% Mizar problem: t64_field_16,field_16,3505,5 
fof(t64_field_16, conjecture,  (! [A] :  ( (v7_ordinal1(A) & v1_int_2(A))  =>  (! [B] :  ( (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  &  ( ~ (v6_struct_0(C))  &  (v13_algstr_0(C) &  (v33_algstr_0(C) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v4_vectsp_1(C) &  (v5_vectsp_1(C) &  (v3_group_1(C) &  (v5_group_1(C) & l6_algstr_0(C)) ) ) ) ) ) ) ) ) ) )  =>  (k7_struct_0(C)=k1_newton(A, B) => k1_card_1(a_2_3_field_16(B, C))=B) ) ) ) ) ) ) ).
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_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (v14_algstr_0(A) =>  (v12_algstr_0(A) & v13_algstr_0(A)) ) ) ) ).
fof(cc10_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A))  => v3_card_1(A, 1)) ) ).
fof(cc10_field_9, axiom,  (! [A] :  (m1_subset_1(A, u1_struct_0(k12_polynom3(k9_int_3(2)))) =>  (v1_uproots(A, k9_int_3(2)) =>  (v1_uproots(A, k9_int_3(2)) & v2_ratfunc1(A, k9_int_3(2))) ) ) ) ).
fof(cc10_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v6_membered(A)) ) ).
fof(cc10_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_int_1(B)) ) ) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc10_ring_2, axiom,  (! [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) &  (v3_group_1(A) &  (v5_group_1(A) &  (v8_ideal_1(A) &  (v1_vectsp_2(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v5_ring_2(B, A) => v4_ring_2(B, A)) ) ) ) ) ).
fof(cc10_ring_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k12_polynom3(A))) =>  ( (v1_uproots(B, A) & v3_ring_4(B, A))  => v1_gcd_1(B, k12_polynom3(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(cc11_algstr_0, axiom,  (! [A] :  ( (v12_algstr_0(A) & l2_algstr_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => v9_algstr_0(B, A)) ) ) ) ).
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_field_9, 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) &  (v3_group_1(A) & v2_polynom5(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) &  (v3_group_1(A) & v3_field_9(A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc11_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_finseq_1(A)) ) ).
fof(cc11_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v7_ordinal1(B)) ) ) ) ).
fof(cc11_mod_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  &  ( ~ (v2_struct_0(B))  & l6_algstr_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) =>  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v7_mod_4(C, A, B)) )  =>  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) &  (v2_funct_2(C, u1_struct_0(B)) & v3_mod_4(C, A, B)) ) ) ) ) ) ) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc11_ring_2, 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) &  (v5_group_1(A) & v1_int_3(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) &  (v5_group_1(A) & v8_ideal_1(A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc11_ring_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k12_polynom3(A))) =>  (v1_gcd_1(B, k12_polynom3(A)) =>  (v1_uproots(B, A) & v3_ring_4(B, A)) ) ) ) ) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc12_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_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v6_membered(A)) ) ).
fof(cc12_mod_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  &  ( ~ (v2_struct_0(B))  & l6_algstr_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) =>  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) &  (v2_funct_2(C, u1_struct_0(B)) & v3_mod_4(C, A, B)) ) )  =>  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v7_mod_4(C, A, B)) ) ) ) ) ) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc12_ring_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k12_polynom3(A))) =>  (v3_ring_4(B, A) =>  ~ (v5_ring_2(B, k12_polynom3(A))) ) ) ) ) ) ).
fof(cc13_field_9, 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) &  ~ (v3_field_9(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) & v3_group_1(A)) ) ) ) ) ) ) ) ) ) ) ).
fof(cc13_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finseq_1(B)) ) ) ) ).
fof(cc13_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_membered(B)) ) ) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc13_ring_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & l6_algstr_0(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v7_ring_2(B, A) => v6_ring_2(B, A)) ) ) ) ) ).
fof(cc13_ring_3, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & v3_ring_3(A, k5_numbers)) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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) &  (v1_ring_3(A, k11_gaussint) & v3_ring_3(A, k5_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc13_ring_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k12_polynom3(A))) =>  (v3_ring_4(B, A) =>  ~ (v5_ring_2(B, k12_polynom3(A))) ) ) ) ) ) ).
fof(cc14_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_finseq_1(B)) ) ) ) ).
fof(cc14_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_membered(B)) ) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc14_ring_2, axiom,  (! [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) &  (v3_group_1(A) &  (v5_group_1(A) &  (v1_vectsp_2(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v6_ring_2(B, A) =>  ( ~ (v9_struct_0(B, A))  &  ~ (v1_gcd_1(B, A)) ) ) ) ) ) ) ).
fof(cc14_ring_3, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_int_2(A))  =>  (! [B] :  (l6_algstr_0(B) =>  ( ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  (v13_algstr_0(B) &  (v33_algstr_0(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) & v3_ring_3(B, A)) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  (v13_algstr_0(B) &  (v33_algstr_0(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v1_ring_3(B, k9_int_3(A)) & v3_ring_3(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc14_ring_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k12_polynom3(A))) =>  (v5_ring_2(B, k12_polynom3(A)) =>  ~ (v3_ring_4(B, A)) ) ) ) ) ) ).
fof(cc15_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_membered(B)) ) ) ) ).
fof(cc15_mod_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)))) =>  ( (v1_funct_1(B) &  (v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v9_mod_4(B, A)) )  =>  (v1_funct_1(B) &  (v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_ringcat1(B, A, A)) ) ) ) ) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc15_ring_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & l6_algstr_0(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v5_ring_2(B, A) => v6_ring_2(B, A)) ) ) ) ) ).
fof(cc15_ring_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k12_polynom3(A))) =>  (v5_ring_2(B, k12_polynom3(A)) =>  ~ (v3_ring_4(B, A)) ) ) ) ) ) ).
fof(cc16_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finset_1(A) & v2_finseq_1(A)) ) ) ) ) ).
fof(cc16_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_membered(B)) ) ) ) ).
fof(cc16_mod_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)))) =>  ( (v1_funct_1(B) &  (v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_ringcat1(B, A, A)) )  =>  (v1_funct_1(B) &  (v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v9_mod_4(B, A)) ) ) ) ) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc16_ring_2, axiom,  (! [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) &  (v3_group_1(A) &  (v5_group_1(A) &  (v8_ideal_1(A) &  (v1_vectsp_2(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v6_ring_2(B, A) => v7_ring_2(B, A)) ) ) ) ) ).
fof(cc17_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_membered(B)) ) ) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc17_ring_2, axiom,  (! [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) &  (v3_group_1(A) &  (v8_ring_2(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  ( ( ~ (v9_struct_0(B, A))  &  ~ (v1_gcd_1(B, A)) )  => v6_ring_2(B, A)) ) ) ) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc18_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_membered(B)) ) ) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc18_ring_2, 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) &  (v3_group_1(A) &  (v5_group_1(A) &  (v8_ideal_1(A) & v1_vectsp_2(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) &  (v3_group_1(A) &  (v5_group_1(A) &  (v1_vectsp_2(A) & v8_ring_2(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc19_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v7_membered(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_field_1, axiom,  (! [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) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (! [B] :  (l6_algstr_0(B) =>  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) & v1_ring_3(B, A)) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) & v3_ring_2(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc1_field_12, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (l6_algstr_0(B) =>  ( ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  (v13_algstr_0(B) &  (v33_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v3_group_1(B) &  (v5_group_1(B) & v1_field_4(B, A)) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  (v13_algstr_0(B) &  (v33_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v3_ring_2(B, A) &  (v1_ring_3(B, A) & v1_field_4(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc1_field_15, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k12_polynom3(A))) =>  (v2_ratfunc1(B, A) => v1_uproots(B, A)) ) ) ) ) ).
fof(cc1_field_16, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_field_16(B, A) =>  ( ~ (v1_xboole_0(B))  & v1_field_16(B, A)) ) ) ) ) ) ).
fof(cc1_field_6, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (l6_algstr_0(B) =>  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v3_group_1(B) &  (v5_group_1(B) & v1_field_4(B, A)) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v3_ring_2(B, k12_polynom3(A)) & v1_field_4(B, 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_gaussint, axiom,  (! [A] :  (v1_int_1(A) =>  (v1_int_1(A) & v1_gaussint(A)) ) ) ).
fof(cc1_group_1, axiom,  (! [A] :  (l3_algstr_0(A) =>  (v2_group_1(A) => v1_group_1(A)) ) ) ).
fof(cc1_int_3, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v6_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) &  (v1_vectsp_1(A) &  (v4_vectsp_1(A) &  (v1_vectsp_2(A) & v1_int_3(A)) ) ) ) ) ) ) ) ) )  =>  ( ~ (v6_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) &  (v1_vectsp_1(A) &  (v4_vectsp_1(A) &  (v1_vectsp_2(A) & v3_gcd_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc1_membered, axiom,  (! [A] :  (v6_membered(A) => v5_membered(A)) ) ).
fof(cc1_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v3_ordinal1(A) & v7_ordinal1(A)) ) ) ).
fof(cc1_nat_6, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_int_2(A))  =>  ( ~ (v1_zfmisc_1(A))  & v7_ordinal1(A)) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(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_ratfunc1, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v1_vectsp_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & v1_vectsp_2(A)) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v30_algstr_0(A) &  (v1_vectsp_1(A) &  (v3_rlvect_1(A) & v4_rlvect_1(A)) ) ) ) ) ) ) ) ).
fof(cc1_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc1_ring_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v3_ring_2(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) )  =>  (! [C] :  (l6_algstr_0(C) =>  ( ( ~ (v2_struct_0(C))  &  (v13_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) & v3_ring_2(C, B)) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(C))  &  (v13_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) &  (v3_ring_2(C, A) & v3_ring_2(C, B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc1_ring_3, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ~ (v2_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) &  (v1_ring_3(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) )  =>  (! [C] :  (l6_algstr_0(C) =>  ( ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v3_group_1(C) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v4_vectsp_1(C) &  (v5_vectsp_1(C) & v1_ring_3(C, B)) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v3_group_1(C) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v4_vectsp_1(C) &  (v5_vectsp_1(C) &  (v1_ring_3(C, A) & v1_ring_3(C, B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc1_ring_4, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) & v5_group_1(A)) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v34_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)) ) ) ) ) ) ) ) ) ) ) ).
fof(cc1_ringcat1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  &  ( ~ (v2_struct_0(B))  & l6_algstr_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) =>  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_ringcat1(C, A, B)) )  =>  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) &  (v6_group_1(C, A, B) &  (v1_group_6(C, A, B) & v13_vectsp_1(C, A, B)) ) ) ) ) ) ) ) ) ).
fof(cc1_rlvect_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v9_rlvect_1(A))  =>  ( ~ (v2_struct_0(A))  & v4_rlvect_1(A)) ) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc1_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc1_vectsp_1, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v5_vectsp_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v1_vectsp_1(A) & v2_vectsp_1(A)) ) ) ) ) ).
fof(cc1_xcmplx_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xcmplx_0(A)) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc25_algstr_0, axiom,  (! [A] :  (l5_algstr_0(A) =>  ( (v30_algstr_0(A) & v31_algstr_0(A))  => v32_algstr_0(A)) ) ) ).
fof(cc26_algstr_0, axiom,  (! [A] :  (l5_algstr_0(A) =>  (v32_algstr_0(A) =>  (v30_algstr_0(A) & v31_algstr_0(A)) ) ) ) ).
fof(cc27_algstr_0, axiom,  (! [A] :  (l5_algstr_0(A) =>  ( (v33_algstr_0(A) & v34_algstr_0(A))  => v35_algstr_0(A)) ) ) ).
fof(cc28_algstr_0, axiom,  (! [A] :  (l5_algstr_0(A) =>  (v35_algstr_0(A) =>  (v33_algstr_0(A) & v34_algstr_0(A)) ) ) ) ).
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_field_15, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_int_2(A))  =>  (! [B] :  (l6_algstr_0(B) =>  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v3_group_1(B) &  (v5_group_1(B) & v3_ring_3(B, A)) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v3_group_1(B) &  (v5_group_1(B) & v3_ring_3(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc2_field_16, axiom,  (! [A] :  ( (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) )  =>  (! [B] :  ( (v7_ordinal1(B) & v2_field_16(B, A))  =>  (v7_ordinal1(B) &  ( ~ (v8_ordinal1(B))  & v2_field_16(B, 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_gaussint, axiom,  (! [A] :  (v1_rat_1(A) =>  (v1_rat_1(A) & v2_gaussint(A)) ) ) ).
fof(cc2_group_1, axiom,  (! [A] :  (l3_algstr_0(A) =>  (v2_struct_0(A) => v3_group_1(A)) ) ) ).
fof(cc2_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_int_1(A)) ) ).
fof(cc2_int_3, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_rlvect_1(A) & v4_vectsp_1(A)) ) ) ) )  =>  ( ~ (v2_struct_0(A))  & v1_int_3(A)) ) ) ) ).
fof(cc2_membered, axiom,  (! [A] :  (v5_membered(A) => v4_membered(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_ratfunc1, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_vectsp_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & v1_vectsp_2(A)) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v31_algstr_0(A) &  (v2_vectsp_1(A) &  (v3_rlvect_1(A) & v4_rlvect_1(A)) ) ) ) ) ) ) ) ).
fof(cc2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(B)) ) ) ) ).
fof(cc2_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(cc2_ring_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  (v13_algstr_0(B) &  (v33_algstr_0(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v5_group_1(B) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) =>  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) &  (v13_vectsp_1(C, A, B) &  (v6_group_1(C, A, B) & v1_group_6(C, A, B)) ) ) )  =>  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v3_mod_4(C, A, B)) ) ) ) ) ) ) ).
fof(cc2_ring_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (! [B] :  (l6_algstr_0(B) =>  ( ( ~ (v2_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) & v1_ring_3(B, A)) ) ) ) ) ) ) )  =>  ( ~ (v2_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) &  (v3_ring_2(B, A) & v1_ring_3(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc2_ring_4, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v34_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)) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & v3_group_1(A)) ) ) ) ) ) ) ) ) ) ) ).
fof(cc2_ringcat1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  &  ( ~ (v2_struct_0(B))  & l6_algstr_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) =>  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) &  (v6_group_1(C, A, B) &  (v1_group_6(C, A, B) & v13_vectsp_1(C, A, B)) ) ) )  =>  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_ringcat1(C, A, B)) ) ) ) ) ) ) ).
fof(cc2_rlvect_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v2_rlvect_1(A) & v4_rlvect_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v9_rlvect_1(A)) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc2_vectsp_1, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v1_vectsp_1(A) & v2_vectsp_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v5_vectsp_1(A)) ) ) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc2_xxreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xxreal_0(A)) ) ).
