% Mizar problem: l19_field_2,field_2,495,8 
fof(l19_field_2, conjecture,  (! [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) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v1_ring_3(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (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) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) ) )  =>  (r1_tsep_1(A, B) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k7_field_2(A, B, C))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(k7_field_2(A, B, C))) =>  (r2_tarski(D, k2_struct_0(A)) =>  (r2_tarski(E, k2_struct_0(A)) |  (! [F] :  (m1_subset_1(F, k2_field_2(A, B, C)) =>  (! [G] :  (m1_subset_1(G, k2_field_2(A, B, C)) =>  ( (F=D & G=E)  =>  (k1_algstr_0(k7_field_2(A, B, C), D, E)=k1_binop_1(u1_algstr_0(B), k1_funct_1(C, F), G) &  (k1_algstr_0(k7_field_2(A, B, C), E, D)=k1_binop_1(u1_algstr_0(B), G, k1_funct_1(C, F)) &  ( ~ (r2_tarski(k1_algstr_0(k7_field_2(A, B, C), D, E), k2_struct_0(A)))  &  ~ (r2_tarski(k1_algstr_0(k7_field_2(A, B, C), E, D), k2_struct_0(A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(abstractness_v36_algstr_0, axiom,  (! [A] :  (l6_algstr_0(A) =>  (v36_algstr_0(A) => A=g6_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_algstr_0(A), u3_struct_0(A), u2_struct_0(A))) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(cc10_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (v14_algstr_0(A) =>  (v12_algstr_0(A) & v13_algstr_0(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_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(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(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(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(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
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_quofield, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) & v5_vectsp_1(A)) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v5_group_1(A) &  (v3_vectsp_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & v1_vectsp_2(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_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_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_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(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_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_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_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_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(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_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_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_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_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(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_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_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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc4_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & v6_vectsp_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v1_group_1(A)) ) ) ) ).
fof(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_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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc5_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_vectsp_1(A))  =>  ( ~ (v2_struct_0(A))  & v1_group_1(A)) ) ) ) ).
fof(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_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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc6_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v5_group_1(A) & v6_vectsp_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v3_vectsp_1(A)) ) ) ) ).
fof(cc7_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_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_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_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc8_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v5_relat_1(B, A)) ) ) ) ) ) ).
fof(cc8_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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc9_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( (v12_algstr_0(A) & v13_algstr_0(A))  => v14_algstr_0(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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_0(B, A)) ).
fof(commutativity_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, C)=k9_subset_1(A, C, B)) ) ).
fof(d1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k1_algstr_0(A, B, C)=k4_binop_1(u1_struct_0(A), u1_algstr_0(A), B, C)) ) ) ) ) ) ).
fof(d1_binop_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (! [C] : k1_binop_1(A, B, C)=k1_funct_1(A, k4_tarski(B, C))) ) ) ) ).
fof(d1_field_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) & l6_algstr_0(B)) ) ) ) ) ) ) )  =>  (r1_tsep_1(A, B) <=> k9_subset_1(u1_struct_0(B), k2_struct_0(A), k2_struct_0(B))=k1_xboole_0) ) ) ) ) ).
fof(d2_field_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v1_ring_3(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (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) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) ) )  => k2_field_2(A, B, C)=k2_xboole_0(k7_subset_1(u1_struct_0(B), k2_struct_0(B), k2_relset_1(u1_struct_0(B), C)), k2_struct_0(A))) ) ) ) ) ) ).
