% Mizar problem: t31_latwal_2,latwal_2,1525,7 
fof(t31_latwal_2, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) & l1_orders_2(A)) ) ) ) )  =>  (? [B] :  ( ( ~ (v2_struct_0(B))  &  (v3_lattices(B) &  (v4_lattices(B) &  (v6_lattices(B) &  (v7_robbins1(B) &  (v5_sheffer1(B) &  (v1_latwal_1(B) &  (v2_latwal_1(B) & l3_lattices(B)) ) ) ) ) ) ) )  & g1_orders_2(u1_struct_0(A), u1_orders_2(A))=k4_latwal_2(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_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_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v5_lattices(A) &  (v6_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) & l3_lattices(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v19_lattices(B, A) => v21_lattices(B, A)) ) ) ) ) ).
fof(cc10_latwal_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) & v3_robbins3(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) & v8_lattices(A)) ) ) ) ) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc11_latwal_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  (v4_latwal_1(A) &  (v5_latwal_1(A) &  (v6_latwal_1(A) &  (v7_latwal_1(A) & v8_latwal_1(A)) ) ) ) ) ) ) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc12_latwal_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_latwal_1(A) &  (v5_latwal_1(A) &  (v6_latwal_1(A) &  (v7_latwal_1(A) & v8_latwal_1(A)) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v7_robbins1(A) & v5_sheffer1(A)) ) ) ) ) ) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc13_latwal_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  =>  ( ~ (v2_struct_0(A))  & v9_latwal_1(A)) ) ) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc14_latwal_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v9_latwal_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v7_robbins1(A) & v5_sheffer1(A)) ) ) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_lattad_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  =>  ( ~ (v2_struct_0(A))  & v11_lattices(A)) ) ) ) ).
fof(cc1_lattice3, axiom,  (! [A] :  (l1_orders_2(A) =>  (v1_lattice3(A) =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc1_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v10_lattices(A))  =>  ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) &  (v6_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) & v9_lattices(A)) ) ) ) ) ) ) ) ) ).
fof(cc1_latwal_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v7_robbins1(A) & v2_latwal_1(A)) ) ) )  =>  ( ~ (v2_struct_0(A))  & v3_robbins3(A)) ) ) ) ).
fof(cc1_orders_2, axiom,  (! [A] :  (l1_orders_2(A) =>  (v3_orders_2(A) => v2_orders_2(A)) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc1_pcs_0, axiom,  (! [A] :  (l1_orders_2(A) =>  (v2_struct_0(A) => v2_orders_2(A)) ) ) ).
fof(cc1_relat_2, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) &  (v1_relat_2(A) &  (v2_relat_2(A) &  (v3_relat_2(A) &  (v4_relat_2(A) &  (v5_relat_2(A) &  (v6_relat_2(A) &  (v7_relat_2(A) & v8_relat_2(A)) ) ) ) ) ) ) ) ) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc1_robbins3, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v10_lattices(A))  =>  ( ~ (v2_struct_0(A))  &  (v1_robbins3(A) &  (v2_robbins3(A) & v3_robbins3(A)) ) ) ) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc1_zfmisc_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_zfmisc_1(A)) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_lattad_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  (v3_robbins3(A) &  (v1_lattad_1(A) &  (v2_lattad_1(A) & v3_lattad_1(A)) ) ) ) ) ) ) ).
fof(cc2_lattice3, axiom,  (! [A] :  (l1_orders_2(A) =>  (v2_lattice3(A) =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v5_lattices(A) &  (v6_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) & v9_lattices(A)) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  & v10_lattices(A)) ) ) ) ).
fof(cc2_latwal_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v5_sheffer1(A) & v1_latwal_1(A)) ) ) )  =>  ( ~ (v2_struct_0(A))  & v9_lattices(A)) ) ) ) ).
fof(cc2_orders_2, axiom,  (! [A] :  (l1_orders_2(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_xboole_0(B) => v6_orders_2(B, A)) ) ) ) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc2_relat_2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v3_relat_2(A) & v8_relat_2(A)) )  =>  (v1_relat_1(A) & v1_relat_2(A)) ) ) ).
