% Mizar problem: l79_lattice3,lattice3,2119,8 
fof(l79_lattice3, conjecture,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, k9_setfam_1(A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A), A)))) )  =>  ~ ( ( (! [C] :  (m1_subset_1(C, A) => k3_funct_2(k1_zfmisc_1(A), A, B, k6_domain_1(A, C))=C) )  &  ( (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) => k3_funct_2(k1_zfmisc_1(A), A, B, k7_relset_1(k9_setfam_1(A), A, B, C))=k3_funct_2(k1_zfmisc_1(A), A, B, k5_setfam_1(A, C))) )  &  (! [C] :  ( ( ~ (v2_struct_0(C))  &  (v3_lattices(C) &  (v10_lattices(C) & l3_lattices(C)) ) )  =>  ~ ( (u1_struct_0(C)=A &  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(C))) => k15_lattice3(C, D)=k1_funct_1(B, D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_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(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(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_orders_2, axiom,  (! [A] :  (l1_orders_2(A) =>  (v3_orders_2(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_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_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_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_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_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_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_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_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_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_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_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, 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_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_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
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(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_k7_domain_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) & m1_subset_1(C, A)) )  => k7_domain_1(A, B, C)=k7_domain_1(A, C, B)) ) ).
fof(d10_xboole_0, axiom,  (! [A] :  (! [B] :  (A=B <=>  (r1_tarski(A, B) & r1_tarski(B, A)) ) ) ) ).
fof(d12_lattice3, axiom,  (! [A] :  (l1_orders_2(A) =>  (v3_lattice3(A) <=>  (! [B] :  (? [C] :  (m1_subset_1(C, u1_struct_0(A)) &  (r2_lattice3(A, B, C) &  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r2_lattice3(A, B, D) => r1_orders_2(A, C, D)) ) ) ) ) ) ) ) ) ) ).
fof(d12_relat_2, axiom,  (! [A] :  (v1_relat_1(A) =>  (v4_relat_2(A) <=> r4_relat_2(A, k1_relat_1(A))) ) ) ).
fof(d15_lattice3, axiom,  (! [A] :  (l1_orders_2(A) =>  ( (v3_orders_2(A) &  (v4_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) &  (v10_lattices(B) & l3_lattices(B)) ) )  =>  (B=k14_lattice3(A) <=> g1_orders_2(u1_struct_0(A), u1_orders_2(A))=k3_lattice3(B)) ) ) ) ) ) ).
fof(d16_relat_2, axiom,  (! [A] :  (v1_relat_1(A) =>  (v8_relat_2(A) <=> r8_relat_2(A, k1_relat_1(A))) ) ) ).
fof(d17_lattice3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (r4_lattice3(A, B, C) <=>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r2_tarski(D, C) => r1_lattices(A, D, B)) ) ) ) ) ) ) ) ) ).
fof(d1_funct_2, axiom,  (! [A] :  (! [B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( ( ~ (B=k1_xboole_0)  =>  (v1_funct_2(C, A, B) <=> A=k1_relset_1(A, C)) )  &  (B=k1_xboole_0 =>  (v1_funct_2(C, A, B) <=> C=k1_xboole_0) ) ) ) ) ) ) ).
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_relat_2, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (r1_relat_2(A, B) <=>  (! [C] :  (r2_hidden(C, B) => r2_hidden(k4_tarski(C, C), A)) ) ) ) ) ) ).
fof(d1_tarski, axiom,  (! [A] :  (! [B] :  (B=k1_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=> C=A) ) ) ) ) ).
fof(d21_lattice3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_lattices(A))  =>  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) &  (v4_lattice3(A) & l3_lattices(A)) ) )  =>  (! [B] :  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (C=k15_lattice3(A, B) <=>  (r4_lattice3(A, C, B) &  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r4_lattice3(A, D, B) => r1_lattices(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_tarski, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k2_tarski(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (D=A | D=B) ) ) ) ) ) ) ).