fof(d3_field_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v1_ring_3(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (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) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) ) )  =>  (! [D] :  (m1_subset_1(D, k2_field_2(A, B, C)) =>  (! [E] :  (m1_subset_1(E, k2_field_2(A, B, C)) =>  ( ( (r2_tarski(D, k2_struct_0(A)) & r2_tarski(E, k2_struct_0(A)))  => k3_field_2(A, B, C, D, E)=k1_binop_1(u1_algstr_0(A), D, E))  &  ( (r2_tarski(D, k2_struct_0(A)) =>  (r2_tarski(E, k2_struct_0(A)) | k3_field_2(A, B, C, D, E)=k1_binop_1(u1_algstr_0(B), k1_funct_1(C, D), E)) )  &  ( (r2_tarski(E, k2_struct_0(A)) =>  (r2_tarski(D, k2_struct_0(A)) | k3_field_2(A, B, C, D, E)=k1_binop_1(u1_algstr_0(B), D, k1_funct_1(C, E))) )  &  ( (r2_tarski(k1_binop_1(u1_algstr_0(B), D, E), k2_relset_1(u1_struct_0(B), C)) =>  (r2_tarski(D, k2_struct_0(A)) |  (r2_tarski(E, k2_struct_0(A)) | k3_field_2(A, B, C, D, E)=k1_funct_1(k1_field_2(A, B, C), k1_binop_1(u1_algstr_0(B), D, E))) ) )  &  ~ ( ( ~ ( (r2_tarski(D, k2_struct_0(A)) & r2_tarski(E, k2_struct_0(A))) )  &  ( ~ ( (r2_tarski(D, k2_struct_0(A)) &  ~ (r2_tarski(E, k2_struct_0(A))) ) )  &  ( ~ ( (r2_tarski(E, k2_struct_0(A)) &  ~ (r2_tarski(D, k2_struct_0(A))) ) )  &  ( ~ ( ( ~ (r2_tarski(D, k2_struct_0(A)))  &  ( ~ (r2_tarski(E, k2_struct_0(A)))  & r2_tarski(k1_binop_1(u1_algstr_0(B), D, E), k2_relset_1(u1_struct_0(B), C))) ) )  &  ~ (k3_field_2(A, B, C, D, E)=k1_binop_1(u1_algstr_0(B), D, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_struct_0, axiom,  (! [A] :  (l1_struct_0(A) => k2_struct_0(A)=u1_struct_0(A)) ) ).
fof(d4_field_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v1_ring_3(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (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) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) ) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(k2_field_2(A, B, C), k2_field_2(A, B, C)), k2_field_2(A, B, C)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_field_2(A, B, C), k2_field_2(A, B, C)), k2_field_2(A, B, C))))) )  =>  (D=k4_field_2(A, B, C) <=>  (! [E] :  (m1_subset_1(E, k2_field_2(A, B, C)) =>  (! [F] :  (m1_subset_1(F, k2_field_2(A, B, C)) => k4_binop_1(k2_field_2(A, B, C), D, E, F)=k3_field_2(A, B, C, E, F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k3_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) & r2_hidden(D, B)) ) ) ) ) ) ) ).
fof(d6_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => k4_struct_0(A)=u2_struct_0(A)) ) ).
fof(d7_field_2, 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) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v5_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v1_ring_3(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (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) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) ) )  =>  (! [D] :  ( (v36_algstr_0(D) & l6_algstr_0(D))  =>  (D=k7_field_2(A, B, C) <=>  (u1_struct_0(D)=k2_field_2(A, B, C) &  (u1_algstr_0(D)=k4_field_2(A, B, C) &  (u2_algstr_0(D)=k6_field_2(A, B, C) &  (u3_struct_0(D)=k5_struct_0(A) & u2_struct_0(D)=k4_struct_0(A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_struct_0, axiom,  (! [A] :  (l3_struct_0(A) => k5_struct_0(A)=u3_struct_0(A)) ) ).
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_k1_algstr_0, axiom,  (! [A, B, C] :  ( (l1_algstr_0(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k1_algstr_0(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k1_binop_1, axiom, $true).
fof(dt_k1_field_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v1_ring_3(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) )  &  (v1_funct_1(C) &  (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) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) ) ) ) )  =>  (v1_funct_1(k1_field_2(A, B, C)) &  (v1_funct_2(k1_field_2(A, B, C), k2_relset_1(u1_struct_0(B), C), u1_struct_0(A)) & m1_subset_1(k1_field_2(A, B, C), k1_zfmisc_1(k2_zfmisc_1(k2_relset_1(u1_struct_0(B), C), u1_struct_0(A))))) ) ) ) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_int_3, axiom, l6_algstr_0(k1_int_3)).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_field_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v1_ring_3(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) )  &  (v1_funct_1(C) &  (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) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) ) ) ) )  =>  ~ (v1_xboole_0(k2_field_2(A, B, C))) ) ) ).
