% Mizar problem: t5_conlat_2,conlat_2,406,5 
fof(t5_conlat_2, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  =>  (k3_conlat_2(A, k1_struct_0(k11_conlat_1(A)))=k6_conlat_1(A) & k2_conlat_2(A, k1_struct_0(k11_conlat_1(A)))=k5_conlat_1(A)) ) ) ).
fof(abstractness_v3_conlat_1, axiom,  (! [A, B] :  ( (l5_struct_0(A) & l2_conlat_1(B, A))  =>  (v3_conlat_1(B, A) => B=g2_conlat_1(A, u2_conlat_1(A, B), u3_conlat_1(A, B))) ) ) ).
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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
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_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  ( ~ (v2_struct_0(A))  => v14_struct_0(A)) ) ) ).
fof(cc13_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  (v11_struct_0(A) => v14_struct_0(A)) ) ) ).
fof(cc14_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  ( (v2_struct_0(A) & v14_struct_0(A))  => v11_struct_0(A)) ) ) ).
fof(cc15_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  ( ( ~ (v11_struct_0(A))  & v14_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc16_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  (v11_struct_0(A) => v15_struct_0(A)) ) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc1_conlat_1, axiom,  (! [A] :  ( (v2_struct_0(A) &  (v11_struct_0(A) & l5_struct_0(A)) )  =>  (! [B] :  (l2_conlat_1(B, A) => v4_conlat_1(B, A)) ) ) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_partfun1(C, A) => v1_funct_2(C, A, B)) ) ) ) ).
fof(cc1_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_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(cc2_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ) ).
fof(cc2_funct_2, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc2_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_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(cc3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_funct_1(B)) ) ) ) ).
fof(cc3_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc3_lattice2, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v8_struct_0(A) & v10_lattices(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & v13_lattices(A)) ) ) ) ) ).
fof(cc3_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_lattices(A) & v14_lattices(A)) )  =>  ( ~ (v2_struct_0(A))  & v15_lattices(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(cc4_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc4_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  (v1_funct_2(B, A, A) => v1_partfun1(B, A)) ) ) ) ).
fof(cc4_lattice2, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v8_struct_0(A) & v10_lattices(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & v14_lattices(A)) ) ) ) ) ).
fof(cc4_lattices, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  & v15_lattices(A))  =>  ( ~ (v2_struct_0(A))  &  (v13_lattices(A) & v14_lattices(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(cc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc5_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A))) =>  (v1_funct_2(B, k2_zfmisc_1(A, A), A) => v1_partfun1(B, k2_zfmisc_1(A, A))) ) ) ) ).
fof(cc5_lattice2, axiom,  (! [A] :  (l3_lattices(A) =>  ( ( ~ (v2_struct_0(A))  &  (v8_struct_0(A) & v10_lattices(A)) )  =>  ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & v15_lattices(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(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc8_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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(cc9_funct_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(cc9_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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(d16_lattice3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (r3_lattice3(A, B, C) <=>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r2_tarski(D, C) => r1_lattices(A, B, D)) ) ) ) ) ) ) ) ) ).
fof(d1_conlat_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  =>  (! [B] :  ( (v3_conlat_1(B, A) &  ( ~ (v4_conlat_1(B, A))  &  (v6_conlat_1(B, A) & l2_conlat_1(B, A)) ) )  => k1_conlat_2(A, B)=B) ) ) ) ).
fof(d21_conlat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k11_conlat_1(A))) => k12_conlat_1(A, B)=B) ) ) ) ).
fof(d22_lattice3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  =>  (! [B] : k16_lattice3(A, B)=k15_lattice3(A, a_2_1_lattice3(A, B))) ) ) ).
fof(d2_conlat_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) => k2_conlat_2(A, B)=k16_lattice3(k11_conlat_1(A), B)) ) ) ) ).
fof(d2_xboole_0, axiom, k1_xboole_0=o_0_0_xboole_0).
fof(d3_conlat_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) => k3_conlat_2(A, B)=k15_lattice3(k11_conlat_1(A), B)) ) ) ) ).
fof(dt_g2_conlat_1, axiom,  (! [A, B, C] :  ( (l5_struct_0(A) &  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C, k1_zfmisc_1(u4_struct_0(A)))) )  =>  (v3_conlat_1(g2_conlat_1(A, B, C), A) & l2_conlat_1(g2_conlat_1(A, B, C), A)) ) ) ).