fof(d3_lattice3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => k4_lattice3(A, B)=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(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d3_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k2_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) | r2_hidden(D, B)) ) ) ) ) ) ) ).
fof(d4_lattice3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k3_lattice3(A))) => k5_lattice3(A, B)=B) ) ) ) ).
fof(d4_relat_2, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (r4_relat_2(A, B) <=>  (! [C] :  (! [D] :  ( (r2_hidden(C, B) &  (r2_hidden(D, B) &  (r2_hidden(k4_tarski(C, D), A) & r2_hidden(k4_tarski(D, C), A)) ) )  => C=D) ) ) ) ) ) ) ).
fof(d4_tarski, axiom,  (! [A] :  (! [B] :  (B=k3_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=>  (? [D] :  (r2_hidden(C, D) & r2_hidden(D, A)) ) ) ) ) ) ) ).
fof(d4_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k3_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) & r2_hidden(D, B)) ) ) ) ) ) ) ).
fof(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(d8_relat_2, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (r8_relat_2(A, B) <=>  (! [C] :  (! [D] :  (! [E] :  ( (r2_hidden(C, B) &  (r2_hidden(D, B) &  (r2_hidden(E, B) &  (r2_hidden(k4_tarski(C, D), A) & r2_hidden(k4_tarski(D, E), A)) ) ) )  => r2_hidden(k4_tarski(C, E), A)) ) ) ) ) ) ) ) ).
fof(d9_lattice3, axiom,  (! [A] :  (l1_orders_2(A) =>  (! [B] :  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r2_lattice3(A, B, C) <=>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r2_tarski(D, B) => r1_orders_2(A, D, C)) ) ) ) ) ) ) ) ) ).
fof(d9_relat_2, axiom,  (! [A] :  (v1_relat_1(A) =>  (v1_relat_2(A) <=> r1_relat_2(A, k1_relat_1(A))) ) ) ).
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_k14_lattice3, axiom,  (! [A] :  (l1_orders_2(A) =>  ( ~ (v2_struct_0(k14_lattice3(A)))  &  (v3_lattices(k14_lattice3(A)) &  (v10_lattices(k14_lattice3(A)) & l3_lattices(k14_lattice3(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_k1_binop_1, axiom, $true).
fof(dt_k1_domain_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, A) & m1_subset_1(D, B)) ) )  => m1_subset_1(k1_domain_1(A, B, C, D), k2_zfmisc_1(A, B))) ) ).
fof(dt_k1_enumset1, axiom, $true).
fof(dt_k1_funct_1, axiom, $true).
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_relat_1, axiom, $true).
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_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_xboole_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => m1_subset_1(k3_funct_2(A, B, C, D), B)) ) ).
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_tarski, axiom, $true).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k4_binop_1, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  &  (m1_subset_1(C, A) & m1_subset_1(D, A)) )  => m1_subset_1(k4_binop_1(A, B, C, D), A)) ) ).
fof(dt_k4_lattice3, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  & m1_subset_1(B, u1_struct_0(A)))  => m1_subset_1(k4_lattice3(A, B), u1_struct_0(k3_lattice3(A)))) ) ).
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_tarski, axiom, $true).
fof(dt_k5_lattice3, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  & m1_subset_1(B, u1_struct_0(k3_lattice3(A))))  => m1_subset_1(k5_lattice3(A, B), u1_struct_0(A))) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_setfam_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k5_setfam_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k6_domain_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k7_domain_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) & m1_subset_1(C, A)) )  => m1_subset_1(k7_domain_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k7_relat_1, axiom, $true).
fof(dt_k7_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => m1_subset_1(k7_relset_1(A, B, C, D), k1_zfmisc_1(B))) ) ).
fof(dt_k8_domain_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) &  (m1_subset_1(C, A) & m1_subset_1(D, A)) ) )  => m1_subset_1(k8_domain_1(A, B, C, D), k1_zfmisc_1(A))) ) ).
