% Mizar problem: t42_closure2,closure2,1736,5 
fof(t42_closure2, conjecture,  (! [A] :  (l1_struct_0(A) =>  (! [B] :  ( (v15_closure2(B, A) & l1_closure2(B, A))  => k10_closure2(A, u3_msualg_1(A, B), k12_closure2(A, B))=g1_closure2(A, u3_msualg_1(A, B), u1_closure2(A, B))) ) ) ) ).
fof(abstractness_v11_closure2, axiom,  (! [A, B] :  ( (l1_struct_0(A) & l1_closure2(B, A))  =>  (v11_closure2(B, A) => B=g1_closure2(A, u3_msualg_1(A, B), u1_closure2(A, B))) ) ) ).
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_closure2, axiom,  (! [A] :  (l1_struct_0(A) =>  (! [B] :  (l1_closure2(B, A) =>  (v15_closure2(B, A) => v16_closure2(B, A)) ) ) ) ) ).
fof(cc11_closure2, axiom,  (! [A] :  (l1_struct_0(A) =>  (! [B] :  (l1_closure2(B, A) =>  (v13_closure2(B, A) => v17_closure2(B, A)) ) ) ) ) ).
fof(cc1_closure2, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) =>  (v2_closure2(C, A, B) => v1_closure2(C, A, B)) ) ) ) ) ).
fof(cc1_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_finset_1(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_pboole, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  =>  (v1_relat_1(B) &  ( ~ (v3_relat_1(B))  &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ) ) ).
fof(cc1_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(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_closure2, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) =>  (v4_closure2(C, A, B) => v3_closure2(C, A, B)) ) ) ) ) ).
fof(cc2_finset_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_finset_1(B)) ) ) ) ).
fof(cc2_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funcop_1(A)) ) ) ) ).
fof(cc2_funct_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_pboole, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v3_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  =>  (v1_relat_1(B) &  ( ~ (v2_relat_1(B))  &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ) ) ).
fof(cc2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(B)) ) ) ) ).
fof(cc2_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_closure2, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) =>  (v4_closure2(C, A, B) => v5_closure2(C, A, B)) ) ) ) ) ).
fof(cc3_finset_1, axiom,  (! [A, B] :  (v1_finset_1(A) =>  (! [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_funct_2(C, A, B) & v1_finset_1(C)) ) ) ) ) ) ) ).
fof(cc3_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ) ).
fof(cc3_funct_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_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(A)) ) ) ).
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_closure2, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) =>  (v5_closure2(C, A, B) =>  ~ (v1_xboole_0(C)) ) ) ) ) ) ).
fof(cc4_finset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) => v1_finset_1(A)) ) ).
fof(cc4_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc4_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  (v1_funct_2(B, A, A) => v1_partfun1(B, A)) ) ) ) ).
fof(cc4_pboole, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  =>  (v1_relat_1(B) &  ( ~ (v3_relat_1(B))  &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ) ) ).
fof(cc4_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_1(A)) ) ) ).
fof(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(cc5_closure2, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) =>  (v2_closure2(C, A, B) => v6_closure2(C, A, B)) ) ) ) ) ).
fof(cc5_finset_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_zfmisc_1(A)) ) ) ).
fof(cc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc5_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A))) =>  (v1_funct_2(B, k2_zfmisc_1(A, A), A) => v1_partfun1(B, k2_zfmisc_1(A, A))) ) ) ) ).
fof(cc5_pboole, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  ( ~ (v1_xboole_0(B))  &  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ) ) ).
fof(cc5_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v4_relat_1(C, A)) ) ) ) ).
fof(cc5_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc6_closure2, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) =>  (v6_closure2(C, A, B) =>  ~ (v1_xboole_0(C)) ) ) ) ) ) ).
fof(cc6_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_finset_1(A)) ) ).
fof(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc7_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finset_1(B)) ) ) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v4_relat_1(B, A)) ) ) ) ) ) ).
fof(cc8_closure2, axiom,  (! [A] :  (l1_struct_0(A) =>  (! [B] :  (l1_closure2(B, A) =>  (v13_closure2(B, A) => v12_closure2(B, A)) ) ) ) ) ).
fof(cc8_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_finset_1(B)) ) ) ) ).
