% Mizar problem: t37_groeb_1,groeb_1,3506,5 
fof(t37_groeb_1, conjecture,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v6_relat_2(B) &  (v8_relat_2(B) &  (v2_bagorder(B, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A))))) ) ) ) ) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  &  ( ~ (v6_struct_0(C))  &  (v13_algstr_0(C) &  (v33_algstr_0(C) &  (v4_vectsp_1(C) &  (v5_vectsp_1(C) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v3_group_1(C) &  (v5_group_1(C) & l6_algstr_0(C)) ) ) ) ) ) ) ) ) ) )  =>  (! [D] :  ( (v1_ideal_1(D, k12_polynom1(A, C)) &  (v2_ideal_1(D, k12_polynom1(A, C)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k12_polynom1(A, C))))) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, k15_pre_poly(A), u1_struct_0(C)) &  (v3_polynom7(E, A, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  =>  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(F, C) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  =>  (! [G] :  ( (v1_funct_1(G) &  (v1_funct_2(G, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(G, C) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  =>  ( (r2_tarski(F, D) &  (r2_tarski(G, D) &  (k5_termord(A, B, C, F)=E &  (k5_termord(A, B, C, G)=E &  ( (! [H] :  ( (v1_funct_1(H) &  (v1_funct_2(H, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(H, C) & m1_subset_1(H, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  =>  ~ ( (r2_tarski(H, D) &  (r2_polyred(A, B, C, H, F) & k5_termord(A, B, C, H)=E) ) ) ) )  &  (! [H] :  ( (v1_funct_1(H) &  (v1_funct_2(H, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(H, C) & m1_subset_1(H, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  =>  ~ ( (r2_tarski(H, D) &  (r2_polyred(A, B, C, H, G) & k5_termord(A, B, C, H)=E) ) ) ) ) ) ) ) ) )  => F=G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A))  => v3_card_1(A, 1)) ) ).
fof(cc10_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v6_membered(A)) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc10_pre_poly, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k15_pre_poly(A))) =>  (! [C] :  (m1_subset_1(C, B) => v4_relat_1(C, A)) ) ) ) ).
fof(cc10_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_rewrite1(A))  =>  (v1_relat_1(A) & v4_rewrite1(A)) ) ) ).
fof(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc10_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_valued_0(B)) ) ) ) ).
fof(cc11_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_card_1(A))  =>  (! [B] :  (v3_card_1(B, A) =>  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(cc11_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_finseq_1(A)) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc11_pre_poly, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(k15_pre_poly(A))))  =>  (! [C] :  (m1_subset_1(C, B) =>  (v1_partfun1(C, A) &  (v6_valued_0(C) & v2_pre_poly(C)) ) ) ) ) ) ).
fof(cc11_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v2_rewrite1(A) & v4_rewrite1(A)) )  =>  (v1_relat_1(A) & v8_rewrite1(A)) ) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc11_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_valued_0(B)) ) ) ) ).
fof(cc12_algstr_0, axiom,  (! [A] :  ( (v13_algstr_0(A) & l2_algstr_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => v10_algstr_0(B, A)) ) ) ) ).
fof(cc12_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) => v4_funct_1(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc12_rewrite1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v6_rewrite1(A)) ) ) ).
fof(cc12_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_valued_0(B)) ) ) ) ).
fof(cc13_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finseq_1(B)) ) ) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc13_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v3_rewrite1(A) & v9_rewrite1(A)) )  =>  (v1_relat_1(A) & v7_rewrite1(A)) ) ) ).
fof(cc13_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_valued_0(B)) ) ) ) ).
fof(cc14_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_finseq_1(B)) ) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc14_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v10_rewrite1(A))  =>  (v1_relat_1(A) &  (v3_rewrite1(A) & v7_rewrite1(A)) ) ) ) ).
fof(cc14_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_valued_0(B)) ) ) ) ).
fof(cc15_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v3_valued_0(A) & v7_valued_0(A)) ) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_funct_1(A) & v3_valued_0(A)) ) ) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc15_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v3_rewrite1(A) & v7_rewrite1(A)) )  =>  (v1_relat_1(A) & v10_rewrite1(A)) ) ) ).
fof(cc15_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_valued_0(B)) ) ) ) ).
fof(cc16_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finset_1(A) & v2_finseq_1(A)) ) ) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(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_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  ( (v2_algstr_0(B, A) & v3_algstr_0(B, A))  => v4_algstr_0(B, 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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc1_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_finset_1(A)) ) ).
fof(cc1_funcop_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_funcop_1(B)) ) ) ) ) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_partfun1(C, A) => v1_funct_2(C, A, B)) ) ) ) ).
fof(cc1_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_ideal_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v5_group_1(A) & l3_algstr_0(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  ( ( ~ (v1_xboole_0(B))  & v2_ideal_1(B, A))  =>  ( ~ (v1_xboole_0(B))  & v3_ideal_1(B, A)) ) ) ) ) ) ).
fof(cc1_int_1, axiom,  (! [A] :  (m1_subset_1(A, k4_numbers) => v1_int_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_polynom1, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v6_struct_0(A) &  (v13_algstr_0(A) &  (v1_vectsp_1(A) &  (v3_vectsp_1(A) &  (v3_rlvect_1(A) & v4_rlvect_1(A)) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v7_struct_0(A) &  (v13_algstr_0(A) &  (v1_vectsp_1(A) &  (v3_vectsp_1(A) &  (v3_rlvect_1(A) & v4_rlvect_1(A)) ) ) ) ) ) ) ) ) ).
fof(cc1_polynom4, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v6_algstr_0(A) &  (v33_algstr_0(A) &  (v1_vectsp_1(A) &  (v4_vectsp_1(A) &  (v3_group_1(A) & v1_algstr_1(A)) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v6_algstr_0(A) &  (v1_vectsp_1(A) &  (v4_vectsp_1(A) &  (v3_group_1(A) &  (v1_vectsp_2(A) & v1_algstr_1(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_termord, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A)))) =>  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v8_relat_2(B) & v2_bagorder(B, A)) ) ) )  =>  (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v8_relat_2(B) &  (v1_wellord1(B) & v2_bagorder(B, A)) ) ) ) ) ) ) ) ) ) ).
fof(cc1_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v5_valued_0(A)) ) ) ).
fof(cc1_vectsp_1, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v5_vectsp_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v1_vectsp_1(A) & v2_vectsp_1(A)) ) ) ) ) ).
fof(cc1_xreal_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xreal_0(A)) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc21_valued_0, axiom,  (! [A, B] :  (v6_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v6_valued_0(C)) ) ) ) ).
fof(cc22_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_zfmisc_1(A) & v2_valued_0(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) &  (v7_valued_0(A) & v8_valued_0(A)) ) ) ) ) ) ).
fof(cc23_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v7_valued_0(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v9_valued_0(A)) ) ) ) ) ).
fof(cc24_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v8_valued_0(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v10_valued_0(A)) ) ) ) ) ).
fof(cc28_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k2_numbers))  =>  (v1_relat_1(A) & v1_valued_0(A)) ) ) ).
fof(cc29_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k2_numbers)) ) ) ).
fof(cc2_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v4_algstr_0(B, A) =>  (v2_algstr_0(B, A) & v3_algstr_0(B, 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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(cc2_finset_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_finset_1(B)) ) ) ) ).
fof(cc2_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funcop_1(A)) ) ) ) ).
fof(cc2_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ) ).
fof(cc2_funct_2, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc2_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_ideal_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v5_group_1(A) & l3_algstr_0(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  ( ( ~ (v1_xboole_0(B))  & v3_ideal_1(B, A))  =>  ( ~ (v1_xboole_0(B))  & v2_ideal_1(B, 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_polynom1, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v1_vectsp_1(A) &  (v3_vectsp_1(A) &  (v3_rlvect_1(A) & v4_rlvect_1(A)) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v1_vectsp_1(A) &  (v3_vectsp_1(A) &  (v3_rlvect_1(A) & v4_rlvect_1(A)) ) ) ) ) ) ) ) ) ).
fof(cc2_polynom7, axiom,  (! [A, B] :  ( ( ~ (v2_struct_0(B))  & l2_struct_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B)))) =>  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & v3_polynom7(C, A, B)) )  =>  (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & v1_polynom1(C, B)) ) ) ) ) ) ) ).