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_k11_conlat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  =>  ( ~ (v2_struct_0(k11_conlat_1(A)))  &  (v3_lattices(k11_conlat_1(A)) & l3_lattices(k11_conlat_1(A))) ) ) ) ).
fof(dt_k12_conlat_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  & m1_subset_1(B, u1_struct_0(k11_conlat_1(A))))  =>  (v3_conlat_1(k12_conlat_1(A, B), A) &  ( ~ (v4_conlat_1(k12_conlat_1(A, B), A))  &  (v6_conlat_1(k12_conlat_1(A, B), A) & l2_conlat_1(k12_conlat_1(A, B), A)) ) ) ) ) ).
fof(dt_k15_lattice3, axiom,  (! [A, B] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  => m1_subset_1(k15_lattice3(A, B), u1_struct_0(A))) ) ).
fof(dt_k16_lattice3, axiom,  (! [A, B] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  => m1_subset_1(k16_lattice3(A, B), u1_struct_0(A))) ) ).
fof(dt_k1_conlat_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  &  (v3_conlat_1(B, A) &  ( ~ (v4_conlat_1(B, A))  &  (v6_conlat_1(B, A) & l2_conlat_1(B, A)) ) ) )  => m1_subset_1(k1_conlat_2(A, B), u1_struct_0(k11_conlat_1(A)))) ) ).
fof(dt_k1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) => m1_subset_1(k1_struct_0(A), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_conlat_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))))  =>  ( ~ (v4_conlat_1(k2_conlat_2(A, B), A))  &  (v6_conlat_1(k2_conlat_2(A, B), A) & l2_conlat_1(k2_conlat_2(A, B), A)) ) ) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_conlat_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))))  =>  ( ~ (v4_conlat_1(k3_conlat_2(A, B), A))  &  (v6_conlat_1(k3_conlat_2(A, B), A) & l2_conlat_1(k3_conlat_2(A, B), A)) ) ) ) ).
fof(dt_k5_conlat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  =>  (v3_conlat_1(k5_conlat_1(A), A) &  ( ~ (v4_conlat_1(k5_conlat_1(A), A))  &  (v6_conlat_1(k5_conlat_1(A), A) &  (v7_conlat_1(k5_conlat_1(A), A) & l2_conlat_1(k5_conlat_1(A), A)) ) ) ) ) ) ).
fof(dt_k5_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_lattices(A))  => m1_subset_1(k5_lattices(A), u1_struct_0(A))) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k6_conlat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  =>  (v3_conlat_1(k6_conlat_1(A), A) &  ( ~ (v4_conlat_1(k6_conlat_1(A), A))  &  (v6_conlat_1(k6_conlat_1(A), A) &  (v8_conlat_1(k6_conlat_1(A), A) & l2_conlat_1(k6_conlat_1(A), A)) ) ) ) ) ) ).
fof(dt_k6_lattices, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_lattices(A))  => m1_subset_1(k6_lattices(A), u1_struct_0(A))) ) ).
fof(dt_l1_conlat_1, axiom,  (! [A] :  (l1_conlat_1(A) => l5_struct_0(A)) ) ).
fof(dt_l1_lattices, axiom,  (! [A] :  (l1_lattices(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_conlat_1, 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_l5_struct_0, axiom,  (! [A] :  (l5_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_o_0_0_xboole_0, axiom, v1_xboole_0(o_0_0_xboole_0)).
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_struct_0, axiom, $true).
fof(dt_u2_conlat_1, axiom,  (! [A, B] :  ( (l5_struct_0(A) & l2_conlat_1(B, A))  => m1_subset_1(u2_conlat_1(A, B), k1_zfmisc_1(u1_struct_0(A)))) ) ).
