% Mizar problem: t17_waybel18,waybel18,2670,5 
fof(t17_waybel18, conjecture,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v4_waybel11(B) & m1_yellow_9(B, k4_yellow_1(A, k7_funcop_1(A, k2_yellow_1(k1_tarski(k5_numbers))))))  => v2_waybel18(B)) ) ) ) ).
fof(abstractness_v1_orders_2, axiom,  (! [A] :  (l1_orders_2(A) =>  (v1_orders_2(A) => A=g1_orders_2(u1_struct_0(A), u1_orders_2(A))) ) ) ).
fof(abstractness_v1_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) =>  (v1_pre_topc(A) => A=g1_pre_topc(u1_struct_0(A), u1_pre_topc(A))) ) ) ).
fof(abstractness_v3_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  (v3_lattices(A) => A=g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(cc10_card_3, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) ) )  =>  (! [C] :  (m1_subset_1(C, k4_card_3(B)) => v4_relat_1(C, A)) ) ) ) ).
fof(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc10_waybel_0, axiom,  (! [A] :  (l1_orders_2(A) =>  ( (v3_orders_2(A) &  (v1_lattice3(A) & v24_waybel_0(A)) )  =>  (v3_orders_2(A) &  (v1_lattice3(A) & v2_yellow_0(A)) ) ) ) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc11_waybel_0, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) & v3_lattice3(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v24_waybel_0(A) & v25_waybel_0(A)) ) ) ) ) ) ).
fof(cc12_waybel_0, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) & v25_waybel_0(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) & v1_yellow_0(A)) ) ) ) ) ).
fof(cc13_card_3, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  =>  (! [C] :  (m1_subset_1(C, k4_card_3(B)) => v1_partfun1(C, A)) ) ) ) ).
fof(cc13_waybel_0, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v1_yellow_0(A) & v24_waybel_0(A)) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) & v3_lattice3(A)) ) ) ) ) ) ) ).
fof(cc14_card_3, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  =>  (! [C] :  (m1_subset_1(C, k4_card_3(B)) => v1_partfun1(C, A)) ) ) ) ).
fof(cc14_waybel_0, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v5_orders_2(A) & v25_waybel_0(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v5_orders_2(A) & v2_lattice3(A)) ) ) ) ) ) ).
fof(cc15_card_3, axiom,  (! [A] :  ( ~ (v4_card_3(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc15_waybel_0, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v5_orders_2(A) &  (v2_yellow_0(A) & v25_waybel_0(A)) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) & v2_yellow_0(A)) ) ) ) ) ) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc1_card_3, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_card_3(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_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_lattice3, axiom,  (! [A] :  (l1_orders_2(A) =>  (v1_lattice3(A) =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc1_monoid_0, axiom,  (! [A] :  ( (v1_monoid_0(A) & l1_struct_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
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_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_waybel11, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => v1_finset_1(B)) ) ) ) ).
fof(cc1_waybel18, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_waybel18(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_pralg_1(A)) ) ) ) ).
fof(cc1_waybel_0, axiom,  (! [A] :  (l1_orders_2(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_xboole_0(B) =>  (v1_waybel_0(B, A) & v2_waybel_0(B, A)) ) ) ) ) ) ).
fof(cc1_waybel_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v16_waybel_0(A) & l1_orders_2(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_waybel_0(B, A) & v2_waybel_0(B, A)) ) ) ) ) ).
fof(cc1_waybel_8, axiom,  (! [A] :  (l1_orders_2(A) =>  ( (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) & v2_waybel_8(A)) ) ) ) )  =>  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) & v3_waybel_3(A)) ) ) ) ) ) ) ) ).
fof(cc1_yellow_0, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  & v3_lattice3(A))  =>  ( ~ (v2_struct_0(A))  &  (v1_lattice3(A) & v2_lattice3(A)) ) ) ) ) ).
fof(cc1_yellow_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_yellow_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_pralg_1(A)) ) ) ) ).
fof(cc1_yellow_9, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_orders_2(A))  =>  (! [B] :  (m1_yellow_9(B, A) =>  ~ (v2_struct_0(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_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_lattice3, axiom,  (! [A] :  (l1_orders_2(A) =>  (v2_lattice3(A) =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_pre_topc, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_xboole_0(B) => v4_pre_topc(B, 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_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_waybel11, axiom,  (! [A] :  (l1_orders_2(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_xboole_0(B) =>  (v12_waybel_0(B, A) & v13_waybel_0(B, A)) ) ) ) ) ) ).
fof(cc2_waybel_3, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_yellow_0(A) &  (v16_waybel_0(A) & v24_waybel_0(A)) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v3_lattice3(A) & v16_waybel_0(A)) ) ) ) ) ) ) ) ).
fof(cc2_waybel_8, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) & v2_waybel_8(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v24_waybel_0(A) & v1_waybel_8(A)) ) ) ) ) ) ).
fof(cc2_yellow_0, axiom,  (! [A] :  (l1_orders_2(A) =>  ( (v13_struct_0(A, 1) & v3_orders_2(A))  =>  (v13_struct_0(A, 1) &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) & v3_lattice3(A)) ) ) ) ) ) ) ).
fof(cc2_yellow_9, axiom,  (! [A] :  ( (v3_orders_2(A) & l1_orders_2(A))  =>  (! [B] :  (m1_yellow_9(B, A) => v3_orders_2(B)) ) ) ) ).
fof(cc3_card_3, axiom,  (! [A] :  (v3_card_3(A) =>  (v4_funct_1(A) & v2_card_3(A)) ) ) ).