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_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_rewrite1(A))  =>  (v1_relat_1(A) &  (v2_relat_2(A) & v1_rewrite1(A)) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v4_valued_0(A)) ) ) ).
fof(cc2_vectsp_1, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v1_vectsp_1(A) & v2_vectsp_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v5_vectsp_1(A)) ) ) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc30_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k6_numbers))  =>  (v1_relat_1(A) & v2_valued_0(A)) ) ) ).
fof(cc31_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k6_numbers)) ) ) ).
fof(cc32_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k1_numbers))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc33_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k1_numbers)) ) ) ).
fof(cc34_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k3_numbers))  =>  (v1_relat_1(A) & v4_valued_0(A)) ) ) ).
fof(cc35_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k3_numbers)) ) ) ).
fof(cc36_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k4_numbers))  =>  (v1_relat_1(A) & v5_valued_0(A)) ) ) ).
fof(cc37_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k4_numbers)) ) ) ).
fof(cc38_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k4_ordinal1))  =>  (v1_relat_1(A) & v6_valued_0(A)) ) ) ).
fof(cc39_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k4_ordinal1)) ) ) ).
fof(cc3_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  ( (v5_algstr_0(A) & v6_algstr_0(A))  => v7_algstr_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_finset_1, axiom,  (! [A, B] :  (v1_finset_1(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  (v1_funct_2(C, A, B) & v1_finset_1(C)) ) ) ) ) ) ) ).
fof(cc3_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ) ).
fof(cc3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_funct_1(B)) ) ) ) ).
fof(cc3_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc3_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_polynom7, axiom,  (! [A, B] :  ( ( ~ (v2_struct_0(B))  & l2_struct_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B)))) =>  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & v4_polynom7(C, A, B)) )  =>  (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & v3_polynom7(C, A, B)) ) ) ) ) ) ) ).
fof(cc3_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(A)) ) ) ).
fof(cc3_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v2_relat_2(A) & v1_rewrite1(A)) )  =>  (v1_relat_1(A) & v3_rewrite1(A)) ) ) ).
fof(cc3_struct_0, axiom,  (! [A] :  (l4_struct_0(A) =>  ( ~ (v6_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc3_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc3_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_vectsp_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & v6_vectsp_1(A)) ) ) ) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc4_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  (v7_algstr_0(A) =>  (v5_algstr_0(A) & v6_algstr_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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc4_finset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) => v1_finset_1(A)) ) ).
fof(cc4_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc4_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  (v1_funct_2(B, A, A) => v1_partfun1(B, A)) ) ) ) ).
fof(cc4_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_pre_poly, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_pre_poly(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(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_rewrite1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) &  (v2_rewrite1(A) & v3_rewrite1(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_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc4_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & v6_vectsp_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v1_group_1(A)) ) ) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc50_valued_0, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k4_ordinal1)) ) ) ) ) ).
fof(cc51_valued_0, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v6_valued_0(B)) ) ) ) ) ).
fof(cc5_algstr_0, axiom,  (! [A] :  ( (v5_algstr_0(A) & l1_algstr_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => v2_algstr_0(B, A)) ) ) ) ).
fof(cc5_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_finset_1(A)) ) ).
fof(cc5_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) ) ) ).
fof(cc5_finset_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_zfmisc_1(A)) ) ) ).
fof(cc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc5_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A))) =>  (v1_funct_2(B, k2_zfmisc_1(A, A), A) => v1_partfun1(B, k2_zfmisc_1(A, A))) ) ) ) ).
fof(cc5_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_pre_poly, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_pre_poly(A)) ) ) ) ).
fof(cc5_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v4_relat_1(C, A)) ) ) ) ).
fof(cc5_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_rewrite1(A))  =>  (v1_relat_1(A) & v2_rewrite1(A)) ) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc5_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v2_valued_0(A)) ) ) ).
fof(cc5_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_vectsp_1(A))  =>  ( ~ (v2_struct_0(A))  & v1_group_1(A)) ) ) ) ).
fof(cc6_algstr_0, axiom,  (! [A] :  ( (v6_algstr_0(A) & l1_algstr_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => v3_algstr_0(B, A)) ) ) ) ).
fof(cc6_card_1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v1_finset_1(A))  => v7_ordinal1(A)) ) ).
fof(cc6_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ).
fof(cc6_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_finset_1(A)) ) ).
fof(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc6_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v3_funct_2(C, A, B))  =>  (v1_funct_1(C) &  (v2_funct_1(C) & v2_funct_2(C, B)) ) ) ) ) ) ).
fof(cc6_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc6_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v5_relat_1(C, A)) ) ) ) ).
fof(cc6_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v8_rewrite1(A))  =>  (v1_relat_1(A) & v7_rewrite1(A)) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc6_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v1_valued_0(A)) ) ) ).
fof(cc6_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v5_group_1(A) & v6_vectsp_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v3_vectsp_1(A)) ) ) ) ).
fof(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_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ) ).
fof(cc7_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finset_1(B)) ) ) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) &  (v2_funct_1(C) & v2_funct_2(C, B)) )  =>  (v1_funct_1(C) & v3_funct_2(C, A, B)) ) ) ) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_pre_poly, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_pre_poly(A)) ) ) ) ).
fof(cc7_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v4_relat_1(B, A)) ) ) ) ) ) ).
fof(cc7_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v7_rewrite1(A))  =>  (v1_relat_1(A) &  (v8_rewrite1(A) & v9_rewrite1(A)) ) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc7_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v4_valued_0(A)) ) ) ).
fof(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_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_finseq_1(A)) ) ).
fof(cc8_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_finset_1(B)) ) ) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc8_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  ( (v1_relat_2(B) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_funct_2(B, A, A)) ) )  =>  (v1_funct_1(B) &  (v1_funct_2(B, A, A) & v3_funct_2(B, A, A)) ) ) ) ) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc8_pre_poly, axiom,  (! [A] :  (v1_finset_1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v2_pre_poly(B)) ) ) ) ) ) ) ) ).
fof(cc8_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v5_relat_1(B, A)) ) ) ) ) ) ).
fof(cc8_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_rewrite1(A))  =>  (v1_relat_1(A) & v7_rewrite1(A)) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc8_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(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_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v1_finset_1(A)) ) ).
fof(cc9_finset_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_finset_1(A)) ) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(cc9_funct_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(cc9_pre_poly, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k15_pre_poly(A))) => v4_funct_1(B)) ) ) ).
fof(cc9_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v8_rewrite1(A))  =>  (v1_relat_1(A) & v5_rewrite1(A)) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(cc9_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v6_valued_0(A)) ) ) ).
fof(commutativity_k11_polynom1, axiom,  (! [A, B, C, D] :  ( (v3_ordinal1(A) &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v5_group_1(B) & l6_algstr_0(B)) ) ) ) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) )  => k11_polynom1(A, B, C, D)=k11_polynom1(A, B, D, C)) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(commutativity_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => k4_subset_1(A, B, C)=k4_subset_1(A, C, B)) ) ).
fof(commutativity_k6_polynom1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  &  (v2_rlvect_1(B) &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) )  => k6_polynom1(A, B, C, D)=k6_polynom1(A, B, D, C)) ) ).
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(d10_vectsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) & l6_algstr_0(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  ( ~ (B=k4_struct_0(A))  =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (C=k9_algstr_0(A, B) <=> k8_group_1(A, C, B)=k5_struct_0(A)) ) ) ) ) ) ) ) ).
fof(d11_polynom1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( ( ~ (v7_struct_0(B))  &  (v13_algstr_0(B) &  (v3_vectsp_1(B) &  (v5_vectsp_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) ) ) ) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  &  (v36_algstr_0(C) & l6_algstr_0(C)) )  =>  (C=k12_polynom1(A, B) <=>  ( (! [D] :  (r2_tarski(D, u1_struct_0(C)) <=>  (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(B)) &  (v1_polynom1(D, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) )  &  ( (! [D] :  (m1_subset_1(D, u1_struct_0(C)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(C)) =>  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, k15_pre_poly(A), u1_struct_0(B)) &  (v1_polynom1(F, B) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) )  =>  (! [G] :  ( (v1_funct_1(G) &  (v1_funct_2(G, k15_pre_poly(A), u1_struct_0(B)) &  (v1_polynom1(G, B) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) )  =>  ( (D=F & E=G)  => k1_algstr_0(C, D, E)=k5_polynom1(A, B, F, G)) ) ) ) ) ) ) ) )  &  ( (! [D] :  (m1_subset_1(D, u1_struct_0(C)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(C)) =>  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, k15_pre_poly(A), u1_struct_0(B)) &  (v1_polynom1(F, B) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) )  =>  (! [G] :  ( (v1_funct_1(G) &  (v1_funct_2(G, k15_pre_poly(A), u1_struct_0(B)) &  (v1_polynom1(G, B) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) )  =>  ( (D=F & E=G)  => k6_algstr_0(C, D, E)=k10_polynom1(A, B, F, G)) ) ) ) ) ) ) ) )  &  (k4_struct_0(C)=k8_polynom1(A, B) & k5_struct_0(C)=k9_polynom1(A, 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_ideal_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_algstr_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v2_ideal_1(B, A) <=>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r2_tarski(D, B) => r2_tarski(k6_algstr_0(A, C, D), B)) ) ) ) ) ) ) ) ) ) ).