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(dt_u3_conlat_1, axiom,  (! [A, B] :  ( (l5_struct_0(A) & l2_conlat_1(B, A))  => m1_subset_1(u3_conlat_1(A, B), k1_zfmisc_1(u4_struct_0(A)))) ) ).
fof(dt_u4_struct_0, axiom, $true).
fof(existence_l1_conlat_1, axiom,  (? [A] : l1_conlat_1(A)) ).
fof(existence_l1_lattices, axiom,  (? [A] : l1_lattices(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_conlat_1, axiom,  (! [A] :  (l5_struct_0(A) =>  (? [B] : l2_conlat_1(B, A)) ) ) ).
fof(existence_l2_lattices, axiom,  (? [A] : l2_lattices(A)) ).
fof(existence_l3_lattices, axiom,  (? [A] : l3_lattices(A)) ).
fof(existence_l5_struct_0, axiom,  (? [A] : l5_struct_0(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc10_lattice2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v14_lattices(A) & l3_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)) & v1_setwiseo(u1_lattices(A), u1_struct_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(fc13_struct_0, axiom,  (! [A] :  ( (v11_struct_0(A) & l5_struct_0(A))  => v1_xboole_0(u4_struct_0(A))) ) ).
fof(fc14_struct_0, axiom,  (! [A] :  ( ( ~ (v11_struct_0(A))  & l5_struct_0(A))  =>  ~ (v1_xboole_0(u4_struct_0(A))) ) ) ).
fof(fc1_conlat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l5_struct_0(A)) )  =>  ~ (v1_xboole_0(u4_struct_0(A))) ) ) ).
fof(fc1_conlat_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  =>  ( ~ (v2_struct_0(k11_conlat_1(A)))  &  (v3_lattices(k11_conlat_1(A)) & v15_lattices(k11_conlat_1(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(fc20_struct_0, axiom,  (! [A] :  ( (v15_struct_0(A) & l5_struct_0(A))  => v1_zfmisc_1(u4_struct_0(A))) ) ).
fof(fc21_struct_0, axiom,  (! [A] :  ( ( ~ (v15_struct_0(A))  & l5_struct_0(A))  =>  ~ (v1_zfmisc_1(u4_struct_0(A))) ) ) ).
fof(fc2_conlat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l5_struct_0(A)) )  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc2_lattice2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_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)) & v3_binop_1(u2_lattices(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(fc3_lattice2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_lattices(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)) & v1_binop_1(u2_lattices(A), u1_struct_0(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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) => v1_xboole_0(k1_struct_0(A))) ) ).
fof(fc4_conlat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  =>  ( ~ (v2_struct_0(k11_conlat_1(A)))  &  (v3_lattices(k11_conlat_1(A)) & v10_lattices(k11_conlat_1(A))) ) ) ) ).
fof(fc4_lattice2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v5_lattices(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)) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) ) ) ) ).
fof(fc5_conlat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  =>  ( ~ (v2_struct_0(k11_conlat_1(A)))  &  (v3_lattices(k11_conlat_1(A)) & v4_lattice3(k11_conlat_1(A))) ) ) ) ).
fof(fc5_lattice2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_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)) & v3_binop_1(u1_lattices(A), u1_struct_0(A))) ) ) ) ).
fof(fc6_lattice2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v6_lattices(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)) & v1_binop_1(u1_lattices(A), u1_struct_0(A))) ) ) ) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc7_lattice2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v7_lattices(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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) ) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_lattice2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v13_lattices(A) & l3_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)) & v1_setwiseo(u2_lattices(A), u1_struct_0(A))) ) ) ) ).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(fraenkel_a_2_1_lattice3, axiom,  (! [A, B, C] :  ( ( ~ (v2_struct_0(B))  & l3_lattices(B))  =>  (r2_hidden(A, a_2_1_lattice3(B, C)) <=>  (? [D] :  (m1_subset_1(D, u1_struct_0(B)) &  (A=D & r3_lattice3(B, D, C)) ) ) ) ) ) ).
fof(free_g2_conlat_1, axiom,  (! [A, B, C] :  ( (l5_struct_0(A) &  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C, k1_zfmisc_1(u4_struct_0(A)))) )  =>  (! [D, E, F] :  (g2_conlat_1(A, B, C)=g2_conlat_1(D, E, F) =>  (A=D &  (B=E & C=F) ) ) ) ) ) ).