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_field_15, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v3_ring_3(A, k5_numbers) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k12_polynom3(A))) =>  (v5_ring_2(B, k12_polynom3(A)) =>  (v5_ring_2(B, k12_polynom3(A)) & v1_field_15(B, A)) ) ) ) ) ) ).
fof(cc3_field_16, axiom,  (! [A] :  ( ( ~ (v1_zfmisc_1(A))  & v7_ordinal1(A))  =>  (! [B] :  ( (v7_ordinal1(B) & v2_field_16(B, A))  =>  ( ~ (v1_zfmisc_1(B))  &  (v7_ordinal1(B) & v2_field_16(B, 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_gaussint, axiom,  (! [A] :  ( (v1_xcmplx_0(A) & v1_gaussint(A))  =>  (v1_xcmplx_0(A) &  (v1_gaussint(A) & v2_gaussint(A)) ) ) ) ).
fof(cc3_int_1, axiom,  (! [A] :  (v1_int_1(A) => v1_xreal_0(A)) ) ).
fof(cc3_int_3, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_int_2(A))  =>  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  & v1_int_2(A)) ) ) ) ).
fof(cc3_membered, axiom,  (! [A] :  (v4_membered(A) => v3_membered(A)) ) ).
fof(cc3_mod_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  &  ( ~ (v2_struct_0(B))  & l6_algstr_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) =>  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v3_mod_4(C, A, B)) )  =>  (v1_funct_1(C) &  (v2_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_ringcat1(C, A, B)) ) ) ) ) ) ) ) ).
fof(cc3_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc3_nat_6, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  ( (v7_ordinal1(B) & v1_ec_pf_2(B, k2_xcmplx_0(A, 1)))  =>  (v7_ordinal1(B) & v1_ec_pf_2(B, A)) ) ) ) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc3_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(A)) ) ) ).
fof(cc3_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_xboole_0(C)) ) ) ) ).
fof(cc3_ring_2, axiom,  (! [A] :  ( ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v2_vectsp_1(A) &  (v3_vectsp_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v1_gcd_1(B, A) =>  ( ~ (v9_struct_0(B, A))  & v1_gcd_1(B, A)) ) ) ) ) ) ).
fof(cc3_ring_4, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v30_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)) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v31_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)) ) ) ) ) ) ) ) ) ) ) ).
fof(cc3_rlvect_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) & v2_rlvect_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v12_algstr_0(A)) ) ) ) ).
fof(cc3_struct_0, axiom,  (! [A] :  (l4_struct_0(A) =>  ( ~ (v6_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc3_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc3_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_vectsp_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & v6_vectsp_1(A)) ) ) ) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc3_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v2_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc4_algstr_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_field_12, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & v2_polynom5(A)) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  ( ~ (v8_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) & v5_group_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc4_field_15, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & v3_ring_3(A, k5_numbers)) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v3_ring_3(A, k5_numbers) & v2_field_15(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc4_field_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v1_field_4(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) )  =>  (! [C] :  (l6_algstr_0(C) =>  ( ( ~ (v2_struct_0(C))  &  (v13_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) & v1_field_4(C, B)) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(C))  &  (v13_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) &  (v1_field_4(C, A) & v1_field_4(C, B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_gaussint, axiom,  (! [A] :  (m1_subset_1(A, u1_struct_0(k11_gaussint)) => v1_rat_1(A)) ) ).
fof(cc4_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v2_int_1(A)) ) ).
fof(cc4_membered, axiom,  (! [A] :  (v3_membered(A) => v2_membered(A)) ) ).
fof(cc4_mod_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  &  ( ~ (v2_struct_0(B))  & l6_algstr_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) =>  ( (v1_funct_1(C) &  (v2_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_ringcat1(C, A, B)) ) )  =>  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v3_mod_4(C, A, B)) ) ) ) ) ) ) ).
fof(cc4_nat_1, axiom,  (! [A] :  ( (v7_ordinal1(A) & v8_ordinal1(A))  =>  (v7_ordinal1(A) &  ~ (v2_xxreal_0(A)) ) ) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(A)) ) ).
fof(cc4_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_1(A)) ) ) ).
fof(cc4_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => v1_xboole_0(C)) ) ) ) ).
fof(cc4_ring_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  ( ~ (v9_struct_0(B, A))  =>  ( ~ (v9_struct_0(B, A))  & v1_gcd_1(B, A)) ) ) ) ) ) ).
fof(cc4_ring_4, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v31_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)) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v30_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)) ) ) ) ) ) ) ) ) ) ) ).
fof(cc4_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & v6_vectsp_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v1_group_1(A)) ) ) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc4_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ) ).
fof(cc5_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_field_15, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v8_struct_0(A) &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) & v5_group_1(A)) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v8_struct_0(A) &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & v2_field_15(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc5_field_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v1_field_4(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) ) )  =>  (! [C] :  (l6_algstr_0(C) =>  ( ( ~ (v2_struct_0(C))  &  (v13_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) & v1_field_4(C, B)) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(C))  &  (v13_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) &  (v1_field_4(C, A) & v1_field_4(C, B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_int_1, axiom,  (! [A] :  (v2_int_1(A) => v1_int_1(A)) ) ).
fof(cc5_membered, axiom,  (! [A] :  (v3_membered(A) => v1_membered(A)) ) ).
fof(cc5_nat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v8_ordinal1(A)) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc5_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v4_relat_1(C, A)) ) ) ) ).
fof(cc5_ring_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & l6_algstr_0(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v4_ring_2(B, A) =>  ( ~ (v9_struct_0(B, A))  &  ~ (v1_gcd_1(B, A)) ) ) ) ) ) ) ).
fof(cc5_ring_4, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_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) & v3_ring_3(A, k5_numbers)) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  ( ~ (v8_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) & v3_ring_3(A, k5_numbers)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc5_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc5_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_vectsp_1(A))  =>  ( ~ (v2_struct_0(A))  & v1_group_1(A)) ) ) ) ).
fof(cc5_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v3_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) ) ) ) ).
fof(cc6_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_field_15, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & v2_polynom5(A)) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v2_polynom5(A) & v2_field_15(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc6_field_4, axiom,  (! [A, B] :  ( ( ( ~ (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) &  (v3_group_1(A) &  (v5_group_1(A) &  (v1_vectsp_2(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_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) &  (v5_group_1(B) &  (v1_vectsp_2(B) &  (v1_field_4(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C] :  (l6_algstr_0(C) =>  ( ( ~ (v2_struct_0(C))  &  ( ~ (v6_struct_0(C))  &  (v13_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) &  (v1_vectsp_2(C) & v1_field_4(C, B)) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(C))  &  ( ~ (v6_struct_0(C))  &  (v13_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) &  (v1_vectsp_2(C) &  (v1_field_4(C, A) & v1_field_4(C, B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xcmplx_0(B)) ) ) ) ).
fof(cc6_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc6_nat_6, axiom,  (! [A] :  ( ( ~ (v1_zfmisc_1(A))  & v7_ordinal1(A))  =>  (! [B] :  ( (v7_ordinal1(B) & v1_ec_pf_2(B, A))  =>  ( ~ (v1_zfmisc_1(B))  & v7_ordinal1(B)) ) ) ) ) ).
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_ring_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & l6_algstr_0(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v5_ring_2(B, A) =>  ( ~ (v9_struct_0(B, A))  &  ~ (v1_gcd_1(B, A)) ) ) ) ) ) ) ).
fof(cc6_ring_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k12_polynom3(A))) =>  ( ~ (v3_ring_4(B, A))  =>  ( ~ (v9_struct_0(B, k12_polynom3(A)))  &  ~ (v1_gcd_1(B, k12_polynom3(A))) ) ) ) ) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc6_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v5_group_1(A) & v6_vectsp_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v3_vectsp_1(A)) ) ) ) ).
fof(cc6_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ) ).
fof(cc7_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  ( (v9_algstr_0(B, A) & v10_algstr_0(B, A))  => v11_algstr_0(B, 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_field_16, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v1_topzari1(B, A) =>  ~ (v1_gcd_1(B, A)) ) ) ) ) ) ).
fof(cc7_field_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  (v13_algstr_0(B) &  (v33_algstr_0(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v1_field_4(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C] :  (l6_algstr_0(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) & v1_field_4(C, B)) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (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) &  (v1_field_4(C, A) & v1_field_4(C, B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xxreal_0(B)) ) ) ) ).
fof(cc7_mod_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  &  ( ~ (v2_struct_0(B))  & l6_algstr_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) =>  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_mod_4(C, A, B)) )  =>  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) &  (v2_funct_2(C, u1_struct_0(B)) & v1_ringcat1(C, A, B)) ) ) ) ) ) ) ) ).
fof(cc7_nat_6, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_ec_pf_2(A, 2))  =>  ( ~ (v1_zfmisc_1(A))  & v7_ordinal1(A)) ) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v4_relat_1(B, A)) ) ) ) ) ) ).
fof(cc7_ring_2, axiom,  (! [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) &  (v3_group_1(A) &  (v5_group_1(A) &  (v1_vectsp_2(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v4_ring_2(B, A) => v5_ring_2(B, A)) ) ) ) ) ).
fof(cc7_ring_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k12_polynom3(A))) =>  ( ~ (v3_ring_4(B, A))  =>  (v1_uproots(B, A) &  ~ (v1_gcd_1(B, k12_polynom3(A))) ) ) ) ) ) ) ).
fof(cc7_ring_5, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v8_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) & v1_vectsp_2(A)) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v8_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) &  (v1_vectsp_2(A) &  ~ (v2_polynom5(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc7_xxreal_0, axiom,  (! [A] :  ( (v8_ordinal1(A) & v1_xxreal_0(A))  =>  (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc8_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v11_algstr_0(B, A) =>  (v9_algstr_0(B, A) & v10_algstr_0(B, 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_field_16, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_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)) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  ( ~ (v6_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) & v3_field_16(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc8_field_4, axiom,  (! [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) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  (l6_algstr_0(B) =>  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) & v1_field_4(B, A)) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(B))  &  ( ~ (v6_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) & v1_field_4(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc8_field_9, axiom,  (! [A] :  (m1_subset_1(A, u1_struct_0(k9_int_3(2))) => v1_o_ring_1(A, k9_int_3(2))) ) ).
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_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xreal_0(B)) ) ) ) ).
fof(cc8_mod_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  &  ( ~ (v2_struct_0(B))  & l6_algstr_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) =>  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) &  (v2_funct_2(C, u1_struct_0(B)) & v1_ringcat1(C, A, B)) ) )  =>  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v5_mod_4(C, A, B)) ) ) ) ) ) ) ).
fof(cc8_nat_6, axiom,  (! [A] :  ( ( ~ (v1_zfmisc_1(A))  & v7_ordinal1(A))  =>  (v7_ordinal1(A) & v1_ec_pf_2(A, 2)) ) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc8_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v5_relat_1(B, A)) ) ) ) ) ) ).
fof(cc8_ring_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  ~ (v5_ring_2(B, A)) ) ) ) ) ).
fof(cc8_ring_3, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) & v5_vectsp_1(A)) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & v3_ring_2(A, k1_int_3)) ) ) ) ) ) ) ) ) ) ) ).
fof(cc8_ring_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k12_polynom3(A))) =>  ( ( ~ (v9_struct_0(B, k12_polynom3(A)))  & v3_ring_4(B, A))  => v1_gcd_1(B, k12_polynom3(A))) ) ) ) ) ).
fof(cc8_ring_5, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & v2_polynom5(A)) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v34_algstr_0(A) &  (v3_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) & v5_vectsp_1(A)) ) ) ) ) ) ) ) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc8_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) )  =>  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ) ).
fof(cc9_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( (v12_algstr_0(A) & v13_algstr_0(A))  => v14_algstr_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_field_16, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  ( ~ (v9_struct_0(B, A))  =>  ( ~ (v9_struct_0(B, A))  &  ~ (v1_topzari1(B, 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_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_rat_1(B)) ) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(cc9_ring_2, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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)) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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) & v8_ideal_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc9_ring_3, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  ( ~ (v2_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) &  (v3_ring_3(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) )  =>  (! [C] :  (l6_algstr_0(C) =>  ( ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v3_group_1(C) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v4_vectsp_1(C) &  (v5_vectsp_1(C) & v1_ring_3(C, B)) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v3_group_1(C) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v4_vectsp_1(C) &  (v5_vectsp_1(C) & v3_ring_3(C, A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(cc9_ring_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k12_polynom3(A))) =>  (v1_gcd_1(B, k12_polynom3(A)) =>  ( ~ (v9_struct_0(B, k12_polynom3(A)))  & v3_ring_4(B, A)) ) ) ) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(commutativity_k1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_subset_1(B, k4_ordinal1))  => k1_nat_1(A, B)=k1_nat_1(B, A)) ) ).
fof(commutativity_k2_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(A, B)=k2_xcmplx_0(B, A)) ) ).
fof(commutativity_k3_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k3_xcmplx_0(A, B)=k3_xcmplx_0(B, A)) ) ).
fof(connectedness_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  =>  (r1_xxreal_0(A, B) | r1_xxreal_0(B, A)) ) ) ).
fof(d16_struct_0, axiom,  (! [A] :  (l1_struct_0(A) => k7_struct_0(A)=k1_card_1(u1_struct_0(A))) ) ).
fof(d3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (B=k10_xtuple_0(A) <=>  (! [C] :  (r2_hidden(C, B) <=>  (? [D] :  (r2_hidden(D, k9_xtuple_0(A)) & C=k1_funct_1(A, D)) ) ) ) ) ) ) ) ).
fof(d7_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) =>  (! [B] :  (v1_xcmplx_0(B) => k6_xcmplx_0(A, B)=k2_xcmplx_0(A, k4_xcmplx_0(B))) ) ) ) ).
fof(d8_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) =>  (! [B] :  (v1_xcmplx_0(B) => k7_xcmplx_0(A, B)=k3_xcmplx_0(A, k5_xcmplx_0(B))) ) ) ) ).
fof(dt_g6_algstr_0, axiom,  (! [A, B, C, D, E] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (m1_subset_1(D, A) & m1_subset_1(E, A)) ) )  =>  (v36_algstr_0(g6_algstr_0(A, B, C, D, E)) & l6_algstr_0(g6_algstr_0(A, B, C, D, E))) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k11_gaussint, axiom,  ( ~ (v2_struct_0(k11_gaussint))  &  (v36_algstr_0(k11_gaussint) & l6_algstr_0(k11_gaussint)) ) ).
fof(dt_k12_polynom3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom3(A)))  &  (v36_algstr_0(k12_polynom3(A)) & l6_algstr_0(k12_polynom3(A))) ) ) ) ).
fof(dt_k1_card_1, axiom,  (! [A] : v1_card_1(k1_card_1(A))) ).
fof(dt_k1_finseq_1, axiom, $true).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_int_3, axiom, l6_algstr_0(k1_int_3)).
fof(dt_k1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_subset_1(B, k4_ordinal1))  => m1_subset_1(k1_nat_1(A, B), k4_ordinal1)) ) ).
fof(dt_k1_newton, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_field_16, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) )  & v7_ordinal1(C)) )  =>  (v1_funct_1(k2_field_16(A, B, C)) &  (v1_funct_2(k2_field_16(A, B, C), u1_struct_0(A), u1_struct_0(A)) & m1_subset_1(k2_field_16(A, B, C), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) ) ) ) ).
fof(dt_k2_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => m1_subset_1(k2_finseq_1(A), k1_zfmisc_1(k4_ordinal1))) ) ).
fof(dt_k2_xcmplx_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_xcmplx_0, axiom, $true).
fof(dt_k4_card_1, axiom,  (! [A] :  (v1_finset_1(A) => m1_subset_1(k4_card_1(A), k4_ordinal1)) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A))) ) ).
fof(dt_k5_field_16, axiom,  (! [A] :  ( ( ~ (v2_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) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (v1_funct_1(k5_field_16(A)) &  (v1_funct_2(k5_field_16(A), u1_struct_0(A), u1_struct_0(A)) & m1_subset_1(k5_field_16(A), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) ) ) ) ).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k5_xcmplx_0(A))) ) ).
fof(dt_k6_xcmplx_0, axiom, $true).
fof(dt_k7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) => v1_card_1(k7_struct_0(A))) ) ).
fof(dt_k7_xcmplx_0, axiom, $true).
fof(dt_k9_int_3, axiom,  (! [A] :  (v7_ordinal1(A) => l6_algstr_0(k9_int_3(A))) ) ).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_l1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (l2_struct_0(A) & l1_algstr_0(A)) ) ) ).
fof(dt_l2_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_l3_algstr_0, axiom,  (! [A] :  (l3_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l3_struct_0, axiom,  (! [A] :  (l3_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_l4_algstr_0, axiom,  (! [A] :  (l4_algstr_0(A) =>  (l3_struct_0(A) & l3_algstr_0(A)) ) ) ).
fof(dt_l4_struct_0, axiom,  (! [A] :  (l4_struct_0(A) =>  (l2_struct_0(A) & l3_struct_0(A)) ) ) ).
fof(dt_l5_algstr_0, axiom,  (! [A] :  (l5_algstr_0(A) =>  (l4_algstr_0(A) & l4_struct_0(A)) ) ) ).