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(d3_polyred, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v6_relat_2(B) &  (v8_relat_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A))))) ) ) ) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  & l2_struct_0(C))  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(D, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(E, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  =>  (r2_polyred(A, B, C, D, E) <=>  (r1_polyred(A, B, C, D, E) &  ~ (k3_polynom1(k15_pre_poly(A), C, D)=k3_polynom1(k15_pre_poly(A), C, E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d3_termord, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v8_relat_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A))))) ) ) )  =>  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) &  (v1_partfun1(C, A) &  (v6_valued_0(C) & v2_pre_poly(C)) ) ) ) )  =>  (! [D] :  ( (v1_relat_1(D) &  (v4_relat_1(D, A) &  (v1_funct_1(D) &  (v1_partfun1(D, A) &  (v6_valued_0(D) & v2_pre_poly(D)) ) ) ) )  =>  (r2_termord(A, B, C, D) <=>  (r1_termord(A, B, C, D) &  ~ (C=D) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_polynom1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  & l2_struct_0(B))  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, A, u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, u1_struct_0(B))))) )  =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(A)) =>  (D=k3_polynom1(A, B, C) <=>  (! [E] :  (m1_subset_1(E, A) =>  (r2_tarski(E, D) <=>  ~ (k3_funct_2(A, u1_struct_0(B), C, E)=k4_struct_0(B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_rlvect_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  (v4_rlvect_1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k1_algstr_0(A, B, k4_struct_0(A))=B) ) ) ) ) ).
fof(d6_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => k4_struct_0(A)=u2_struct_0(A)) ) ).
fof(d6_termord, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v6_relat_2(B) &  (v8_relat_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A))))) ) ) ) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  & l2_struct_0(C))  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(D, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  =>  (! [E] :  (m2_subset_1(E, k14_pre_poly(A), k15_pre_poly(A)) =>  (E=k3_termord(A, B, C, D) <=>  ( (k3_polynom1(k15_pre_poly(A), C, D)=k1_xboole_0 & r6_pboole(A, E, k16_pre_poly(A)))  |  (r2_tarski(E, k3_polynom1(k15_pre_poly(A), C, D)) &  (! [F] :  ( (v1_relat_1(F) &  (v4_relat_1(F, A) &  (v1_funct_1(F) &  (v1_partfun1(F, A) &  (v6_valued_0(F) & v2_pre_poly(F)) ) ) ) )  =>  (r2_tarski(F, k3_polynom1(k15_pre_poly(A), C, D)) => r1_termord(A, B, F, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_polynom1, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  => k7_polynom1(A, B, C, D)=k5_polynom1(A, B, C, k5_vfunct_1(k15_pre_poly(A), B, D))) ) ) ) ) ) ) ).
fof(d7_struct_0, axiom,  (! [A] :  (l3_struct_0(A) => k5_struct_0(A)=u3_struct_0(A)) ) ).
fof(d7_termord, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v6_relat_2(B) &  (v8_relat_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A))))) ) ) ) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  & l2_struct_0(C))  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(D, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  => k4_termord(A, B, C, D)=k4_polynom1(A, C, D, k3_termord(A, B, C, D))) ) ) ) ) ) ) ) ).
fof(d8_termord, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v6_relat_2(B) &  (v8_relat_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A))))) ) ) ) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  & l2_struct_0(C))  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(D, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  => k5_termord(A, B, C, D)=k1_polynom7(A, C, k4_termord(A, B, C, D), k3_termord(A, B, C, D))) ) ) ) ) ) ) ) ).
fof(d9_polynom7, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  & l5_algstr_0(B))  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  =>  (! [D] :  (m1_subset_1(D, u1_struct_0(B)) =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  =>  (E=k5_polynom7(A, B, C, D) <=>  (! [F] :  ( (v1_relat_1(F) &  (v4_relat_1(F, A) &  (v1_funct_1(F) &  (v1_partfun1(F, A) &  (v6_valued_0(F) & v2_pre_poly(F)) ) ) ) )  => k4_polynom1(A, B, E, F)=k6_algstr_0(B, D, k4_polynom1(A, B, C, F))) ) ) ) ) ) ) ) ) ) ) ) ).
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_k10_polynom1, axiom,  (! [A, B, C, D] :  ( (v3_ordinal1(A) &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) )  =>  (v1_funct_1(k10_polynom1(A, B, C, D)) &  (v1_funct_2(k10_polynom1(A, B, C, D), k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(k10_polynom1(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) ).
fof(dt_k11_polynom1, axiom,  (! [A, B, C, D] :  ( (v3_ordinal1(A) &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v5_group_1(B) & l6_algstr_0(B)) ) ) ) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) )  =>  (v1_funct_1(k11_polynom1(A, B, C, D)) &  (v1_funct_2(k11_polynom1(A, B, C, D), k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(k11_polynom1(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) ).
fof(dt_k12_polynom1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) &  ( ~ (v7_struct_0(B))  &  (v13_algstr_0(B) &  (v3_vectsp_1(B) &  (v5_vectsp_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom1(A, B)))  &  (v36_algstr_0(k12_polynom1(A, B)) & l6_algstr_0(k12_polynom1(A, B))) ) ) ) ).
fof(dt_k14_pre_poly, axiom, $true).
fof(dt_k15_pre_poly, axiom,  (! [A] : m1_subset_1(k15_pre_poly(A), k1_zfmisc_1(k14_pre_poly(A)))) ).
fof(dt_k16_pre_poly, axiom,  (! [A] : m2_subset_1(k16_pre_poly(A), k14_pre_poly(A), k15_pre_poly(A))) ).
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_funct_1, axiom, $true).
fof(dt_k1_numbers, axiom, $true).
fof(dt_k1_pboole, axiom,  (! [A] :  (v1_relat_1(k1_pboole(A)) &  (v4_relat_1(k1_pboole(A), A) &  (v1_funct_1(k1_pboole(A)) & v1_partfun1(k1_pboole(A), A)) ) ) ) ).
fof(dt_k1_polynom7, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  & l2_struct_0(B))  &  (m1_subset_1(C, u1_struct_0(B)) &  (v1_relat_1(D) &  (v4_relat_1(D, A) &  (v1_funct_1(D) &  (v1_partfun1(D, A) &  (v6_valued_0(D) & v2_pre_poly(D)) ) ) ) ) ) )  =>  (v1_funct_1(k1_polynom7(A, B, C, D)) &  (v1_funct_2(k1_polynom7(A, B, C, D), k15_pre_poly(A), u1_struct_0(B)) &  (v3_polynom7(k1_polynom7(A, B, C, D), A, B) & m1_subset_1(k1_polynom7(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_numbers, axiom, $true).
fof(dt_k2_polynom1, axiom, $true).
fof(dt_k2_polynom7, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  & l2_struct_0(B))  &  (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) &  (v3_polynom7(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) )  =>  (v1_relat_1(k2_polynom7(A, B, C)) &  (v4_relat_1(k2_polynom7(A, B, C), A) &  (v1_funct_1(k2_polynom7(A, B, C)) &  (v1_partfun1(k2_polynom7(A, B, C), A) &  (v6_valued_0(k2_polynom7(A, B, C)) & v2_pre_poly(k2_polynom7(A, B, C))) ) ) ) ) ) ) ).
fof(dt_k2_termord, axiom,  (! [A, B, C, D] :  ( (v3_ordinal1(A) &  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v8_relat_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A))))) ) ) )  &  ( (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) &  (v1_partfun1(C, A) &  (v6_valued_0(C) & v2_pre_poly(C)) ) ) ) )  &  (v1_relat_1(D) &  (v4_relat_1(D, A) &  (v1_funct_1(D) &  (v1_partfun1(D, A) &  (v6_valued_0(D) & v2_pre_poly(D)) ) ) ) ) ) ) )  =>  (v1_relat_1(k2_termord(A, B, C, D)) &  (v4_relat_1(k2_termord(A, B, C, D), A) &  (v1_funct_1(k2_termord(A, B, C, D)) &  (v1_partfun1(k2_termord(A, B, C, D), A) &  (v6_valued_0(k2_termord(A, B, C, D)) & v2_pre_poly(k2_termord(A, B, C, D))) ) ) ) ) ) ) ).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => m1_subset_1(k3_funct_2(A, B, C, D), B)) ) ).
fof(dt_k3_numbers, axiom, $true).
fof(dt_k3_polynom1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v2_struct_0(B))  & l2_struct_0(B))  &  (v1_funct_1(C) &  (v1_funct_2(C, A, u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, u1_struct_0(B))))) ) ) )  => m1_subset_1(k3_polynom1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k3_polynom7, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  & l2_struct_0(B))  &  (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) &  (v3_polynom7(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) )  => m1_subset_1(k3_polynom7(A, B, C), u1_struct_0(B))) ) ).
fof(dt_k3_termord, axiom,  (! [A, B, C, D] :  ( (v3_ordinal1(A) &  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v6_relat_2(B) &  (v8_relat_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A))))) ) ) ) )  &  ( ( ~ (v2_struct_0(C))  & l2_struct_0(C))  &  (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(D, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) ) ) ) )  => m2_subset_1(k3_termord(A, B, C, D), k14_pre_poly(A), k15_pre_poly(A))) ) ).