fof(dt_k2_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_relat_1(k2_funct_1(A)) & v1_funct_1(k2_funct_1(A))) ) ) ).
fof(dt_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => m1_subset_1(k2_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) => m1_subset_1(k2_struct_0(A), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_field_2, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v1_ring_3(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) )  &  ( (v1_funct_1(C) &  (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) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) ) )  &  (m1_subset_1(D, k2_field_2(A, B, C)) & m1_subset_1(E, k2_field_2(A, B, C))) ) ) )  => m1_subset_1(k3_field_2(A, B, C, D, E), k2_field_2(A, B, C))) ) ).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k4_binop_1, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (m1_subset_1(C, A) & m1_subset_1(D, A)) )  => m1_subset_1(k4_binop_1(A, B, C, D), A)) ) ).
fof(dt_k4_field_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v1_ring_3(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) )  &  (v1_funct_1(C) &  (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) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) ) ) ) )  =>  (v1_funct_1(k4_field_2(A, B, C)) &  (v1_funct_2(k4_field_2(A, B, C), k2_zfmisc_1(k2_field_2(A, B, C), k2_field_2(A, B, C)), k2_field_2(A, B, C)) & m1_subset_1(k4_field_2(A, B, C), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_field_2(A, B, C), k2_field_2(A, B, C)), k2_field_2(A, B, C))))) ) ) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => m1_subset_1(k4_struct_0(A), u1_struct_0(A))) ) ).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k4_xboole_0, axiom, $true).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_struct_0, axiom,  (! [A] :  (l3_struct_0(A) => m1_subset_1(k5_struct_0(A), u1_struct_0(A))) ) ).
fof(dt_k6_field_2, axiom,  (! [A, B, C] :  ( ( ( ~ (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) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_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) &  (v3_group_1(B) &  (v5_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v1_ring_3(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) )  &  (v1_funct_1(C) &  (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) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) ) ) ) )  =>  (v1_funct_1(k6_field_2(A, B, C)) &  (v1_funct_2(k6_field_2(A, B, C), k2_zfmisc_1(k2_field_2(A, B, C), k2_field_2(A, B, C)), k2_field_2(A, B, C)) & m1_subset_1(k6_field_2(A, B, C), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_field_2(A, B, C), k2_field_2(A, B, C)), k2_field_2(A, B, C))))) ) ) ) ).
fof(dt_k7_field_2, axiom,  (! [A, B, C] :  ( ( ( ~ (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) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_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) &  (v3_group_1(B) &  (v5_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v1_ring_3(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) )  &  (v1_funct_1(C) &  (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) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) ) ) ) )  =>  (v36_algstr_0(k7_field_2(A, B, C)) & l6_algstr_0(k7_field_2(A, B, C))) ) ) ).
fof(dt_k7_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => m1_subset_1(k7_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => m1_subset_1(k9_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_l1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (l2_struct_0(A) & l1_algstr_0(A)) ) ) ).
fof(dt_l2_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_l3_algstr_0, axiom,  (! [A] :  (l3_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l3_struct_0, axiom,  (! [A] :  (l3_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_l4_algstr_0, axiom,  (! [A] :  (l4_algstr_0(A) =>  (l3_struct_0(A) & l3_algstr_0(A)) ) ) ).
fof(dt_l4_struct_0, axiom,  (! [A] :  (l4_struct_0(A) =>  (l2_struct_0(A) & l3_struct_0(A)) ) ) ).
fof(dt_l5_algstr_0, axiom,  (! [A] :  (l5_algstr_0(A) =>  (l4_algstr_0(A) & l4_struct_0(A)) ) ) ).
fof(dt_l6_algstr_0, axiom,  (! [A] :  (l6_algstr_0(A) =>  (l2_algstr_0(A) & l5_algstr_0(A)) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_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(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_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => v9_struct_0(k4_struct_0(A), A)) ) ).
fof(fc11_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc11_struct_0, axiom,  (! [A] :  ( ( ~ (v6_struct_0(A))  & l4_struct_0(A))  =>  ~ (v9_struct_0(k5_struct_0(A), 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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ~ (v1_subset_1(k2_struct_0(A), u1_struct_0(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(fc16_ring_3, axiom,  ( ~ (v2_struct_0(k11_gaussint))  &  (v36_algstr_0(k11_gaussint) & v3_ring_3(k11_gaussint, k5_numbers)) ) ).