fof(dt_l6_algstr_0, axiom,  (! [A] :  (l6_algstr_0(A) =>  (l2_algstr_0(A) & l5_algstr_0(A)) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_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_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ( ~ (v1_finset_1(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc10_field_12, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_vectsp_1(A) & l6_algstr_0(A)) )  =>  (v36_algstr_0(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A))) & v2_vectsp_1(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A)))) ) ) ).
fof(fc10_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) )  => v1_setfam_1(k10_xtuple_0(A))) ) ).
fof(fc10_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_ordinal1(A))  =>  ~ (v10_ordinal1(k10_xtuple_0(A))) ) ) ).
fof(fc10_polynom3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom3(A)))  &  (v36_algstr_0(k12_polynom3(A)) & v3_rlvect_1(k12_polynom3(A))) ) ) ) ).
fof(fc10_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc10_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k2_xcmplx_0(A, B))) ) ) ).
fof(fc11_field_12, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_vectsp_1(A) & l6_algstr_0(A)) )  =>  (v36_algstr_0(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A))) & v1_vectsp_1(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A)))) ) ) ).
fof(fc11_funct_1, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) )  & m1_subset_1(B, k9_xtuple_0(A)))  =>  ~ (v1_xboole_0(k1_funct_1(A, B))) ) ) ).
fof(fc11_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  ~ (v9_ordinal1(A)) )  => v10_ordinal1(k10_xtuple_0(A))) ) ).
fof(fc11_polynom3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom3(A)))  &  (v36_algstr_0(k12_polynom3(A)) & v4_rlvect_1(k12_polynom3(A))) ) ) ) ).
fof(fc11_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc11_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc12_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k1_zfmisc_1(A))) ) ) ).
fof(fc12_field_12, axiom,  (! [A] :  ( (v5_group_1(A) & l6_algstr_0(A))  =>  (v36_algstr_0(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A))) & v5_group_1(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A)))) ) ) ).
fof(fc12_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) )  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc12_polynom3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom3(A)))  &  (v13_algstr_0(k12_polynom3(A)) & v36_algstr_0(k12_polynom3(A))) ) ) ) ).
fof(fc12_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k2_xcmplx_0(B, A))) ) ).
fof(fc13_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(A, B))) ) ) ).
fof(fc13_field_12, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_vectsp_2(A) & l6_algstr_0(A)) )  =>  (v36_algstr_0(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A))) & v1_vectsp_2(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A)))) ) ) ).
fof(fc13_field_16, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  => v2_field_16(k1_newton(A, B), A)) ) ).
fof(fc13_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ~ (v1_zfmisc_1(k10_xtuple_0(A))) ) ) ).
fof(fc13_polynom3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_vectsp_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom3(A)))  &  (v36_algstr_0(k12_polynom3(A)) & v5_group_1(k12_polynom3(A))) ) ) ) ).
fof(fc13_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc14_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(B, A))) ) ) ).
fof(fc14_field_12, axiom,  (! [A] :  ( (v33_algstr_0(A) & l6_algstr_0(A))  =>  (v33_algstr_0(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A))) & v36_algstr_0(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A)))) ) ) ).
fof(fc14_field_16, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v8_struct_0(A) &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (v7_ordinal1(k7_struct_0(A)) & v1_card_1(k7_struct_0(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(fc14_polynom3, axiom,  (! [A] :  ( ( ~ (v2_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) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom3(A)))  &  (v36_algstr_0(k12_polynom3(A)) & v3_group_1(k12_polynom3(A))) ) ) ) ).
fof(fc14_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k2_xcmplx_0(B, A))) ) ).
fof(fc15_field_16, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v8_struct_0(A) &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v1_zfmisc_1(k7_struct_0(A)))  & v1_card_1(k7_struct_0(A))) ) ) ).
fof(fc15_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_finseq_1(k1_finseq_1(A))) ) ).
fof(fc15_polynom3, axiom,  (! [A] :  ( ( ~ (v2_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) & l6_algstr_0(A)) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom3(A)))  &  (v36_algstr_0(k12_polynom3(A)) & v4_vectsp_1(k12_polynom3(A))) ) ) ) ).
fof(fc15_xreal_0, axiom,  (! [A] :  ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k4_xcmplx_0(A)) &  ~ (v3_xxreal_0(k4_xcmplx_0(A))) ) ) ) ).
fof(fc16_field_16, axiom,  (! [A, B] :  ( ( (v7_ordinal1(A) & v1_int_2(A))  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v3_ring_3(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) ) )  =>  (v1_funct_1(k5_field_16(B)) &  (v1_funct_2(k5_field_16(B), u1_struct_0(B), u1_struct_0(B)) &  (v13_vectsp_1(k5_field_16(B), B, B) &  (v6_group_1(k5_field_16(B), B, B) & v1_group_6(k5_field_16(B), B, B)) ) ) ) ) ) ).
fof(fc16_polynom3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom3(A)))  &  (v36_algstr_0(k12_polynom3(A)) & v5_vectsp_1(k12_polynom3(A))) ) ) ) ).
fof(fc16_ring_3, axiom,  ( ~ (v2_struct_0(k11_gaussint))  &  (v36_algstr_0(k11_gaussint) & v3_ring_3(k11_gaussint, k5_numbers)) ) ).
fof(fc16_ring_4, axiom,  (! [A] :  ( ( ~ (v2_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) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom3(A)))  &  (v36_algstr_0(k12_polynom3(A)) &  (v3_ring_2(k12_polynom3(A), A) & v1_ring_3(k12_polynom3(A), A)) ) ) ) ) ).
fof(fc16_xreal_0, axiom,  (! [A] :  ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k4_xcmplx_0(A)) &  ~ (v2_xxreal_0(k4_xcmplx_0(A))) ) ) ) ).
fof(fc17_card_1, axiom,  (! [A, B] :  ( (v1_card_1(A) &  (v1_relat_1(B) &  (v1_funct_1(B) & v3_card_1(B, A)) ) )  => v3_card_1(k9_xtuple_0(B), A)) ) ).
fof(fc17_field_16, axiom,  (! [A, B] :  ( ( (v7_ordinal1(A) & v1_int_2(A))  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v3_ring_3(B, A) &  (v3_field_16(B) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) ) ) )  =>  (v1_funct_1(k5_field_16(B)) &  (v2_funct_1(k5_field_16(B)) & v1_funct_2(k5_field_16(B), u1_struct_0(B), u1_struct_0(B))) ) ) ) ).
fof(fc17_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => v3_finseq_1(k9_xtuple_0(A))) ) ).
fof(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(fc17_ring_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom3(A)))  &  ( ~ (v8_struct_0(k12_polynom3(A)))  & v36_algstr_0(k12_polynom3(A))) ) ) ) ).
fof(fc17_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  =>  (v7_ordinal1(k7_struct_0(A)) & v1_card_1(k7_struct_0(A))) ) ) ).
fof(fc17_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k6_xcmplx_0(A, B))) ) ) ).
fof(fc18_field_16, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v8_struct_0(A) &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (v1_funct_1(k5_field_16(A)) &  (v1_funct_2(k5_field_16(A), u1_struct_0(A), u1_struct_0(A)) & v2_funct_2(k5_field_16(A), u1_struct_0(A))) ) ) ) ).
fof(fc18_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  => v3_finseq_1(k9_xtuple_0(A))) ) ).
fof(fc18_funct_1, axiom,  (! [A] :  ( ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  ~ (v1_zfmisc_1(k9_xtuple_0(A))) ) ) ).
fof(fc18_ring_4, axiom,  (! [A] :  ( ( ~ (v1_zfmisc_1(A))  & v7_ordinal1(A))  =>  ( ~ (v2_struct_0(k12_polynom3(k9_int_3(A))))  &  ( ~ (v8_struct_0(k12_polynom3(k9_int_3(A))))  & v36_algstr_0(k12_polynom3(k9_int_3(A)))) ) ) ) ).
fof(fc18_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v8_struct_0(A) & l1_struct_0(A)) )  =>  (v7_ordinal1(k7_struct_0(A)) &  ~ (v8_ordinal1(k7_struct_0(A))) ) ) ) ).
fof(fc18_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k6_xcmplx_0(B, A))) ) ) ).
fof(fc19_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_finset_1(A))  => v1_finset_1(k9_xtuple_0(A))) ) ).
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_ring_4, axiom,  ~ (v33_algstr_0(k1_int_3)) ).
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(fc19_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k6_xcmplx_0(A, B))) ) ).
fof(fc1_card_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v1_xboole_0(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc1_ec_pf_1, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_int_2(A))  => v8_struct_0(k9_int_3(A))) ) ).
fof(fc1_field_12, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  =>  ( ~ (v2_struct_0(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A))))  & v36_algstr_0(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A)))) ) ) ).
fof(fc1_field_14, axiom,  (! [A] :  ( (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) )  => v7_ordinal1(k6_xcmplx_0(A, 1))) ) ).
fof(fc1_field_8, axiom,  (! [A, B] :  ( ( ( ~ (v2_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) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v3_group_1(B) &  (v3_ring_2(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom3(B)))  &  (v36_algstr_0(k12_polynom3(B)) & v3_ring_2(k12_polynom3(B), k12_polynom3(A))) ) ) ) ).
fof(fc1_finseq_1, axiom,  (! [A] :  ( (v7_ordinal1(A) & v8_ordinal1(A))  => v1_xboole_0(k1_finseq_1(A))) ) ).
fof(fc1_int_1, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => v1_int_1(k2_xcmplx_0(A, B))) ) ).
fof(fc1_int_3, axiom,  ( ~ (v2_struct_0(k1_int_3))  & v36_algstr_0(k1_int_3)) ).
fof(fc1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v7_ordinal1(k2_xcmplx_0(A, B))) ) ).
fof(fc1_nat_6, axiom,  (! [A] :  ( (v7_ordinal1(A) & v2_xxreal_0(A))  => v7_ordinal1(k6_xcmplx_0(A, 1))) ) ).
fof(fc1_ring_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l2_struct_0(A))  &  ( ~ (v2_struct_0(B))  &  (v2_ring_4(B, A) & l1_struct_0(B)) ) )  => v1_ring_4(u1_struct_0(B), A)) ) ).
fof(fc1_ring_5, axiom,  ( ~ (v7_struct_0(k9_int_3(2)))  & v33_algstr_0(k9_int_3(2))) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc20_ring_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom3(A)))  &  ( ~ (v33_algstr_0(k12_polynom3(A)))  & v36_algstr_0(k12_polynom3(A))) ) ) ) ).
fof(fc20_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k6_xcmplx_0(B, A))) ) ).
fof(fc21_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k6_xcmplx_0(A, B))) ) ).
fof(fc22_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_finset_1(A))  => v1_finset_1(k10_xtuple_0(A))) ) ).
fof(fc22_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k6_xcmplx_0(B, A))) ) ).
fof(fc23_field_9, axiom, v3_field_3(k9_int_3(2))).
fof(fc23_gaussint, axiom,  (! [A, B] :  ( ( (v1_xcmplx_0(A) & v2_gaussint(A))  &  (v1_xcmplx_0(B) & v2_gaussint(B)) )  => v2_gaussint(k2_xcmplx_0(A, B))) ) ).
fof(fc23_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k3_xcmplx_0(A, B))) ) ) ).
fof(fc24_gaussint, axiom,  (! [A, B] :  ( ( (v1_xcmplx_0(A) & v2_gaussint(A))  &  (v1_xcmplx_0(B) & v2_gaussint(B)) )  => v2_gaussint(k6_xcmplx_0(A, B))) ) ).
fof(fc24_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k9_xtuple_0(A))) ) ).
fof(fc24_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k3_xcmplx_0(B, A))) ) ) ).
fof(fc25_field_16, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v8_struct_0(A) &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) ) )  & v7_ordinal1(B))  =>  (v1_funct_1(k2_field_16(A, k5_field_16(A), B)) &  (v1_funct_2(k2_field_16(A, k5_field_16(A), B), u1_struct_0(A), u1_struct_0(A)) & v7_mod_4(k2_field_16(A, k5_field_16(A), B), A, A)) ) ) ) ).
fof(fc25_gaussint, axiom,  (! [A, B] :  ( ( (v1_xcmplx_0(A) & v2_gaussint(A))  &  (v1_xcmplx_0(B) & v2_gaussint(B)) )  => v2_gaussint(k3_xcmplx_0(A, B))) ) ).
fof(fc25_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc25_ring_3, axiom,  ( ~ (v2_struct_0(k11_gaussint))  &  (v36_algstr_0(k11_gaussint) & v3_ring_2(k11_gaussint, k11_gaussint)) ) ).
fof(fc25_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k3_xcmplx_0(A, B))) ) ) ).
fof(fc26_field_16, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v8_struct_0(A) &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (v1_funct_1(k5_field_16(A)) &  (v1_funct_2(k5_field_16(A), u1_struct_0(A), u1_struct_0(A)) & v7_mod_4(k5_field_16(A), A, A)) ) ) ) ).
fof(fc26_gaussint, axiom,  (! [A, B] :  ( ( (v1_xcmplx_0(A) & v2_gaussint(A))  & v1_rat_1(B))  => v2_gaussint(k3_xcmplx_0(B, A))) ) ).
fof(fc26_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k3_xcmplx_0(A, B))) ) ) ).
fof(fc27_gaussint, axiom,  (! [A] :  ( (v1_xcmplx_0(A) & v2_gaussint(A))  =>  (v1_xcmplx_0(k4_xcmplx_0(A)) & v2_gaussint(k4_xcmplx_0(A))) ) ) ).
fof(fc27_xreal_0, axiom,  (! [A] :  ( (v2_xxreal_0(A) & v1_xreal_0(A))  =>  (v1_xcmplx_0(k5_xcmplx_0(A)) & v2_xxreal_0(k5_xcmplx_0(A))) ) ) ).
fof(fc28_gaussint, axiom,  (! [A] :  ( (v1_xcmplx_0(A) & v2_gaussint(A))  =>  (v1_xcmplx_0(k5_xcmplx_0(A)) & v2_gaussint(k5_xcmplx_0(A))) ) ) ).
fof(fc28_xreal_0, axiom,  (! [A] :  ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k5_xcmplx_0(A)) &  ~ (v2_xxreal_0(k5_xcmplx_0(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(fc29_ring_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom3(A)))  &  (v36_algstr_0(k12_polynom3(A)) & v1_int_3(k12_polynom3(A))) ) ) ) ).
fof(fc29_xreal_0, axiom,  (! [A] :  ( (v3_xxreal_0(A) & v1_xreal_0(A))  =>  (v1_xcmplx_0(k5_xcmplx_0(A)) & v3_xxreal_0(k5_xcmplx_0(A))) ) ) ).
fof(fc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v8_ordinal1(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc2_ec_pf_1, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_int_2(A))  => v1_ec_pf_1(k9_int_3(A))) ) ).
fof(fc2_field_12, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l6_algstr_0(A))  =>  ( ~ (v7_struct_0(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A))))  & v36_algstr_0(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A)))) ) ) ).
fof(fc2_field_16, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_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) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( (v1_funct_1(B) &  (v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) &  (v7_mod_4(B, A, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) ) )  & v7_ordinal1(C)) )  =>  (v1_funct_1(k2_field_16(A, B, C)) &  (v1_funct_2(k2_field_16(A, B, C), u1_struct_0(A), u1_struct_0(A)) & v7_mod_4(k2_field_16(A, B, C), A, A)) ) ) ) ).
fof(fc2_finseq_1, axiom,  (! [A] :  ( (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) )  =>  ~ (v1_xboole_0(k1_finseq_1(A))) ) ) ).
fof(fc2_int_1, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => v1_int_1(k3_xcmplx_0(A, B))) ) ).
fof(fc2_int_3, axiom, v5_membered(u1_struct_0(k1_int_3))).
fof(fc2_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v7_ordinal1(k3_xcmplx_0(A, B))) ) ).
fof(fc2_nat_6, axiom,  (! [A] :  ( ( ~ (v1_zfmisc_1(A))  & v7_ordinal1(A))  => v2_xxreal_0(k6_xcmplx_0(A, 1))) ) ).
fof(fc2_newton, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v7_ordinal1(B))  => v1_xreal_0(k1_newton(A, B))) ) ).
fof(fc2_ring_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom3(A)))  &  (v36_algstr_0(k12_polynom3(A)) & v2_ring_4(k12_polynom3(A), A)) ) ) ) ).
fof(fc2_ring_5, axiom,  (! [A] :  ( ( ~ (v1_zfmisc_1(A))  &  (v7_ordinal1(A) &  ~ (v1_int_2(A)) ) )  =>  ~ (v1_vectsp_2(k9_int_3(A))) ) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc2_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_xcmplx_0(k2_xcmplx_0(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(fc30_gaussint, axiom,  ( ~ (v2_struct_0(k11_gaussint))  &  ( ~ (v6_struct_0(k11_gaussint))  &  (v13_algstr_0(k11_gaussint) &  (v33_algstr_0(k11_gaussint) &  (v36_algstr_0(k11_gaussint) &  (v3_group_1(k11_gaussint) &  (v5_group_1(k11_gaussint) &  (v2_rlvect_1(k11_gaussint) &  (v3_rlvect_1(k11_gaussint) &  (v4_rlvect_1(k11_gaussint) &  (v3_vectsp_1(k11_gaussint) &  (v5_vectsp_1(k11_gaussint) & v6_vectsp_1(k11_gaussint)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(fc30_ring_3, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_int_2(A))  => v3_ring_2(k9_int_3(A), k9_int_3(A))) ) ).
fof(fc30_xreal_0, axiom,  (! [A] :  ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k5_xcmplx_0(A)) &  ~ (v3_xxreal_0(k5_xcmplx_0(A))) ) ) ) ).