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(cc9_closure2, axiom,  (! [A] :  (l1_struct_0(A) =>  (! [B] :  (l1_closure2(B, A) =>  (v15_closure2(B, A) => v14_closure2(B, A)) ) ) ) ) ).
fof(cc9_finset_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_finset_1(A)) ) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(cc9_funct_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(d10_pboole, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) )  =>  (r6_pboole(A, B, C) <=>  (! [D] :  (r2_hidden(D, A) => k1_funct_1(B, D)=k1_funct_1(C, D)) ) ) ) ) ) ) ) ).
fof(d10_xboole_0, axiom,  (! [A] :  (! [B] :  (A=B <=>  (r1_tarski(A, B) & r1_tarski(B, A)) ) ) ) ).
fof(d18_pboole, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) )  =>  (m3_pboole(C, A, B) <=> r2_pboole(A, C, B)) ) ) ) ) ) ).
fof(d1_mssubfam, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  (m3_pboole(C, A, k1_mboolean(A, B)) =>  (! [D] :  ( (v1_relat_1(D) &  (v4_relat_1(D, A) &  (v1_funct_1(D) & v1_partfun1(D, A)) ) )  =>  (D=k3_mssubfam(A, B, C) <=>  (! [E] :  ~ ( (r2_hidden(E, A) &  (! [F] :  (m1_subset_1(F, k1_zfmisc_1(k1_zfmisc_1(k1_funct_1(B, E)))) =>  ~ ( (F=k1_funct_1(C, E) & k1_funct_1(D, E)=k8_setfam_1(k1_funct_1(B, E), F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d21_closure2, axiom,  (! [A] :  (l1_struct_0(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k6_closure2(u1_struct_0(A), B), k6_closure2(u1_struct_0(A), B)) &  (v7_closure2(C, u1_struct_0(A), B) &  (v8_closure2(C, u1_struct_0(A), B) &  (v9_closure2(C, u1_struct_0(A), B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k6_closure2(u1_struct_0(A), B), k6_closure2(u1_struct_0(A), B))))) ) ) ) )  =>  (! [D] :  ( (v11_closure2(D, A) & l1_closure2(D, A))  =>  (D=k10_closure2(A, B, C) <=>  (r6_pboole(u1_struct_0(A), u3_msualg_1(A, D), B) & u1_closure2(A, D)=a_3_0_closure2(A, B, C)) ) ) ) ) ) ) ) ) ) ).
fof(d22_closure2, axiom,  (! [A] :  (l1_struct_0(A) =>  (! [B] :  ( (v15_closure2(B, A) & l1_closure2(B, A))  =>  (! [C] :  (m3_pboole(C, u1_struct_0(A), u3_msualg_1(A, B)) =>  (! [D] :  (m1_closure2(D, u1_struct_0(A), u3_msualg_1(A, B), k6_closure2(u1_struct_0(A), u3_msualg_1(A, B))) =>  (D=k11_closure2(A, B, C) <=>  (? [E] :  (m1_subset_1(E, k1_zfmisc_1(k1_closure2(u1_struct_0(A), u3_msualg_1(A, B)))) &  (r6_pboole(u1_struct_0(A), D, k4_mssubfam(u1_struct_0(A), u3_msualg_1(A, B), k5_closure2(u1_struct_0(A), u3_msualg_1(A, B), E))) & E=a_3_1_closure2(A, B, C)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d23_closure2, axiom,  (! [A] :  (l1_struct_0(A) =>  (! [B] :  ( (v15_closure2(B, A) & l1_closure2(B, A))  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k6_closure2(u1_struct_0(A), u3_msualg_1(A, B)), k6_closure2(u1_struct_0(A), u3_msualg_1(A, B))) &  (v7_closure2(C, u1_struct_0(A), u3_msualg_1(A, B)) &  (v8_closure2(C, u1_struct_0(A), u3_msualg_1(A, B)) &  (v9_closure2(C, u1_struct_0(A), u3_msualg_1(A, B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k6_closure2(u1_struct_0(A), u3_msualg_1(A, B)), k6_closure2(u1_struct_0(A), u3_msualg_1(A, B)))))) ) ) ) )  =>  (C=k12_closure2(A, B) <=>  (! [D] :  (m1_closure2(D, u1_struct_0(A), u3_msualg_1(A, B), k6_closure2(u1_struct_0(A), u3_msualg_1(A, B))) => r6_pboole(u1_struct_0(A), k7_closure2(u1_struct_0(A), u3_msualg_1(A, B), C, D), k11_closure2(A, B, D))) ) ) ) ) ) ) ) ) ).
fof(d2_pboole, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) )  =>  (r2_pboole(A, B, C) <=>  (! [D] :  (r2_hidden(D, A) => r1_tarski(k1_funct_1(B, D), k1_funct_1(C, D))) ) ) ) ) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d7_closure2, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) =>  (v4_closure2(C, A, B) <=>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(k1_closure2(A, B))) =>  (r1_tarski(D, C) => r2_tarski(k4_mssubfam(A, B, k5_closure2(A, B, D)), C)) ) ) ) ) ) ) ) ) ).
fof(d8_closure2, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) =>  (v5_closure2(C, A, B) <=> r2_tarski(B, C)) ) ) ) ) ) ).