fof(cc2_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(cc2_robbins3, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v9_lattices(A) &  (v1_robbins3(A) &  (v2_robbins3(A) & v3_robbins3(A)) ) ) )  =>  ( ~ (v2_struct_0(A))  & v10_lattices(A)) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_xxreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xxreal_0(A)) ) ).
fof(cc2_zfmisc_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc3_lattad_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  =>  ( ~ (v2_struct_0(A))  & v10_lattices(A)) ) ) ) ).
fof(cc3_latwal_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  =>  ( ~ (v2_struct_0(A))  & v2_latwal_1(A)) ) ) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc3_relat_2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v2_relat_2(A) & v8_relat_2(A)) )  =>  (v1_relat_1(A) & v5_relat_2(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_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v2_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc4_lattad_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  (v7_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) & v4_lattad_1(A)) ) ) ) ) ) ) ).
fof(cc4_latwal_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v5_lattices(A) &  (v8_lattices(A) & v10_lattices(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v5_lattices(A) &  (v8_lattices(A) &  (v10_lattices(A) & v2_latwal_1(A)) ) ) ) ) ) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(A)) ) ).
fof(cc4_relat_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_2(A))  =>  (v1_relat_1(A) &  (v2_relat_2(A) & v4_relat_2(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_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ) ).
fof(cc5_lattad_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) & v4_lattad_1(A)) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) &  (v4_lattad_1(A) & v5_lattad_1(A)) ) ) ) ) ) ) ) ) ) ).
fof(cc5_latwal_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) & v3_robbins3(A)) ) )  =>  ( ~ (v2_struct_0(A))  & v8_lattices(A)) ) ) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc5_pcs_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) &  (v9_pcs_0(A) &  (v10_pcs_0(A) & v11_pcs_0(A)) ) ) ) ) ).
fof(cc5_relat_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v7_relat_2(A))  =>  (v1_relat_1(A) &  (v1_relat_2(A) & v6_relat_2(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_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v3_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) ) ) ) ).
fof(cc6_lattad_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) &  (v4_lattad_1(A) & v5_lattad_1(A)) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) & v4_lattad_1(A)) ) ) ) ) ) ) ) ) ) ).
fof(cc6_latwal_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v7_robbins1(A) &  (v5_sheffer1(A) &  (v1_latwal_1(A) & v2_latwal_1(A)) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v8_lattices(A) &  (v7_robbins1(A) &  (v5_sheffer1(A) &  (v1_latwal_1(A) & v2_latwal_1(A)) ) ) ) ) ) ) ) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc6_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ) ).
fof(cc7_lattad_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) & v4_lattad_1(A)) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v6_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) & v4_lattad_1(A)) ) ) ) ) ) ) ) ) ) ).
fof(cc7_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & v11_lattices(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & v12_lattices(A)) ) ) ) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc7_xxreal_0, axiom,  (! [A] :  ( (v8_ordinal1(A) & v1_xxreal_0(A))  =>  (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc8_lattad_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) & v4_lattad_1(A)) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) & v4_lattad_1(A)) ) ) ) ) ) ) ) ) ) ).
fof(cc8_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_xboole_0(B) =>  (v18_lattices(B, A) & v19_lattices(B, A)) ) ) ) ) ) ).
fof(cc8_latwal_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v9_lattices(A) &  (v5_sheffer1(A) & v3_robbins3(A)) ) ) ) ) ) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc8_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) )  =>  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ) ).
fof(cc9_lattad_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v7_struct_0(A) &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) & v4_lattad_1(A)) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(A))  &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) &  (v4_lattad_1(A) & v6_lattad_1(A)) ) ) ) ) ) ) ) ) ) ).
fof(cc9_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) &  (v8_lattices(A) & l3_lattices(A)) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v18_lattices(B, A) => v20_lattices(B, A)) ) ) ) ) ).
fof(cc9_latwal_1, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) & v8_lattices(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) & v3_robbins3(A)) ) ) ) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(commutativity_k12_lattice3, axiom,  (! [A, B, C] :  ( ( (v5_orders_2(A) &  (v2_lattice3(A) & l1_orders_2(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k12_lattice3(A, B, C)=k12_lattice3(A, C, B)) ) ).