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_numbers, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_polynom1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  & l1_struct_0(B))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  &  (v1_relat_1(D) &  (v4_relat_1(D, A) &  (v1_funct_1(D) &  (v1_partfun1(D, A) &  (v6_valued_0(D) & v2_pre_poly(D)) ) ) ) ) ) )  => m1_subset_1(k4_polynom1(A, B, C, D), u1_struct_0(B))) ) ).
fof(dt_k4_polynom7, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  & l2_struct_0(B))  & m1_subset_1(C, u1_struct_0(B)))  =>  (v1_funct_1(k4_polynom7(A, B, C)) &  (v1_funct_2(k4_polynom7(A, B, C), k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(k4_polynom7(A, B, C), k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) ).
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_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k4_termord, axiom,  (! [A, B, C, D] :  ( (v3_ordinal1(A) &  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v6_relat_2(B) &  (v8_relat_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A))))) ) ) ) )  &  ( ( ~ (v2_struct_0(C))  & l2_struct_0(C))  &  (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(D, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) ) ) ) )  => m1_subset_1(k4_termord(A, B, C, D), u1_struct_0(C))) ) ).
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_ordinal1, axiom, $true).
fof(dt_k5_polynom1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  & l2_algstr_0(B))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) )  =>  (v1_funct_1(k5_polynom1(A, B, C, D)) &  (v1_funct_2(k5_polynom1(A, B, C, D), k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(k5_polynom1(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) ).
fof(dt_k5_polynom7, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  & l5_algstr_0(B))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  & m1_subset_1(D, u1_struct_0(B))) )  =>  (v1_funct_1(k5_polynom7(A, B, C, D)) &  (v1_funct_2(k5_polynom7(A, B, C, D), k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(k5_polynom7(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) ).
fof(dt_k5_struct_0, axiom,  (! [A] :  (l3_struct_0(A) => m1_subset_1(k5_struct_0(A), u1_struct_0(A))) ) ).
fof(dt_k5_termord, axiom,  (! [A, B, C, D] :  ( (v3_ordinal1(A) &  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v6_relat_2(B) &  (v8_relat_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A))))) ) ) ) )  &  ( ( ~ (v2_struct_0(C))  & l2_struct_0(C))  &  (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(D, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) ) ) ) )  =>  (v1_funct_1(k5_termord(A, B, C, D)) &  (v1_funct_2(k5_termord(A, B, C, D), k15_pre_poly(A), u1_struct_0(C)) &  (v3_polynom7(k5_termord(A, B, C, D), A, C) & m1_subset_1(k5_termord(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) ) ) ) ).
fof(dt_k5_vfunct_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v2_struct_0(B))  & l2_algstr_0(B))  &  (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, u1_struct_0(B))))) ) )  =>  (v1_funct_1(k5_vfunct_1(A, B, C)) & m1_subset_1(k5_vfunct_1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(A, 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_k6_numbers, axiom, $true).
fof(dt_k6_polynom1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  &  (v2_rlvect_1(B) &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) )  =>  (v1_funct_1(k6_polynom1(A, B, C, D)) &  (v1_funct_2(k6_polynom1(A, B, C, D), k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(k6_polynom1(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) ).
fof(dt_k7_polynom1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) )  =>  (v1_funct_1(k7_polynom1(A, B, C, D)) &  (v1_funct_2(k7_polynom1(A, B, C, D), k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(k7_polynom1(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) ).
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_polynom1, axiom,  (! [A, B] :  ( ( ~ (v2_struct_0(B))  & l2_struct_0(B))  =>  (v1_funct_1(k8_polynom1(A, B)) &  (v1_funct_2(k8_polynom1(A, B), k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(k8_polynom1(A, B), k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) ).
fof(dt_k9_algstr_0, axiom,  (! [A, B] :  ( (l4_algstr_0(A) & m1_subset_1(B, u1_struct_0(A)))  => m1_subset_1(k9_algstr_0(A, B), u1_struct_0(A))) ) ).
fof(dt_k9_polynom1, axiom,  (! [A, B] :  ( ( ~ (v2_struct_0(B))  &  (v3_vectsp_1(B) & l5_algstr_0(B)) )  =>  (v1_funct_1(k9_polynom1(A, B)) &  (v1_funct_2(k9_polynom1(A, B), k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(k9_polynom1(A, B), k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) ).
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_polynom1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) &  ( ~ (v7_struct_0(B))  &  (v13_algstr_0(B) &  (v3_vectsp_1(B) &  (v5_vectsp_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom1(A, B)))  &  (v13_algstr_0(k12_polynom1(A, B)) & v36_algstr_0(k12_polynom1(A, B))) ) ) ) ).
fof(fc10_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => v9_struct_0(k4_struct_0(A), A)) ) ).
fof(fc10_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v4_valued_0(A))  &  (v1_relat_1(B) & v4_valued_0(B)) )  => v4_valued_0(k2_xboole_0(A, B))) ) ).
fof(fc11_polynom1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) &  ( ~ (v2_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v13_algstr_0(B) &  (v3_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v5_group_1(B) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom1(A, B)))  &  (v36_algstr_0(k12_polynom1(A, B)) & v5_group_1(k12_polynom1(A, B))) ) ) ) ).
fof(fc11_struct_0, axiom,  (! [A] :  ( ( ~ (v6_struct_0(A))  & l4_struct_0(A))  =>  ~ (v9_struct_0(k5_struct_0(A), A)) ) ) ).
fof(fc11_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v5_valued_0(A))  &  (v1_relat_1(B) & v5_valued_0(B)) )  => v5_valued_0(k2_xboole_0(A, B))) ) ).
fof(fc12_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k1_zfmisc_1(A))) ) ) ).
fof(fc12_polynom1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) &  ( ~ (v2_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v13_algstr_0(B) &  (v3_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom1(A, B)))  &  (v36_algstr_0(k12_polynom1(A, B)) & v3_group_1(k12_polynom1(A, B))) ) ) ) ).
fof(fc12_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v6_valued_0(A))  &  (v1_relat_1(B) & v6_valued_0(B)) )  => v6_valued_0(k2_xboole_0(A, B))) ) ).
fof(fc13_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(A, B))) ) ) ).
fof(fc13_polynom1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) &  ( ~ (v2_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v13_algstr_0(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom1(A, B)))  &  (v36_algstr_0(k12_polynom1(A, B)) &  (v1_vectsp_1(k12_polynom1(A, B)) & v4_vectsp_1(k12_polynom1(A, B))) ) ) ) ) ).
fof(fc14_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(B, A))) ) ) ).
fof(fc14_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v1_finset_1(k2_zfmisc_1(A, B))) ) ).
fof(fc17_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v1_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc17_funct_1, axiom,  (! [A, B, C] :  ( (v4_funct_1(A) &  (v1_relat_1(C) &  (v5_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_1(C, B)) & v1_funct_1(k1_funct_1(C, B))) ) ) ).
fof(fc19_finseq_1, axiom,  (! [A, B] :  ( (v3_finseq_1(A) & v3_finseq_1(B))  => v3_finseq_1(k2_xboole_0(A, B))) ) ).
fof(fc19_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v3_relat_1(A) & v1_funct_1(A)) )  => v1_xboole_0(k1_funct_1(A, B))) ) ).