fof(dt_g1_closure2, axiom,  (! [A, B, C] :  ( (l1_struct_0(A) &  ( (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) )  & m1_subset_1(C, k1_zfmisc_1(k1_closure2(u1_struct_0(A), B)))) )  =>  (v11_closure2(g1_closure2(A, B, C), A) & l1_closure2(g1_closure2(A, B, C), A)) ) ) ).
fof(dt_k10_closure2, axiom,  (! [A, B, C] :  ( (l1_struct_0(A) &  ( (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) )  &  (v1_funct_1(C) &  (v1_funct_2(C, k6_closure2(u1_struct_0(A), B), k6_closure2(u1_struct_0(A), B)) &  (v7_closure2(C, u1_struct_0(A), B) &  (v8_closure2(C, u1_struct_0(A), B) &  (v9_closure2(C, u1_struct_0(A), B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k6_closure2(u1_struct_0(A), B), k6_closure2(u1_struct_0(A), B))))) ) ) ) ) ) )  =>  (v11_closure2(k10_closure2(A, B, C), A) & l1_closure2(k10_closure2(A, B, C), A)) ) ) ).
fof(dt_k11_closure2, axiom,  (! [A, B, C] :  ( (l1_struct_0(A) &  ( (v15_closure2(B, A) & l1_closure2(B, A))  & m3_pboole(C, u1_struct_0(A), u3_msualg_1(A, B))) )  => m1_closure2(k11_closure2(A, B, C), u1_struct_0(A), u3_msualg_1(A, B), k6_closure2(u1_struct_0(A), u3_msualg_1(A, B)))) ) ).
fof(dt_k12_closure2, axiom,  (! [A, B] :  ( (l1_struct_0(A) &  (v15_closure2(B, A) & l1_closure2(B, A)) )  =>  (v1_funct_1(k12_closure2(A, B)) &  (v1_funct_2(k12_closure2(A, B), k6_closure2(u1_struct_0(A), u3_msualg_1(A, B)), k6_closure2(u1_struct_0(A), u3_msualg_1(A, B))) &  (v7_closure2(k12_closure2(A, B), u1_struct_0(A), u3_msualg_1(A, B)) &  (v8_closure2(k12_closure2(A, B), u1_struct_0(A), u3_msualg_1(A, B)) &  (v9_closure2(k12_closure2(A, B), u1_struct_0(A), u3_msualg_1(A, B)) & m1_subset_1(k12_closure2(A, B), k1_zfmisc_1(k2_zfmisc_1(k6_closure2(u1_struct_0(A), u3_msualg_1(A, B)), k6_closure2(u1_struct_0(A), u3_msualg_1(A, B)))))) ) ) ) ) ) ) ).
fof(dt_k1_closure2, axiom, $true).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_mboolean, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (v1_relat_1(k1_mboolean(A, B)) &  (v4_relat_1(k1_mboolean(A, B), A) &  (v1_funct_1(k1_mboolean(A, B)) & v1_partfun1(k1_mboolean(A, B), A)) ) ) ) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_closure2, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  => m1_subset_1(k2_closure2(A, B), k1_zfmisc_1(k1_closure2(A, B)))) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_mssubfam, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  & m3_pboole(C, A, k1_mboolean(A, B)))  =>  (v1_relat_1(k3_mssubfam(A, B, C)) &  (v4_relat_1(k3_mssubfam(A, B, C), A) &  (v1_funct_1(k3_mssubfam(A, B, C)) & v1_partfun1(k3_mssubfam(A, B, C), A)) ) ) ) ) ).
fof(dt_k4_closure2, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  & m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))))  =>  (v1_relat_1(k4_closure2(A, B, C)) &  (v4_relat_1(k4_closure2(A, B, C), A) &  (v1_funct_1(k4_closure2(A, B, C)) & v1_partfun1(k4_closure2(A, B, C), A)) ) ) ) ) ).
fof(dt_k4_mssubfam, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  & m3_pboole(C, A, k1_mboolean(A, B)))  => m3_pboole(k4_mssubfam(A, B, C), A, B)) ) ).
fof(dt_k5_closure2, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  & m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))))  => m3_pboole(k5_closure2(A, B, C), A, k1_mboolean(A, B))) ) ).
fof(dt_k6_closure2, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (v1_closure2(k6_closure2(A, B), A, B) &  (v2_closure2(k6_closure2(A, B), A, B) &  (v3_closure2(k6_closure2(A, B), A, B) &  (v4_closure2(k6_closure2(A, B), A, B) &  (v5_closure2(k6_closure2(A, B), A, B) &  (v6_closure2(k6_closure2(A, B), A, B) & m1_subset_1(k6_closure2(A, B), k1_zfmisc_1(k1_closure2(A, B)))) ) ) ) ) ) ) ) ).