fof(commutativity_k13_lattice3, axiom,  (! [A, B, C] :  ( ( (v5_orders_2(A) &  (v1_lattice3(A) & l1_orders_2(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k13_lattice3(A, B, C)=k13_lattice3(A, C, B)) ) ).
fof(commutativity_k3_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) & l2_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k3_lattices(A, B, C)=k3_lattices(A, C, B)) ) ).
fof(d1_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_lattices(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k1_lattices(A, B, C)=k4_binop_1(u1_struct_0(A), u2_lattices(A), B, C)) ) ) ) ) ) ).
fof(d1_latwal_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  =>  (v1_latwal_1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) => k2_lattices(A, k2_lattices(A, k1_lattices(A, D, C), k1_lattices(A, B, C)), C)=C) ) ) ) ) ) ) ) ) ).
fof(d2_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_lattices(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k2_lattices(A, B, C)=k4_binop_1(u1_struct_0(A), u1_lattices(A), B, C)) ) ) ) ) ) ).
fof(d2_latwal_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  =>  (v2_latwal_1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) => k1_lattices(A, k1_lattices(A, k2_lattices(A, D, C), k2_lattices(A, B, C)), C)=C) ) ) ) ) ) ) ) ) ).
fof(d2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (v1_relat_1(B) =>  (A=B <=>  (! [C] :  (! [D] :  (r2_hidden(k4_tarski(C, D), A) <=> r2_hidden(k4_tarski(C, D), B)) ) ) ) ) ) ) ) ).
fof(d3_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_lattices(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r1_lattices(A, B, C) <=> k1_lattices(A, B, C)=C) ) ) ) ) ) ) ).
fof(d4_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_lattices(A))  =>  (v4_lattices(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k1_lattices(A, B, C)=k1_lattices(A, C, B)) ) ) ) ) ) ) ).
fof(d5_latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v7_robbins1(A) &  (v5_sheffer1(A) &  (v1_latwal_1(A) &  (v2_latwal_1(A) & l3_lattices(A)) ) ) ) ) ) )  => k4_latwal_2(A)=g1_orders_2(u1_struct_0(A), k3_latwal_2(A))) ) ).
fof(d5_orders_2, axiom,  (! [A] :  (l1_orders_2(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))) ) ) ) ) ) ) ).
fof(d6_lattad_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  => k1_lattad_1(A)=a_1_0_lattad_1(A)) ) ).
fof(d6_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_lattices(A))  =>  (v6_lattices(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k2_lattices(A, B, C)=k2_lattices(A, C, B)) ) ) ) ) ) ) ).
fof(d7_robbins1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_lattices(A))  =>  (v7_robbins1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k1_lattices(A, B, B)=B) ) ) ) ) ).
fof(d9_sheffer1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_lattices(A))  =>  (v5_sheffer1(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k2_lattices(A, B, B)=B) ) ) ) ) ).
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_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_k10_lattice3, axiom,  (! [A, B, C] :  ( (l1_orders_2(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k10_lattice3(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k11_lattice3, axiom,  (! [A, B, C] :  ( (l1_orders_2(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k11_lattice3(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k12_lattice3, axiom,  (! [A, B, C] :  ( ( (v5_orders_2(A) &  (v2_lattice3(A) & l1_orders_2(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k12_lattice3(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k13_lattice3, axiom,  (! [A, B, C] :  ( ( (v5_orders_2(A) &  (v1_lattice3(A) & l1_orders_2(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k13_lattice3(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k1_binop_1, axiom, $true).
fof(dt_k1_lattad_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  => v1_relat_1(k1_lattad_1(A))) ) ).
fof(dt_k1_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l2_lattices(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_binop_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C)))) )  &  (m1_subset_1(E, A) & m1_subset_1(F, B)) ) ) )  => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) ) ).
fof(dt_k2_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_lattices(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) & l2_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k3_latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v7_robbins1(A) &  (v5_sheffer1(A) &  (v1_latwal_1(A) &  (v2_latwal_1(A) & l3_lattices(A)) ) ) ) ) ) )  => m1_subset_1(k3_latwal_2(A), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) ) ).