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_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_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_o_2_11_lattice3, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, k1_zfmisc_1(A)))  => m1_subset_1(o_2_11_lattice3(A, B), 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_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_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_relat_2, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v3_relat_2(A))  &  (v1_relat_1(B) & v3_relat_2(B)) )  => v3_relat_2(k2_xboole_0(A, B))) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc11_relat_2, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v3_relat_2(A))  &  (v1_relat_1(B) & v3_relat_2(B)) )  => v3_relat_2(k3_xboole_0(A, B))) ) ).
fof(fc11_relset_1, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(k9_xtuple_0(A)))) )  =>  ~ (v1_xboole_0(k7_relat_1(A, B))) ) ) ).
fof(fc14_relat_2, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_relat_1(B) & v5_relat_2(B)) )  => v5_relat_2(k3_xboole_0(A, B))) ) ).
fof(fc15_relat_2, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_relat_1(B) & v5_relat_2(B)) )  => v5_relat_2(k3_xboole_0(B, A))) ) ).
fof(fc18_relat_2, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v4_relat_2(A))  & v1_relat_1(B))  => v4_relat_2(k3_xboole_0(A, B))) ) ).
fof(fc19_relat_2, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v4_relat_2(A))  & v1_relat_1(B))  => v4_relat_2(k3_xboole_0(B, 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_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_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc22_relat_2, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v8_relat_2(A))  &  (v1_relat_1(B) & v8_relat_2(B)) )  => v8_relat_2(k3_xboole_0(A, B))) ) ).
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_orders_2, axiom,  (! [A] :  ( (v2_orders_2(A) & l1_orders_2(A))  => v1_partfun1(u1_orders_2(A), u1_struct_0(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_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(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_orders_2, axiom,  (! [A] :  ( (v3_orders_2(A) & l1_orders_2(A))  => v1_relat_2(u1_orders_2(A))) ) ).
fof(fc3_xboole_0, axiom,  (! [A, B] :  ~ (v1_xboole_0(k2_tarski(A, B))) ) ).
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(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_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_relat_2, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_relat_2(A))  &  (v1_relat_1(B) & v1_relat_2(B)) )  => v1_relat_2(k2_xboole_0(A, B))) ) ).
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_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
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(fc5_orders_2, axiom,  (! [A] :  ( (v4_orders_2(A) & l1_orders_2(A))  => v8_relat_2(u1_orders_2(A))) ) ).
fof(fc5_relat_2, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_relat_2(A))  &  (v1_relat_1(B) & v1_relat_2(B)) )  => v1_relat_2(k3_xboole_0(A, B))) ) ).
fof(fc5_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  => v5_relat_1(k3_xboole_0(B, C), A)) ) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, 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_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_relat_2, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v2_relat_2(A))  &  (v1_relat_1(B) & v2_relat_2(B)) )  => v2_relat_2(k2_xboole_0(A, B))) ) ).
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_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_relat_2, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v2_relat_2(A))  &  (v1_relat_1(B) & v2_relat_2(B)) )  => v2_relat_2(k3_xboole_0(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_lattice3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v3_lattice3(A) & l1_orders_2(A)) ) ) ) )  =>  ( ~ (v2_struct_0(k14_lattice3(A)))  &  (v3_lattices(k14_lattice3(A)) &  (v10_lattices(k14_lattice3(A)) & v4_lattice3(k14_lattice3(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_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(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_3_22_lattice3, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, B) & m1_subset_1(D, k1_zfmisc_1(B))) )  =>  (r2_hidden(A, a_3_22_lattice3(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, B) &  (A=k7_domain_1(B, E, C) & r2_tarski(E, D)) ) ) ) ) ) ).