fof(dt_k7_closure2, axiom,  (! [A, B, C, D] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k6_closure2(A, B), k6_closure2(A, B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k6_closure2(A, B), k6_closure2(A, B))))) )  & m1_subset_1(D, k6_closure2(A, B))) )  => m1_closure2(k7_closure2(A, B, C, D), A, B, k6_closure2(A, B))) ) ).
fof(dt_k8_setfam_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k8_setfam_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_l1_closure2, axiom,  (! [A] :  (l1_struct_0(A) =>  (! [B] :  (l1_closure2(B, A) => l2_msualg_1(B, A)) ) ) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_msualg_1, axiom, $true).
fof(dt_m1_closure2, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) )  =>  (! [D] :  (m1_closure2(D, A, B, C) => m3_pboole(D, A, B)) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m3_pboole, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  (m3_pboole(C, A, B) =>  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) ) ) ) ).
fof(dt_u1_closure2, axiom,  (! [A, B] :  ( (l1_struct_0(A) & l1_closure2(B, A))  => m1_subset_1(u1_closure2(A, B), k1_zfmisc_1(k1_closure2(u1_struct_0(A), u3_msualg_1(A, B))))) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u3_msualg_1, axiom,  (! [A, B] :  ( (l1_struct_0(A) & l2_msualg_1(B, A))  =>  (v1_relat_1(u3_msualg_1(A, B)) &  (v4_relat_1(u3_msualg_1(A, B), u1_struct_0(A)) &  (v1_funct_1(u3_msualg_1(A, B)) & v1_partfun1(u3_msualg_1(A, B), u1_struct_0(A))) ) ) ) ) ).
fof(existence_l1_closure2, axiom,  (! [A] :  (l1_struct_0(A) =>  (? [B] : l1_closure2(B, A)) ) ) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_msualg_1, axiom,  (! [A] :  (l1_struct_0(A) =>  (? [B] : l2_msualg_1(B, A)) ) ) ).
fof(existence_m1_closure2, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) )  =>  (? [D] : m1_closure2(D, A, B, C)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m3_pboole, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (? [C] : m3_pboole(C, A, B)) ) ) ).
fof(fc10_closure2, axiom,  (! [A, B] :  ( (l1_struct_0(A) &  (v15_closure2(B, A) & l1_closure2(B, A)) )  => v4_closure2(u1_closure2(A, B), u1_struct_0(A), u3_msualg_1(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_closure2, axiom,  (! [A, B] :  ( (l1_struct_0(A) &  (v16_closure2(B, A) & l1_closure2(B, A)) )  => v5_closure2(u1_closure2(A, B), u1_struct_0(A), u3_msualg_1(A, B))) ) ).
fof(fc12_closure2, axiom,  (! [A, B] :  ( (l1_struct_0(A) &  (v17_closure2(B, A) & l1_closure2(B, A)) )  => v6_closure2(u1_closure2(A, B), u1_struct_0(A), u3_msualg_1(A, B))) ) ).
fof(fc13_closure2, axiom,  (! [A, B, C] :  ( (l1_struct_0(A) &  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) ) )  & m1_subset_1(C, k1_zfmisc_1(k1_closure2(u1_struct_0(A), B)))) )  =>  (v4_msualg_1(g1_closure2(A, B, C), A) & v11_closure2(g1_closure2(A, B, C), A)) ) ) ).
fof(fc14_closure2, axiom,  (! [A, B, C] :  ( (l1_struct_0(A) &  (l2_msualg_1(B, A) &  (v1_closure2(C, u1_struct_0(A), u3_msualg_1(A, B)) & m1_subset_1(C, k1_zfmisc_1(k1_closure2(u1_struct_0(A), u3_msualg_1(A, B))))) ) )  =>  (v11_closure2(g1_closure2(A, u3_msualg_1(A, B), C), A) & v12_closure2(g1_closure2(A, u3_msualg_1(A, B), C), A)) ) ) ).
fof(fc14_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v1_finset_1(k2_zfmisc_1(A, B))) ) ).
fof(fc15_closure2, axiom,  (! [A, B, C] :  ( (l1_struct_0(A) &  (l2_msualg_1(B, A) &  (v2_closure2(C, u1_struct_0(A), u3_msualg_1(A, B)) & m1_subset_1(C, k1_zfmisc_1(k1_closure2(u1_struct_0(A), u3_msualg_1(A, B))))) ) )  =>  (v11_closure2(g1_closure2(A, u3_msualg_1(A, B), C), A) & v13_closure2(g1_closure2(A, u3_msualg_1(A, B), C), A)) ) ) ).
fof(fc16_closure2, axiom,  (! [A, B, C] :  ( (l1_struct_0(A) &  (l2_msualg_1(B, A) &  (v3_closure2(C, u1_struct_0(A), u3_msualg_1(A, B)) & m1_subset_1(C, k1_zfmisc_1(k1_closure2(u1_struct_0(A), u3_msualg_1(A, B))))) ) )  =>  (v11_closure2(g1_closure2(A, u3_msualg_1(A, B), C), A) & v14_closure2(g1_closure2(A, u3_msualg_1(A, B), C), A)) ) ) ).
