% Mizar problem: t1_birkhoff,birkhoff,69,5 
fof(t1_birkhoff, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  ( (v4_msualg_1(B, A) & l3_msualg_1(B, A))  =>  (! [C] :  ( (v1_relat_1(C) &  (v2_relat_1(C) &  (v4_relat_1(C, u1_struct_0(A)) &  (v1_funct_1(C) & v1_partfun1(C, u1_struct_0(A))) ) ) )  =>  (! [D] :  (m2_pboole(D, u1_struct_0(A), C, u3_msualg_1(A, B)) => r2_pboole(u1_struct_0(A), k2_funct_6(D), k2_funct_6(k1_birkhoff(A, C, B, D)))) ) ) ) ) ) ) ) ).
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_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc12_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  ( ~ (v2_struct_0(A))  => v14_struct_0(A)) ) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc13_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  (v11_struct_0(A) => v14_struct_0(A)) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(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_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(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_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc16_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  (v11_struct_0(A) => v15_struct_0(A)) ) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_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_msafree1, axiom,  (! [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) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_prob_2(B)) ) ) ) ) ) ) ).
fof(cc1_msafree2, axiom,  (! [A] :  (l1_msualg_1(A) =>  ( ( ~ (v2_struct_0(A))  & v11_struct_0(A))  =>  ( ~ (v2_struct_0(A))  & v2_msafree2(A)) ) ) ) ).
fof(cc1_mssubfam, axiom,  (! [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) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v2_finset_1(B)) ) ) ) ) ) ) ).
fof(cc1_msualg_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  &  (v4_msualg_1(B, A) & l3_msualg_1(B, A)) )  =>  (! [C] :  (m1_subset_1(C, k10_xtuple_0(u3_msualg_1(A, B))) =>  ~ (v1_xboole_0(C)) ) ) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
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_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(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funcop_1(A)) ) ) ) ).
fof(cc2_funct_2, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc2_mssubfam, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v2_finset_1(B)) ) ) )  =>  (! [C] :  (m3_pboole(C, A, B) => v2_finset_1(C)) ) ) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(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_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(cc3_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ) ).
fof(cc3_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc3_msafree2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(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, u1_struct_0(A))) )  =>  (! [D] :  (m1_subset_1(D, k1_funct_1(u3_msualg_1(A, k11_msafree(A, B)), C)) =>  (v1_relat_1(D) &  ( ~ (v1_xboole_0(D))  &  (v1_funct_1(D) & v1_finset_1(D)) ) ) ) ) ) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc3_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)) ) ) )  =>  (! [D] :  (m2_pboole(D, A, B, C) => v1_funcop_1(D)) ) ) ) ).
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(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_msafree2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(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, u1_struct_0(A))) )  =>  (! [D] :  (m1_subset_1(D, k1_funct_1(u3_msualg_1(A, k11_msafree(A, B)), C)) =>  ( (v1_relat_1(D) & v1_funct_1(D))  =>  (v1_relat_1(D) &  (v1_funct_1(D) & v3_trees_2(D)) ) ) ) ) ) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(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_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(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_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
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_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(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(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_birkhoff, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  ( (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))) ) ) )  =>  (! [C] :  ( (v4_msualg_1(C, A) & l3_msualg_1(C, A))  =>  (! [D] :  (m2_pboole(D, u1_struct_0(A), B, u3_msualg_1(A, C)) =>  (! [E] :  (m2_pboole(E, u1_struct_0(A), u3_msualg_1(A, k11_msafree(A, B)), u3_msualg_1(A, C)) =>  (E=k1_birkhoff(A, B, C, D) <=>  (r1_msualg_3(A, k11_msafree(A, B), C, E) & r8_pboole(u1_struct_0(A), k1_msafree(u1_struct_0(A), u3_msualg_1(A, k11_msafree(A, B)), u3_msualg_1(A, C), k13_msafree(A, B), E), k3_msualg_3(u1_struct_0(A), k13_msafree(A, B), B, u3_msualg_1(A, C), k15_msafree(A, B), D))) ) ) ) ) ) ) ) ) ) ) ) ).