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_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_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_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_waybel11, axiom,  (! [A] :  ( (v13_struct_0(A, 1) & l1_orders_2(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => v13_waybel_0(B, A)) ) ) ) ).
fof(cc3_waybel_3, axiom,  (! [A] :  (l1_orders_2(A) =>  ( (v13_struct_0(A, 1) & v3_orders_2(A))  =>  (v13_struct_0(A, 1) &  (v3_orders_2(A) & v2_waybel_3(A)) ) ) ) ) ).
fof(cc3_waybel_8, axiom,  (! [A] :  (l1_orders_2(A) =>  ( (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) & v3_waybel_8(A)) ) ) ) )  =>  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) & v2_waybel_8(A)) ) ) ) ) ) ) ) ).
fof(cc3_yellow_0, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  & v3_lattice3(A))  =>  ( ~ (v2_struct_0(A))  & v3_yellow_0(A)) ) ) ) ).
fof(cc3_yellow_9, axiom,  (! [A] :  ( (v4_orders_2(A) & l1_orders_2(A))  =>  (! [B] :  (m1_yellow_9(B, A) => v4_orders_2(B)) ) ) ) ).
fof(cc4_card_3, axiom,  (! [A] :  (v5_card_3(A) =>  ( ~ (v1_finset_1(A))  & v4_card_3(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_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_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_waybel11, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) & l1_orders_2(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_xboole_0(B) =>  (v2_waybel11(B, A) & v3_waybel11(B, A)) ) ) ) ) ) ).
fof(cc4_waybel_3, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) & v3_waybel_3(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v24_waybel_0(A) & v2_waybel_3(A)) ) ) ) ) ) ).
fof(cc4_waybel_8, axiom,  (! [A] :  (l1_orders_2(A) =>  ( (v7_struct_0(A) &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) & v2_lattice3(A)) ) ) ) )  =>  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) & v3_waybel_8(A)) ) ) ) ) ) ) ) ).
fof(cc4_yellow_0, axiom,  (! [A] :  (l1_orders_2(A) =>  (v3_yellow_0(A) =>  (v1_yellow_0(A) & v2_yellow_0(A)) ) ) ) ).
fof(cc4_yellow_9, axiom,  (! [A] :  ( (v5_orders_2(A) & l1_orders_2(A))  =>  (! [B] :  (m1_yellow_9(B, A) => v5_orders_2(B)) ) ) ) ).
fof(cc5_card_3, axiom,  (! [A] :  ( ( ~ (v1_finset_1(A))  & v4_card_3(A))  => v5_card_3(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_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc5_waybel11, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v8_struct_0(A) &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) & l1_orders_2(A)) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => v1_waybel11(B, A)) ) ) ) ).
fof(cc5_waybel_3, axiom,  (! [A] :  (l1_orders_2(A) =>  ( (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_yellow_0(A) &  (v1_lattice3(A) &  (v24_waybel_0(A) & v2_waybel_3(A)) ) ) ) ) )  =>  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_yellow_0(A) &  (v1_lattice3(A) & v3_waybel_3(A)) ) ) ) ) ) ) ) ).
fof(cc5_yellow_0, axiom,  (! [A] :  (l1_orders_2(A) =>  ( (v1_yellow_0(A) & v2_yellow_0(A))  => v3_yellow_0(A)) ) ) ).
fof(cc5_yellow_9, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_lattice3(A) & l1_orders_2(A)) )  =>  (! [B] :  (m1_yellow_9(B, A) => v3_lattice3(B)) ) ) ) ).
fof(cc6_card_3, axiom,  (! [A] :  (v1_finset_1(A) => v4_card_3(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_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_waybel11, axiom,  (! [A] :  ( (v2_pre_topc(A) &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) &  (v3_lattice3(A) & l1_waybel_9(A)) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v12_waybel_0(B, A) => v3_waybel11(B, A)) ) ) ) ) ).
fof(cc6_waybel_0, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  &  (v7_struct_0(A) & v3_orders_2(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) & v16_waybel_0(A)) ) ) ) ) ).
fof(cc6_waybel_3, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v3_lattice3(A) & v16_waybel_0(A)) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v16_waybel_0(A) & v2_waybel_3(A)) ) ) ) ) ) ) ) ).
fof(cc6_yellow_9, axiom,  (! [A] :  ( (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) &  (v3_lattice3(A) & l1_orders_2(A)) ) ) ) ) )  =>  (! [B] :  (m1_yellow_9(B, A) =>  (v4_waybel11(B) => v2_pre_topc(B)) ) ) ) ) ).
fof(cc7_card_3, axiom,  (! [A] :  (v4_card_3(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_card_3(B)) ) ) ) ).
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_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_card_3, axiom,  (! [A] :  (v2_card_3(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_card_3(B)) ) ) ) ).
fof(cc8_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  ( (v1_relat_2(B) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_funct_2(B, A, A)) ) )  =>  (v1_funct_1(B) &  (v1_funct_2(B, A, A) & v3_funct_2(B, A, A)) ) ) ) ) ) ).
fof(cc8_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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc9_card_3, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) )  =>  (! [B] :  (m1_subset_1(B, k4_card_3(A)) => v5_funct_1(B, A)) ) ) ) ).