fof(fc17_closure2, axiom,  (! [A, B, C] :  ( (l1_struct_0(A) &  (l2_msualg_1(B, A) &  (v4_closure2(C, u1_struct_0(A), u3_msualg_1(A, B)) & m1_subset_1(C, k1_zfmisc_1(k1_closure2(u1_struct_0(A), u3_msualg_1(A, B))))) ) )  =>  (v11_closure2(g1_closure2(A, u3_msualg_1(A, B), C), A) & v15_closure2(g1_closure2(A, u3_msualg_1(A, B), C), A)) ) ) ).
fof(fc17_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v1_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc18_closure2, axiom,  (! [A, B, C] :  ( (l1_struct_0(A) &  (l2_msualg_1(B, A) &  (v5_closure2(C, u1_struct_0(A), u3_msualg_1(A, B)) & m1_subset_1(C, k1_zfmisc_1(k1_closure2(u1_struct_0(A), u3_msualg_1(A, B))))) ) )  =>  (v11_closure2(g1_closure2(A, u3_msualg_1(A, B), C), A) & v16_closure2(g1_closure2(A, u3_msualg_1(A, B), C), A)) ) ) ).
fof(fc19_closure2, axiom,  (! [A, B, C] :  ( (l1_struct_0(A) &  (l2_msualg_1(B, A) &  (v6_closure2(C, u1_struct_0(A), u3_msualg_1(A, B)) & m1_subset_1(C, k1_zfmisc_1(k1_closure2(u1_struct_0(A), u3_msualg_1(A, B))))) ) )  =>  (v11_closure2(g1_closure2(A, u3_msualg_1(A, B), C), A) & v17_closure2(g1_closure2(A, u3_msualg_1(A, B), C), A)) ) ) ).
fof(fc19_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v3_relat_1(A) & v1_funct_1(A)) )  => v1_xboole_0(k1_funct_1(A, B))) ) ).
fof(fc1_closure2, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  ( ~ (v1_xboole_0(k1_closure2(A, B)))  &  (v4_funct_1(k1_closure2(A, B)) & v2_card_3(k1_closure2(A, B))) ) ) ) ).
fof(fc1_msualg_1, axiom,  (! [A, B] :  ( (l1_struct_0(A) &  (v4_msualg_1(B, A) & l2_msualg_1(B, A)) )  =>  (v1_relat_1(u3_msualg_1(A, B)) &  (v2_relat_1(u3_msualg_1(A, B)) &  (v4_relat_1(u3_msualg_1(A, B), u1_struct_0(A)) &  (v1_funct_1(u3_msualg_1(A, B)) & v1_partfun1(u3_msualg_1(A, B), 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(fc20_closure2, axiom,  (! [A, B, C] :  ( (l1_struct_0(A) &  ( (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) )  &  (v1_funct_1(C) &  (v1_funct_2(C, k6_closure2(u1_struct_0(A), B), k6_closure2(u1_struct_0(A), B)) &  (v7_closure2(C, u1_struct_0(A), B) &  (v8_closure2(C, u1_struct_0(A), B) &  (v9_closure2(C, u1_struct_0(A), B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k6_closure2(u1_struct_0(A), B), k6_closure2(u1_struct_0(A), B))))) ) ) ) ) ) )  =>  (v11_closure2(k10_closure2(A, B, C), A) & v15_closure2(k10_closure2(A, B, C), A)) ) ) ).
fof(fc2_pboole, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  & m1_subset_1(C, A)) )  =>  ~ (v1_xboole_0(k1_funct_1(B, C))) ) ) ).
fof(fc31_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v5_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc35_finset_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) )  => v1_finset_1(k1_funct_1(A, B))) ) ).
fof(fc3_closure2, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_xboole_0(C) & m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) )  =>  (v1_relat_1(k4_closure2(A, B, C)) &  (v3_relat_1(k4_closure2(A, B, C)) &  (v4_relat_1(k4_closure2(A, B, C), A) &  (v1_funct_1(k4_closure2(A, B, C)) & v1_partfun1(k4_closure2(A, B, C), A)) ) ) ) ) ) ).
fof(fc4_closure2, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) )  =>  (v1_relat_1(k4_closure2(A, B, C)) &  (v2_relat_1(k4_closure2(A, B, C)) &  (v4_relat_1(k4_closure2(A, B, C), A) &  (v1_funct_1(k4_closure2(A, B, C)) & v1_partfun1(k4_closure2(A, B, C), A)) ) ) ) ) ) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc7_closure2, axiom,  (! [A, B] :  ( (l1_struct_0(A) &  (v12_closure2(B, A) & l1_closure2(B, A)) )  => v1_closure2(u1_closure2(A, B), u1_struct_0(A), u3_msualg_1(A, B))) ) ).