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_field_9, axiom,  ( ~ (v2_struct_0(k11_gaussint))  &  (v36_algstr_0(k11_gaussint) &  ~ (v3_field_9(k11_gaussint)) ) ) ).
fof(fc31_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v5_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc31_gaussint, axiom,  ( ~ (v2_struct_0(k11_gaussint))  &  (v36_algstr_0(k11_gaussint) & v4_vectsp_1(k11_gaussint)) ) ).
fof(fc31_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k7_xcmplx_0(A, B))) ) ) ).
fof(fc32_gaussint, axiom,  ( ~ (v2_struct_0(k11_gaussint))  &  (v36_algstr_0(k11_gaussint) & v1_ec_pf_1(k11_gaussint)) ) ).
fof(fc32_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k7_xcmplx_0(B, A))) ) ) ).
fof(fc33_ring_3, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_int_2(A))  => v1_ec_pf_1(k9_int_3(A))) ) ).
fof(fc33_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k7_xcmplx_0(A, B))) ) ) ).
fof(fc34_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k7_xcmplx_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_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_finset_1(A))  => v5_finset_1(k10_xtuple_0(A))) ) ).
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_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v1_xboole_0(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc3_field_12, axiom,  (! [A] :  ( ( ~ (v6_struct_0(A))  & l6_algstr_0(A))  =>  ( ~ (v6_struct_0(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A))))  & v36_algstr_0(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A)))) ) ) ).
fof(fc3_field_4, axiom,  ( ~ (v2_struct_0(k11_gaussint))  &  (v36_algstr_0(k11_gaussint) & v1_field_4(k11_gaussint, k1_int_3)) ) ).
fof(fc3_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_finset_1(k1_finseq_1(A))) ) ).
fof(fc3_gaussint, axiom,  (! [A, B] :  ( ( (v1_xcmplx_0(A) & v1_gaussint(A))  &  (v1_xcmplx_0(B) & v1_gaussint(B)) )  => v1_gaussint(k2_xcmplx_0(A, B))) ) ).
fof(fc3_int_1, axiom,  (! [A] :  (v1_int_1(A) =>  (v1_xcmplx_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A))) ) ) ).
fof(fc3_int_3, axiom, v4_vectsp_1(k1_int_3)).
fof(fc3_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  ~ (v8_ordinal1(k2_xcmplx_0(A, B))) ) ) ).
fof(fc3_newton, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v7_ordinal1(B))  => v1_xcmplx_0(k1_newton(A, B))) ) ).
fof(fc3_ring_3, axiom,  (! [A] :  (v7_ordinal1(A) => v8_struct_0(k9_int_3(A))) ) ).
fof(fc3_ring_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom3(A)))  &  (v36_algstr_0(k12_polynom3(A)) & v4_vectsp_1(k12_polynom3(A))) ) ) ) ).
fof(fc3_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_xcmplx_0(k3_xcmplx_0(A, B))) ) ).
fof(fc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) =>  (v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A))) ) ) ).
fof(fc4_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v8_ordinal1(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc4_field_12, axiom,  (! [A] :  ( (v3_rlvect_1(A) & l6_algstr_0(A))  =>  (v36_algstr_0(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A))) & v3_rlvect_1(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A)))) ) ) ).
fof(fc4_field_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v1_field_4(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom3(B)))  &  (v36_algstr_0(k12_polynom3(B)) & v1_field_4(k12_polynom3(B), k12_polynom3(A))) ) ) ) ).
fof(fc4_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_card_1(k1_finseq_1(A), A)) ) ).
fof(fc4_gaussint, axiom,  (! [A, B] :  ( ( (v1_xcmplx_0(A) & v1_gaussint(A))  &  (v1_xcmplx_0(B) & v1_gaussint(B)) )  => v1_gaussint(k6_xcmplx_0(A, B))) ) ).
fof(fc4_group_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_group_1(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)) & v2_binop_1(u2_algstr_0(A), u1_struct_0(A))) ) ) ) ).
fof(fc4_int_1, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => v1_int_1(k6_xcmplx_0(A, B))) ) ).
fof(fc4_int_3, axiom,  ( ~ (v6_struct_0(k1_int_3))  &  (v13_algstr_0(k1_int_3) &  (v3_group_1(k1_int_3) &  (v5_group_1(k1_int_3) &  (v2_rlvect_1(k1_int_3) &  (v3_rlvect_1(k1_int_3) &  (v4_rlvect_1(k1_int_3) &  (v5_vectsp_1(k1_int_3) & v1_vectsp_2(k1_int_3)) ) ) ) ) ) ) ) ).
fof(fc4_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  ~ (v8_ordinal1(k2_xcmplx_0(B, A))) ) ) ).
fof(fc4_newton, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v7_ordinal1(k1_newton(A, B))) ) ).
fof(fc4_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  => v3_ordinal1(k9_xtuple_0(A))) ) ).
fof(fc4_ring_3, axiom,  (! [A] :  ( ( ~ (v1_zfmisc_1(A))  & v7_ordinal1(A))  =>  ~ (v6_struct_0(k9_int_3(A))) ) ) ).
fof(fc4_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_xcmplx_0(k6_xcmplx_0(A, B))) ) ).
fof(fc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) =>  (v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A))) ) ) ).
fof(fc59_membered, axiom, v7_membered(k4_ordinal1)).
fof(fc5_field_12, axiom,  (! [A] :  ( (v4_rlvect_1(A) & l6_algstr_0(A))  =>  (v36_algstr_0(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A))) & v4_rlvect_1(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A)))) ) ) ).
fof(fc5_gaussint, axiom,  (! [A, B] :  ( ( (v1_xcmplx_0(A) & v1_gaussint(A))  &  (v1_xcmplx_0(B) & v1_gaussint(B)) )  => v1_gaussint(k3_xcmplx_0(A, B))) ) ).
fof(fc5_group_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_group_1(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)) & v1_setwiseo(u2_algstr_0(A), u1_struct_0(A))) ) ) ) ).
fof(fc5_int_3, axiom, v1_int_3(k1_int_3)).
fof(fc5_nat_6, axiom,  (! [A, B, C] :  ( ( (v7_ordinal1(A) & v2_xxreal_0(A))  &  (v7_ordinal1(B) &  (v7_ordinal1(C) & v1_ec_pf_2(C, B)) ) )  => v1_ec_pf_2(k1_newton(A, C), k1_newton(A, B))) ) ).
fof(fc5_ring_3, axiom,  (! [A] :  ( (v7_ordinal1(A) & v2_xxreal_0(A))  =>  (v13_algstr_0(k9_int_3(A)) &  (v2_rlvect_1(k9_int_3(A)) &  (v3_rlvect_1(k9_int_3(A)) & v4_rlvect_1(k9_int_3(A))) ) ) ) ) ).
fof(fc5_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_xcmplx_0(k7_xcmplx_0(A, B))) ) ).
fof(fc5_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc6_card_1, axiom, v1_card_1(k4_ordinal1)).
fof(fc6_field_12, axiom,  (! [A] :  ( (v13_algstr_0(A) & l6_algstr_0(A))  =>  (v13_algstr_0(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A))) & v36_algstr_0(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A)))) ) ) ).
fof(fc6_group_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_group_1(A) &  (v3_group_1(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)) & v1_finseqop(u2_algstr_0(A), u1_struct_0(A))) ) ) ) ).
fof(fc6_int_1, axiom, v2_int_1(k4_xcmplx_0(1))).
fof(fc6_int_3, axiom,  (! [A] :  ( (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) )  =>  ( ~ (v2_struct_0(k9_int_3(A)))  & v36_algstr_0(k9_int_3(A))) ) ) ).
fof(fc6_membered, axiom, v6_membered(k4_ordinal1)).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc6_ring_3, axiom,  (! [A] :  ( (v7_ordinal1(A) & v2_xxreal_0(A))  =>  (v3_group_1(k9_int_3(A)) &  (v5_group_1(k9_int_3(A)) &  (v4_vectsp_1(k9_int_3(A)) & v5_vectsp_1(k9_int_3(A))) ) ) ) ) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc6_xcmplx_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A))  =>  ( ~ (v8_ordinal1(k4_xcmplx_0(A)))  & v1_xcmplx_0(k4_xcmplx_0(A))) ) ) ).
fof(fc6_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k3_xcmplx_0(A, B))) ) ).
fof(fc7_card_1, axiom, v2_card_1(k4_ordinal1)).
fof(fc7_field_12, axiom,  (! [A] :  ( (v2_rlvect_1(A) & l6_algstr_0(A))  =>  (v36_algstr_0(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A))) & v2_rlvect_1(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A)))) ) ) ).
fof(fc7_gaussint, axiom,  (! [A] :  ( (v1_xcmplx_0(A) & v1_gaussint(A))  =>  (v1_xcmplx_0(k4_xcmplx_0(A)) & v1_gaussint(k4_xcmplx_0(A))) ) ) ).
fof(fc7_int_1, axiom,  (! [A] :  (v2_int_1(A) => v7_ordinal1(k2_xcmplx_0(A, 1))) ) ).
fof(fc7_int_3, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_int_2(A))  =>  ( ~ (v6_struct_0(k9_int_3(A)))  &  (v13_algstr_0(k9_int_3(A)) &  (v33_algstr_0(k9_int_3(A)) &  (v3_group_1(k9_int_3(A)) &  (v5_group_1(k9_int_3(A)) &  (v2_rlvect_1(k9_int_3(A)) &  (v3_rlvect_1(k9_int_3(A)) &  (v4_rlvect_1(k9_int_3(A)) &  (v4_vectsp_1(k9_int_3(A)) & v5_vectsp_1(k9_int_3(A))) ) ) ) ) ) ) ) ) ) ) ).
fof(fc7_ring_3, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_int_2(A))  => v33_algstr_0(k9_int_3(A))) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc7_xcmplx_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A))  =>  ( ~ (v8_ordinal1(k5_xcmplx_0(A)))  & v1_xcmplx_0(k5_xcmplx_0(A))) ) ) ).
fof(fc7_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k6_xcmplx_0(A, B))) ) ).
fof(fc8_card_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc8_field_12, axiom,  (! [A] :  ( (v3_group_1(A) & l6_algstr_0(A))  =>  (v36_algstr_0(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A))) & v3_group_1(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A)))) ) ) ).
fof(fc8_field_16, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  => v1_field_16(u1_struct_0(A), A)) ) ).
fof(fc8_int_1, axiom,  (! [A, B] :  ( (v2_int_1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  => v7_ordinal1(k2_xcmplx_0(A, B))) ) ).
fof(fc8_int_3, axiom,  ~ (v8_struct_0(k1_int_3)) ).
fof(fc8_nat_6, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_ec_pf_2(A, 2))  => v7_ordinal1(k6_xcmplx_0(A, 2))) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_ratfunc1, axiom,  (! [A] :  ( ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v5_vectsp_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom3(A)))  &  ( ~ (v6_struct_0(k12_polynom3(A)))  & v36_algstr_0(k12_polynom3(A))) ) ) ) ).
fof(fc8_relat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  =>  ~ (v1_xboole_0(k9_xtuple_0(A))) ) ) ).
fof(fc8_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C))) => v1_relat_1(k9_xtuple_0(D))) ) ).
fof(fc8_ring_3, axiom, v3_ring_3(k1_int_3, k5_numbers)).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc8_xcmplx_0, axiom,  (! [A, B] :  ( ( ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A))  &  ( ~ (v8_ordinal1(B))  & v1_xcmplx_0(B)) )  =>  ~ (v8_ordinal1(k3_xcmplx_0(A, B))) ) ) ).
fof(fc8_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k7_xcmplx_0(A, B))) ) ).
fof(fc9_card_1, axiom,  ~ (v1_finset_1(k4_ordinal1)) ).
fof(fc9_field_12, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_vectsp_1(A) & l6_algstr_0(A)) )  =>  (v36_algstr_0(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A))) & v4_vectsp_1(g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A)))) ) ) ).
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_gaussint, axiom,  (! [A, B] :  ( ( (v1_xcmplx_0(A) & v1_gaussint(A))  & v1_int_1(B))  => v1_gaussint(k3_xcmplx_0(B, A))) ) ).
fof(fc9_nat_6, axiom,  (! [A, B] :  ( ( (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) )  &  (v7_ordinal1(B) & v1_ec_pf_2(B, A)) )  => v7_ordinal1(k6_xcmplx_0(B, 1))) ) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_polynom3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom3(A)))  &  (v36_algstr_0(k12_polynom3(A)) & v2_rlvect_1(k12_polynom3(A))) ) ) ) ).
fof(fc9_ratfunc1, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v5_vectsp_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_2(A) & l6_algstr_0(A)) ) ) ) ) )  =>  ( ~ (v2_struct_0(k12_polynom3(A)))  &  (v36_algstr_0(k12_polynom3(A)) & v1_vectsp_2(k12_polynom3(A))) ) ) ) ).
fof(fc9_relat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  =>  ~ (v1_xboole_0(k10_xtuple_0(A))) ) ) ).
fof(fc9_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k2_zfmisc_1(B, C)))) => v1_relat_1(k10_xtuple_0(D))) ) ).
fof(fc9_ring_3, axiom,  (! [A] :  ( (v7_ordinal1(A) & v2_xxreal_0(A))  => v3_ring_3(k9_int_3(A), A)) ) ).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(fc9_xcmplx_0, axiom,  (! [A, B] :  ( ( ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A))  &  ( ~ (v8_ordinal1(B))  & v1_xcmplx_0(B)) )  =>  ~ (v8_ordinal1(k7_xcmplx_0(A, B))) ) ) ).
fof(fc9_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k2_xcmplx_0(A, B))) ) ) ).
fof(fraenkel_a_2_3_field_16, axiom,  (! [A, B, C] :  ( ( (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) )  &  ( ~ (v2_struct_0(C))  &  ( ~ (v6_struct_0(C))  &  (v13_algstr_0(C) &  (v33_algstr_0(C) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v4_vectsp_1(C) &  (v5_vectsp_1(C) &  (v3_group_1(C) &  (v5_group_1(C) & l6_algstr_0(C)) ) ) ) ) ) ) ) ) ) ) )  =>  (r2_hidden(A, a_2_3_field_16(B, C)) <=>  (? [D] :  (v7_ordinal1(D) &  (A=k2_field_16(C, k5_field_16(C), D) &  (r1_xxreal_0(k5_numbers, D) & r1_xxreal_0(D, k6_xcmplx_0(B, 1))) ) ) ) ) ) ) ).