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(rc10_conlat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  =>  (? [B] :  (l2_conlat_1(B, A) &  (v3_conlat_1(B, A) &  ( ~ (v4_conlat_1(B, A))  & v6_conlat_1(B, A)) ) ) ) ) ) ).
fof(rc11_conlat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  =>  (? [B] :  (l2_conlat_1(B, A) &  (v3_conlat_1(B, A) &  ( ~ (v4_conlat_1(B, A))  &  (v6_conlat_1(B, A) & v7_conlat_1(B, A)) ) ) ) ) ) ) ).
fof(rc11_lattices, axiom,  (? [A] :  (l3_lattices(A) &  ( ~ (v2_struct_0(A))  &  (v3_lattices(A) &  (v4_lattices(A) &  (v5_lattices(A) &  (v6_lattices(A) &  (v7_lattices(A) &  (v8_lattices(A) &  (v9_lattices(A) &  (v10_lattices(A) & v15_lattices(A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc12_conlat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  =>  (? [B] :  (l2_conlat_1(B, A) &  (v3_conlat_1(B, A) &  ( ~ (v4_conlat_1(B, A))  &  (v6_conlat_1(B, A) & v8_conlat_1(B, 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_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_funct_2, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(rc1_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(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(rc25_struct_0, axiom,  (? [A] :  (l5_struct_0(A) &  ~ (v15_struct_0(A)) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc3_lattices, axiom,  (? [A] :  (l3_lattices(A) & v3_lattices(A)) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc4_conlat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l5_struct_0(A)) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_xboole_0(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_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
fof(rc5_conlat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l5_struct_0(A)) )  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u4_struct_0(A))) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(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(rc6_conlat_1, axiom,  (! [A] :  (l5_struct_0(A) =>  (? [B] :  (l2_conlat_1(B, A) & v3_conlat_1(B, A)) ) ) ) ).
fof(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(rc6_lattices, axiom,  (? [A] :  (l3_lattices(A) &  (v13_struct_0(A, 1) & v3_lattices(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_conlat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l5_struct_0(A)) )  =>  (? [B] :  (l2_conlat_1(B, A) &  (v3_conlat_1(B, A) &  ~ (v4_conlat_1(B, A)) ) ) ) ) ) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc9_conlat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  =>  (? [B] :  (l2_conlat_1(B, A) &  ( ~ (v4_conlat_1(B, A))  & v6_conlat_1(B, A)) ) ) ) ) ).
fof(rc9_lattices, axiom,  (? [A] :  (l3_lattices(A) &  ( ~ (v2_struct_0(A))  &  (v3_lattices(A) & v10_lattices(A)) ) ) ) ).
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(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(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(t1_conlat_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  =>  (k5_lattices(k11_conlat_1(A))=k6_conlat_1(A) & k6_lattices(k11_conlat_1(A))=k5_conlat_1(A)) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
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(t30_conlat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  =>  (! [B] :  ( ( ~ (v4_conlat_1(B, A))  &  (v6_conlat_1(B, A) & l2_conlat_1(B, A)) )  =>  (r2_conlat_1(A, B, k5_conlat_1(A)) & r2_conlat_1(A, k6_conlat_1(A), B)) ) ) ) ) ).
fof(t34_lattice3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v4_lattice3(A) & l3_lattices(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (B=k16_lattice3(A, C) <=>  (r3_lattice3(A, B, C) &  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r3_lattice3(A, D, C) => r3_lattices(A, D, B)) ) ) ) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t43_conlat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_conlat_1(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k11_conlat_1(A))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k11_conlat_1(A))) =>  (r3_lattices(k11_conlat_1(A), B, C) <=> r2_conlat_1(A, k12_conlat_1(A, B), k12_conlat_1(A, C))) ) ) ) ) ) ) ).
fof(t49_lattice3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v4_lattice3(A) & l3_lattices(A)) ) )  =>  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v13_lattices(A) & l3_lattices(A)) ) )  & k5_lattices(A)=k15_lattice3(A, k1_xboole_0)) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