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_polynom1, axiom,  (! [A, B, C, D] :  ( (v3_ordinal1(A) &  ( ( ~ (v2_struct_0(B))  &  (v4_rlvect_1(B) & l2_algstr_0(B)) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) &  (v1_polynom1(C, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(B)) &  (v1_polynom1(D, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) ) )  =>  (v1_funct_1(k5_polynom1(A, B, C, D)) &  (v1_funct_2(k5_polynom1(A, B, C, D), k15_pre_poly(A), u1_struct_0(B)) & v1_polynom1(k5_polynom1(A, B, C, D), B)) ) ) ) ).
fof(fc1_polynom2, axiom,  (! [A, B, C, D] :  ( (v3_ordinal1(A) &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) &  (v1_polynom1(C, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(B)) &  (v1_polynom1(D, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) ) )  =>  (v1_funct_1(k7_polynom1(A, B, C, D)) &  (v1_funct_2(k7_polynom1(A, B, C, D), k15_pre_poly(A), u1_struct_0(B)) & v1_polynom1(k7_polynom1(A, B, C, D), B)) ) ) ) ).
fof(fc1_polynom7, axiom,  (! [A, B] :  ( ( ~ (v2_struct_0(B))  & l2_struct_0(B))  =>  (v1_funct_1(k8_polynom1(A, B)) &  (v1_funct_2(k8_polynom1(A, B), k15_pre_poly(A), u1_struct_0(B)) & v4_polynom7(k8_polynom1(A, B), 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_termord, axiom,  (! [A, B, C, D] :  ( (v3_ordinal1(A) &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) ) ) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) &  (v3_polynom7(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(B)) &  (v3_polynom7(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) ) )  =>  (v1_funct_1(k10_polynom1(A, B, C, D)) &  (v1_funct_2(k10_polynom1(A, B, C, D), k15_pre_poly(A), u1_struct_0(B)) & v3_polynom7(k10_polynom1(A, B, C, D), A, B)) ) ) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc25_funcop_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_binop_1(A, B, C)) & v1_funct_1(k1_binop_1(A, B, C))) ) ) ).
fof(fc25_pre_poly, axiom,  (! [A] :  ~ (v1_xboole_0(k14_pre_poly(A))) ) ).
fof(fc29_algstr_0, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( (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)) ) ) )  =>  ( ~ (v2_struct_0(g6_algstr_0(A, B, C, D, E)))  & v36_algstr_0(g6_algstr_0(A, B, C, D, E))) ) ) ).
fof(fc2_polynom1, axiom,  (! [A, B, C] :  ( (v3_ordinal1(A) &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) ) )  &  (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) &  (v1_polynom1(C, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) )  =>  (v1_funct_1(k5_vfunct_1(k15_pre_poly(A), B, C)) & v1_polynom1(k5_vfunct_1(k15_pre_poly(A), B, C), B)) ) ) ).
fof(fc2_polynom2, axiom,  (! [A, B, C] :  ( (v3_ordinal1(A) &  ( ( ~ (v7_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) & l6_algstr_0(B)) ) ) ) ) )  &  (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) &  (v1_polynom1(C, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) )  => v1_finset_1(k2_polynom1(B, C))) ) ).
fof(fc2_polynom7, axiom,  (! [A, B] :  ( ( ~ (v2_struct_0(B))  &  (v4_vectsp_1(B) & l6_algstr_0(B)) )  =>  (v1_funct_1(k9_polynom1(A, B)) &  (v1_funct_2(k9_polynom1(A, B), k15_pre_poly(A), u1_struct_0(B)) & v4_polynom7(k9_polynom1(A, B), 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_termord, axiom,  (! [A, B, C, D] :  ( (v3_ordinal1(A) &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v5_vectsp_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) ) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) &  (v4_polynom7(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(B)) &  (v4_polynom7(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) ) )  =>  (v1_funct_1(k10_polynom1(A, B, C, D)) &  (v1_funct_2(k10_polynom1(A, B, C, D), k15_pre_poly(A), u1_struct_0(B)) & v4_polynom7(k10_polynom1(A, B, C, D), A, B)) ) ) ) ).
fof(fc30_algstr_0, axiom,  (! [A, B, C, D, E] :  ( (v1_zfmisc_1(A) &  ( (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)) ) ) )  =>  (v7_struct_0(g6_algstr_0(A, B, C, D, E)) & v36_algstr_0(g6_algstr_0(A, B, C, D, E))) ) ) ).
fof(fc31_algstr_0, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_zfmisc_1(A))  &  ( (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)) ) ) )  =>  ( ~ (v7_struct_0(g6_algstr_0(A, B, C, D, E)))  & v36_algstr_0(g6_algstr_0(A, B, C, D, E))) ) ) ).
fof(fc31_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v5_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc33_finset_1, axiom,  (! [A, B] :  ( (v5_finset_1(A) & v5_finset_1(B))  => v5_finset_1(k2_xboole_0(A, B))) ) ).
fof(fc35_finset_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) )  => v1_finset_1(k1_funct_1(A, B))) ) ).
fof(fc36_finseq_1, axiom,  (! [A, B] :  ( (v4_finseq_1(A) & v4_finseq_1(B))  => v4_finseq_1(k2_xboole_0(A, B))) ) ).
fof(fc39_finseq_1, axiom,  (! [A, B, C] :  ( (v4_finseq_1(A) &  (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) ) )  => v1_finseq_1(k1_funct_1(B, C))) ) ).
fof(fc3_polynom1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(A, k4_ordinal1) &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) &  (v1_polynom1(C, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(B)) &  (v1_polynom1(D, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) ) )  =>  (v1_funct_1(k7_polynom1(A, B, C, D)) &  (v1_funct_2(k7_polynom1(A, B, C, D), k15_pre_poly(A), u1_struct_0(B)) & v1_polynom1(k7_polynom1(A, B, C, D), B)) ) ) ) ).
fof(fc3_polynom2, axiom,  (! [A, B] :  ( (v3_ordinal1(A) &  ( ~ (v2_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v13_algstr_0(B) &  (v3_group_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom1(A, B)))  &  (v36_algstr_0(k12_polynom1(A, B)) & v4_vectsp_1(k12_polynom1(A, B))) ) ) ) ).
fof(fc3_polynom7, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  & l2_struct_0(B))  & m1_subset_1(C, u1_struct_0(B)))  =>  (v1_funct_1(k4_polynom7(A, B, C)) &  (v1_funct_2(k4_polynom7(A, B, C), k15_pre_poly(A), u1_struct_0(B)) & v4_polynom7(k4_polynom7(A, B, C), A, B)) ) ) ) ).
fof(fc3_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_relat_1(B))  => v1_relat_1(k2_xboole_0(A, B))) ) ).
fof(fc4_polynom1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) &  ( ~ (v2_struct_0(B))  & l2_struct_0(B)) )  =>  (v1_funct_1(k8_polynom1(A, B)) &  (v1_funct_2(k8_polynom1(A, B), k15_pre_poly(A), u1_struct_0(B)) & v1_polynom1(k8_polynom1(A, B), B)) ) ) ) ).
fof(fc4_polynom7, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  &  (v7_algstr_0(B) &  (v4_rlvect_1(B) &  (v5_vectsp_1(B) &  (v1_algstr_1(B) & l6_algstr_0(B)) ) ) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) &  (v1_polynom1(C, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) )  & m1_subset_1(D, u1_struct_0(B))) )  =>  (v1_funct_1(k5_polynom7(A, B, C, D)) &  (v1_funct_2(k5_polynom7(A, B, C, D), k15_pre_poly(A), u1_struct_0(B)) & v1_polynom1(k5_polynom7(A, B, C, D), B)) ) ) ) ).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc5_polynom1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) &  ( ~ (v7_struct_0(B))  &  (v13_algstr_0(B) &  (v1_vectsp_1(B) &  (v3_vectsp_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) ) ) ) ) )  =>  (v1_funct_1(k9_polynom1(A, B)) &  (v1_funct_2(k9_polynom1(A, B), k15_pre_poly(A), u1_struct_0(B)) & v1_polynom1(k9_polynom1(A, B), B)) ) ) ) ).
fof(fc5_vfunct_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v2_struct_0(B))  & l2_algstr_0(B))  &  (v1_funct_1(C) &  (v1_funct_2(C, A, u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, u1_struct_0(B))))) ) ) )  =>  (v1_funct_1(k5_vfunct_1(A, B, C)) & v1_partfun1(k5_vfunct_1(A, B, C), A)) ) ) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc61_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  => v1_xcmplx_0(k1_funct_1(A, B))) ) ).
fof(fc62_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_valued_0(A)) )  => v1_xxreal_0(k1_funct_1(A, B))) ) ).
fof(fc63_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_valued_0(A)) )  => v1_xreal_0(k1_funct_1(A, B))) ) ).
fof(fc64_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v4_valued_0(A)) )  => v1_rat_1(k1_funct_1(A, B))) ) ).
fof(fc65_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_valued_0(A)) )  => v1_int_1(k1_funct_1(A, B))) ) ).
fof(fc66_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v6_valued_0(A)) )  => v7_ordinal1(k1_funct_1(A, B))) ) ).
fof(fc6_card_1, axiom, v1_card_1(k4_ordinal1)).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc6_polynom1, axiom,  (! [A, B, C, D] :  ( (v3_ordinal1(A) &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_vectsp_1(B) &  (v5_vectsp_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) ) ) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) &  (v1_polynom1(C, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(B)) &  (v1_polynom1(D, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) ) )  =>  (v1_funct_1(k10_polynom1(A, B, C, D)) &  (v1_funct_2(k10_polynom1(A, B, C, D), k15_pre_poly(A), u1_struct_0(B)) & v1_polynom1(k10_polynom1(A, B, C, D), B)) ) ) ) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc7_card_1, axiom, v2_card_1(k4_ordinal1)).