fof(fraenkel_a_4_0_lattice3, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k9_setfam_1(B), B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(B), B)))) )  &  (m1_subset_1(D, B) & m1_subset_1(E, k1_zfmisc_1(B))) ) )  =>  (r2_hidden(A, a_4_0_lattice3(B, C, D, E)) <=>  (? [F] :  (m1_subset_1(F, B) &  (A=k3_funct_2(k1_zfmisc_1(B), B, C, k7_domain_1(B, F, D)) & r2_tarski(F, E)) ) ) ) ) ) ).
fof(fraenkel_a_4_1_lattice3, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(B))  &  ( (v1_partfun1(C, B) &  (v1_relat_2(C) &  (v4_relat_2(C) &  (v8_relat_2(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, B)))) ) ) )  &  (m1_subset_1(D, k1_zfmisc_1(B)) & m1_subset_1(E, u1_struct_0(g1_orders_2(B, C)))) ) )  =>  (r2_hidden(A, a_4_1_lattice3(B, C, D, E)) <=>  (? [F] :  (m1_subset_1(F, B) &  (A=E & r2_tarski(F, D)) ) ) ) ) ) ).
fof(fraenkel_a_4_2_lattice3, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(B))  &  ( ( ~ (v2_struct_0(C))  &  (v3_lattices(C) &  (v10_lattices(C) & l3_lattices(C)) ) )  &  (m1_subset_1(D, k1_zfmisc_1(B)) & m1_subset_1(E, u1_struct_0(k3_lattice3(C)))) ) )  =>  (r2_hidden(A, a_4_2_lattice3(B, C, D, E)) <=>  (? [F] :  (m1_subset_1(F, B) &  (A=E & r2_tarski(F, D)) ) ) ) ) ) ).
fof(fraenkel_a_4_3_lattice3, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k9_setfam_1(B), B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(B), B)))) )  &  (m1_subset_1(D, B) & m1_subset_1(E, k1_zfmisc_1(B))) ) )  =>  (r2_hidden(A, a_4_3_lattice3(B, C, D, E)) <=>  (? [F] :  (m1_subset_1(F, B) &  (A=k1_funct_1(C, k7_domain_1(B, F, D)) & r2_tarski(F, E)) ) ) ) ) ) ).
fof(fraenkel_a_5_0_lattice3, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k9_setfam_1(B), B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(B), B)))) )  &  ( (v1_partfun1(D, B) &  (v1_relat_2(D) &  (v4_relat_2(D) &  (v8_relat_2(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B, B)))) ) ) )  &  (m1_subset_1(E, k1_zfmisc_1(B)) & m1_subset_1(F, u1_struct_0(g1_orders_2(B, D)))) ) ) )  =>  (r2_hidden(A, a_5_0_lattice3(B, C, D, E, F)) <=>  (? [G] :  (m1_subset_1(G, B) &  (A=k1_funct_1(C, k2_tarski(G, F)) & r2_tarski(G, E)) ) ) ) ) ) ).
fof(fraenkel_a_5_1_lattice3, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k9_setfam_1(B), B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(B), B)))) )  &  ( ( ~ (v2_struct_0(D))  &  (v3_lattices(D) &  (v10_lattices(D) & l3_lattices(D)) ) )  &  (m1_subset_1(E, k1_zfmisc_1(B)) & m1_subset_1(F, u1_struct_0(k3_lattice3(D)))) ) ) )  =>  (r2_hidden(A, a_5_1_lattice3(B, C, D, E, F)) <=>  (? [G] :  (m1_subset_1(G, B) &  (A=k1_funct_1(C, k2_tarski(G, F)) & r2_tarski(G, E)) ) ) ) ) ) ).