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_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) =>  (v2_struct_0(A) => v6_pre_topc(A)) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(commutativity_k2_tarski, axiom,  (! [A, B] : k2_tarski(A, B)=k2_tarski(B, 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_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => k4_subset_1(A, B, C)=k4_subset_1(A, C, B)) ) ).
fof(commutativity_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(d13_ordinal1, axiom, k5_ordinal1=k1_xboole_0).
fof(d15_pralg_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v2_pralg_1(B)) ) ) )  =>  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) )  =>  (C=k14_pralg_1(A, B) <=>  (! [D] :  ~ ( (r2_tarski(D, A) &  (! [E] :  (l1_struct_0(E) =>  ~ ( (E=k1_funct_1(B, D) & k1_funct_1(C, D)=u1_struct_0(E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_lattice3, axiom,  (! [A] :  (! [B] :  ( (v3_lattices(B) & l3_lattices(B))  =>  (B=k1_lattice3(A) <=>  (u1_struct_0(B)=k9_setfam_1(A) &  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(A)) =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(A)) =>  (k1_binop_1(u2_lattices(B), C, D)=k4_subset_1(A, C, D) & k1_binop_1(u1_lattices(B), C, D)=k9_subset_1(A, C, D)) ) ) ) ) ) ) ) ) ) ).
fof(d2_lattice3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  => k3_lattice3(A)=g1_orders_2(u1_struct_0(A), k2_lattice3(A))) ) ).
fof(d2_partfun1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (v1_partfun1(B, A) <=> k1_relset_1(A, B)=A) ) ) ) ).
fof(d2_yellow_1, axiom,  (! [A] : k2_yellow_1(A)=k3_lattice3(k1_lattice3(A))) ).
fof(d3_waybel18, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v4_waybel_3(B) & v1_waybel18(B)) ) ) ) )  =>  (! [C] :  ( (v1_pre_topc(C) &  (v2_pre_topc(C) & l1_pre_topc(C)) )  =>  (C=k3_waybel18(A, B) <=>  (u1_struct_0(C)=k4_card_3(k14_pralg_1(A, B)) &  (v1_tops_2(k2_waybel18(A, B), C) &  (v2_cantor_1(k2_waybel18(A, B), C) & m1_subset_1(k2_waybel18(A, B), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C))))) ) ) ) ) ) ) ) ) ).
fof(d4_yellow_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_yellow_1(B)) ) ) )  =>  (! [C] :  ( (v1_orders_2(C) & l1_orders_2(C))  =>  (C=k4_yellow_1(A, B) <=>  (u1_struct_0(C)=k4_card_3(k14_pralg_1(A, B)) &  (! [D] :  (m1_subset_1(D, u1_struct_0(C)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(C)) =>  (r2_tarski(D, k4_card_3(k14_pralg_1(A, B))) =>  (r1_orders_2(C, D, E) <=>  (? [F] :  ( (v1_relat_1(F) & v1_funct_1(F))  &  (? [G] :  ( (v1_relat_1(G) & v1_funct_1(G))  &  (F=D &  (G=E &  (! [H] :  ~ ( (r2_hidden(H, A) &  (! [I] :  (l1_orders_2(I) =>  (! [J] :  (m1_subset_1(J, u1_struct_0(I)) =>  (! [K] :  (m1_subset_1(K, u1_struct_0(I)) =>  ~ ( (I=k1_funct_1(B, H) &  (J=k1_funct_1(F, H) &  (K=k1_funct_1(G, H) & r1_orders_2(I, J, K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_yellow_9, axiom,  (! [A] :  (l1_orders_2(A) =>  (! [B] :  (l1_waybel_9(B) =>  (m1_yellow_9(B, A) <=> g1_orders_2(u1_struct_0(B), u1_orders_2(B))=g1_orders_2(u1_struct_0(A), u1_orders_2(A))) ) ) ) ) ).
fof(d9_waybel18, axiom,  (! [A] :  ( (v1_pre_topc(A) & l1_pre_topc(A))  =>  (A=k9_waybel18 <=>  (u1_struct_0(A)=k2_tarski(k5_numbers, 1) & u1_pre_topc(A)=k1_enumset1(k1_xboole_0, k1_tarski(1), k2_tarski(k5_numbers, 1))) ) ) ) ).
fof(dt_g1_orders_2, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  (v1_orders_2(g1_orders_2(A, B)) & l1_orders_2(g1_orders_2(A, B))) ) ) ).
fof(dt_g1_pre_topc, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) =>  (v1_pre_topc(g1_pre_topc(A, B)) & l1_pre_topc(g1_pre_topc(A, B))) ) ) ).
fof(dt_g3_lattices, axiom,  (! [A, B, C] :  ( ( (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)))) ) )  =>  (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))) ) ) ).
fof(dt_k13_pralg_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_pralg_1(A)) )  =>  (v1_relat_1(k13_pralg_1(A)) & v1_funct_1(k13_pralg_1(A))) ) ) ).
fof(dt_k14_pralg_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v2_pralg_1(B)) ) ) )  =>  (v1_relat_1(k14_pralg_1(A, B)) &  (v4_relat_1(k14_pralg_1(A, B), A) &  (v1_funct_1(k14_pralg_1(A, B)) & v1_partfun1(k14_pralg_1(A, B), A)) ) ) ) ) ).
fof(dt_k1_binop_1, axiom, $true).
fof(dt_k1_enumset1, axiom, $true).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_lattice3, axiom,  (! [A] :  (v3_lattices(k1_lattice3(A)) & l3_lattices(k1_lattice3(A))) ) ).
fof(dt_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => m1_subset_1(k1_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_funcop_1, axiom, $true).