fof(fc7_polynom1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) &  ( ~ (v7_struct_0(B))  &  (v13_algstr_0(B) &  (v3_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom1(A, B)))  &  (v36_algstr_0(k12_polynom1(A, B)) & v2_rlvect_1(k12_polynom1(A, B))) ) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc7_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_valued_0(A))  &  (v1_relat_1(B) & v1_valued_0(B)) )  => v1_valued_0(k2_xboole_0(A, B))) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_polynom1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) &  ( ~ (v7_struct_0(B))  &  (v13_algstr_0(B) &  (v3_vectsp_1(B) &  (v5_vectsp_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom1(A, B)))  &  (v36_algstr_0(k12_polynom1(A, B)) & v3_rlvect_1(k12_polynom1(A, B))) ) ) ) ).
fof(fc8_pre_poly, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_pre_poly(A)) )  => v1_finseq_1(k1_funct_1(A, B))) ) ).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc8_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v2_valued_0(A))  &  (v1_relat_1(B) & v2_valued_0(B)) )  => v2_valued_0(k2_xboole_0(A, B))) ) ).
fof(fc90_valued_0, axiom,  (! [A, B] :  (v6_membered(B) => v6_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc9_card_1, axiom,  ~ (v1_finset_1(k4_ordinal1)) ).
fof(fc9_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v1_finset_1(k2_xboole_0(A, B))) ) ).
fof(fc9_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_funct_1(A, B)) & v1_funct_1(k1_funct_1(A, B))) ) ) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_polynom1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) &  ( ~ (v7_struct_0(B))  &  (v13_algstr_0(B) &  (v3_vectsp_1(B) &  (v5_vectsp_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom1(A, B)))  &  (v36_algstr_0(k12_polynom1(A, B)) & v4_rlvect_1(k12_polynom1(A, B))) ) ) ) ).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(fc9_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v3_valued_0(A))  &  (v1_relat_1(B) & v3_valued_0(B)) )  => v3_valued_0(k2_xboole_0(A, 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(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(idempotence_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => k4_subset_1(A, B, B)=B) ) ).
fof(l4_groeb_1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v6_relat_2(B) &  (v8_relat_2(B) &  (v2_bagorder(B, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A))))) ) ) ) ) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  &  ( ~ (v6_struct_0(C))  &  (v13_algstr_0(C) &  (v33_algstr_0(C) &  (v4_vectsp_1(C) &  (v5_vectsp_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v3_group_1(C) &  (v5_group_1(C) & l6_algstr_0(C)) ) ) ) ) ) ) ) ) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(D, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(E, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  =>  (! [F] :  (m1_subset_1(F, u1_struct_0(k12_polynom1(A, C))) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(k12_polynom1(A, C))) =>  ( (F=D & G=E)  => k5_algstr_0(k12_polynom1(A, C), F, G)=k7_polynom1(A, C, D, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc10_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_card_1(B)) ) ) ) ).
fof(rc10_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v3_card_1(B, A) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ).
fof(rc10_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) ) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_finseq_1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc11_vectsp_1, axiom,  (? [A] :  (l4_algstr_0(A) &  ( ~ (v2_struct_0(A))  & v4_vectsp_1(A)) ) ) ).
fof(rc12_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc12_pre_poly, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v6_valued_0(A) & v2_pre_poly(A)) ) ) ) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc13_pre_poly, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k4_ordinal1))) &  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v1_funct_2(B, A, k4_ordinal1) &  (v1_valued_0(B) &  (v2_valued_0(B) &  (v3_valued_0(B) &  (v4_valued_0(B) &  (v5_valued_0(B) &  (v6_valued_0(B) & v2_pre_poly(B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc14_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v2_funct_1(A) &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(rc14_pre_poly, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v6_valued_0(B) & v2_pre_poly(B)) ) ) ) ) ) ) ).
fof(rc15_pre_poly, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (v1_relat_1(B) &  ( ~ (v3_relat_1(B))  &  (v4_relat_1(B, A) &  (v5_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_partfun1(B, A) &  (v1_valued_0(B) &  (v2_valued_0(B) &  (v3_valued_0(B) &  (v4_valued_0(B) &  (v5_valued_0(B) &  (v6_valued_0(B) & v2_pre_poly(B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc16_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v6_valued_0(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ) ).
fof(rc17_algstr_0, axiom,  (? [A] :  (l6_algstr_0(A) & v36_algstr_0(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(rc18_algstr_0, axiom,  (? [A] :  (l6_algstr_0(A) &  (v13_struct_0(A, 1) & v36_algstr_0(A)) ) ) ).
fof(rc19_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l2_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, u1_struct_0(A)) &  ~ (v9_struct_0(B, A)) ) ) ) ) ).
fof(rc1_card_1, axiom,  (? [A] : v1_card_1(A)) ).
fof(rc1_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A))) &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ).
fof(rc1_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_finset_1(A)) ) ).
fof(rc1_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_funct_2, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(rc1_gcd_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) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & v1_vectsp_2(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_ideal_1, axiom,  (? [A] :  (l2_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & v1_algstr_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_polynom2, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) & v5_vectsp_1(A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_polynom4, 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) &  (v5_vectsp_1(A) &  (v1_group_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & v1_vectsp_2(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_polynom7, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v1_vectsp_2(A) & v1_algstr_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_rewrite1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) & v10_rewrite1(A)) ) ) ).
fof(rc1_termord, axiom,  (? [A] :  (l2_algstr_0(A) &  ~ (v7_struct_0(A)) ) ) ).
fof(rc1_valued_0, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v6_valued_0(A)) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc20_struct_0, axiom,  (? [A] :  (l2_struct_0(A) &  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ).
fof(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc23_struct_0, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (l1_struct_0(B) & v13_struct_0(B, A)) ) ) ) ).
fof(rc2_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v1_finset_1(A) & v1_card_1(A)) ) ) ) ) ).
fof(rc2_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) & v1_finseq_1(B)) ) ) ) ) ) ).
fof(rc2_finset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_finset_1(B)) ) ) ).
fof(rc2_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_funct_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_funct_2, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) &  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v1_funct_2(B, A, A) & v3_funct_2(B, A, 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_ideal_1, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v7_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & v1_algstr_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_polynom1, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v36_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & v5_group_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_polyred, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v5_algstr_0(A) &  (v6_algstr_0(A) &  (v7_algstr_0(A) &  (v13_algstr_0(A) &  (v33_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) &  (v1_algstr_1(A) &  (v2_algstr_1(A) &  (v3_algstr_1(A) & v4_algstr_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_termord, axiom,  (? [A] :  (l2_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) & v4_rlvect_1(A)) ) ) ) ) ) ).
fof(rc2_valued_0, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v4_valued_0(A) &  (v5_valued_0(A) & v6_valued_0(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(rc3_card_1, axiom,  (? [A] :  ~ (v1_finset_1(A)) ) ).
fof(rc3_finset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc3_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) &  (v3_funct_1(C) &  (v1_partfun1(C, A) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ) ) ) ).
fof(rc3_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_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_ideal_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_algstr_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_ideal_1(B, 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_polynom1, axiom,  (! [A, B] :  ( ( ~ (v2_struct_0(B))  & l2_struct_0(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B)))) &  (v1_relat_1(C) &  (v4_relat_1(C, k15_pre_poly(A)) &  (v5_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  &  (v1_partfun1(C, k15_pre_poly(A)) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & v1_polynom1(C, B)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_relat_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(rc3_termord, axiom,  (! [A] :  (v3_ordinal1(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A)))) &  (v1_relat_1(B) &  (v4_relat_1(B, k15_pre_poly(A)) &  (v5_relat_1(B, k15_pre_poly(A)) &  (v1_partfun1(B, k15_pre_poly(A)) &  (v1_funct_2(B, k15_pre_poly(A), k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v6_relat_2(B) &  (v8_relat_2(B) & v2_bagorder(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_valued_0, axiom,  (? [A] :  (m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k4_ordinal1))) &  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v5_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_partfun1(A, k4_ordinal1) &  (v1_funct_2(A, k4_ordinal1, k4_ordinal1) &  (v1_valued_0(A) &  (v2_valued_0(A) &  (v3_valued_0(A) &  (v4_valued_0(A) &  (v5_valued_0(A) &  (v6_valued_0(A) & v7_valued_0(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_vectsp_1, axiom,  (? [A] :  (l3_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v3_group_1(A) & v5_group_1(A)) ) ) ) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_card_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc4_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ).
fof(rc4_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(rc4_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) ) ) ) ) ).