fof(dt_k4_binop_1, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (m1_subset_1(C, A) & m1_subset_1(D, A)) )  => m1_subset_1(k4_binop_1(A, B, C, D), A)) ) ).
fof(dt_k4_latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v7_robbins1(A) &  (v5_sheffer1(A) &  (v1_latwal_1(A) &  (v2_latwal_1(A) & l3_lattices(A)) ) ) ) ) ) )  =>  (v1_orders_2(k4_latwal_2(A)) & l1_orders_2(k4_latwal_2(A))) ) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k5_ordinal1, 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_struct_0, axiom, $true).
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_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_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_struct_0, axiom,  (? [A] : l1_struct_0(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(fc10_latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v7_robbins1(A) &  (v5_sheffer1(A) &  (v1_latwal_1(A) &  (v2_latwal_1(A) & l3_lattices(A)) ) ) ) ) ) )  =>  (v1_orders_2(k4_latwal_2(A)) &  (v3_orders_2(k4_latwal_2(A)) & v5_orders_2(k4_latwal_2(A))) ) ) ) ).
fof(fc11_latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v7_robbins1(A) &  (v5_sheffer1(A) &  (v1_latwal_1(A) &  (v2_latwal_1(A) & l3_lattices(A)) ) ) ) ) ) )  =>  (v1_orders_2(k4_latwal_2(A)) &  (v1_lattice3(k4_latwal_2(A)) & v2_lattice3(k4_latwal_2(A))) ) ) ) ).
fof(fc1_lattad_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) &  (v4_lattad_1(A) & l3_lattices(A)) ) ) ) ) ) )  => v1_partfun1(k1_lattad_1(A), u1_struct_0(A))) ) ).
fof(fc1_orders_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))))  =>  ( ~ (v2_struct_0(g1_orders_2(A, B)))  & v1_orders_2(g1_orders_2(A, B))) ) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc2_orders_2, axiom,  (! [A] :  ( (v2_orders_2(A) & l1_orders_2(A))  => v1_partfun1(u1_orders_2(A), u1_struct_0(A))) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc2_zfmisc_1, axiom,  (! [A, B] :  (v1_xboole_0(B) => v1_xboole_0(k2_zfmisc_1(A, B))) ) ).
fof(fc3_lattad_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) &  (v4_lattad_1(A) & l3_lattices(A)) ) ) ) ) ) )  =>  (v1_relat_1(k1_lattad_1(A)) & v1_relat_2(k1_lattad_1(A))) ) ) ).
fof(fc3_lattices, axiom,  (! [A, B, C] :  ( ( ~ (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)))) ) ) )  =>  ( ~ (v2_struct_0(g3_lattices(A, B, C)))  & v3_lattices(g3_lattices(A, B, C))) ) ) ).
fof(fc3_orders_2, axiom,  (! [A] :  ( (v3_orders_2(A) & l1_orders_2(A))  => v1_relat_2(u1_orders_2(A))) ) ).
fof(fc3_zfmisc_1, axiom,  (! [A, B] :  (v1_xboole_0(A) => v1_xboole_0(k2_zfmisc_1(A, B))) ) ).
fof(fc4_lattad_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) &  (v4_lattad_1(A) & l3_lattices(A)) ) ) ) ) ) )  =>  (v1_relat_1(k1_lattad_1(A)) & v8_relat_2(k1_lattad_1(A))) ) ) ).
fof(fc4_latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v7_robbins1(A) &  (v5_sheffer1(A) &  (v1_latwal_1(A) &  (v2_latwal_1(A) & l3_lattices(A)) ) ) ) ) ) )  =>  (v1_relat_1(k1_lattad_1(A)) & v4_relat_1(k1_lattad_1(A), u1_struct_0(A))) ) ) ).
fof(fc4_orders_2, axiom,  (! [A] :  ( (v2_orders_2(A) &  (v5_orders_2(A) & l1_orders_2(A)) )  => v4_relat_2(u1_orders_2(A))) ) ).