fof(fc8_closure2, axiom,  (! [A, B] :  ( (l1_struct_0(A) &  (v13_closure2(B, A) & l1_closure2(B, A)) )  => v2_closure2(u1_closure2(A, B), u1_struct_0(A), u3_msualg_1(A, B))) ) ).
fof(fc9_closure2, axiom,  (! [A, B] :  ( (l1_struct_0(A) &  (v14_closure2(B, A) & l1_closure2(B, A)) )  => v3_closure2(u1_closure2(A, B), u1_struct_0(A), u3_msualg_1(A, B))) ) ).
fof(fc9_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_funct_1(A, B)) & v1_funct_1(k1_funct_1(A, B))) ) ) ).
fof(fraenkel_a_2_2_closure2, axiom,  (! [A, B, C] :  ( (l1_struct_0(B) &  (v15_closure2(C, B) & l1_closure2(C, B)) )  =>  (r2_hidden(A, a_2_2_closure2(B, C)) <=>  (? [D] :  (m1_closure2(D, u1_struct_0(B), u3_msualg_1(B, C), k6_closure2(u1_struct_0(B), u3_msualg_1(B, C))) &  (A=D & r6_pboole(u1_struct_0(B), k7_closure2(u1_struct_0(B), u3_msualg_1(B, C), k12_closure2(B, C), D), D)) ) ) ) ) ) ).
fof(fraenkel_a_3_0_closure2, axiom,  (! [A, B, C, D] :  ( (l1_struct_0(B) &  ( (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) & v1_partfun1(C, u1_struct_0(B))) ) )  &  (v1_funct_1(D) &  (v1_funct_2(D, k6_closure2(u1_struct_0(B), C), k6_closure2(u1_struct_0(B), C)) &  (v7_closure2(D, u1_struct_0(B), C) &  (v8_closure2(D, u1_struct_0(B), C) &  (v9_closure2(D, u1_struct_0(B), C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k6_closure2(u1_struct_0(B), C), k6_closure2(u1_struct_0(B), C))))) ) ) ) ) ) )  =>  (r2_hidden(A, a_3_0_closure2(B, C, D)) <=>  (? [E] :  (m1_closure2(E, u1_struct_0(B), C, k6_closure2(u1_struct_0(B), C)) &  (A=E & r6_pboole(u1_struct_0(B), k7_closure2(u1_struct_0(B), C, D, E), E)) ) ) ) ) ) ).
fof(fraenkel_a_3_10_closure2, axiom,  (! [A, B, C, D] :  ( (l1_struct_0(B) &  ( (v15_closure2(C, B) & l1_closure2(C, B))  & m1_closure2(D, u1_struct_0(B), u3_msualg_1(B, C), k6_closure2(u1_struct_0(B), u3_msualg_1(B, C)))) )  =>  (r2_hidden(A, a_3_10_closure2(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, k6_closure2(u1_struct_0(B), u3_msualg_1(B, C))) &  (A=E &  (r2_tarski(E, u1_closure2(B, C)) & r2_pboole(u1_struct_0(B), D, E)) ) ) ) ) ) ) ).
fof(fraenkel_a_3_1_closure2, axiom,  (! [A, B, C, D] :  ( (l1_struct_0(B) &  ( (v15_closure2(C, B) & l1_closure2(C, B))  & m3_pboole(D, u1_struct_0(B), u3_msualg_1(B, C))) )  =>  (r2_hidden(A, a_3_1_closure2(B, C, D)) <=>  (? [E] :  (m1_closure2(E, u1_struct_0(B), u3_msualg_1(B, C), k6_closure2(u1_struct_0(B), u3_msualg_1(B, C))) &  (A=E &  (r2_pboole(u1_struct_0(B), D, E) & r2_tarski(E, u1_closure2(B, C))) ) ) ) ) ) ) ).
fof(fraenkel_a_3_4_closure2, axiom,  (! [A, B, C, D] :  ( (l1_struct_0(B) &  ( (v15_closure2(C, B) & l1_closure2(C, B))  & m1_closure2(D, u1_struct_0(B), u3_msualg_1(B, C), k6_closure2(u1_struct_0(B), u3_msualg_1(B, C)))) )  =>  (r2_hidden(A, a_3_4_closure2(B, C, D)) <=>  (? [E] :  (m1_closure2(E, u1_struct_0(B), u3_msualg_1(B, C), k6_closure2(u1_struct_0(B), u3_msualg_1(B, C))) &  (A=E &  (r2_pboole(u1_struct_0(B), D, E) & r2_tarski(E, u1_closure2(B, C))) ) ) ) ) ) ) ).