fof(dt_k2_lattice3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  =>  (v1_partfun1(k2_lattice3(A), u1_struct_0(A)) &  (v1_relat_2(k2_lattice3(A)) &  (v4_relat_2(k2_lattice3(A)) &  (v8_relat_2(k2_lattice3(A)) & m1_subset_1(k2_lattice3(A), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) ) ) ) ) ) ).
fof(dt_k2_tarski, axiom, $true).
fof(dt_k2_waybel18, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_waybel18(B)) ) ) )  => m1_subset_1(k2_waybel18(A, B), k1_zfmisc_1(k1_zfmisc_1(k4_card_3(k14_pralg_1(A, B)))))) ) ).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_yellow_1, axiom,  (! [A] :  (v1_orders_2(k2_yellow_1(A)) & l1_orders_2(k2_yellow_1(A))) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_lattice3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  =>  (v1_orders_2(k3_lattice3(A)) &  (v3_orders_2(k3_lattice3(A)) &  (v4_orders_2(k3_lattice3(A)) &  (v5_orders_2(k3_lattice3(A)) & l1_orders_2(k3_lattice3(A))) ) ) ) ) ) ).
fof(dt_k3_waybel18, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v4_waybel_3(B) & v1_waybel18(B)) ) ) ) )  =>  (v1_pre_topc(k3_waybel18(A, B)) &  (v2_pre_topc(k3_waybel18(A, B)) & l1_pre_topc(k3_waybel18(A, B))) ) ) ) ).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k4_card_3, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k4_waybel18, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v4_waybel_3(B) & v1_waybel18(B)) ) ) ) )  & m1_subset_1(C, A)) )  =>  ( ~ (v2_struct_0(k4_waybel18(A, B, C)))  & l1_pre_topc(k4_waybel18(A, B, C))) ) ) ).
fof(dt_k4_yellow_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_yellow_1(B)) ) ) )  =>  (v1_orders_2(k4_yellow_1(A, B)) & l1_orders_2(k4_yellow_1(A, B))) ) ) ).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k7_funcop_1, axiom,  (! [A, B] :  (v1_funct_1(k7_funcop_1(A, B)) &  (v1_funct_2(k7_funcop_1(A, B), A, k1_tarski(B)) & m1_subset_1(k7_funcop_1(A, B), k1_zfmisc_1(k2_zfmisc_1(A, k1_tarski(B))))) ) ) ).
fof(dt_k8_filter_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  => v1_relat_1(k8_filter_1(A))) ) ).
fof(dt_k9_setfam_1, axiom,  (! [A] : m1_subset_1(k9_setfam_1(A), k1_zfmisc_1(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_k9_waybel18, axiom,  (v1_pre_topc(k9_waybel18) & l1_pre_topc(k9_waybel18)) ).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_l1_lattices, axiom,  (! [A] :  (l1_lattices(A) => l1_struct_0(A)) ) ).
fof(dt_l1_orders_2, axiom,  (! [A] :  (l1_orders_2(A) => l1_struct_0(A)) ) ).
fof(dt_l1_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l1_waybel_9, axiom,  (! [A] :  (l1_waybel_9(A) =>  (l1_pre_topc(A) & l1_orders_2(A)) ) ) ).
fof(dt_l2_lattices, axiom,  (! [A] :  (l2_lattices(A) => l1_struct_0(A)) ) ).
fof(dt_l3_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  (l1_lattices(A) & l2_lattices(A)) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m1_yellow_9, axiom,  (! [A] :  (l1_orders_2(A) =>  (! [B] :  (m1_yellow_9(B, A) => l1_waybel_9(B)) ) ) ) ).
fof(dt_u1_lattices, axiom,  (! [A] :  (l1_lattices(A) =>  (v1_funct_1(u1_lattices(A)) &  (v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u1_lattices(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_orders_2, axiom,  (! [A] :  (l1_orders_2(A) => m1_subset_1(u1_orders_2(A), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) ) ).
fof(dt_u1_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) => m1_subset_1(u1_pre_topc(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u2_lattices, axiom,  (! [A] :  (l2_lattices(A) =>  (v1_funct_1(u2_lattices(A)) &  (v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u2_lattices(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(existence_l1_lattices, axiom,  (? [A] : l1_lattices(A)) ).
fof(existence_l1_orders_2, axiom,  (? [A] : l1_orders_2(A)) ).
fof(existence_l1_pre_topc, axiom,  (? [A] : l1_pre_topc(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l1_waybel_9, axiom,  (? [A] : l1_waybel_9(A)) ).
fof(existence_l2_lattices, axiom,  (? [A] : l2_lattices(A)) ).
fof(existence_l3_lattices, axiom,  (? [A] : l3_lattices(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m1_yellow_9, axiom,  (! [A] :  (l1_orders_2(A) =>  (? [B] : m1_yellow_9(B, A)) ) ) ).
fof(fc10_card_3, axiom, v5_card_3(k4_ordinal1)).