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_msafree, 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)) ) )  =>  (! [D] :  (m3_pboole(D, A, B) =>  (! [E] :  (m2_pboole(E, A, B, C) =>  (! [F] :  (m2_pboole(F, A, D, C) =>  (F=k1_msafree(A, B, C, D, E) <=>  (! [G] :  (r2_tarski(G, A) => k1_funct_1(F, G)=k5_relat_1(k1_funct_1(E, G), k1_funct_1(D, G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d21_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)) ) )  =>  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) )  =>  (r8_pboole(A, B, C) <=>  (! [D] :  (m1_subset_1(D, A) => k1_funct_1(B, D)=k1_funct_1(C, 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_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (B=k10_xtuple_0(A) <=>  (! [C] :  (r2_hidden(C, B) <=>  (? [D] :  (r2_hidden(D, k9_xtuple_0(A)) & C=k1_funct_1(A, D)) ) ) ) ) ) ) ) ).
fof(d3_msualg_3, 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)) ) )  =>  (! [D] :  (m2_pboole(D, A, B, C) =>  (v2_msualg_3(D, A, B, C) <=>  (! [E] :  (r2_tarski(E, A) => k10_xtuple_0(k1_funct_1(D, E))=k1_funct_1(C, E)) ) ) ) ) ) ) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k11_msafree, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(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))) ) ) ) )  => l3_msualg_1(k11_msafree(A, B), A)) ) ).
fof(dt_k13_msafree, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(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_msafree(k13_msafree(A, B), A, k11_msafree(A, B))) ) ).
fof(dt_k15_msafree, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(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))) ) ) ) )  => m2_pboole(k15_msafree(A, B), u1_struct_0(A), k13_msafree(A, B), B)) ) ).
fof(dt_k1_birkhoff, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(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))) ) ) )  &  ( (v4_msualg_1(C, A) & l3_msualg_1(C, A))  & m2_pboole(D, u1_struct_0(A), B, u3_msualg_1(A, C))) ) )  => m2_pboole(k1_birkhoff(A, B, C, D), u1_struct_0(A), u3_msualg_1(A, k11_msafree(A, B)), u3_msualg_1(A, C))) ) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_msafree, axiom,  (! [A, B, C, D, E] :  ( ( (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)) ) )  &  (m3_pboole(D, A, B) & m2_pboole(E, A, B, C)) ) )  => m2_pboole(k1_msafree(A, B, C, D, E), A, D, C)) ) ).
fof(dt_k1_msualg_3, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( (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)) ) )  &  (m2_pboole(D, A, B, C) & m1_subset_1(E, A)) ) ) )  =>  (v1_funct_1(k1_msualg_3(A, B, C, D, E)) &  (v1_funct_2(k1_msualg_3(A, B, C, D, E), k1_funct_1(B, E), k1_funct_1(C, E)) & m1_subset_1(k1_msualg_3(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(k1_funct_1(B, E), k1_funct_1(C, E))))) ) ) ) ).
fof(dt_k1_partfun1, axiom,  (! [A, B, C, D, E, F] :  ( ( (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))))  &  (v1_funct_1(F) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D)))) )  =>  (v1_funct_1(k1_partfun1(A, B, C, D, E, F)) & m1_subset_1(k1_partfun1(A, B, C, D, E, F), k1_zfmisc_1(k2_zfmisc_1(A, D)))) ) ) ).
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_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_funct_6, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k2_funct_6(A)) & v1_funct_1(k2_funct_6(A))) ) ) ).
fof(dt_k2_partfun1, axiom,  (! [A, B, C, D] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))  =>  (v1_funct_1(k2_partfun1(A, B, C, D)) & m1_subset_1(k2_partfun1(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ).
fof(dt_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => m1_subset_1(k2_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_msualg_3, axiom,  (! [A, B, C, D, E, F] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  ( (v1_relat_1(C) &  (v2_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) )  &  ( (v1_relat_1(D) &  (v2_relat_1(D) &  (v4_relat_1(D, A) &  (v1_funct_1(D) & v1_partfun1(D, A)) ) ) )  &  (m2_pboole(E, A, B, C) & m2_pboole(F, A, C, D)) ) ) )  => m2_pboole(k3_msualg_3(A, B, C, D, E, F), A, B, D)) ) ).