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(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(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(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_lattice3, axiom,  (? [A] :  (l1_orders_2(A) &  ( ~ (v2_struct_0(A))  &  (v1_orders_2(A) &  (v2_orders_2(A) &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) & v3_lattice3(A)) ) ) ) ) ) ) ) ).
fof(rc1_orders_2, axiom,  (? [A] :  (l1_orders_2(A) & v1_orders_2(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_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc2_lattice3, axiom,  (? [A] :  (l1_orders_2(A) &  ( ~ (v2_struct_0(A))  &  (v1_orders_2(A) &  (v2_orders_2(A) &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v1_lattice3(A) &  (v2_lattice3(A) & v3_lattice3(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_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(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_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc4_orders_2, axiom,  (? [A] :  (l1_orders_2(A) &  (v2_struct_0(A) & v1_orders_2(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_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_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(rc9_lattices, axiom,  (? [A] :  (l3_lattices(A) &  ( ~ (v2_struct_0(A))  &  (v3_lattices(A) & v10_lattices(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_k1_domain_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, A) & m1_subset_1(D, B)) ) )  => k1_domain_1(A, B, C, D)=k4_tarski(C, D)) ) ).
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_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => k3_funct_2(A, B, C, D)=k1_funct_1(C, D)) ) ).
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_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_k5_setfam_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => k5_setfam_1(A, B)=k3_tarski(B)) ) ).
fof(redefinition_k6_domain_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => k6_domain_1(A, B)=k1_tarski(B)) ) ).
fof(redefinition_k7_domain_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) & m1_subset_1(C, A)) )  => k7_domain_1(A, B, C)=k2_tarski(B, C)) ) ).
fof(redefinition_k7_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => k7_relset_1(A, B, C, D)=k7_relat_1(C, D)) ) ).
fof(redefinition_k8_domain_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) &  (m1_subset_1(C, A) & m1_subset_1(D, A)) ) )  => k8_domain_1(A, B, C, D)=k1_enumset1(B, C, D)) ) ).
fof(redefinition_k9_setfam_1, axiom,  (! [A] : k9_setfam_1(A)=k1_zfmisc_1(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(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(s1_lattice3__e3_91_6_3_1_1_2__lattice3, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_partfun1(B, A) &  (v1_relat_2(B) &  (v4_relat_2(B) &  (v8_relat_2(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A)))) ) ) )  &  (m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, u1_struct_0(g1_orders_2(A, B)))) ) )  =>  ( (? [E] :  (m1_subset_1(E, A) & r2_tarski(E, C)) )  => a_4_1_lattice3(A, B, C, D)=k1_tarski(D)) ) ) ).
fof(s1_lattice3__e3_91_8_2_1_1_2__lattice3, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v2_struct_0(B))  &  (v3_lattices(B) &  (v10_lattices(B) & l3_lattices(B)) ) )  &  (m1_subset_1(C, k1_zfmisc_1(A)) & m1_subset_1(D, u1_struct_0(k3_lattice3(B)))) ) )  =>  ( (? [E] :  (m1_subset_1(E, A) & r2_tarski(E, C)) )  => a_4_2_lattice3(A, B, C, D)=k1_tarski(D)) ) ) ).
fof(s1_relset_1__e3_91__lattice3, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  (v1_funct_1(B) &  (v1_funct_2(B, k9_setfam_1(A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A), A)))) ) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, A))) &  (! [D] :  (! [E] :  (r2_hidden(k4_tarski(D, E), C) <=>  (r2_hidden(D, A) &  (r2_hidden(E, A) & k1_funct_1(B, k2_tarski(D, E))=E) ) ) ) ) ) ) ) ) ).
fof(s2_lattice3__e6_91_2__lattice3, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k9_setfam_1(A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A), A)))) )  &  (m1_subset_1(C, A) & m1_subset_1(D, k1_zfmisc_1(A))) ) )  =>  (r1_tarski(k1_zfmisc_1(A), k9_xtuple_0(B)) => k7_relat_1(B, a_3_22_lattice3(A, C, D))=a_4_3_lattice3(A, B, C, D)) ) ) ).