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_waybel18, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v2_struct_0(B))  &  (v5_orders_2(B) & l1_orders_2(B)) ) )  =>  (v1_orders_2(k4_yellow_1(A, k7_funcop_1(A, B))) & v5_orders_2(k4_yellow_1(A, k7_funcop_1(A, B)))) ) ) ).
fof(fc10_waybel_3, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v1_yellow_1(B) & v5_waybel_3(B)) ) ) ) )  & m1_subset_1(C, A)) )  => v3_orders_2(k1_funct_1(B, C))) ) ).
fof(fc10_waybel_8, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v24_waybel_0(A) & l1_orders_2(A)) ) )  =>  (v1_orders_2(g1_orders_2(u1_struct_0(A), u1_orders_2(A))) & v24_waybel_0(g1_orders_2(u1_struct_0(A), u1_orders_2(A)))) ) ) ).
fof(fc10_yellow_1, axiom,  (! [A, B] :  (l1_orders_2(B) => v1_yellow_1(k2_funcop_1(A, B))) ) ).
fof(fc11_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => v2_relat_1(k2_funcop_1(A, B))) ) ).
fof(fc11_waybel18, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v2_struct_0(B))  &  (v4_orders_2(B) & l1_orders_2(B)) ) )  =>  (v1_orders_2(k4_yellow_1(A, k7_funcop_1(A, B))) & v4_orders_2(k4_yellow_1(A, k7_funcop_1(A, B)))) ) ) ).
fof(fc11_waybel_3, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v1_yellow_1(B) &  (v4_waybel_3(B) & v5_waybel_3(B)) ) ) ) ) ) )  =>  (v1_orders_2(k4_yellow_1(A, B)) & v3_orders_2(k4_yellow_1(A, B))) ) ) ).
fof(fc11_waybel_8, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v5_orders_2(A) &  (v2_waybel_8(A) & l1_orders_2(A)) ) ) )  =>  (v1_orders_2(g1_orders_2(u1_struct_0(A), u1_orders_2(A))) & v2_waybel_8(g1_orders_2(u1_struct_0(A), u1_orders_2(A)))) ) ) ).
fof(fc12_waybel18, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  (v3_orders_2(B) &  (v4_orders_2(B) &  (v5_orders_2(B) &  (v1_lattice3(B) &  (v2_lattice3(B) &  (v3_lattice3(B) & l1_orders_2(B)) ) ) ) ) ) )  =>  (v1_orders_2(k4_yellow_1(A, k7_funcop_1(A, B))) &  (v1_lattice3(k4_yellow_1(A, k7_funcop_1(A, B))) & v3_lattice3(k4_yellow_1(A, k7_funcop_1(A, B)))) ) ) ) ).
fof(fc12_waybel_8, axiom,  (! [A] :  ( (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) &  (v3_waybel_8(A) & l1_orders_2(A)) ) ) ) ) )  =>  (v1_orders_2(g1_orders_2(u1_struct_0(A), u1_orders_2(A))) & v3_waybel_8(g1_orders_2(u1_struct_0(A), u1_orders_2(A)))) ) ) ).
fof(fc13_card_3, axiom,  (! [A, B] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k2_funcop_1(A, B))) ) ) ).
fof(fc13_waybel18, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  (v3_orders_2(B) &  (v4_orders_2(B) &  (v5_orders_2(B) &  (v1_lattice3(B) &  (v2_lattice3(B) &  (v1_yellow_0(B) &  (v2_waybel_8(B) & l1_orders_2(B)) ) ) ) ) ) ) )  =>  (v1_orders_2(k4_yellow_1(A, k7_funcop_1(A, B))) & v2_waybel_8(k4_yellow_1(A, k7_funcop_1(A, B)))) ) ) ).
fof(fc14_waybel_8, axiom,  (! [A] :  (v1_orders_2(k2_yellow_1(A)) & v2_waybel_8(k2_yellow_1(A))) ) ).
fof(fc15_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v1_funct_1(B))  => v1_funcop_1(k2_funcop_1(A, B))) ) ).
fof(fc16_funcop_1, axiom,  (! [A, B] : v3_funct_1(k2_funcop_1(A, B))) ).
fof(fc18_funcop_1, axiom,  (! [A, B] : v4_relat_1(k2_funcop_1(A, B), A)) ).
fof(fc1_funcop_1, axiom,  (! [A, B] :  (v1_relat_1(k2_funcop_1(A, B)) & v1_funct_1(k2_funcop_1(A, B))) ) ).
fof(fc1_lattice3, axiom,  (! [A] :  ( ~ (v2_struct_0(k1_lattice3(A)))  & v3_lattices(k1_lattice3(A))) ) ).
fof(fc1_pre_topc, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  ~ (v1_xboole_0(u1_pre_topc(A))) ) ) ).
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_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_waybel17, axiom,  (! [A, B] :  ( (v3_orders_2(B) & l1_orders_2(B))  => v5_waybel_3(k2_funcop_1(A, B))) ) ).
fof(fc1_waybel18, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v4_waybel_3(B) & v1_waybel18(B)) ) ) ) )  =>  ( ~ (v2_struct_0(k3_waybel18(A, B)))  &  (v1_pre_topc(k3_waybel18(A, B)) & v2_pre_topc(k3_waybel18(A, B))) ) ) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc1_yellow_0, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k1_tarski(A), k1_tarski(A)))) =>  (v13_struct_0(g1_orders_2(k1_tarski(A), B), 1) & v1_orders_2(g1_orders_2(k1_tarski(A), B))) ) ) ).
fof(fc1_yellow_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  =>  (v1_orders_2(k3_lattice3(A)) &  (v3_orders_2(k3_lattice3(A)) &  (v4_orders_2(k3_lattice3(A)) &  (v5_orders_2(k3_lattice3(A)) &  (v1_lattice3(k3_lattice3(A)) & v2_lattice3(k3_lattice3(A))) ) ) ) ) ) ) ).
fof(fc21_funcop_1, axiom,  (! [A, B] :  (v1_relat_1(k2_funcop_1(A, B)) &  (v4_relat_1(k2_funcop_1(A, B), A) &  (v1_funct_1(k2_funcop_1(A, B)) & v1_partfun1(k2_funcop_1(A, B), A)) ) ) ) ).