fof(fc17_funct_1, axiom,  (! [A, B, C] :  ( (v4_funct_1(A) &  (v1_relat_1(C) &  (v5_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_1(C, B)) & v1_funct_1(k1_funct_1(C, B))) ) ) ).
fof(fc19_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(fc1_field_2, axiom,  (! [A, B, C] :  ( ( ( ~ (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) &  (v3_group_1(A) &  (v5_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_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) &  (v3_group_1(B) &  (v5_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v1_ring_3(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) ) )  &  (v1_funct_1(C) &  (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) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) ) ) ) )  =>  ( ~ (v6_struct_0(k7_field_2(A, B, C)))  & v36_algstr_0(k7_field_2(A, B, C))) ) ) ).
fof(fc1_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k3_xboole_0(A, B))) ) ).
fof(fc1_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  &  (v1_relat_1(C) & v4_relat_1(C, A)) )  => v4_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(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(fc29_algstr_0, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (m1_subset_1(D, A) & m1_subset_1(E, A)) ) ) )  =>  ( ~ (v2_struct_0(g6_algstr_0(A, B, C, D, E)))  & v36_algstr_0(g6_algstr_0(A, B, C, D, E))) ) ) ).
fof(fc2_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k4_xboole_0(A, B))) ) ).
fof(fc2_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  => v4_relat_1(k3_xboole_0(B, C), A)) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc30_algstr_0, axiom,  (! [A, B, C, D, E] :  ( (v1_zfmisc_1(A) &  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (m1_subset_1(D, A) & m1_subset_1(E, A)) ) ) )  =>  (v7_struct_0(g6_algstr_0(A, B, C, D, E)) & v36_algstr_0(g6_algstr_0(A, B, C, D, E))) ) ) ).
fof(fc31_algstr_0, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_zfmisc_1(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (m1_subset_1(D, A) & m1_subset_1(E, A)) ) ) )  =>  ( ~ (v7_struct_0(g6_algstr_0(A, B, C, D, E)))  & v36_algstr_0(g6_algstr_0(A, B, C, D, E))) ) ) ).
fof(fc3_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_relat_1(B))  => v1_relat_1(k2_xboole_0(A, B))) ) ).
fof(fc3_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  => v4_relat_1(k4_xboole_0(B, C), A)) ) ).
fof(fc4_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  &  (v1_relat_1(C) & v5_relat_1(C, A)) )  => v5_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc4_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(k2_struct_0(A))) ) ).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc5_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  => v5_relat_1(k3_xboole_0(B, C), A)) ) ).
fof(fc5_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(k2_struct_0(A))) ) ) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc6_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) )  =>  (v1_relat_1(k2_funct_1(A)) &  (v1_funct_1(k2_funct_1(A)) & v2_funct_1(k2_funct_1(A))) ) ) ) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc6_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  => v5_relat_1(k4_xboole_0(B, C), A)) ) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
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(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_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(free_g6_algstr_0, axiom,  (! [A, B, C, D, E] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (m1_subset_1(D, A) & m1_subset_1(E, A)) ) )  =>  (! [F, G, H, I, J] :  (g6_algstr_0(A, B, C, D, E)=g6_algstr_0(F, G, H, I, J) =>  (A=F &  (B=G &  (C=H &  (D=I & E=J) ) ) ) ) ) ) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(idempotence_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, A)=A) ).
fof(idempotence_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, B)=B) ) ).