fof(s6_fraenkel__e1_91_6_3_1_1_2__lattice3, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k9_setfam_1(A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A), A)))) )  &  ( (v1_partfun1(C, A) &  (v1_relat_2(C) &  (v4_relat_2(C) &  (v8_relat_2(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, A)))) ) ) )  &  (m1_subset_1(D, k1_zfmisc_1(A)) & m1_subset_1(E, u1_struct_0(g1_orders_2(A, C)))) ) ) )  =>  ( (! [F] :  (m1_subset_1(F, A) =>  (r2_tarski(F, D) => k1_funct_1(B, k2_tarski(F, E))=E) ) )  => a_5_0_lattice3(A, B, C, D, E)=a_4_1_lattice3(A, C, D, E)) ) ) ).
fof(s6_fraenkel__e1_91_8_2_1_1_2__lattice3, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k9_setfam_1(A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A), A)))) )  &  ( ( ~ (v2_struct_0(C))  &  (v3_lattices(C) &  (v10_lattices(C) & l3_lattices(C)) ) )  &  (m1_subset_1(D, k1_zfmisc_1(A)) & m1_subset_1(E, u1_struct_0(k3_lattice3(C)))) ) ) )  =>  ( (! [F] :  (m1_subset_1(F, A) =>  (r2_tarski(F, D) => k1_funct_1(B, k2_tarski(F, E))=E) ) )  => a_5_1_lattice3(A, B, C, D, E)=a_4_2_lattice3(A, C, D, E)) ) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(t12_lattice3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_orders_2(A))  =>  (v3_lattice3(A) =>  (v1_lattice3(A) & v2_lattice3(A)) ) ) ) ).
fof(t13_orders_1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  (r1_relat_2(B, A) =>  (k1_relset_1(A, B)=A & k1_relat_1(B)=A) ) ) ) ) ).
fof(t17_xboole_1, axiom,  (! [A] :  (! [B] : r1_tarski(k3_xboole_0(A, B), A)) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t1_tarski, axiom, $true).
fof(t1_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r1_tarski(A, B) & r1_tarski(B, C))  => r1_tarski(A, C)) ) ) ) ).
fof(t29_enumset1, axiom,  (! [A] : k2_tarski(A, A)=k1_tarski(A)) ).
fof(t2_boole, axiom,  (! [A] : k3_xboole_0(A, k1_xboole_0)=k1_xboole_0) ).
fof(t2_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] : k1_enumset1(A, B, C)=k2_xboole_0(k1_tarski(A), k2_tarski(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(t30_lattice3, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v10_lattices(B) & l3_lattices(B)) )  =>  (! [C] :  (m1_subset_1(C, u1_struct_0(B)) =>  (r4_lattice3(B, C, A) <=> r2_lattice3(k3_lattice3(B), A, k4_lattice3(B, C))) ) ) ) ) ) ).
fof(t31_lattice3, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v10_lattices(B) & l3_lattices(B)) )  =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k3_lattice3(B))) =>  (r2_lattice3(k3_lattice3(B), A, C) <=> r4_lattice3(B, k5_lattice3(B, C), A)) ) ) ) ) ) ).
fof(t3_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] : k1_enumset1(A, B, C)=k2_xboole_0(k2_tarski(A, B), k1_tarski(C))) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t40_zfmisc_1, axiom,  (! [A] :  (! [B] :  (r2_hidden(A, B) => k2_xboole_0(k1_tarski(A), B)=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(t60_funct_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  ( (r2_hidden(A, k9_xtuple_0(C)) & r2_hidden(B, k9_xtuple_0(C)))  => k7_relat_1(C, k2_tarski(A, B))=k2_tarski(k1_funct_1(C, A), k1_funct_1(C, B))) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t74_zfmisc_1, axiom,  (! [A] :  (! [B] :  (r2_tarski(B, A) => r1_tarski(B, k3_tarski(A))) ) ) ).
fof(t75_zfmisc_1, axiom,  (! [A] :  (! [B] : k3_tarski(k2_tarski(A, B))=k2_xboole_0(A, B)) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_lattice3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v10_lattices(A) & l3_lattices(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r3_lattices(A, B, C) <=> r3_orders_2(k3_lattice3(A), k4_lattice3(A, B), k4_lattice3(A, C))) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