fof(fc23_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_subset_1(C, B))  => v5_relat_1(k2_funcop_1(A, C), B)) ) ).
fof(fc24_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k9_xtuple_0(A))) ) ).
fof(fc25_funcop_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_binop_1(A, B, C)) & v1_funct_1(k1_binop_1(A, B, C))) ) ) ).
fof(fc2_borsuk_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  & m1_subset_1(B, u1_struct_0(A)))  => v2_compts_1(k1_tarski(B), A)) ) ).
fof(fc2_funcop_1, axiom,  (! [A] : v1_xboole_0(k2_funcop_1(k1_xboole_0, A))) ).
fof(fc2_lattice3, axiom,  (! [A] :  (v3_lattices(k1_lattice3(A)) & v10_lattices(k1_lattice3(A))) ) ).
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(fc2_subset_1, axiom,  (! [A, B, C] :  ~ (v1_xboole_0(k1_enumset1(A, B, C))) ) ).
fof(fc2_waybel18, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v4_waybel_3(B) & v1_waybel18(B)) ) ) ) )  =>  (v1_pre_topc(k3_waybel18(A, B)) &  (v2_pre_topc(k3_waybel18(A, B)) & v1_monoid_0(k3_waybel18(A, B))) ) ) ) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc3_funcop_1, axiom,  (! [A, B] :  (v1_xboole_0(B) => v1_xboole_0(k2_funcop_1(B, A))) ) ).
fof(fc3_lattice3, axiom,  (! [A] :  (v3_lattices(k1_lattice3(A)) & v17_lattices(k1_lattice3(A))) ) ).
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_xboole_0, axiom,  (! [A, B] :  ~ (v1_xboole_0(k2_tarski(A, B))) ) ).
fof(fc4_card_3, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => v4_funct_1(k4_card_3(A))) ) ).
fof(fc4_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  ~ (v1_xboole_0(k2_funcop_1(B, A))) ) ) ).
fof(fc4_lattice3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  =>  ( ~ (v2_struct_0(k3_lattice3(A)))  &  (v1_orders_2(k3_lattice3(A)) &  (v3_orders_2(k3_lattice3(A)) &  (v4_orders_2(k3_lattice3(A)) & v5_orders_2(k3_lattice3(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_waybel_8, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_orders_2(A))  =>  ( ~ (v2_struct_0(g1_orders_2(u1_struct_0(A), u1_orders_2(A))))  & v1_orders_2(g1_orders_2(u1_struct_0(A), u1_orders_2(A)))) ) ) ).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc4_yellow_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v4_lattice3(A) & l3_lattices(A)) ) )  =>  (v1_orders_2(k3_lattice3(A)) &  (v3_orders_2(k3_lattice3(A)) &  (v4_orders_2(k3_lattice3(A)) &  (v5_orders_2(k3_lattice3(A)) & v3_lattice3(k3_lattice3(A))) ) ) ) ) ) ).
fof(fc5_card_3, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) )  =>  ~ (v1_xboole_0(k4_card_3(A))) ) ) ).
fof(fc5_funcop_1, axiom,  (! [A] : v3_relat_1(k2_funcop_1(A, k1_xboole_0))) ).
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_waybel18, axiom,  ( ~ (v2_struct_0(k9_waybel18))  &  (v1_pre_topc(k9_waybel18) & v2_pre_topc(k9_waybel18)) ) ).
fof(fc5_waybel_8, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) & l1_orders_2(A)) )  =>  (v1_orders_2(g1_orders_2(u1_struct_0(A), u1_orders_2(A))) & v3_orders_2(g1_orders_2(u1_struct_0(A), u1_orders_2(A)))) ) ) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc6_pre_topc, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (v1_pre_topc(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A))) & v2_pre_topc(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)))) ) ) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc6_waybel18, axiom,  (v1_pre_topc(k9_waybel18) & v6_pre_topc(k9_waybel18)) ).
fof(fc6_waybel_8, axiom,  (! [A] :  ( (v4_orders_2(A) & l1_orders_2(A))  =>  (v1_orders_2(g1_orders_2(u1_struct_0(A), u1_orders_2(A))) & v4_orders_2(g1_orders_2(u1_struct_0(A), u1_orders_2(A)))) ) ) ).
fof(fc7_card_3, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => v2_card_3(k1_tarski(A))) ) ).
fof(fc7_lattice3, axiom,  (! [A] :  (v3_lattices(k1_lattice3(A)) & v4_lattice3(k1_lattice3(A))) ) ).
fof(fc7_pre_topc, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_pre_topc(A))  =>  ( ~ (v2_struct_0(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A))))  & v1_pre_topc(g1_pre_topc(u1_struct_0(A), u1_pre_topc(A)))) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc7_waybel18, axiom,  (v1_pre_topc(k9_waybel18) & v2_waybel18(k9_waybel18)) ).
fof(fc7_waybel_3, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v1_yellow_1(B) & v4_waybel_3(B)) ) ) ) )  =>  ( ~ (v2_struct_0(k4_yellow_1(A, B)))  & v1_orders_2(k4_yellow_1(A, B))) ) ) ).
fof(fc7_waybel_8, axiom,  (! [A] :  ( (v5_orders_2(A) & l1_orders_2(A))  =>  (v1_orders_2(g1_orders_2(u1_struct_0(A), u1_orders_2(A))) & v5_orders_2(g1_orders_2(u1_struct_0(A), u1_orders_2(A)))) ) ) ).