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(involutiveness_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A))=A) ) ).
fof(involutiveness_k5_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k5_xcmplx_0(k5_xcmplx_0(A))=A) ) ).
fof(projectivity_k1_card_1, axiom,  (! [A] : k1_card_1(k1_card_1(A))=k1_card_1(A)) ).
fof(projectivity_k4_card_1, axiom,  (! [A] :  (v1_finset_1(A) => k4_card_1(k4_card_1(A))=k4_card_1(A)) ) ).
fof(rc10_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_card_1(B)) ) ) ) ).
fof(rc10_field_12, axiom,  (! [A, B] :  ( ( ( ~ (v2_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) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v3_group_1(B) &  (v3_ring_2(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) )  =>  (? [C] :  (l6_algstr_0(C) &  ( ~ (v2_struct_0(C))  &  (v12_algstr_0(C) &  (v13_algstr_0(C) &  (v14_algstr_0(C) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v9_rlvect_1(C) &  (v1_vectsp_1(C) &  (v2_vectsp_1(C) &  (v3_vectsp_1(C) &  (v4_vectsp_1(C) &  (v5_vectsp_1(C) &  (v6_vectsp_1(C) &  (v1_group_1(C) &  (v3_group_1(C) &  (v3_ring_2(C, A) &  (v3_ring_2(C, B) &  (v3_ring_2(C, k1_int_3) & v3_ring_2(C, k1_int_3)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc10_field_9, axiom,  (! [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) &  ( ~ (v3_field_9(A))  & l6_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) &  (v9_algstr_0(B, A) &  (v10_algstr_0(B, A) &  (v11_algstr_0(B, A) &  ~ (v1_o_ring_1(B, A)) ) ) ) ) ) ) ) ) ) ) ).
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(rc10_ring_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) & v3_ring_2(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc10_ring_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_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) &  (v1_vectsp_2(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_vectsp_2(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) & v1_ring_3(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc10_ring_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (m1_subset_1(B, u1_struct_0(k12_polynom3(A))) &  (v2_algstr_0(B, k12_polynom3(A)) &  (v3_algstr_0(B, k12_polynom3(A)) &  (v4_algstr_0(B, k12_polynom3(A)) &  (v9_algstr_0(B, k12_polynom3(A)) &  (v10_algstr_0(B, k12_polynom3(A)) &  (v11_algstr_0(B, k12_polynom3(A)) &  ~ (v3_ring_4(B, A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc11_field_9, 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) &  (v12_algstr_0(A) &  (v13_algstr_0(A) &  (v14_algstr_0(A) &  (v30_algstr_0(A) &  (v31_algstr_0(A) &  (v32_algstr_0(A) &  (v33_algstr_0(A) &  (v34_algstr_0(A) &  (v35_algstr_0(A) &  (v36_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) &  (v9_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) &  (v8_ideal_1(A) &  (v3_ring_2(A, k1_int_3) &  (v8_ring_2(A) &  ( ~ (v3_ring_3(A, 2))  &  (v3_field_3(A) &  ~ (v3_field_9(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_ring_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) & v3_ring_2(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc11_ring_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_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) &  (v1_vectsp_2(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) & v1_ring_3(B, 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_ring_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v3_ring_2(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) &  (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(A)) &  (v5_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  &  (v1_partfun1(C, u1_struct_0(A)) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) &  (v13_vectsp_1(C, A, B) &  (v6_group_1(C, A, B) & v1_group_6(C, A, B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc12_ring_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_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) &  (v1_vectsp_2(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) & v1_ring_3(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc13_ring_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & l4_algstr_0(A)) )  =>  (? [B] :  (m1_subset_1(B, u1_struct_0(A)) & v1_gcd_1(B, A)) ) ) ) ).
fof(rc13_ring_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v33_algstr_0(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_vectsp_2(B) &  (v3_gcd_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) &  (v8_ideal_1(B) &  (v1_int_3(B) &  (v8_ring_2(B) & v1_ring_3(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_ring_2, axiom,  (! [A] :  ( ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v2_vectsp_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_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) &  (v10_algstr_0(B, A) &  ~ (v1_gcd_1(B, A)) ) ) ) ) ) ) ) ) ).
fof(rc14_ring_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_vectsp_2(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) & v1_ring_3(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc15_ring_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & l6_algstr_0(A)) )  =>  (? [B] :  (m1_subset_1(B, u1_struct_0(A)) &  ~ (v4_ring_2(B, A)) ) ) ) ) ).
fof(rc15_ring_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) & v1_ring_3(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc16_ring_2, axiom,  (? [A] :  (m1_subset_1(A, u1_struct_0(k1_int_3)) &  (v2_algstr_0(A, k1_int_3) &  (v3_algstr_0(A, k1_int_3) &  (v4_algstr_0(A, k1_int_3) &  (v9_algstr_0(A, k1_int_3) &  (v10_algstr_0(A, k1_int_3) &  (v11_algstr_0(A, k1_int_3) &  (v1_xreal_0(A) &  (v1_int_1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v1_rat_1(A) & v4_ring_2(A, k1_int_3)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc16_ring_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) & v1_ring_3(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc17_algstr_0, axiom,  (? [A] :  (l6_algstr_0(A) & v36_algstr_0(A)) ) ).
fof(rc17_ring_2, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  & v8_ideal_1(A)) ) ) ).
fof(rc17_ring_3, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ~ (v2_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) &  (v1_ring_3(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) &  (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(A)) &  (v5_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  &  (v1_partfun1(C, u1_struct_0(A)) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) &  (v6_group_1(C, A, B) &  (v13_vectsp_1(C, A, B) &  (v3_mod_4(C, A, B) & v1_group_6(C, A, B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc17_ring_4, axiom,  (! [A] :  ( ( ~ (v1_zfmisc_1(A))  & v7_ordinal1(A))  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  ( ~ (v8_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) &  (v3_ring_2(B, k1_int_3) &  (v3_ring_2(B, k1_int_3) & v3_ring_3(B, 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(rc18_ring_2, 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) &  (v12_algstr_0(A) &  (v13_algstr_0(A) &  (v14_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) &  (v9_rlvect_1(A) &  (v1_group_1(A) &  (v3_group_1(A) &  (v1_algstr_1(A) &  (v2_algstr_1(A) &  (v3_algstr_1(A) &  (v4_algstr_1(A) & v8_ring_2(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc18_ring_4, 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) &  (v12_algstr_0(A) &  (v13_algstr_0(A) &  (v14_algstr_0(A) &  (v30_algstr_0(A) &  (v31_algstr_0(A) &  (v32_algstr_0(A) &  ( ~ (v33_algstr_0(A))  &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v9_rlvect_1(A) &  (v1_vectsp_1(A) &  (v2_vectsp_1(A) &  (v3_vectsp_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v6_vectsp_1(A) &  (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) & v3_ring_2(A, k1_int_3)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc19_ring_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  ( ~ (v33_algstr_0(A))  &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v1_vectsp_2(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (m1_subset_1(B, u1_struct_0(A)) &  ( ~ (v9_struct_0(B, A))  &  (v2_algstr_0(B, A) &  (v3_algstr_0(B, A) &  (v4_algstr_0(B, A) &  (v9_algstr_0(B, A) &  (v10_algstr_0(B, A) &  (v11_algstr_0(B, A) &  ~ (v1_gcd_1(B, A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc19_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l2_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, u1_struct_0(A)) &  ~ (v9_struct_0(B, A)) ) ) ) ) ).
fof(rc1_card_1, axiom,  (? [A] : v1_card_1(A)) ).
fof(rc1_field_1, 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) &  (v12_algstr_0(A) &  (v13_algstr_0(A) &  (v30_algstr_0(A) &  (v31_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) &  (v9_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) &  (v3_ring_2(A, k1_int_3) & v8_ring_2(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_field_12, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v30_algstr_0(B) &  (v31_algstr_0(B) &  (v32_algstr_0(B) &  (v33_algstr_0(B) &  (v34_algstr_0(B) &  (v35_algstr_0(B) &  (v36_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v1_vectsp_2(B) &  (v3_gcd_1(B) &  (v8_ideal_1(B) &  (v1_int_3(B) &  (v3_ring_2(B, k12_polynom3(A)) &  (v8_ring_2(B) & v1_field_4(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_field_15, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_int_2(A))  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v8_struct_0(B) &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v30_algstr_0(B) &  (v31_algstr_0(B) &  (v32_algstr_0(B) &  (v33_algstr_0(B) &  (v34_algstr_0(B) &  (v35_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v1_vectsp_2(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) &  (v8_ideal_1(B) &  (v3_ring_2(B, k1_int_3) &  (v8_ring_2(B) & v3_ring_3(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_field_4, axiom,  (! [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) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) &  (v3_ring_2(B, k1_int_3) &  (v3_ring_2(B, k1_int_3) & v1_field_4(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_field_7, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  (v13_algstr_0(B) &  (v33_algstr_0(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v1_field_4(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [C] :  (l6_algstr_0(C) &  ( ~ (v2_struct_0(C))  &  ( ~ (v6_struct_0(C))  &  ( ~ (v7_struct_0(C))  &  (v5_algstr_0(C) &  (v6_algstr_0(C) &  (v7_algstr_0(C) &  (v12_algstr_0(C) &  (v13_algstr_0(C) &  (v14_algstr_0(C) &  (v30_algstr_0(C) &  (v31_algstr_0(C) &  (v32_algstr_0(C) &  (v33_algstr_0(C) &  (v34_algstr_0(C) &  (v35_algstr_0(C) &  (v1_vectsp_1(C) &  (v2_vectsp_1(C) &  (v3_vectsp_1(C) &  (v4_vectsp_1(C) &  (v5_vectsp_1(C) &  (v6_vectsp_1(C) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v9_rlvect_1(C) &  (v1_group_1(C) &  (v3_group_1(C) &  (v5_group_1(C) &  (v1_vectsp_2(C) &  (v1_algstr_1(C) &  (v2_algstr_1(C) &  (v3_algstr_1(C) &  (v4_algstr_1(C) &  (v8_ideal_1(C) &  (v3_ring_2(C, B) &  (v3_ring_2(C, k12_polynom3(A)) &  (v8_ring_2(C) & v1_field_4(C, 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_int_1, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v1_xcmplx_0(A) &  (v1_xreal_0(A) & v1_int_1(A)) ) ) ) ).
fof(rc1_int_3, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v36_algstr_0(A) &  (v1_group_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) &  (v2_vectsp_1(A) &  (v3_vectsp_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v6_vectsp_1(A) &  (v1_vectsp_2(A) & v1_int_3(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc1_mod_4, 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, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)))) &  ( ~ (v1_xboole_0(B))  &  (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v5_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) &  (v1_partfun1(B, u1_struct_0(A)) &  (v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) &  (v3_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v13_vectsp_1(B, A, A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_nat_1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc1_newton, axiom,  (? [A] :  (m1_subset_1(A, k4_ordinal1) &  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xreal_0(A) &  (v1_xxreal_0(A) &  ( ~ (v3_xxreal_0(A))  &  (v1_int_1(A) &  (v2_int_1(A) &  (v1_int_2(A) &  (v1_finset_1(A) &  (v1_card_1(A) & v1_rat_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(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_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
fof(rc1_ring_3, axiom,  (? [A] :  (m1_subset_1(A, u1_struct_0(k1_int_3)) &  (v1_xreal_0(A) &  (v1_int_1(A) &  (v2_algstr_0(A, k1_int_3) &  (v3_algstr_0(A, k1_int_3) &  (v4_algstr_0(A, k1_int_3) &  (v9_algstr_0(A, k1_int_3) &  (v10_algstr_0(A, k1_int_3) &  (v11_algstr_0(A, k1_int_3) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) &  (v1_xcmplx_0(A) &  (v1_rat_1(A) &  (v1_gaussint(A) & v2_gaussint(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_ring_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_struct_0(A))  =>  (? [B] :  ( ~ (v1_xboole_0(B))  & v1_ring_4(B, A)) ) ) ) ).
fof(rc1_ring_5, axiom,  (? [A] :  ( ~ (v1_zfmisc_1(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  (v1_xreal_0(A) &  (v1_int_1(A) &  (v2_int_1(A) &  (v1_finset_1(A) &  (v1_card_1(A) &  (v1_xxreal_0(A) &  ( ~ (v3_xxreal_0(A))  &  (v1_xcmplx_0(A) &  ~ (v1_int_2(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_topzari1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_group_1(A) & l5_algstr_0(A)) )  =>  (? [B] :  (m1_subset_1(B, u1_struct_0(A)) & v1_topzari1(B, A)) ) ) ) ).
fof(rc1_uniroots, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v8_struct_0(A) &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v1_group_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v1_vectsp_1(A) &  (v2_vectsp_1(A) &  (v3_vectsp_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v6_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & v1_vectsp_2(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_vectsp_9, 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(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xcmplx_0, axiom,  (? [A] : v1_xcmplx_0(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc20_ring_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (m1_subset_1(B, u1_struct_0(k12_polynom3(A))) &  (v2_algstr_0(B, k12_polynom3(A)) &  (v3_algstr_0(B, k12_polynom3(A)) &  (v4_algstr_0(B, k12_polynom3(A)) &  (v9_algstr_0(B, k12_polynom3(A)) &  (v10_algstr_0(B, k12_polynom3(A)) &  (v11_algstr_0(B, k12_polynom3(A)) & v5_ring_2(B, k12_polynom3(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_ring_4, axiom,  (! [A] :  ( ( ~ (v2_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) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (? [B] :  (m1_subset_1(B, u1_struct_0(k12_polynom3(A))) &  (v2_algstr_0(B, k12_polynom3(A)) &  (v3_algstr_0(B, k12_polynom3(A)) &  (v4_algstr_0(B, k12_polynom3(A)) &  (v9_algstr_0(B, k12_polynom3(A)) &  (v10_algstr_0(B, k12_polynom3(A)) &  (v11_algstr_0(B, k12_polynom3(A)) &  ~ (v5_ring_2(B, k12_polynom3(A))) ) ) ) ) ) ) ) ) ) ) ).