fof(rc4_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(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_ideal_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_algstr_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v2_ideal_1(B, A)) ) ) ) ) ).
fof(rc4_nat_1, axiom,  (? [A] :  (m1_subset_1(A, k1_zfmisc_1(k1_numbers)) &  ( ~ (v1_xboole_0(A))  & v3_ordinal1(A)) ) ) ).
fof(rc4_ordinal1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v5_ordinal1(B)) ) ) ) ) ).
fof(rc4_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc4_valued_0, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A))) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v3_funct_1(B) & v1_funct_2(B, k4_ordinal1, 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_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  & v1_card_1(A)) ) ) ) ) ) ).
fof(rc5_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v3_finseq_1(A)) ) ).
fof(rc5_funcop_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_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_ideal_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_algstr_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v3_ideal_1(B, A)) ) ) ) ) ).
fof(rc5_nat_1, axiom,  (? [A] :  (m1_subset_1(A, k4_ordinal1) &  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v1_xreal_0(A) &  (v1_finset_1(A) & v1_card_1(A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_polynom7, axiom,  (! [A, B] :  ( ( ~ (v2_struct_0(B))  & l2_struct_0(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B)))) &  (v1_relat_1(C) &  (v4_relat_1(C, k15_pre_poly(A)) &  (v5_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & v3_polynom7(C, A, 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_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_finset_1(B)) ) ) ) ) ).
fof(rc6_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(rc6_finset_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ).
fof(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(rc6_ideal_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  &  (v1_ideal_1(B, A) &  (v2_ideal_1(B, A) & v3_ideal_1(B, A)) ) ) ) ) ) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_polynom7, axiom,  (! [A, B] :  ( ( ~ (v2_struct_0(B))  & l2_struct_0(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B)))) &  (v1_relat_1(C) &  (v4_relat_1(C, k15_pre_poly(A)) &  (v5_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & v4_polynom7(C, A, B)) ) ) ) ) ) ) ) ) ).
fof(rc6_valued_0, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v6_valued_0(B)) ) ) ) ) ) ).
fof(rc7_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] : v3_card_1(B, A)) ) ) ).
fof(rc7_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ) ).
fof(rc7_finset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (? [C] :  ( ~ (v1_xboole_0(C))  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ) ) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc7_ideal_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  &  (v1_ideal_1(B, A) & v3_ideal_1(B, A)) ) ) ) ) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc7_pre_poly, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_pre_poly(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_finset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_zfmisc_1(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc8_ideal_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  &  (v1_ideal_1(B, A) & v2_ideal_1(B, A)) ) ) ) ) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc8_pre_poly, axiom,  (? [A] :  (v4_funct_1(A) &  ( ~ (v1_xboole_0(A))  & v1_finset_1(A)) ) ) ).
fof(rc9_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v3_card_1(B, 1)) ) ) ) ).
fof(rc9_finseq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ).
fof(rc9_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) & v5_finset_1(A)) ) ) ).
fof(rc9_funct_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) ) ) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rd1_vectsp_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_vectsp_1(A) & l5_algstr_0(A)) )  & m1_subset_1(B, u1_struct_0(A)))  => k6_algstr_0(A, B, k5_struct_0(A))=B) ) ).
fof(rd2_vectsp_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_vectsp_1(A) & l5_algstr_0(A)) )  & m1_subset_1(B, u1_struct_0(A)))  => k6_algstr_0(A, k5_struct_0(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(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(rd6_vectsp_1, axiom,  (! [A, B] :  ( ( ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(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)) ) ) ) ) ) ) ) )  &  ( ~ (v9_struct_0(B, A))  & m1_subset_1(B, u1_struct_0(A))) )  => k9_algstr_0(A, k9_algstr_0(A, B))=B) ) ).
fof(rd7_vectsp_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & l4_algstr_0(A)) )  & m1_subset_1(B, u1_struct_0(A)))  => k6_algstr_0(A, B, k5_struct_0(A))=B) ) ).
fof(rd8_vectsp_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v6_vectsp_1(A) & l4_algstr_0(A)) )  & m1_subset_1(B, u1_struct_0(A)))  => k6_algstr_0(A, k5_struct_0(A), B)=B) ) ).
fof(redefinition_k11_polynom1, axiom,  (! [A, B, C, D] :  ( (v3_ordinal1(A) &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v5_group_1(B) & l6_algstr_0(B)) ) ) ) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) ) )  => k11_polynom1(A, B, C, D)=k10_polynom1(A, B, C, D)) ) ).
fof(redefinition_k15_pre_poly, axiom,  (! [A] : k15_pre_poly(A)=k14_pre_poly(A)) ).
fof(redefinition_k16_pre_poly, axiom,  (! [A] : k16_pre_poly(A)=k1_pboole(A)) ).
fof(redefinition_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => k3_funct_2(A, B, C, D)=k1_funct_1(C, D)) ) ).
fof(redefinition_k3_polynom1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v2_struct_0(B))  & l2_struct_0(B))  &  (v1_funct_1(C) &  (v1_funct_2(C, A, u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, u1_struct_0(B))))) ) ) )  => k3_polynom1(A, B, C)=k2_polynom1(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_polynom1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  & l1_struct_0(B))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  &  (v1_relat_1(D) &  (v4_relat_1(D, A) &  (v1_funct_1(D) &  (v1_partfun1(D, A) &  (v6_valued_0(D) & v2_pre_poly(D)) ) ) ) ) ) )  => k4_polynom1(A, B, C, D)=k1_funct_1(C, D)) ) ).
fof(redefinition_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => k4_subset_1(A, B, C)=k2_xboole_0(B, C)) ) ).
fof(redefinition_k6_polynom1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  &  (v2_rlvect_1(B) &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) ) )  => k6_polynom1(A, B, C, D)=k5_polynom1(A, 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_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_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(redefinition_r6_pboole, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) )  =>  (r6_pboole(A, B, C) <=> B=C) ) ) ).
fof(redefinition_r8_pboole, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) )  =>  (r8_pboole(A, B, C) <=> B=C) ) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(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(reflexivity_r6_pboole, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) )  => r6_pboole(A, B, B)) ) ).
fof(reflexivity_r8_pboole, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) )  => r8_pboole(A, B, B)) ) ).
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(symmetry_r6_pboole, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) )  =>  (r6_pboole(A, B, C) => r6_pboole(A, C, B)) ) ) ).
fof(symmetry_r8_pboole, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) )  =>  (r8_pboole(A, B, C) => r8_pboole(A, C, B)) ) ) ).
fof(t12_rlvect_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  => k4_algstr_0(A, k4_struct_0(A))=k4_struct_0(A)) ) ).
fof(t12_termord, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v8_relat_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A))))) ) ) )  =>  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) &  (v1_partfun1(C, A) &  (v6_valued_0(C) & v2_pre_poly(C)) ) ) ) )  =>  (! [D] :  ( (v1_relat_1(D) &  (v4_relat_1(D, A) &  (v1_funct_1(D) &  (v1_partfun1(D, A) &  (v6_valued_0(D) & v2_pre_poly(D)) ) ) ) )  =>  (r6_pboole(A, k2_termord(A, B, C, D), C) | r6_pboole(A, k2_termord(A, B, C, D), D)) ) ) ) ) ) ) ) ) ).
fof(t15_ideal_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v2_vectsp_1(A) &  (v6_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_ideal_1(B, A) &  (v2_ideal_1(B, A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) ) )  =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  ( (r2_tarski(C, B) & r2_tarski(D, B))  => r2_tarski(k5_algstr_0(A, C, D), B)) ) ) ) ) ) ) ) ) ).
fof(t15_polynom1, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  & l2_algstr_0(B))  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  =>  (! [E] :  ( (v1_relat_1(E) &  (v4_relat_1(E, A) &  (v1_funct_1(E) &  (v1_partfun1(E, A) &  (v6_valued_0(E) & v2_pre_poly(E)) ) ) ) )  => k4_polynom1(A, B, k5_polynom1(A, B, C, D), E)=k1_algstr_0(B, k4_polynom1(A, B, C, E), k4_polynom1(A, B, D, E))) ) ) ) ) ) ) ) ) ).
fof(t17_polynom1, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  =>  (! [D] :  ( (v1_relat_1(D) &  (v4_relat_1(D, A) &  (v1_funct_1(D) &  (v1_partfun1(D, A) &  (v6_valued_0(D) & v2_pre_poly(D)) ) ) ) )  => k4_polynom1(A, B, k5_vfunct_1(k15_pre_poly(A), B, C), D)=k4_algstr_0(B, k4_polynom1(A, B, C, D))) ) ) ) ) ) ) ).