fof(fc7_yellow_1, axiom,  (! [A] :  ( ~ (v2_struct_0(k2_yellow_1(A)))  &  (v1_orders_2(k2_yellow_1(A)) &  (v3_orders_2(k2_yellow_1(A)) &  (v4_orders_2(k2_yellow_1(A)) & v5_orders_2(k2_yellow_1(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_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc8_waybel18, axiom,  (! [A, B] :  ( ( ~ (v2_struct_0(B))  & l1_struct_0(B))  => v4_waybel_3(k2_funcop_1(A, B))) ) ).
fof(fc8_waybel_3, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v1_yellow_1(B) & v4_waybel_3(B)) ) ) ) )  & m1_subset_1(C, A)) )  =>  ~ (v2_struct_0(k1_funct_1(B, C))) ) ) ).
fof(fc8_waybel_8, axiom,  (! [A] :  ( (v2_lattice3(A) & l1_orders_2(A))  =>  (v1_orders_2(g1_orders_2(u1_struct_0(A), u1_orders_2(A))) & v2_lattice3(g1_orders_2(u1_struct_0(A), u1_orders_2(A)))) ) ) ).
fof(fc8_yellow_1, axiom,  (! [A] :  (v1_orders_2(k2_yellow_1(A)) & v3_lattice3(k2_yellow_1(A))) ) ).
fof(fc9_card_3, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => v3_card_3(k4_card_3(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_pre_topc, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))))  =>  ( ~ (v2_struct_0(g1_pre_topc(A, B)))  & v1_pre_topc(g1_pre_topc(A, B))) ) ) ).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(fc9_waybel18, axiom,  (! [A, B] :  (l1_pre_topc(B) => v1_waybel18(k2_funcop_1(A, B))) ) ).
fof(fc9_waybel_3, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v1_yellow_1(B) & v4_waybel_3(B)) ) ) ) )  =>  (v1_monoid_0(k4_yellow_1(A, B)) & v1_orders_2(k4_yellow_1(A, B))) ) ) ).
fof(fc9_waybel_8, axiom,  (! [A] :  ( (v1_lattice3(A) & l1_orders_2(A))  =>  (v1_orders_2(g1_orders_2(u1_struct_0(A), u1_orders_2(A))) & v1_lattice3(g1_orders_2(u1_struct_0(A), u1_orders_2(A)))) ) ) ).
fof(free_g1_orders_2, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  (! [C, D] :  (g1_orders_2(A, B)=g1_orders_2(C, D) =>  (A=C & B=D) ) ) ) ) ).
fof(free_g1_pre_topc, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) =>  (! [C, D] :  (g1_pre_topc(A, B)=g1_pre_topc(C, D) =>  (A=C & B=D) ) ) ) ) ).
fof(free_g3_lattices, axiom,  (! [A, B, C] :  ( ( (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)))) ) )  =>  (! [D, E, F] :  (g3_lattices(A, B, C)=g3_lattices(D, E, F) =>  (A=D &  (B=E & C=F) ) ) ) ) ) ).
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_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => k4_subset_1(A, B, B)=B) ) ).
fof(idempotence_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, B)=B) ) ).
fof(rc10_waybel_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) & l1_orders_2(A)) ) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  &  (v2_waybel_0(B, A) & v13_waybel_0(B, A)) ) ) ) ) ) ).
fof(rc11_pre_topc, axiom,  (? [A] :  (l1_pre_topc(A) &  (v2_struct_0(A) & v1_pre_topc(A)) ) ) ).
fof(rc11_waybel_0, axiom,  (! [A] :  ( (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) & l1_orders_2(A)) ) ) ) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  &  (v1_waybel_0(B, A) &  (v2_waybel_0(B, A) &  (v12_waybel_0(B, A) & v13_waybel_0(B, A)) ) ) ) ) ) ) ) ).
fof(rc12_pre_topc, axiom,  (? [A] :  (l1_pre_topc(A) &  (v2_struct_0(A) &  (v1_pre_topc(A) & v2_pre_topc(A)) ) ) ) ).
fof(rc1_card_3, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_card_3(A)) ) ) ).
fof(rc1_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_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_monoid_0, axiom,  (? [A] :  (l1_struct_0(A) & v1_monoid_0(A)) ) ).
fof(rc1_pre_topc, axiom,  (? [A] :  (l1_pre_topc(A) & v1_pre_topc(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_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_waybel11, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) & l1_orders_2(A)) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  &  (v1_finset_1(B) & v1_waybel_0(B, A)) ) ) ) ) ) ).
fof(rc1_waybel18, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_waybel18(B)) ) ) ) ) ) ).
fof(rc1_waybel_0, axiom,  (! [A] :  (l1_orders_2(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  (v1_waybel_0(B, A) & v2_waybel_0(B, A)) ) ) ) ) ).
fof(rc1_waybel_8, axiom,  (? [A] :  (l1_orders_2(A) &  ( ~ (v2_struct_0(A))  &  (v13_struct_0(A, 1) &  (v1_orders_2(A) &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) & v2_lattice3(A)) ) ) ) ) ) ) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_yellow_0, axiom,  (? [A] :  (l1_orders_2(A) &  (v13_struct_0(A, 1) &  (v1_orders_2(A) & v3_orders_2(A)) ) ) ) ).
fof(rc1_yellow_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_yellow_1(B)) ) ) ) ) ) ).