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_field_1, axiom,  (! [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) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) &  (v3_ring_2(B, A) &  (v3_ring_2(B, k1_int_3) &  (v3_ring_2(B, k1_int_3) & v1_ring_3(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_field_12, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  (v13_algstr_0(B) &  (v33_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v1_ring_3(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [C] :  (l6_algstr_0(C) &  ( ~ (v2_struct_0(C))  &  ( ~ (v6_struct_0(C))  &  ( ~ (v7_struct_0(C))  &  (v12_algstr_0(C) &  (v13_algstr_0(C) &  (v14_algstr_0(C) &  (v30_algstr_0(C) &  (v31_algstr_0(C) &  (v32_algstr_0(C) &  (v33_algstr_0(C) &  (v34_algstr_0(C) &  (v35_algstr_0(C) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v9_rlvect_1(C) &  (v1_vectsp_1(C) &  (v2_vectsp_1(C) &  (v3_vectsp_1(C) &  (v4_vectsp_1(C) &  (v5_vectsp_1(C) &  (v6_vectsp_1(C) &  (v1_group_1(C) &  (v3_group_1(C) &  (v5_group_1(C) &  (v1_vectsp_2(C) &  (v3_gcd_1(C) &  (v8_ideal_1(C) &  (v1_int_3(C) &  (v3_ring_2(C, A) &  (v3_ring_2(C, k12_polynom3(B)) &  (v8_ring_2(C) &  (v1_ring_3(C, A) & v1_field_4(C, B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_field_14, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  (v13_algstr_0(B) &  (v33_algstr_0(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v1_field_4(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(C))  &  ( ~ (v6_struct_0(C))  &  (v13_algstr_0(C) &  (v33_algstr_0(C) &  (v3_group_1(C) &  (v5_group_1(C) &  (v4_vectsp_1(C) &  (v5_vectsp_1(C) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v1_field_4(C, B) & l6_algstr_0(C)) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [D] :  (l6_algstr_0(D) &  ( ~ (v2_struct_0(D))  &  ( ~ (v6_struct_0(D))  &  ( ~ (v7_struct_0(D))  &  (v5_algstr_0(D) &  (v6_algstr_0(D) &  (v7_algstr_0(D) &  (v12_algstr_0(D) &  (v13_algstr_0(D) &  (v14_algstr_0(D) &  (v30_algstr_0(D) &  (v31_algstr_0(D) &  (v32_algstr_0(D) &  (v33_algstr_0(D) &  (v34_algstr_0(D) &  (v35_algstr_0(D) &  (v1_group_1(D) &  (v3_group_1(D) &  (v5_group_1(D) &  (v1_vectsp_1(D) &  (v2_vectsp_1(D) &  (v3_vectsp_1(D) &  (v4_vectsp_1(D) &  (v5_vectsp_1(D) &  (v6_vectsp_1(D) &  (v2_rlvect_1(D) &  (v3_rlvect_1(D) &  (v4_rlvect_1(D) &  (v9_rlvect_1(D) &  (v1_vectsp_2(D) &  (v1_algstr_1(D) &  (v2_algstr_1(D) &  (v3_algstr_1(D) &  (v4_algstr_1(D) &  (v8_ideal_1(D) &  (v1_int_3(D) &  (v3_ring_2(D, A) &  (v8_ring_2(D) &  (v1_ring_3(D, A) &  (v1_field_4(D, A) &  (v1_field_4(D, B) &  (v1_field_4(D, C) & v3_gcd_1(D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_field_4, axiom,  (! [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) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) &  (v3_ring_2(B, k1_int_3) & v1_field_4(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_field_6, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v30_algstr_0(B) &  (v31_algstr_0(B) &  (v32_algstr_0(B) &  (v33_algstr_0(B) &  (v34_algstr_0(B) &  (v35_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v1_vectsp_2(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) &  (v8_ideal_1(B) &  (v3_ring_2(B, k12_polynom3(A)) &  (v3_ring_2(B, k1_int_3) &  (v8_ring_2(B) & v1_field_4(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_field_7, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  (v13_algstr_0(B) &  (v33_algstr_0(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v1_field_4(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [C] :  (l6_algstr_0(C) &  ( ~ (v2_struct_0(C))  &  ( ~ (v6_struct_0(C))  &  ( ~ (v7_struct_0(C))  &  (v5_algstr_0(C) &  (v6_algstr_0(C) &  (v7_algstr_0(C) &  (v12_algstr_0(C) &  (v13_algstr_0(C) &  (v14_algstr_0(C) &  (v30_algstr_0(C) &  (v31_algstr_0(C) &  (v32_algstr_0(C) &  (v33_algstr_0(C) &  (v34_algstr_0(C) &  (v35_algstr_0(C) &  (v1_vectsp_1(C) &  (v2_vectsp_1(C) &  (v3_vectsp_1(C) &  (v4_vectsp_1(C) &  (v5_vectsp_1(C) &  (v6_vectsp_1(C) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v9_rlvect_1(C) &  (v1_group_1(C) &  (v3_group_1(C) &  (v5_group_1(C) &  (v1_vectsp_2(C) &  (v1_algstr_1(C) &  (v2_algstr_1(C) &  (v3_algstr_1(C) &  (v4_algstr_1(C) &  (v8_ideal_1(C) &  (v3_ring_2(C, k12_polynom3(A)) &  (v8_ring_2(C) &  (v1_field_4(C, A) & v1_ring_3(C, B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_field_9, 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) &  (v12_algstr_0(A) &  (v13_algstr_0(A) &  (v14_algstr_0(A) &  (v30_algstr_0(A) &  (v31_algstr_0(A) &  (v32_algstr_0(A) &  (v33_algstr_0(A) &  (v34_algstr_0(A) &  (v35_algstr_0(A) &  (v36_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) &  (v9_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) &  (v8_ideal_1(A) &  (v3_ring_2(A, k1_int_3) &  (v8_ring_2(A) &  ~ (v3_ring_3(A, 2)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_int_1, axiom,  (? [A] : v1_int_1(A)) ).
fof(rc2_int_3, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v6_struct_0(A) &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v36_algstr_0(A) &  (v1_group_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) &  (v2_vectsp_1(A) &  (v3_vectsp_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & v6_vectsp_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc2_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) & v8_ordinal1(A)) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_ring_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  &  ( ~ (v2_struct_0(B))  &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) &  (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(A)) &  (v5_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  &  (v1_partfun1(C, u1_struct_0(A)) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v13_vectsp_1(C, A, B)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_ring_3, axiom,  (? [A] :  (m1_subset_1(A, u1_struct_0(k1_int_3)) &  (v1_xreal_0(A) &  (v1_int_1(A) &  (v2_algstr_0(A, k1_int_3) &  (v3_algstr_0(A, k1_int_3) &  (v4_algstr_0(A, k1_int_3) &  (v9_algstr_0(A, k1_int_3) &  (v10_algstr_0(A, k1_int_3) &  (v11_algstr_0(A, k1_int_3) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) &  (v1_xcmplx_0(A) &  (v1_rat_1(A) &  (v1_gaussint(A) & v2_gaussint(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_ring_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_struct_0(A))  =>  (? [B] :  (l1_struct_0(B) &  ( ~ (v2_struct_0(B))  & v2_ring_4(B, A)) ) ) ) ) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_topzari1, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v6_struct_0(A) &  (v5_algstr_0(A) &  (v6_algstr_0(A) &  (v7_algstr_0(A) &  (v12_algstr_0(A) &  (v13_algstr_0(A) &  (v14_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v9_rlvect_1(A) &  (v1_group_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v1_vectsp_1(A) &  (v2_vectsp_1(A) &  (v3_vectsp_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v6_vectsp_1(A) &  (v1_algstr_1(A) &  (v2_algstr_1(A) &  (v3_algstr_1(A) & v4_algstr_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_uniroots, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v8_struct_0(A) &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v1_group_1(A) &  (v3_group_1(A) &  (v1_vectsp_1(A) &  (v2_vectsp_1(A) &  (v3_vectsp_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v6_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) & v4_rlvect_1(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_xcmplx_0, axiom,  (? [A] : v1_xcmplx_0(A)) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc30_ring_3, axiom,  (! [A] :  (v7_ordinal1(A) =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) & v3_ring_3(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc31_ring_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_ring_3(A, k5_numbers) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_int_3), u1_struct_0(A)))) &  (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(k1_int_3)) &  (v5_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_partfun1(B, u1_struct_0(k1_int_3)) &  (v1_funct_2(B, u1_struct_0(k1_int_3), u1_struct_0(A)) &  (v6_group_1(B, k1_int_3, A) &  (v13_vectsp_1(B, k1_int_3, A) &  (v3_mod_4(B, k1_int_3, A) & v1_group_6(B, k1_int_3, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc32_ring_3, 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) &  (v12_algstr_0(A) &  (v13_algstr_0(A) &  (v14_algstr_0(A) &  (v33_algstr_0(A) &  (v1_group_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v9_rlvect_1(A) &  (v1_vectsp_1(A) &  (v2_vectsp_1(A) &  (v3_vectsp_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v6_vectsp_1(A) &  (v1_vectsp_2(A) &  (v3_gcd_1(A) &  (v1_algstr_1(A) &  (v2_algstr_1(A) &  (v3_algstr_1(A) &  (v4_algstr_1(A) &  (v8_ideal_1(A) &  (v1_int_3(A) &  (v3_ring_2(A, k1_int_3) &  (v8_ring_2(A) & v3_ring_3(A, k5_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc33_ring_3, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_int_2(A))  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v33_algstr_0(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_vectsp_2(B) &  (v3_gcd_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) &  (v8_ideal_1(B) &  (v1_int_3(B) &  (v3_ring_2(B, k1_int_3) &  (v8_ring_2(B) & v3_ring_3(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc34_ring_3, 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) &  (v12_algstr_0(A) &  (v13_algstr_0(A) &  (v14_algstr_0(A) &  (v33_algstr_0(A) &  (v1_group_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v9_rlvect_1(A) &  (v1_vectsp_1(A) &  (v2_vectsp_1(A) &  (v3_vectsp_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v6_vectsp_1(A) &  (v1_vectsp_2(A) &  (v3_gcd_1(A) &  (v1_algstr_1(A) &  (v2_algstr_1(A) &  (v3_algstr_1(A) &  (v4_algstr_1(A) &  (v8_ideal_1(A) &  (v1_int_3(A) &  (v3_ring_2(A, k1_int_3) &  (v3_ring_2(A, k11_gaussint) &  (v8_ring_2(A) & v3_ring_3(A, k5_numbers)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc35_ring_3, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_int_2(A))  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v33_algstr_0(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_vectsp_2(B) &  (v3_gcd_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) &  (v8_ideal_1(B) &  (v1_int_3(B) &  (v3_ring_2(B, k1_int_3) &  (v3_ring_2(B, k9_int_3(A)) &  (v8_ring_2(B) & v3_ring_3(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_card_1, axiom,  (? [A] :  ~ (v1_finset_1(A)) ) ).
fof(rc3_ec_pf_1, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v8_struct_0(A) &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v36_algstr_0(A) &  (v1_group_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v1_int_3(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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_field_16, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)))) &  (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v5_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_partfun1(B, u1_struct_0(A)) &  (v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v7_mod_4(B, A, A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_field_4, axiom,  (! [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) &  (v3_group_1(A) &  (v5_group_1(A) &  (v1_vectsp_2(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v30_algstr_0(B) &  (v31_algstr_0(B) &  (v32_algstr_0(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v1_vectsp_2(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) &  (v3_ring_2(B, k1_int_3) & v1_field_4(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_field_8, axiom,  (! [A] :  ( ( ~ (v2_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) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)))) &  (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v5_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_partfun1(B, u1_struct_0(A)) &  (v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v7_mod_4(B, A, A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_field_9, 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) &  (v12_algstr_0(A) &  (v13_algstr_0(A) &  (v14_algstr_0(A) &  (v30_algstr_0(A) &  (v31_algstr_0(A) &  (v32_algstr_0(A) &  (v33_algstr_0(A) &  (v34_algstr_0(A) &  (v35_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) &  (v9_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) &  (v8_ideal_1(A) &  (v3_ring_2(A, k1_int_3) &  (v8_ring_2(A) &  ( ~ (v2_polynom5(A))  & v3_field_3(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_int_1, axiom,  (? [A] : v2_int_1(A)) ).
fof(rc3_int_3, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v8_struct_0(A))  &  (v13_algstr_0(A) &  (v36_algstr_0(A) &  (v1_group_1(A) &  (v3_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) &  (v2_vectsp_1(A) &  (v3_vectsp_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & v6_vectsp_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v6_membered(A) & v7_membered(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_relat_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(rc3_ring_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v1_vectsp_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) ) ) ) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) &  (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(A)) &  (v5_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  &  (v1_partfun1(C, u1_struct_0(A)) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_ring_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_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) &  (v1_vectsp_2(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_vectsp_2(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) & v3_ring_2(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc3_vectsp_1, axiom,  (? [A] :  (l3_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v3_group_1(A) & v5_group_1(A)) ) ) ) ).
fof(rc3_xcmplx_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xcmplx_0(A)) ) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc3_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ).
fof(rc4_card_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc4_ec_pf_1, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v1_group_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v1_int_3(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_ec_pf_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc4_field_16, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_field_16(B, A)) ) ) ) ).
fof(rc4_field_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v30_algstr_0(B) &  (v31_algstr_0(B) &  (v32_algstr_0(B) &  (v33_algstr_0(B) &  (v34_algstr_0(B) &  (v35_algstr_0(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v1_vectsp_2(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) &  (v8_ideal_1(B) &  (v3_gcd_1(B) &  (v1_int_3(B) &  (v3_ring_2(B, k1_int_3) &  (v8_ring_2(B) & v1_field_4(B, 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_ordinal1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v5_ordinal1(B)) ) ) ) ) ).
fof(rc4_ring_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_vectsp_1(A) & l6_algstr_0(A)) )  &  ( ~ (v2_struct_0(B))  &  (v4_vectsp_1(B) & l6_algstr_0(B)) ) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) &  (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(A)) &  (v5_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  &  (v1_partfun1(C, u1_struct_0(A)) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v6_group_1(C, A, B)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc4_ring_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_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) &  (v1_vectsp_2(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) & v3_ring_2(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc4_ring_4, axiom,  (! [A] :  ( ( ~ (v2_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) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (? [B] :  (m1_subset_1(B, u1_struct_0(k12_polynom3(A))) &  (v9_struct_0(B, k12_polynom3(A)) &  (v2_algstr_0(B, k12_polynom3(A)) &  (v3_algstr_0(B, k12_polynom3(A)) &  (v4_algstr_0(B, k12_polynom3(A)) &  (v9_algstr_0(B, k12_polynom3(A)) &  (v10_algstr_0(B, k12_polynom3(A)) & v11_algstr_0(B, k12_polynom3(A))) ) ) ) ) ) ) ) ) ) ).
fof(rc4_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc4_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
fof(rc4_vectsp_1, axiom,  (? [A] :  (l4_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v1_group_1(A) &  (v3_group_1(A) & v5_group_1(A)) ) ) ) ) ).
fof(rc4_xcmplx_0, axiom,  (? [A] :  ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A)) ) ).
fof(rc4_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ).
fof(rc5_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  & v1_card_1(A)) ) ) ) ) ) ).
fof(rc5_field_12, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  (v13_algstr_0(B) &  (v33_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v1_field_4(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [C] :  (l6_algstr_0(C) &  ( ~ (v2_struct_0(C))  &  ( ~ (v6_struct_0(C))  &  ( ~ (v7_struct_0(C))  &  (v12_algstr_0(C) &  (v13_algstr_0(C) &  (v14_algstr_0(C) &  (v30_algstr_0(C) &  (v31_algstr_0(C) &  (v32_algstr_0(C) &  (v33_algstr_0(C) &  (v34_algstr_0(C) &  (v35_algstr_0(C) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v9_rlvect_1(C) &  (v1_vectsp_1(C) &  (v2_vectsp_1(C) &  (v3_vectsp_1(C) &  (v4_vectsp_1(C) &  (v5_vectsp_1(C) &  (v6_vectsp_1(C) &  (v1_group_1(C) &  (v3_group_1(C) &  (v5_group_1(C) &  (v1_vectsp_2(C) &  (v3_gcd_1(C) &  (v8_ideal_1(C) &  (v1_int_3(C) &  (v3_ring_2(C, A) &  (v3_ring_2(C, B) &  (v3_ring_2(C, k1_int_3) &  (v8_ring_2(C) &  (v1_ring_3(C, A) & v1_ring_3(C, B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc5_field_16, axiom,  (! [A] :  (v7_ordinal1(A) =>  (? [B] :  (v1_ordinal1(B) &  (v2_ordinal1(B) &  (v3_ordinal1(B) &  (v7_ordinal1(B) &  (v1_xreal_0(B) &  (v1_finset_1(B) &  (v1_card_1(B) &  (v1_xcmplx_0(B) &  (v1_int_1(B) &  (v2_int_1(B) &  (v1_xxreal_0(B) &  ( ~ (v3_xxreal_0(B))  &  (v1_gaussint(B) &  (v2_gaussint(B) & v2_field_16(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc5_field_7, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  (v13_algstr_0(B) &  (v33_algstr_0(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v1_field_4(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [C] :  (l6_algstr_0(C) &  ( ~ (v2_struct_0(C))  &  ( ~ (v6_struct_0(C))  &  ( ~ (v7_struct_0(C))  &  (v5_algstr_0(C) &  (v6_algstr_0(C) &  (v7_algstr_0(C) &  (v12_algstr_0(C) &  (v13_algstr_0(C) &  (v14_algstr_0(C) &  (v30_algstr_0(C) &  (v31_algstr_0(C) &  (v32_algstr_0(C) &  (v33_algstr_0(C) &  (v34_algstr_0(C) &  (v35_algstr_0(C) &  (v1_vectsp_1(C) &  (v2_vectsp_1(C) &  (v3_vectsp_1(C) &  (v4_vectsp_1(C) &  (v5_vectsp_1(C) &  (v6_vectsp_1(C) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v9_rlvect_1(C) &  (v1_group_1(C) &  (v3_group_1(C) &  (v5_group_1(C) &  (v1_vectsp_2(C) &  (v1_algstr_1(C) &  (v2_algstr_1(C) &  (v3_algstr_1(C) &  (v4_algstr_1(C) &  (v8_ideal_1(C) &  (v3_ring_2(C, k12_polynom3(B)) &  (v8_ring_2(C) &  (v1_field_4(C, A) & v1_field_4(C, B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_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_ring_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l6_algstr_0(A))  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v1_vectsp_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l6_algstr_0(B)) ) ) ) ) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) &  (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(A)) &  (v5_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  &  (v1_partfun1(C, u1_struct_0(A)) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) &  (v13_vectsp_1(C, A, B) & v1_group_6(C, A, B)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc5_ring_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_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) &  (v1_vectsp_2(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) & v3_ring_2(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc5_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc5_vectsp_1, axiom,  (? [A] :  (l6_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v36_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v3_vectsp_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & v6_vectsp_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc5_xcmplx_0, axiom,  (? [A] :  ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A)) ) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc5_xxreal_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ).