fof(fc4_zfmisc_1, axiom,  (! [A, B] :  ( (v1_zfmisc_1(A) & v1_zfmisc_1(B))  => v1_zfmisc_1(k2_zfmisc_1(A, B))) ) ).
fof(fc5_latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v7_robbins1(A) &  (v5_sheffer1(A) &  (v1_latwal_1(A) &  (v2_latwal_1(A) & l3_lattices(A)) ) ) ) ) ) )  =>  (v1_relat_1(k1_lattad_1(A)) & v5_relat_1(k1_lattad_1(A), u1_struct_0(A))) ) ) ).
fof(fc5_orders_2, axiom,  (! [A] :  ( (v4_orders_2(A) & l1_orders_2(A))  => v8_relat_2(u1_orders_2(A))) ) ).
fof(fc6_latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v7_robbins1(A) &  (v5_sheffer1(A) &  (v1_latwal_1(A) &  (v2_latwal_1(A) & l3_lattices(A)) ) ) ) ) ) )  => v1_partfun1(k1_lattad_1(A), u1_struct_0(A))) ) ).
fof(fc6_orders_2, axiom,  (! [A, B] :  ( (v1_relat_2(B) &  (v1_partfun1(B, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A)))) )  =>  (v1_orders_2(g1_orders_2(A, B)) & v3_orders_2(g1_orders_2(A, B))) ) ) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc7_latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v7_robbins1(A) &  (v5_sheffer1(A) &  (v1_latwal_1(A) &  (v2_latwal_1(A) & l3_lattices(A)) ) ) ) ) ) )  =>  (v1_relat_1(k1_lattad_1(A)) & v1_relat_2(k1_lattad_1(A))) ) ) ).
fof(fc7_orders_2, axiom,  (! [A, B] :  ( (v8_relat_2(B) &  (v1_partfun1(B, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A)))) )  =>  (v1_orders_2(g1_orders_2(A, B)) & v4_orders_2(g1_orders_2(A, B))) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v7_robbins1(A) &  (v5_sheffer1(A) &  (v1_latwal_1(A) &  (v2_latwal_1(A) & l3_lattices(A)) ) ) ) ) ) )  =>  (v1_relat_1(k1_lattad_1(A)) & v4_relat_2(k1_lattad_1(A))) ) ) ).
fof(fc8_orders_2, axiom,  (! [A, B] :  ( (v4_relat_2(B) &  (v1_partfun1(B, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A)))) )  =>  (v1_orders_2(g1_orders_2(A, B)) & v5_orders_2(g1_orders_2(A, B))) ) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(fraenkel_a_1_0_lattad_1, axiom,  (! [A, B] :  ( ( ~ (v2_struct_0(B))  & l3_lattices(B))  =>  (r2_hidden(A, a_1_0_lattad_1(B)) <=>  (? [C, D] :  ( (m1_subset_1(C, u1_struct_0(B)) & m1_subset_1(D, u1_struct_0(B)))  &  (A=k4_tarski(C, D) & r1_lattices(B, C, D)) ) ) ) ) ) ).
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_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(l52_latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v5_orders_2(A) &  (v1_lattice3(A) & l1_orders_2(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (D=k13_lattice3(A, B, C) <=>  (r1_orders_2(A, B, D) &  (r1_orders_2(A, C, D) &  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  ( (r1_orders_2(A, B, E) & r1_orders_2(A, C, E))  => r1_orders_2(A, D, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc14_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  &  (v18_lattices(B, A) & v19_lattices(B, A)) ) ) ) ) ) ).
fof(rc15_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  &  (v18_lattices(B, A) & v19_lattices(B, A)) ) ) ) ) ) ).
fof(rc1_lattad_1, axiom,  (? [A] :  (l3_lattices(A) &  ( ~ (v2_struct_0(A))  &  (v7_struct_0(A) &  (v4_lattices(A) &  (v5_lattices(A) &  (v6_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) & v10_lattices(A)) ) ) ) ) ) ) ) ) ) ).