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_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_funct_1(A) &  ~ (v1_xboole_0(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_pre_topc, axiom,  (? [A] :  (l1_pre_topc(A) &  ( ~ (v2_struct_0(A))  &  (v1_pre_topc(A) & v2_pre_topc(A)) ) ) ) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_waybel11, axiom,  (? [A] :  (l1_orders_2(A) &  (v8_struct_0(A) &  (v13_struct_0(A, 1) &  (v1_orders_2(A) &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) & v2_lattice3(A)) ) ) ) ) ) ) ) ) ).
fof(rc2_waybel18, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v4_waybel_3(B) & v1_waybel18(B)) ) ) ) ) ) ) ).
fof(rc2_waybel_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) & l1_orders_2(A)) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  &  (v1_finset_1(B) &  (v1_waybel_0(B, A) & v2_waybel_0(B, A)) ) ) ) ) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc3_card_3, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v4_funct_1(A) & v2_card_3(A)) ) ) ).
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_relat_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc3_waybel11, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) & l1_orders_2(A)) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  (v2_waybel11(B, A) & v3_waybel11(B, A)) ) ) ) ) ).
fof(rc3_waybel_3, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v1_yellow_1(B) &  (v4_waybel_3(B) & v5_waybel_3(B)) ) ) ) ) ) ) ) ).
fof(rc4_card_3, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v3_card_3(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_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(rc5_card_3, axiom,  (? [A] : v5_card_3(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_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_waybel11, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) & l1_orders_2(A)) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  (v12_waybel_0(B, A) &  (v13_waybel_0(B, A) &  (v1_waybel11(B, A) & v2_waybel11(B, A)) ) ) ) ) ) ) ).
fof(rc6_card_3, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v1_finset_1(A)) ) ) ) ).
fof(rc6_pre_topc, axiom,  (! [A] :  ( (v2_pre_topc(A) & l1_pre_topc(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(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_pre_topc, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v4_pre_topc(B, A)) ) ) ) ) ).
fof(rc7_waybel_0, axiom,  (! [A] :  (l1_orders_2(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  (v12_waybel_0(B, A) & v13_waybel_0(B, A)) ) ) ) ) ).
fof(rc8_waybel_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_orders_2(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  &  (v12_waybel_0(B, A) & v13_waybel_0(B, A)) ) ) ) ) ) ).
fof(rc9_waybel_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) & l1_orders_2(A)) ) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  &  (v1_waybel_0(B, A) & v12_waybel_0(B, A)) ) ) ) ) ) ).
fof(rd1_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(C, A))  => k1_funct_1(k2_funcop_1(A, B), C)=B) ) ).
fof(rd2_funcop_1, axiom,  (! [A, B] : k9_xtuple_0(k2_funcop_1(A, B))=A) ).
fof(redefinition_k14_pralg_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v2_pralg_1(B)) ) ) )  => k14_pralg_1(A, B)=k13_pralg_1(B)) ) ).
fof(redefinition_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k1_relset_1(A, B)=k9_xtuple_0(B)) ) ).
fof(redefinition_k2_lattice3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  => k2_lattice3(A)=k8_filter_1(A)) ) ).
fof(redefinition_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => k4_subset_1(A, B, C)=k2_xboole_0(B, C)) ) ).
fof(redefinition_k4_waybel18, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v4_waybel_3(B) & v1_waybel18(B)) ) ) ) )  & m1_subset_1(C, A)) )  => k4_waybel18(A, B, C)=k1_funct_1(B, C)) ) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_k7_funcop_1, axiom,  (! [A, B] : k7_funcop_1(A, B)=k2_funcop_1(A, B)) ).
fof(redefinition_k9_setfam_1, axiom,  (! [A] : k9_setfam_1(A)=k1_zfmisc_1(A)) ).
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(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(t15_waybel18, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v4_waybel11(B) & m1_yellow_9(B, k4_yellow_1(A, k7_funcop_1(A, k2_yellow_1(k1_tarski(k5_numbers))))))  => u1_pre_topc(B)=u1_pre_topc(k3_waybel18(A, k7_funcop_1(A, k9_waybel18)))) ) ) ) ).
fof(t16_waybel18, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_pre_topc(A) & l1_pre_topc(A)) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v2_pre_topc(B) & l1_pre_topc(B)) )  =>  ( (u1_struct_0(A)=u1_struct_0(B) &  (u1_pre_topc(A)=u1_pre_topc(B) & v2_waybel18(A)) )  => v2_waybel18(B)) ) ) ) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t24_zfmisc_1, axiom,  (! [A] : k1_zfmisc_1(k1_tarski(A))=k2_tarski(k1_xboole_0, k1_tarski(A))) ).
fof(t2_boole, axiom,  (! [A] : k3_xboole_0(A, k1_xboole_0)=k1_xboole_0) ).
fof(t2_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  ( (k9_xtuple_0(A)=k9_xtuple_0(B) &  (! [C] :  (r2_hidden(C, k9_xtuple_0(A)) => k1_funct_1(A, C)=k1_funct_1(B, C)) ) )  => A=B) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t49_card_1, axiom, 1=k1_tarski(k5_ordinal1)).
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(t7_funcop_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (r2_hidden(B, A) => k1_funct_1(k2_funcop_1(A, C), B)=C) ) ) ) ).
fof(t7_waybel18, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v4_waybel_3(B) & v1_waybel18(B)) ) ) ) )  =>  ( (! [C] :  (m1_subset_1(C, A) => v2_waybel18(k4_waybel18(A, B, C))) )  => v2_waybel18(k3_waybel18(A, B))) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