fof(t17_termord, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v6_relat_2(B) &  (v8_relat_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A))))) ) ) ) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  & l2_struct_0(C))  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(D, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  =>  (k4_termord(A, B, C, D)=k4_struct_0(C) <=> r8_pboole(k15_pre_poly(A), D, k8_polynom1(A, C))) ) ) ) ) ) ) ) ) ).
fof(t18_termord, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v6_relat_2(B) &  (v8_relat_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A))))) ) ) ) )  =>  (! [C] :  ( ( ~ (v7_struct_0(C))  & l2_struct_0(C))  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(D, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  => k4_polynom1(A, C, k5_termord(A, B, C, D), k3_termord(A, B, C, D))=k4_polynom1(A, C, D, k3_termord(A, B, C, D))) ) ) ) ) ) ) ) ).
fof(t19_polyred, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( ( ~ (v7_struct_0(B))  &  (v13_algstr_0(B) &  (v5_vectsp_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) &  (v1_polynom1(C, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) )  =>  (! [D] :  (m1_subset_1(D, u1_struct_0(B)) => r1_tarski(k3_polynom1(k15_pre_poly(A), B, k5_polynom7(A, B, C, D)), k3_polynom1(k15_pre_poly(A), B, C))) ) ) ) ) ) ) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_polynom7, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  & l2_struct_0(B))  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  =>  (r2_funct_2(k15_pre_poly(A), u1_struct_0(B), C, k8_polynom1(A, B)) <=> k3_polynom1(k15_pre_poly(A), B, C)=k1_xboole_0) ) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t1_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r1_tarski(A, B) & r1_tarski(B, C))  => r1_tarski(A, C)) ) ) ) ).
fof(t20_polynom1, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v4_rlvect_1(B) & l2_algstr_0(B)) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  => r1_tarski(k3_polynom1(k15_pre_poly(A), B, k5_polynom1(A, B, C, D)), k4_subset_1(k15_pre_poly(A), k3_polynom1(k15_pre_poly(A), B, C), k3_polynom1(k15_pre_poly(A), B, D)))) ) ) ) ) ) ) ).
fof(t21_polynom1, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  => r2_funct_2(k15_pre_poly(A), u1_struct_0(B), k5_polynom1(A, B, k5_polynom1(A, B, C, D), E), k5_polynom1(A, B, C, k5_polynom1(A, B, D, E)))) ) ) ) ) ) ) ) ) ).
fof(t22_termord, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v6_relat_2(B) &  (v8_relat_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A))))) ) ) ) )  =>  (! [C] :  ( ( ~ (v7_struct_0(C))  & l2_struct_0(C))  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(D, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  =>  (r6_pboole(A, k2_polynom7(A, C, k5_termord(A, B, C, D)), k3_termord(A, B, C, D)) & k3_polynom7(A, C, k5_termord(A, B, C, D))=k4_termord(A, B, C, D)) ) ) ) ) ) ) ) ) ).
fof(t23_polynom1, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v4_rlvect_1(B) & l2_algstr_0(B)) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  => r2_funct_2(k15_pre_poly(A), u1_struct_0(B), k5_polynom1(A, B, C, k8_polynom1(A, B)), C)) ) ) ) ) ).
fof(t26_polyred, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v6_relat_2(B) &  (v8_relat_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A))))) ) ) ) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  & l2_algstr_0(C))  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(D, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(E, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  =>  ( (r1_polyred(A, B, C, D, E) & r1_polyred(A, B, C, E, D))  <=> k3_polynom1(k15_pre_poly(A), C, D)=k3_polynom1(k15_pre_poly(A), C, E)) ) ) ) ) ) ) ) ) ) ) ).
fof(t27_polynom7, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v2_vectsp_1(B) & l6_algstr_0(B)) ) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  =>  (! [D] :  (m1_subset_1(D, u1_struct_0(B)) => r2_funct_2(k15_pre_poly(A), u1_struct_0(B), k5_polynom7(A, B, C, D), k10_polynom1(A, B, k4_polynom7(A, B, D), C))) ) ) ) ) ) ) ) ).
fof(t29_polyred, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v6_relat_2(B) &  (v8_relat_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A))))) ) ) ) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  & l2_algstr_0(C))  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(D, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(E, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  =>  (r1_polyred(A, B, C, D, E) <=>  ~ (r2_polyred(A, B, C, E, D)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_polyred, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v1_algstr_1(B) & l2_algstr_0(B)) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  => r2_funct_2(k15_pre_poly(A), u1_struct_0(B), k5_polynom1(A, B, k8_polynom1(A, B), C), C)) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_polyred, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  =>  (r2_funct_2(k15_pre_poly(A), u1_struct_0(B), k5_polynom1(A, B, k5_vfunct_1(k15_pre_poly(A), B, C), C), k8_polynom1(A, B)) & r2_funct_2(k15_pre_poly(A), u1_struct_0(B), k5_polynom1(A, B, C, k5_vfunct_1(k15_pre_poly(A), B, C)), k8_polynom1(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_groeb_1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) &  (v1_polynom1(C, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) ) )  => k3_polynom1(k15_pre_poly(A), B, k5_vfunct_1(k15_pre_poly(A), B, C))=k3_polynom1(k15_pre_poly(A), B, C)) ) ) ) ) ) ).
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(t5_termord, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v6_relat_2(B) &  (v8_relat_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A))))) ) ) ) )  =>  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) &  (v1_partfun1(C, A) &  (v6_valued_0(C) & v2_pre_poly(C)) ) ) ) )  =>  (! [D] :  ( (v1_relat_1(D) &  (v4_relat_1(D, A) &  (v1_funct_1(D) &  (v1_partfun1(D, A) &  (v6_valued_0(D) & v2_pre_poly(D)) ) ) ) )  =>  (r1_termord(A, B, C, D) <=>  ~ (r2_termord(A, B, D, 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(t7_groeb_1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v6_relat_2(B) &  (v8_relat_2(B) &  (v2_bagorder(B, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A))))) ) ) ) ) )  =>  (! [C] :  ( ( ~ (v7_struct_0(C))  &  (v13_algstr_0(C) &  (v4_vectsp_1(C) &  (v5_vectsp_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) & l6_algstr_0(C)) ) ) ) ) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(D, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(E, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  => r1_termord(A, B, k3_termord(A, B, C, k7_polynom1(A, C, D, E)), k2_termord(A, B, k3_termord(A, B, C, D), k3_termord(A, B, C, E)))) ) ) ) ) ) ) ) ) ) ).
fof(t7_termord, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v8_relat_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A))))) ) ) )  =>  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) &  (v1_partfun1(C, A) &  (v6_valued_0(C) & v2_pre_poly(C)) ) ) ) )  =>  (! [D] :  ( (v1_relat_1(D) &  (v4_relat_1(D, A) &  (v1_funct_1(D) &  (v1_partfun1(D, A) &  (v6_valued_0(D) & v2_pre_poly(D)) ) ) ) )  =>  ( (r1_termord(A, B, C, D) & r1_termord(A, B, D, C))  => r6_pboole(A, C, D)) ) ) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_groeb_1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  ( (v1_partfun1(B, k15_pre_poly(A)) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v6_relat_2(B) &  (v8_relat_2(B) &  (v2_bagorder(B, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), k15_pre_poly(A))))) ) ) ) ) )  =>  (! [C] :  ( ( ~ (v7_struct_0(C))  &  (v13_algstr_0(C) &  (v33_algstr_0(C) &  (v4_vectsp_1(C) &  (v5_vectsp_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v3_group_1(C) &  (v5_group_1(C) & l6_algstr_0(C)) ) ) ) ) ) ) ) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(D, C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, k15_pre_poly(A), u1_struct_0(C)) &  (v1_polynom1(E, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(C))))) ) )  =>  (r1_tarski(k3_polynom1(k15_pre_poly(A), C, E), k3_polynom1(k15_pre_poly(A), C, D)) => r1_polyred(A, B, C, E, D)) ) ) ) ) ) ) ) ) ) ) ).
fof(t9_polyred, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v5_vectsp_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k15_pre_poly(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A), u1_struct_0(B))))) )  =>  (! [D] :  (m1_subset_1(D, u1_struct_0(B)) =>  (r2_funct_2(k15_pre_poly(A), u1_struct_0(B), k5_vfunct_1(k15_pre_poly(A), B, k5_polynom7(A, B, C, D)), k5_polynom7(A, B, C, k4_algstr_0(B, D))) & r2_funct_2(k15_pre_poly(A), u1_struct_0(B), k5_vfunct_1(k15_pre_poly(A), B, k5_polynom7(A, B, C, D)), k5_polynom7(A, B, k5_vfunct_1(k15_pre_poly(A), B, 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))) ) ) ) ) ) ).
fof(t9_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (r1_tarski(A, B) => r1_tarski(k2_xboole_0(A, C), k2_xboole_0(B, C))) ) ) ) ).