fof(rc1_latwal_1, axiom,  (? [A] :  (l3_lattices(A) &  ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v7_robbins1(A) &  (v5_sheffer1(A) &  (v1_latwal_1(A) & v2_latwal_1(A)) ) ) ) ) ) ) ) ).
fof(rc1_latwal_2, axiom,  (? [A] :  (l1_orders_2(A) &  ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) & v2_lattice3(A)) ) ) ) ) ) ).
fof(rc1_orders_2, axiom,  (? [A] :  (l1_orders_2(A) & v1_orders_2(A)) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
fof(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc1_zfmisc_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(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_lattad_1, axiom,  (? [A] :  (l3_lattices(A) &  ( ~ (v2_struct_0(A))  &  (v11_lattices(A) &  (v3_robbins3(A) &  (v1_lattad_1(A) &  (v2_lattad_1(A) & v3_lattad_1(A)) ) ) ) ) ) ) ).
fof(rc2_orders_2, axiom,  (? [A] :  (l1_orders_2(A) &  (v13_struct_0(A, 1) &  (v1_orders_2(A) &  (v2_orders_2(A) &  (v3_orders_2(A) &  (v4_orders_2(A) & v5_orders_2(A)) ) ) ) ) ) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc2_zfmisc_1, axiom,  (? [A] :  ~ (v1_zfmisc_1(A)) ) ).
fof(rc3_lattad_1, axiom,  (? [A] :  (l3_lattices(A) &  ( ~ (v2_struct_0(A))  &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) & v4_lattad_1(A)) ) ) ) ) ) ) ) ).
fof(rc3_lattices, axiom,  (? [A] :  (l3_lattices(A) & v3_lattices(A)) ) ).
fof(rc3_orders_2, axiom,  (! [A] :  (l1_orders_2(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v6_orders_2(B, A)) ) ) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ).
fof(rc4_lattad_1, axiom,  (? [A] :  (l3_lattices(A) &  ( ~ (v2_struct_0(A))  &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v11_lattices(A) &  (v3_lattad_1(A) &  (v4_lattad_1(A) & v6_lattad_1(A)) ) ) ) ) ) ) ) ) ).
fof(rc4_latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_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(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)))) &  (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v5_relat_1(B, u1_struct_0(A)) &  (v1_partfun1(B, u1_struct_0(A)) &  (v1_relat_2(B) & v3_relat_2(B)) ) ) ) ) ) ) ) ) ).
fof(rc4_orders_2, axiom,  (? [A] :  (l1_orders_2(A) &  (v2_struct_0(A) & v1_orders_2(A)) ) ) ).
fof(rc4_ordinal1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v5_ordinal1(B)) ) ) ) ) ).
fof(rc4_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc4_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_xxreal_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ).
fof(rc6_lattad_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  &  (v20_lattices(B, A) & v21_lattices(B, A)) ) ) ) ) ) ).
fof(rc6_lattices, axiom,  (? [A] :  (l3_lattices(A) &  (v13_struct_0(A, 1) & v3_lattices(A)) ) ) ).
fof(rc6_latwal_2, axiom,  (? [A] :  (l3_lattices(A) &  ( ~ (v2_struct_0(A))  &  (v3_lattices(A) &  (v4_lattices(A) &  (v6_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v7_robbins1(A) &  (v5_sheffer1(A) &  (v3_robbins3(A) &  (v1_latwal_1(A) & v2_latwal_1(A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_lattices, axiom,  (? [A] :  (l3_lattices(A) &  ( ~ (v2_struct_0(A))  &  (v3_lattices(A) & v10_lattices(A)) ) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rd1_lattices, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) & l3_lattices(A)) ) ) )  & m1_subset_1(B, u1_struct_0(A)))  => k1_lattices(A, B, B)=B) ) ).
fof(redefinition_k12_lattice3, axiom,  (! [A, B, C] :  ( ( (v5_orders_2(A) &  (v2_lattice3(A) & l1_orders_2(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k12_lattice3(A, B, C)=k11_lattice3(A, B, C)) ) ).
fof(redefinition_k13_lattice3, axiom,  (! [A, B, C] :  ( ( (v5_orders_2(A) &  (v1_lattice3(A) & l1_orders_2(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k13_lattice3(A, B, C)=k10_lattice3(A, B, C)) ) ).
