2(k10_polynom3(A, B, C), k4_ordinal1, u1_struct_0(A)) & v1_polynom1(k10_polynom3(A, B, C), A)) ) ) ) ).
fof(fc8_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C))) => v1_relat_1(k9_xtuple_0(D))) ) ).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_card_1, axiom,  ~ (v1_finset_1(k4_ordinal1)) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(rc10_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_card_1(B)) ) ) ) ).
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_card_1, axiom,  (? [A] : v1_card_1(A)) ).
fof(rc1_int_1, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v1_xcmplx_0(A) &  (v1_xreal_0(A) & v1_int_1(A)) ) ) ) ).
fof(rc1_nat_1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(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_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc20_struct_0, axiom,  (? [A] :  (l2_struct_0(A) &  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ).
fof(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc23_struct_0, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (l1_struct_0(B) & v13_struct_0(B, A)) ) ) ) ).
fof(rc2_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v1_finset_1(A) & v1_card_1(A)) ) ) ) ) ).
fof(rc2_gcd_1, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(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) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_group_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v1_vectsp_2(A) & v3_gcd_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_int_1, axiom,  (? [A] : v1_int_1(A)) ).
fof(rc2_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) & v8_ordinal1(A)) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_vectsp_1, axiom,  (? [A] :  (l5_algstr_0(A) &  ( ~ (v2_struct_0(A))  & v4_vectsp_1(A)) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc3_card_1, axiom,  (? [A] :  ~ (v1_finset_1(A)) ) ).
fof(rc3_gcd_1, axiom,  (? [A] :  (l4_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v4_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & v3_gcd_1(A)) ) ) ) ) ) ).
fof(rc3_int_1, axiom,  (? [A] : v2_int_1(A)) ).
fof(rc3_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_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(rc3_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ).
fof(rc4_card_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc4_gcd_1, axiom,  (? [A] :  (l5_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v4_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & v3_gcd_1(A)) ) ) ) ) ) ).
fof(rc4_ordinal1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v5_ordinal1(B)) ) ) ) ) ).
fof(rc4_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc4_vectsp_1, axiom,  (? [A] :  (l4_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v1_group_1(A) &  (v3_group_1(A) & v5_group_1(A)) ) ) ) ) ).
fof(rc4_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ).
fof(rc5_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  & v1_card_1(A)) ) ) ) ) ) ).
fof(rc5_gcd_1, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_group_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v1_vectsp_2(A) & v3_gcd_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc5_nat_1, axiom,  (? [A] :  (m1_subset_1(A, k4_ordinal1) &  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v1_xreal_0(A) &  (v1_finset_1(A) & v1_card_1(A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc5_xxreal_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ).
fof(rc6_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_finset_1(B)) ) ) ) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc7_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] : v3_card_1(B, A)) ) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (v1_relat_1(B) &  (v1_funct_1(B) & v3_card_1(B, A)) ) ) ) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v3_card_1(B, 1)) ) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
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(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(redefinition_k11_polynom3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) )  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, u1_struct_0(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) )  &  (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, u1_struct_0(A)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) ) ) )  => k11_polynom3(A, B, C)=k10_polynom3(A, B, C)) ) ).
fof(redefinition_k1_normsp_0, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, u1_struct_0(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) )  & v7_ordinal1(C)) )  => k1_normsp_0(A, B, C)=k1_funct_1(B, C)) ) ).
fof(redefinition_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k1_relset_1(A, B)=k9_xtuple_0(B)) ) ).
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_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_k8_nat_1, axiom,  (! [A, B, C] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A)))) )  & v7_ordinal1(C))  => k8_nat_1(A, B, C)=k1_funct_1(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_r2_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (r2_funct_2(A, B, C, D) <=> C=D) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(reflexivity_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => r1_xxreal_0(A, A)) ) ).
fof(reflexivity_r2_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  => r2_funct_2(A, B, C, C)) ) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_r1, axiom, r1_xxreal_0(1, 1)).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(symmetry_r2_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (r2_funct_2(A, B, C, D) => r2_funct_2(A, B, D, C)) ) ) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v2_xxreal_0(A))  => v2_xxreal_0(B)) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t24_polynom4, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_vectsp_1(A) &  (v6_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k4_ordinal1, u1_struct_0(A)) &  (v1_polynom1(B, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, u1_struct_0(A)) &  (v1_polynom1(C, A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, u1_struct_0(A))))) ) )  =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) => k2_polynom4(A, k11_polynom3(A, B, C), D)=k8_group_1(A, k2_polynom4(A, B, D), k2_polynom4(A, C, D))) ) ) ) ) ) ) ) ).
fof(t2_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  ( (k9_xtuple_0(A)=k9_xtuple_0(B) &  (! [C] :  (r2_hidden(C, k9_xtuple_0(A)) => k1_funct_1(A, C)=k1_funct_1(B, C)) ) )  => A=B) ) ) ) ) ).
fof(t2_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v3_xxreal_0(B))  => v3_xxreal_0(A)) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v3_xxreal_0(A))  & v3_xxreal_0(B)) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v2_xxreal_0(B))  & v2_xxreal_0(A)) ) ) ) ) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(B) |  (v3_xxreal_0(A) | v2_xxreal_0(B)) ) ) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t6_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(A) |  (v2_xxreal_0(B) | v3_xxreal_0(A)) ) ) ) ) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(B)) ) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v3_xxreal_0(B))  &  ~ (v2_xxreal_0(A)) ) ) ) ) ) ) ) ).