fof(l10_field_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v1_ring_3(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (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) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) ) )  =>  (! [D] :  (m1_subset_1(D, k2_field_2(A, B, C)) =>  (! [E] :  (m1_subset_1(E, k2_field_2(A, B, C)) =>  (r2_tarski(E, k2_struct_0(A)) =>  (r2_tarski(D, k2_struct_0(A)) | r2_tarski(k1_binop_1(u1_algstr_0(B), D, k1_funct_1(C, E)), k7_subset_1(u1_struct_0(B), k2_struct_0(B), k2_relset_1(u1_struct_0(B), C)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(l11_field_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v1_ring_3(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (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) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) ) )  =>  (! [D] :  (m1_subset_1(D, k2_field_2(A, B, C)) =>  (! [E] :  (m1_subset_1(E, k2_field_2(A, B, C)) =>  (r2_tarski(D, k2_struct_0(A)) =>  (r2_tarski(E, k2_struct_0(A)) | r2_tarski(k1_binop_1(u1_algstr_0(B), k1_funct_1(C, D), E), k7_subset_1(u1_struct_0(B), k2_struct_0(B), k2_relset_1(u1_struct_0(B), C)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc11_vectsp_1, axiom,  (? [A] :  (l4_algstr_0(A) &  ( ~ (v2_struct_0(A))  & v4_vectsp_1(A)) ) ) ).
fof(rc17_algstr_0, axiom,  (? [A] :  (l6_algstr_0(A) & v36_algstr_0(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_struct_0, axiom,  (! [A] :  (l2_struct_0(A) =>  (? [B] :  (m1_subset_1(B, u1_struct_0(A)) & v9_struct_0(B, A)) ) ) ) ).
fof(rc18_algstr_0, axiom,  (? [A] :  (l6_algstr_0(A) &  (v13_struct_0(A, 1) & v36_algstr_0(A)) ) ) ).
fof(rc19_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l2_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, u1_struct_0(A)) &  ~ (v9_struct_0(B, A)) ) ) ) ) ).
fof(rc1_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_quofield, 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) &  (v3_group_1(A) &  (v5_group_1(A) &  (v5_vectsp_1(A) & v6_vectsp_1(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_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc20_struct_0, axiom,  (? [A] :  (l2_struct_0(A) &  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ).
fof(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_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(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(rc3_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(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_vectsp_1, axiom,  (? [A] :  (l3_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v3_group_1(A) & v5_group_1(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_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc4_vectsp_1, axiom,  (? [A] :  (l4_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v1_group_1(A) &  (v3_group_1(A) & v5_group_1(A)) ) ) ) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
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(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(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_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(rd1_rlvect_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  &  ( (v9_struct_0(B, A) & m1_subset_1(B, u1_struct_0(A)))  & m1_subset_1(C, u1_struct_0(A))) )  => k1_algstr_0(A, B, C)=C) ) ).
fof(rd2_ring_3, axiom,  (! [A, B, C] :  ( ( ( ~ (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)) ) ) ) ) ) ) ) )  &  (v1_funct_1(C) &  (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) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) ) ) ) )  => k2_funct_1(k2_funct_1(C))=C) ) ).
fof(rd2_rlvect_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  &  ( (v9_struct_0(B, A) & m1_subset_1(B, u1_struct_0(A)))  & m1_subset_1(C, u1_struct_0(A))) )  => k1_algstr_0(A, C, B)=C) ) ).
fof(redefinition_k1_field_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v1_ring_3(B, A) & l6_algstr_0(B)) ) ) ) ) ) ) ) )  &  (v1_funct_1(C) &  (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) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) ) ) ) )  => k1_field_2(A, B, C)=k2_funct_1(C)) ) ).
fof(redefinition_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => k2_relset_1(A, B)=k10_xtuple_0(B)) ) ).
fof(redefinition_k4_binop_1, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (m1_subset_1(C, A) & m1_subset_1(D, A)) )  => k4_binop_1(A, B, C, D)=k1_binop_1(B, C, D)) ) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_k7_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => k7_subset_1(A, B, C)=k4_xboole_0(B, C)) ) ).
fof(redefinition_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, C)=k3_xboole_0(B, C)) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(symmetry_r1_tsep_1, axiom,  (! [A, B] :  ( (l1_struct_0(A) & l1_struct_0(B))  =>  (r1_tsep_1(A, B) => r1_tsep_1(B, A)) ) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_boole, axiom,  (! [A] : k3_xboole_0(A, k1_xboole_0)=k1_xboole_0) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_boole, axiom,  (! [A] : k4_xboole_0(A, k1_xboole_0)=A) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_boole, axiom,  (! [A] : k4_xboole_0(k1_xboole_0, A)=k1_xboole_0) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