fof(fraenkel_a_3_5_closure2, axiom,  (! [A, B, C, D] :  ( (l1_struct_0(B) &  ( (v15_closure2(C, B) & l1_closure2(C, B))  & m1_closure2(D, u1_struct_0(B), u3_msualg_1(B, C), k6_closure2(u1_struct_0(B), u3_msualg_1(B, C)))) )  =>  (r2_hidden(A, a_3_5_closure2(B, C, D)) <=>  (? [E] :  (m1_closure2(E, u1_struct_0(B), u3_msualg_1(B, C), k6_closure2(u1_struct_0(B), u3_msualg_1(B, C))) &  (A=E &  (r2_tarski(E, u1_closure2(B, C)) & r2_pboole(u1_struct_0(B), D, E)) ) ) ) ) ) ) ).
fof(fraenkel_a_3_8_closure2, axiom,  (! [A, B, C, D] :  ( (l1_struct_0(B) &  ( (v15_closure2(C, B) & l1_closure2(C, B))  & m1_closure2(D, u1_struct_0(B), u3_msualg_1(B, C), k6_closure2(u1_struct_0(B), u3_msualg_1(B, C)))) )  =>  (r2_hidden(A, a_3_8_closure2(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, k6_closure2(u1_struct_0(B), u3_msualg_1(B, C))) &  (A=E &  (r2_hidden(E, u1_closure2(B, C)) & r2_pboole(u1_struct_0(B), D, E)) ) ) ) ) ) ) ).
fof(fraenkel_a_3_9_closure2, axiom,  (! [A, B, C, D] :  ( (l1_struct_0(B) &  ( (v15_closure2(C, B) & l1_closure2(C, B))  & m1_closure2(D, u1_struct_0(B), u3_msualg_1(B, C), k6_closure2(u1_struct_0(B), u3_msualg_1(B, C)))) )  =>  (r2_hidden(A, a_3_9_closure2(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, k6_closure2(u1_struct_0(B), u3_msualg_1(B, C))) &  (A=E &  (r2_pboole(u1_struct_0(B), D, E) & r2_tarski(E, u1_closure2(B, C))) ) ) ) ) ) ) ).
fof(fraenkel_a_4_0_closure2, axiom,  (! [A, B, C, D, E] :  ( ( (v1_relat_1(C) &  (v4_relat_1(C, B) &  (v1_funct_1(C) & v1_partfun1(C, B)) ) )  & m1_subset_1(D, k1_zfmisc_1(k1_closure2(B, C))))  =>  (r2_hidden(A, a_4_0_closure2(B, C, D, E)) <=>  (? [F] :  (m1_closure2(F, B, C, k2_closure2(B, C)) &  (A=k1_funct_1(F, E) & r2_tarski(F, D)) ) ) ) ) ) ).
fof(fraenkel_a_4_5_closure2, axiom,  (! [A, B, C, D, E] :  ( (l1_struct_0(B) &  ( (v15_closure2(C, B) & l1_closure2(C, B))  &  ( ~ (v1_xboole_0(D))  & m1_subset_1(D, k1_zfmisc_1(k1_closure2(u1_struct_0(B), u3_msualg_1(B, C))))) ) )  =>  (r2_hidden(A, a_4_5_closure2(B, C, D, E)) <=>  (? [F] :  (m1_closure2(F, u1_struct_0(B), u3_msualg_1(B, C), k6_closure2(u1_struct_0(B), u3_msualg_1(B, C))) &  (A=k1_funct_1(F, E) & r2_tarski(F, D)) ) ) ) ) ) ).
fof(free_g1_closure2, axiom,  (! [A, B, C] :  ( (l1_struct_0(A) &  ( (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) )  & m1_subset_1(C, k1_zfmisc_1(k1_closure2(u1_struct_0(A), B)))) )  =>  (! [D, E, F] :  (g1_closure2(A, B, C)=g1_closure2(D, E, F) =>  (A=D &  (B=E & C=F) ) ) ) ) ) ).
fof(rc10_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) ) ) ) ).
fof(rc1_closure2, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) &  ( ~ (v1_xboole_0(C))  &  (v4_funct_1(C) & v2_card_3(C)) ) ) ) ) ) ).
fof(rc1_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_finset_1(A)) ) ).
fof(rc1_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_pboole, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
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(rc2_closure2, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) &  (v1_xboole_0(C) &  (v4_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ).
fof(rc2_finset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_finset_1(B)) ) ) ).
fof(rc2_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_funct_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_pboole, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v3_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc3_closure2, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) &  ( ~ (v1_xboole_0(C))  &  (v4_funct_1(C) &  (v2_card_3(C) &  (v1_closure2(C, A, B) &  (v2_closure2(C, A, B) &  (v3_closure2(C, A, B) &  (v4_closure2(C, A, B) &  (v5_closure2(C, A, B) & v6_closure2(C, A, B)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_finset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc3_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ).