fof(redefinition_k2_binop_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C)))) )  &  (m1_subset_1(E, A) & m1_subset_1(F, B)) ) ) )  => k2_binop_1(A, B, C, D, E, F)=k1_binop_1(D, E, F)) ) ).
fof(redefinition_k3_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) & l2_lattices(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k3_lattices(A, B, C)=k1_lattices(A, B, C)) ) ).
fof(redefinition_k3_latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(A) &  (v6_lattices(A) &  (v7_robbins1(A) &  (v5_sheffer1(A) &  (v1_latwal_1(A) &  (v2_latwal_1(A) & l3_lattices(A)) ) ) ) ) ) )  => k3_latwal_2(A)=k1_lattad_1(A)) ) ).
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_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(redefinition_r3_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) & l3_lattices(A)) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  =>  (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) ) ) ).
fof(redefinition_r3_orders_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) & l1_orders_2(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  =>  (r3_orders_2(A, B, C) <=> r1_orders_2(A, B, C)) ) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(reflexivity_r3_lattices, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v6_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) & l3_lattices(A)) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => r3_lattices(A, B, B)) ) ).
fof(reflexivity_r3_orders_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) & l1_orders_2(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => r3_orders_2(A, B, B)) ) ).
fof(s3_binop_1__e2_57__latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) & l1_orders_2(A)) ) ) ) )  =>  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (? [D] :  (m1_subset_1(D, u1_struct_0(A)) &  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  ( (E=B & F=C)  => D=k13_lattice3(A, E, F)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) )  &  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  ( (G=C & H=D)  => k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), B, C, D)=k13_lattice3(A, G, H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(s3_binop_1__e5_57__latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) & l1_orders_2(A)) ) ) ) )  =>  ( (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (? [D] :  (m1_subset_1(D, u1_struct_0(A)) &  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  ( (E=B & F=C)  => D=k12_lattice3(A, E, F)) ) ) ) ) ) ) ) ) ) )  =>  (? [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) )  &  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  ( (G=C & H=D)  => k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), B, C, D)=k12_lattice3(A, G, H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(t11_latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) & l1_orders_2(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  ( (r3_orders_2(A, B, D) & r3_orders_2(A, C, D))  => r3_orders_2(A, k13_lattice3(A, B, C), D)) ) ) ) ) ) ) ) ) ).
fof(t12_latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) & l1_orders_2(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => r3_orders_2(A, B, k13_lattice3(A, B, C))) ) ) ) ) ) ).
fof(t13_latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) & l1_orders_2(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  ( (r3_orders_2(A, D, B) & r3_orders_2(A, D, C))  => r3_orders_2(A, D, k12_lattice3(A, B, C))) ) ) ) ) ) ) ) ) ).
fof(t1_latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) & l1_orders_2(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r3_orders_2(A, B, C) <=> k13_lattice3(A, B, C)=C) ) ) ) ) ) ) ).
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(t2_latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) & l1_orders_2(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r3_orders_2(A, B, C) <=> k12_lattice3(A, B, C)=B) ) ) ) ) ) ) ).
fof(t2_orders_2, axiom,  (! [A] :  ( (v5_orders_2(A) & l1_orders_2(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  ( (r1_orders_2(A, B, C) & r1_orders_2(A, C, B))  => B=C) ) ) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t2_tarski, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_hidden(C, A) <=> r2_hidden(C, B)) )  => A=B) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_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_latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) & l1_orders_2(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k13_lattice3(A, k12_lattice3(A, B, C), B)=B) ) ) ) ) ) ).
fof(t84_zfmisc_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  ~ ( (r1_tarski(B, k2_zfmisc_1(C, D)) &  (r2_hidden(A, B) &  (! [E] :  (! [F] :  ~ ( (r2_hidden(E, C) &  (r2_hidden(F, D) & A=k4_tarski(E, F)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_latwal_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) & l1_orders_2(A)) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k12_lattice3(A, k13_lattice3(A, B, C), B)=B) ) ) ) ) ) ).