fof(rc6_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_finset_1(B)) ) ) ) ) ).
fof(rc6_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_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_ring_2, axiom,  (! [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) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) & v3_ring_2(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc6_ring_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_vectsp_2(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) & v3_ring_2(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc7_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_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc7_ring_2, axiom,  (! [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) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) & v3_ring_2(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc7_ring_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_group_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) & v1_ring_3(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc7_ring_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  =>  (? [B] :  (m1_subset_1(B, u1_struct_0(k12_polynom3(A))) &  ( ~ (v9_struct_0(B, k12_polynom3(A)))  &  (v2_algstr_0(B, k12_polynom3(A)) &  (v3_algstr_0(B, k12_polynom3(A)) &  (v4_algstr_0(B, k12_polynom3(A)) &  (v9_algstr_0(B, k12_polynom3(A)) &  (v10_algstr_0(B, k12_polynom3(A)) & v11_algstr_0(B, k12_polynom3(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_field_12, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  ( ~ (v8_struct_0(B))  &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v30_algstr_0(B) &  (v31_algstr_0(B) &  (v32_algstr_0(B) &  (v33_algstr_0(B) &  (v34_algstr_0(B) &  (v35_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v1_vectsp_2(B) &  (v3_gcd_1(B) &  (v2_polynom5(B) &  (v8_ideal_1(B) &  (v1_int_3(B) &  (v3_ring_2(B, A) &  (v3_ring_2(B, k1_int_3) &  (v8_ring_2(B) & v1_ring_3(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc8_field_9, 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) &  (v12_algstr_0(A) &  (v13_algstr_0(A) &  (v14_algstr_0(A) &  (v30_algstr_0(A) &  (v31_algstr_0(A) &  (v32_algstr_0(A) &  (v33_algstr_0(A) &  (v34_algstr_0(A) &  (v35_algstr_0(A) &  (v36_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) &  (v9_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) &  (v8_ideal_1(A) &  (v3_ring_2(A, k1_int_3) &  (v8_ring_2(A) &  (v3_field_3(A) &  ~ (v3_field_9(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_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc8_ring_2, axiom,  (! [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) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) & v3_ring_2(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc8_ring_3, axiom,  (! [A] :  ( ( ~ (v2_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) & v1_ring_3(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc8_ring_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  =>  (? [B] :  (m1_subset_1(B, u1_struct_0(k12_polynom3(A))) &  ( ~ (v9_struct_0(B, k12_polynom3(A)))  &  (v2_algstr_0(B, k12_polynom3(A)) &  (v3_algstr_0(B, k12_polynom3(A)) &  (v4_algstr_0(B, k12_polynom3(A)) &  (v9_algstr_0(B, k12_polynom3(A)) &  (v10_algstr_0(B, k12_polynom3(A)) &  (v11_algstr_0(B, k12_polynom3(A)) & v3_ring_4(B, 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_field_9, 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) &  (v12_algstr_0(A) &  (v13_algstr_0(A) &  (v14_algstr_0(A) &  (v30_algstr_0(A) &  (v31_algstr_0(A) &  (v32_algstr_0(A) &  (v33_algstr_0(A) &  (v34_algstr_0(A) &  (v35_algstr_0(A) &  (v36_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) &  (v9_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) &  (v8_ideal_1(A) &  (v3_ring_2(A, k1_int_3) &  (v8_ring_2(A) & v3_field_9(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(rc9_ring_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  ( ~ (v7_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v30_algstr_0(B) &  (v31_algstr_0(B) &  (v32_algstr_0(B) &  (v33_algstr_0(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) &  (v1_vectsp_2(B) &  (v3_gcd_1(B) &  (v1_int_3(B) & v3_ring_2(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc9_ring_3, axiom,  (! [A] :  ( ( ~ (v2_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) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  =>  (? [B] :  (l6_algstr_0(B) &  ( ~ (v2_struct_0(B))  &  (v5_algstr_0(B) &  (v6_algstr_0(B) &  (v7_algstr_0(B) &  (v12_algstr_0(B) &  (v13_algstr_0(B) &  (v14_algstr_0(B) &  (v1_group_1(B) &  (v3_group_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v9_rlvect_1(B) &  (v1_vectsp_1(B) &  (v2_vectsp_1(B) &  (v3_vectsp_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v6_vectsp_1(B) &  (v1_algstr_1(B) &  (v2_algstr_1(B) &  (v3_algstr_1(B) &  (v4_algstr_1(B) & v1_ring_3(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rd1_card_1, axiom,  (! [A] :  (v1_card_1(A) => k1_card_1(A)=A) ) ).
fof(rd1_field_16, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  &  (v1_funct_1(B) &  (v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) ) )  => k2_field_16(A, B, 1)=B) ) ).
fof(rd1_nat_6, axiom,  (! [A] :  (v7_ordinal1(A) => k1_newton(1, A)=1) ) ).
fof(rd1_newton, axiom,  (! [A] :  (v1_xcmplx_0(A) => k1_newton(A, 1)=A) ) ).
fof(rd2_newton, axiom,  (! [A] :  (v7_ordinal1(A) => k1_newton(1, A)=1) ) ).
fof(redefinition_k1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_subset_1(B, k4_ordinal1))  => k1_nat_1(A, B)=k2_xcmplx_0(A, B)) ) ).
fof(redefinition_k2_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => k2_finseq_1(A)=k1_finseq_1(A)) ) ).
fof(redefinition_k4_card_1, axiom,  (! [A] :  (v1_finset_1(A) => k4_card_1(A)=k1_card_1(A)) ) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) ) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(reflexivity_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => r1_xxreal_0(A, A)) ) ).
fof(rqLessOrEqual__r1_xxreal_0__r0_r0, axiom, r1_xxreal_0(0, 0)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r1, axiom, r1_xxreal_0(0, 1)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r2, axiom, r1_xxreal_0(0, 2)).
fof(rqLessOrEqual__r1_xxreal_0__r0_rm1, axiom,  ~ (r1_xxreal_0(0, k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__r0_rm2, axiom,  ~ (r1_xxreal_0(0, k4_xcmplx_0(2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r0_rn1d2, axiom, r1_xxreal_0(0, k7_xcmplx_0(1, 2))).
fof(rqLessOrEqual__r1_xxreal_0__r0_rnm1d2, axiom,  ~ (r1_xxreal_0(0, k7_xcmplx_0(k4_xcmplx_0(1), 2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_r0, axiom,  ~ (r1_xxreal_0(1, 0)) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_r1, axiom, r1_xxreal_0(1, 1)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r2, axiom, r1_xxreal_0(1, 2)).
fof(rqLessOrEqual__r1_xxreal_0__r1_rm1, axiom,  ~ (r1_xxreal_0(1, k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_rm2, axiom,  ~ (r1_xxreal_0(1, k4_xcmplx_0(2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_rn1d2, axiom,  ~ (r1_xxreal_0(1, k7_xcmplx_0(1, 2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_rnm1d2, axiom,  ~ (r1_xxreal_0(1, k7_xcmplx_0(k4_xcmplx_0(1), 2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_r0, axiom,  ~ (r1_xxreal_0(2, 0)) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_r1, axiom,  ~ (r1_xxreal_0(2, 1)) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_r2, axiom, r1_xxreal_0(2, 2)).
fof(rqLessOrEqual__r1_xxreal_0__r2_rm1, axiom,  ~ (r1_xxreal_0(2, k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_rm2, axiom,  ~ (r1_xxreal_0(2, k4_xcmplx_0(2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_rn1d2, axiom,  ~ (r1_xxreal_0(2, k7_xcmplx_0(1, 2))) ).
fof(rqLessOrEqual__r1_xxreal_0__r2_rnm1d2, axiom,  ~ (r1_xxreal_0(2, k7_xcmplx_0(k4_xcmplx_0(1), 2))) ).
fof(rqLessOrEqual__r1_xxreal_0__rm1_r0, axiom, r1_xxreal_0(k4_xcmplx_0(1), 0)).
fof(rqLessOrEqual__r1_xxreal_0__rm1_r1, axiom, r1_xxreal_0(k4_xcmplx_0(1), 1)).
fof(rqLessOrEqual__r1_xxreal_0__rm1_r2, axiom, r1_xxreal_0(k4_xcmplx_0(1), 2)).
fof(rqLessOrEqual__r1_xxreal_0__rm1_rm1, axiom, r1_xxreal_0(k4_xcmplx_0(1), k4_xcmplx_0(1))).
fof(rqLessOrEqual__r1_xxreal_0__rm1_rm2, axiom,  ~ (r1_xxreal_0(k4_xcmplx_0(1), k4_xcmplx_0(2))) ).
fof(rqLessOrEqual__r1_xxreal_0__rm1_rn1d2, axiom, r1_xxreal_0(k4_xcmplx_0(1), k7_xcmplx_0(1, 2))).
fof(rqLessOrEqual__r1_xxreal_0__rm1_rnm1d2, axiom, r1_xxreal_0(k4_xcmplx_0(1), k7_xcmplx_0(k4_xcmplx_0(1), 2))).
fof(rqLessOrEqual__r1_xxreal_0__rm2_r0, axiom, r1_xxreal_0(k4_xcmplx_0(2), 0)).
fof(rqLessOrEqual__r1_xxreal_0__rm2_r1, axiom, r1_xxreal_0(k4_xcmplx_0(2), 1)).
fof(rqLessOrEqual__r1_xxreal_0__rm2_r2, axiom, r1_xxreal_0(k4_xcmplx_0(2), 2)).
fof(rqLessOrEqual__r1_xxreal_0__rm2_rm1, axiom, r1_xxreal_0(k4_xcmplx_0(2), k4_xcmplx_0(1))).
fof(rqLessOrEqual__r1_xxreal_0__rm2_rm2, axiom, r1_xxreal_0(k4_xcmplx_0(2), k4_xcmplx_0(2))).
fof(rqLessOrEqual__r1_xxreal_0__rm2_rn1d2, axiom, r1_xxreal_0(k4_xcmplx_0(2), k7_xcmplx_0(1, 2))).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_r0, axiom,  ~ (r1_xxreal_0(k7_xcmplx_0(1, 2), 0)) ).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_r1, axiom, r1_xxreal_0(k7_xcmplx_0(1, 2), 1)).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_r2, axiom, r1_xxreal_0(k7_xcmplx_0(1, 2), 2)).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_rm1, axiom,  ~ (r1_xxreal_0(k7_xcmplx_0(1, 2), k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_rm2, axiom,  ~ (r1_xxreal_0(k7_xcmplx_0(1, 2), k4_xcmplx_0(2))) ).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_rn1d2, axiom, r1_xxreal_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(1, 2))).
fof(rqLessOrEqual__r1_xxreal_0__rn1d2_rnm1d2, axiom,  ~ (r1_xxreal_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))) ).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_r0, axiom, r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 0)).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_r1, axiom, r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 1)).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_r2, axiom, r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 2)).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_rm1, axiom,  ~ (r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k4_xcmplx_0(1))) ).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_rn1d2, axiom, r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(1, 2))).
fof(rqLessOrEqual__r1_xxreal_0__rnm1d2_rnm1d2, axiom, r1_xxreal_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))).
fof(rqRealAdd__k2_xcmplx_0__r0_r0_r0, axiom, k2_xcmplx_0(0, 0)=0).
fof(rqRealAdd__k2_xcmplx_0__r0_r1_r1, axiom, k2_xcmplx_0(0, 1)=1).
fof(rqRealAdd__k2_xcmplx_0__r0_r2_r2, axiom, k2_xcmplx_0(0, 2)=2).
fof(rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, axiom, k2_xcmplx_0(0, k4_xcmplx_0(1))=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, axiom, k2_xcmplx_0(0, k4_xcmplx_0(2))=k4_xcmplx_0(2)).
fof(rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, axiom, k2_xcmplx_0(0, k7_xcmplx_0(1, 2))=k7_xcmplx_0(1, 2)).
fof(rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, axiom, k2_xcmplx_0(0, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealAdd__k2_xcmplx_0__r1_r0_r1, axiom, k2_xcmplx_0(1, 0)=1).
fof(rqRealAdd__k2_xcmplx_0__r1_r1_r2, axiom, k2_xcmplx_0(1, 1)=2).
fof(rqRealAdd__k2_xcmplx_0__r1_rm1_r0, axiom, k2_xcmplx_0(1, k4_xcmplx_0(1))=0).
fof(rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, axiom, k2_xcmplx_0(1, k4_xcmplx_0(2))=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, axiom, k2_xcmplx_0(1, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(1, 2)).
fof(rqRealAdd__k2_xcmplx_0__r2_r0_r2, axiom, k2_xcmplx_0(2, 0)=2).
fof(rqRealAdd__k2_xcmplx_0__r2_rm1_r1, axiom, k2_xcmplx_0(2, k4_xcmplx_0(1))=1).
fof(rqRealAdd__k2_xcmplx_0__r2_rm2_r0, axiom, k2_xcmplx_0(2, k4_xcmplx_0(2))=0).
fof(rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, axiom, k2_xcmplx_0(k4_xcmplx_0(1), 0)=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__rm1_r1_r0, axiom, k2_xcmplx_0(k4_xcmplx_0(1), 1)=0).
fof(rqRealAdd__k2_xcmplx_0__rm1_r2_r1, axiom, k2_xcmplx_0(k4_xcmplx_0(1), 2)=1).
fof(rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, axiom, k2_xcmplx_0(k4_xcmplx_0(1), k4_xcmplx_0(1))=k4_xcmplx_0(2)).
fof(rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, axiom, k2_xcmplx_0(k4_xcmplx_0(1), k7_xcmplx_0(1, 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealAdd__k2_xcmplx_0__rm2_r0_rm2, axiom, k2_xcmplx_0(k4_xcmplx_0(2), 0)=k4_xcmplx_0(2)).
fof(rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, axiom, k2_xcmplx_0(k4_xcmplx_0(2), 1)=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__rm2_r2_r0, axiom, k2_xcmplx_0(k4_xcmplx_0(2), 2)=0).
fof(rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, axiom, k2_xcmplx_0(k7_xcmplx_0(1, 2), 0)=k7_xcmplx_0(1, 2)).
fof(rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, axiom, k2_xcmplx_0(k7_xcmplx_0(1, 2), k4_xcmplx_0(1))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, axiom, k2_xcmplx_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(1, 2))=1).
fof(rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, axiom, k2_xcmplx_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))=0).
fof(rqRealAdd__k2_xcmplx_0__rnm1d2_r0_rnm1d2, axiom, k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 0)=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, axiom, k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 1)=k7_xcmplx_0(1, 2)).
fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, axiom, k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(1, 2))=0).