fof(rc3_pboole, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc4_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(rc4_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(rc4_pboole, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_funcop_1(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_closure2, axiom,  (! [A] :  (l1_struct_0(A) =>  (? [B] :  (l1_closure2(B, A) & v11_closure2(B, A)) ) ) ) ).
fof(rc5_funcop_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc5_pboole, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  =>  (? [C] :  (m3_pboole(C, A, B) &  (v1_relat_1(C) &  (v2_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, 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_closure2, axiom,  (! [A] :  (l1_struct_0(A) =>  (? [B] :  (l1_closure2(B, A) &  (v4_msualg_1(B, A) &  (v11_closure2(B, A) &  (v12_closure2(B, A) &  (v13_closure2(B, A) &  (v14_closure2(B, A) &  (v15_closure2(B, A) &  (v16_closure2(B, A) & v17_closure2(B, A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc8_finset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_zfmisc_1(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc9_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) & v5_finset_1(A)) ) ) ).
fof(rc9_funct_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) ) ) ) ) ).
fof(redefinition_k2_closure2, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  => k2_closure2(A, B)=k1_closure2(A, B)) ) ).
fof(redefinition_k4_mssubfam, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  & m3_pboole(C, A, k1_mboolean(A, B)))  => k4_mssubfam(A, B, C)=k3_mssubfam(A, B, C)) ) ).
fof(redefinition_k5_closure2, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  & m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))))  => k5_closure2(A, B, C)=k4_closure2(A, B, C)) ) ).
fof(redefinition_k6_closure2, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  => k6_closure2(A, B)=k1_closure2(A, B)) ) ).
fof(redefinition_k7_closure2, axiom,  (! [A, B, C, D] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k6_closure2(A, B), k6_closure2(A, B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k6_closure2(A, B), k6_closure2(A, B))))) )  & m1_subset_1(D, k6_closure2(A, B))) )  => k7_closure2(A, B, C, D)=k1_funct_1(C, D)) ) ).
fof(redefinition_m1_closure2, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B)))) )  =>  (! [D] :  (m1_closure2(D, A, B, C) <=> m1_subset_1(D, C)) ) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(redefinition_r6_pboole, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) )  =>  (r6_pboole(A, B, C) <=> B=C) ) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(reflexivity_r2_pboole, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) )  => r2_pboole(A, B, B)) ) ).
fof(reflexivity_r6_pboole, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) )  => r6_pboole(A, B, B)) ) ).
fof(s17_fraenkel__e5_97_1__closure2, axiom,  (! [A, B, C] :  ( (l1_struct_0(A) &  ( (v15_closure2(B, A) & l1_closure2(B, A))  & m1_closure2(C, u1_struct_0(A), u3_msualg_1(A, B), k6_closure2(u1_struct_0(A), u3_msualg_1(A, B)))) )  => r1_tarski(a_3_8_closure2(A, B, C), u1_closure2(A, B))) ) ).
fof(s3_fraenkel__e7_97_1__closure2, axiom,  (! [A, B, C] :  ( (l1_struct_0(A) &  ( (v15_closure2(B, A) & l1_closure2(B, A))  & m1_closure2(C, u1_struct_0(A), u3_msualg_1(A, B), k6_closure2(u1_struct_0(A), u3_msualg_1(A, B)))) )  =>  ( (! [D] :  (m1_subset_1(D, k6_closure2(u1_struct_0(A), u3_msualg_1(A, B))) =>  ( (r2_pboole(u1_struct_0(A), C, D) & r2_tarski(D, u1_closure2(A, B)))  <=>  (r2_tarski(D, u1_closure2(A, B)) & r2_pboole(u1_struct_0(A), C, D)) ) ) )  => a_3_9_closure2(A, B, C)=a_3_10_closure2(A, B, C)) ) ) ).
fof(symmetry_r6_pboole, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) )  =>  (r6_pboole(A, B, C) => r6_pboole(A, C, B)) ) ) ).
fof(t14_closure2, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k1_closure2(A, B))) =>  ( ~ (v1_xboole_0(C))  =>  (! [D] :  (r2_tarski(D, A) => k1_funct_1(k4_closure2(A, B, C), D)=a_4_0_closure2(A, B, C, D)) ) ) ) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_mssubfam, axiom,  (! [A] :  (! [B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) =>  (r2_tarski(B, C) => r1_tarski(k8_setfam_1(A, C), 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(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_mssubfam, axiom,  (! [A] :  (! [B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))) =>  ( (! [D] :  (r2_tarski(D, C) => r1_tarski(B, D)) )  =>  (C=k1_xboole_0 | r1_tarski(B, k8_setfam_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)) ) ) ) ) ).