fof(rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, axiom, k2_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__r0_r0_r0, axiom, k6_xcmplx_0(0, 0)=0).
fof(rqRealDiff__k6_xcmplx_0__r0_r1_rm1, axiom, k6_xcmplx_0(0, 1)=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__r0_r2_rm2, axiom, k6_xcmplx_0(0, 2)=k4_xcmplx_0(2)).
fof(rqRealDiff__k6_xcmplx_0__r0_rm1_r1, axiom, k6_xcmplx_0(0, k4_xcmplx_0(1))=1).
fof(rqRealDiff__k6_xcmplx_0__r0_rm2_r2, axiom, k6_xcmplx_0(0, k4_xcmplx_0(2))=2).
fof(rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, axiom, k6_xcmplx_0(0, k7_xcmplx_0(1, 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, axiom, k6_xcmplx_0(0, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(1, 2)).
fof(rqRealDiff__k6_xcmplx_0__r1_r0_r1, axiom, k6_xcmplx_0(1, 0)=1).
fof(rqRealDiff__k6_xcmplx_0__r1_r1_r0, axiom, k6_xcmplx_0(1, 1)=0).
fof(rqRealDiff__k6_xcmplx_0__r1_r2_rm1, axiom, k6_xcmplx_0(1, 2)=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__r1_rm1_r2, axiom, k6_xcmplx_0(1, k4_xcmplx_0(1))=2).
fof(rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, axiom, k6_xcmplx_0(1, k7_xcmplx_0(1, 2))=k7_xcmplx_0(1, 2)).
fof(rqRealDiff__k6_xcmplx_0__r2_r0_r2, axiom, k6_xcmplx_0(2, 0)=2).
fof(rqRealDiff__k6_xcmplx_0__r2_r1_r1, axiom, k6_xcmplx_0(2, 1)=1).
fof(rqRealDiff__k6_xcmplx_0__r2_r2_r0, axiom, k6_xcmplx_0(2, 2)=0).
fof(rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, axiom, k6_xcmplx_0(k4_xcmplx_0(1), 0)=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, axiom, k6_xcmplx_0(k4_xcmplx_0(1), 1)=k4_xcmplx_0(2)).
fof(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, axiom, k6_xcmplx_0(k4_xcmplx_0(1), k4_xcmplx_0(1))=0).
fof(rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, axiom, k6_xcmplx_0(k4_xcmplx_0(1), k4_xcmplx_0(2))=1).
fof(rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, axiom, k6_xcmplx_0(k4_xcmplx_0(1), k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, axiom, k6_xcmplx_0(k4_xcmplx_0(2), 0)=k4_xcmplx_0(2)).
fof(rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, axiom, k6_xcmplx_0(k4_xcmplx_0(2), k4_xcmplx_0(1))=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, axiom, k6_xcmplx_0(k4_xcmplx_0(2), k4_xcmplx_0(2))=0).
fof(rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, axiom, k6_xcmplx_0(k7_xcmplx_0(1, 2), 0)=k7_xcmplx_0(1, 2)).
fof(rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, axiom, k6_xcmplx_0(k7_xcmplx_0(1, 2), 1)=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, axiom, k6_xcmplx_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(1, 2))=0).
fof(rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, axiom, k6_xcmplx_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))=1).
fof(rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, axiom, k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 0)=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, axiom, k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k4_xcmplx_0(1))=k7_xcmplx_0(1, 2)).
fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, axiom, k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(1, 2))=k4_xcmplx_0(1)).
fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, axiom, k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k7_xcmplx_0(k4_xcmplx_0(1), 2))=0).
fof(rqRealDiv__k7_xcmplx_0__r1_r1_r1, axiom, k7_xcmplx_0(1, 1)=1).
fof(rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, axiom, k7_xcmplx_0(1, 2)=k7_xcmplx_0(1, 2)).
fof(rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, axiom, k7_xcmplx_0(1, k4_xcmplx_0(1))=k4_xcmplx_0(1)).
fof(rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, axiom, k7_xcmplx_0(1, k4_xcmplx_0(2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, axiom, k7_xcmplx_0(1, k7_xcmplx_0(1, 2))=2).
fof(rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, axiom, k7_xcmplx_0(1, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k4_xcmplx_0(2)).
fof(rqRealDiv__k7_xcmplx_0__r2_r1_r2, axiom, k7_xcmplx_0(2, 1)=2).
fof(rqRealDiv__k7_xcmplx_0__r2_r2_r1, axiom, k7_xcmplx_0(2, 2)=1).
fof(rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, axiom, k7_xcmplx_0(k4_xcmplx_0(1), 1)=k4_xcmplx_0(1)).
fof(rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, axiom, k7_xcmplx_0(k4_xcmplx_0(1), 2)=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, axiom, k7_xcmplx_0(k4_xcmplx_0(2), 2)=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__r0_r0_r0, axiom, k3_xcmplx_0(0, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r0_r1_r0, axiom, k3_xcmplx_0(0, 1)=0).
fof(rqRealMult__k3_xcmplx_0__r0_r2_r0, axiom, k3_xcmplx_0(0, 2)=0).
fof(rqRealMult__k3_xcmplx_0__r0_rm2_r0, axiom, k3_xcmplx_0(0, k4_xcmplx_0(2))=0).
fof(rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, axiom, k3_xcmplx_0(0, k7_xcmplx_0(1, 2))=0).
fof(rqRealMult__k3_xcmplx_0__r1_r0_r0, axiom, k3_xcmplx_0(1, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r1_r1_r1, axiom, k3_xcmplx_0(1, 1)=1).
fof(rqRealMult__k3_xcmplx_0__r1_r2_r2, axiom, k3_xcmplx_0(1, 2)=2).
fof(rqRealMult__k3_xcmplx_0__r1_rm2_rm2, axiom, k3_xcmplx_0(1, k4_xcmplx_0(2))=k4_xcmplx_0(2)).
fof(rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2, axiom, k3_xcmplx_0(1, k7_xcmplx_0(1, 2))=k7_xcmplx_0(1, 2)).
fof(rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, axiom, k3_xcmplx_0(1, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealMult__k3_xcmplx_0__r2_r0_r0, axiom, k3_xcmplx_0(2, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r2_r1_r2, axiom, k3_xcmplx_0(2, 1)=2).
fof(rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, axiom, k3_xcmplx_0(2, k7_xcmplx_0(1, 2))=1).
fof(rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, axiom, k3_xcmplx_0(2, k7_xcmplx_0(k4_xcmplx_0(1), 2))=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__rm2_r0_r0, axiom, k3_xcmplx_0(k4_xcmplx_0(2), 0)=0).
fof(rqRealMult__k3_xcmplx_0__rm2_r1_rm2, axiom, k3_xcmplx_0(k4_xcmplx_0(2), 1)=k4_xcmplx_0(2)).
fof(rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, axiom, k3_xcmplx_0(k4_xcmplx_0(2), k7_xcmplx_0(1, 2))=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, axiom, k3_xcmplx_0(k4_xcmplx_0(2), k7_xcmplx_0(k4_xcmplx_0(1), 2))=1).
fof(rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 2), 0)=0).
fof(rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 2), 1)=k7_xcmplx_0(1, 2)).
fof(rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 2), 2)=1).
fof(rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 2), k4_xcmplx_0(2))=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 1)=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), 2)=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, axiom, k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2), k4_xcmplx_0(2))=1).
fof(rqRealNeg__k4_xcmplx_0__r0_r0, axiom, k4_xcmplx_0(0)=0).
fof(rqRealNeg__k4_xcmplx_0__r1_rm1, axiom, k4_xcmplx_0(1)=k4_xcmplx_0(1)).
fof(rqRealNeg__k4_xcmplx_0__r2_rm2, axiom, k4_xcmplx_0(2)=k4_xcmplx_0(2)).
fof(rqRealNeg__k4_xcmplx_0__rm1_r1, axiom, k4_xcmplx_0(k4_xcmplx_0(1))=1).
fof(rqRealNeg__k4_xcmplx_0__rm2_r2, axiom, k4_xcmplx_0(k4_xcmplx_0(2))=2).
fof(rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, axiom, k4_xcmplx_0(k7_xcmplx_0(1, 2))=k7_xcmplx_0(k4_xcmplx_0(1), 2)).
fof(rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, axiom, k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1), 2))=k7_xcmplx_0(1, 2)).
fof(s2_funct_1__e4_129__field_16, axiom,  (! [A, B] :  ( ( (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) )  &  ( ~ (v2_struct_0(B))  &  ( ~ (v6_struct_0(B))  &  (v13_algstr_0(B) &  (v33_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v3_group_1(B) &  (v5_group_1(B) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) ) ) )  =>  ( ( (! [C] :  (! [D] :  (! [E] :  ( (r2_hidden(C, k2_finseq_1(A)) &  ( (? [F] :  (m2_subset_1(F, k4_ordinal1, k2_finseq_1(A)) &  (? [G] :  (m1_subset_1(G, k4_ordinal1) &  (C=F &  (G=k6_xcmplx_0(F, 1) & D=k2_field_16(B, k5_field_16(B), G)) ) ) ) ) )  &  (? [H] :  (m2_subset_1(H, k4_ordinal1, k2_finseq_1(A)) &  (? [I] :  (m1_subset_1(I, k4_ordinal1) &  (C=H &  (I=k6_xcmplx_0(H, 1) & E=k2_field_16(B, k5_field_16(B), I)) ) ) ) ) ) ) )  => D=E) ) ) )  &  (! [C] :  ~ ( (r2_hidden(C, k2_finseq_1(A)) &  (! [D] :  ~ ( (? [J] :  (m2_subset_1(J, k4_ordinal1, k2_finseq_1(A)) &  (? [K] :  (m1_subset_1(K, k4_ordinal1) &  (C=J &  (K=k6_xcmplx_0(J, 1) & D=k2_field_16(B, k5_field_16(B), K)) ) ) ) ) ) ) ) ) ) ) )  =>  (? [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  &  (k9_xtuple_0(C)=k2_finseq_1(A) &  (! [D] :  (r2_hidden(D, k2_finseq_1(A)) =>  (? [L] :  (m2_subset_1(L, k4_ordinal1, k2_finseq_1(A)) &  (? [M] :  (m1_subset_1(M, k4_ordinal1) &  (D=L &  (M=k6_xcmplx_0(L, 1) & k1_funct_1(C, D)=k2_field_16(B, k5_field_16(B), M)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(spc0_boole, axiom, v1_xboole_0(0)).
fof(spc0_numerals, axiom, m1_subset_1(0, k4_ordinal1)).
fof(spc10_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k3_xcmplx_0(k5_xcmplx_0(A), k5_xcmplx_0(B))=k5_xcmplx_0(k3_xcmplx_0(A, B))) ) ).
fof(spc11_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k7_xcmplx_0(k5_xcmplx_0(A), k5_xcmplx_0(B))=k7_xcmplx_0(B, A)) ) ).
fof(spc12_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k3_xcmplx_0(A, k5_xcmplx_0(B))=k7_xcmplx_0(A, B)) ) ).
fof(spc1_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(A, k4_xcmplx_0(B))=k6_xcmplx_0(A, B)) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(spc2_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(A, k4_xcmplx_0(1))=k4_xcmplx_0(A)) ) ).
fof(spc2_boole, axiom,  ~ (v1_xboole_0(2)) ).
fof(spc2_numerals, axiom,  (v2_xxreal_0(2) & m1_subset_1(2, k4_ordinal1)) ).
fof(spc3_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k7_xcmplx_0(1, A)=k5_xcmplx_0(A)) ) ).
fof(spc4_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k3_xcmplx_0(A, k7_xcmplx_0(B, C))=k7_xcmplx_0(k3_xcmplx_0(A, B), C)) ) ).
fof(spc5_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k3_xcmplx_0(k2_xcmplx_0(A, B), C)=k2_xcmplx_0(k3_xcmplx_0(A, C), k3_xcmplx_0(B, C))) ) ).
fof(spc6_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k2_xcmplx_0(k2_xcmplx_0(A, B), C)=k2_xcmplx_0(A, k2_xcmplx_0(B, C))) ) ).
fof(spc7_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k3_xcmplx_0(k3_xcmplx_0(A, B), C)=k3_xcmplx_0(A, k3_xcmplx_0(B, C))) ) ).
fof(spc8_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(k4_xcmplx_0(A), k4_xcmplx_0(B))=k4_xcmplx_0(k2_xcmplx_0(A, B))) ) ).
fof(spc9_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k6_xcmplx_0(k4_xcmplx_0(A), k4_xcmplx_0(B))=k6_xcmplx_0(B, A)) ) ).
fof(t1_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k2_xcmplx_0(A, k5_numbers)=A) ) ).
fof(t1_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  (v7_ordinal1(B) =>  (r2_hidden(A, k1_finseq_1(B)) <=>  (r1_xxreal_0(1, A) & r1_xxreal_0(A, B)) ) ) ) ) ) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v2_xxreal_0(A))  => v2_xxreal_0(B)) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(A, k5_numbers)=k5_numbers) ) ).
fof(t2_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v3_xxreal_0(B))  => v3_xxreal_0(A)) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t2_tarski, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_hidden(C, A) <=> r2_hidden(C, B)) )  => A=B) ) ) ).
fof(t3_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(1, A)=A) ) ).
fof(t3_int_1, axiom,  (! [A] :  (v1_int_1(A) =>  (r1_xxreal_0(k5_numbers, A) => r2_hidden(A, k4_ordinal1)) ) ) ).
fof(t3_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v3_xxreal_0(A))  & v3_xxreal_0(B)) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k6_xcmplx_0(A, k5_numbers)=A) ) ).
fof(t4_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v2_xxreal_0(B))  & v2_xxreal_0(A)) ) ) ) ) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t57_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => k4_card_1(k2_finseq_1(A))=A) ) ).
fof(t5_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k7_xcmplx_0(k5_numbers, A)=k5_numbers) ) ).
fof(t5_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(B) |  (v3_xxreal_0(A) | v2_xxreal_0(B)) ) ) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t63_field_16, axiom,  (! [A] :  ( (v7_ordinal1(A) & v1_int_2(A))  =>  (! [B] :  ( (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  &  ( ~ (v6_struct_0(C))  &  (v13_algstr_0(C) &  (v33_algstr_0(C) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v4_vectsp_1(C) &  (v5_vectsp_1(C) &  (v3_group_1(C) &  (v5_group_1(C) & l6_algstr_0(C)) ) ) ) ) ) ) ) ) ) )  =>  (k7_struct_0(C)=k1_newton(A, B) =>  (! [D] :  (v7_ordinal1(D) =>  (! [E] :  (v7_ordinal1(E) =>  ~ ( (r1_xxreal_0(k5_numbers, D) &  (r1_xxreal_0(D, k6_xcmplx_0(B, 1)) &  (r1_xxreal_0(k5_numbers, E) &  (r1_xxreal_0(E, k6_xcmplx_0(B, 1)) &  ( ~ (D=E)  & k2_field_16(C, k5_field_16(C), D)=k2_field_16(C, k5_field_16(C), E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t6_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k7_xcmplx_0(A, 1)=A) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t6_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(A) |  (v2_xxreal_0(B) | v3_xxreal_0(A)) ) ) ) ) ) ) ).
fof(t6_xreal_1, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (! [C] :  (v1_xreal_0(C) =>  (r1_xxreal_0(A, B) <=> r1_xxreal_0(k2_xcmplx_0(A, C), k2_xcmplx_0(B, C))) ) ) ) ) ) ) ).
fof(t70_card_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v2_funct_1(A) => k1_card_1(k9_xtuple_0(A))=k1_card_1(k10_xtuple_0(A))) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(B)) ) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v3_xxreal_0(B))  &  ~ (v2_xxreal_0(A)) ) ) ) ) ) ) ) ).
fof(t9_xreal_1, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (! [C] :  (v1_xreal_0(C) =>  (r1_xxreal_0(A, B) <=> r1_xxreal_0(k6_xcmplx_0(A, C), k6_xcmplx_0(B, C))) ) ) ) ) ) ) ).