fof(dt_k3_relat_1, axiom,  (! [A, B] : v1_relat_1(k3_relat_1(A, B))) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k5_relat_1(A, B))) ) ).
fof(dt_k8_pboole, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_funcop_1(B)) ) )  =>  (v1_relat_1(k8_pboole(A, B)) & v1_funct_1(k8_pboole(A, B))) ) ) ).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_l1_msualg_1, axiom,  (! [A] :  (l1_msualg_1(A) => l5_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_msualg_1, axiom, $true).
fof(dt_l3_msualg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  =>  (! [B] :  (l3_msualg_1(B, A) => l2_msualg_1(B, A)) ) ) ) ).
fof(dt_l5_struct_0, axiom,  (! [A] :  (l5_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_m1_msafree, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  & l3_msualg_1(B, A))  =>  (! [C] :  (m1_msafree(C, A, B) => m3_pboole(C, u1_struct_0(A), u3_msualg_1(A, B))) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m2_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)) ) ) )  =>  (! [D] :  (m2_pboole(D, A, B, C) =>  (v1_relat_1(D) &  (v4_relat_1(D, A) &  (v1_funct_1(D) & v1_partfun1(D, A)) ) ) ) ) ) ) ).
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_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_msualg_1, axiom,  (? [A] : l1_msualg_1(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_l3_msualg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  =>  (? [B] : l3_msualg_1(B, A)) ) ) ).
fof(existence_l5_struct_0, axiom,  (? [A] : l5_struct_0(A)) ).
fof(existence_m1_msafree, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  & l3_msualg_1(B, A))  =>  (? [C] : m1_msafree(C, A, B)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m2_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)) ) ) )  =>  (? [D] : m2_pboole(D, A, B, C)) ) ) ).
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_funcop_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k3_relat_1(B, A)) & v1_funcop_1(k3_relat_1(B, A))) ) ) ).
fof(fc10_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_ordinal1(A))  =>  ~ (v10_ordinal1(k10_xtuple_0(A))) ) ) ).
fof(fc10_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(k5_relat_1(A, B)))  & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc11_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  ~ (v9_ordinal1(A)) )  => v10_ordinal1(k10_xtuple_0(A))) ) ).
fof(fc12_ordinal1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v9_ordinal1(A))  & v1_relat_1(B))  =>  (v1_relat_1(k3_relat_1(B, A)) & v9_ordinal1(k3_relat_1(B, A))) ) ) ).
fof(fc14_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_funcop_1(k5_relat_1(A, B))) ) ) ).
fof(fc1_msafree1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  =>  ~ (v1_xboole_0(k10_xtuple_0(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_msualg_9, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(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))) ) ) ) )  =>  (v2_relat_1(k13_msafree(A, B)) & v1_msafree(k13_msafree(A, B), A, k11_msafree(A, B))) ) ) ).
fof(fc1_pboole, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_relat_1(D) &  (v4_relat_1(D, B) &  (v1_funct_1(D) & v1_partfun1(D, B)) ) ) ) )  =>  (v1_relat_1(k3_relat_1(C, D)) &  (v4_relat_1(k3_relat_1(C, D), A) &  (v1_funct_1(k3_relat_1(C, D)) & v1_partfun1(k3_relat_1(C, D), A)) ) ) ) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc2_mssubfam, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_funcop_1(B)) ) ) )  =>  (v1_relat_1(k2_funct_6(B)) &  (v4_relat_1(k2_funct_6(B), A) & v1_funct_1(k2_funct_6(B))) ) ) ) ).
fof(fc2_msualg_9, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(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))) ) ) ) )  => v2_msafree(k11_msafree(A, B), 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(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc3_msafree1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  &  (v1_msafree1(B, A) & l3_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)) & v1_prob_2(u3_msualg_1(A, B))) ) ) ) ) ) ).
fof(fc3_pboole, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_funcop_1(B)) ) )  =>  (v1_relat_1(k8_pboole(A, B)) &  (v1_funct_1(k8_pboole(A, B)) & v1_funcop_1(k8_pboole(A, B))) ) ) ) ).
fof(fc4_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, A) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, A)))) ) )  =>  (v1_funct_1(k3_relat_1(D, C)) & v1_funct_2(k3_relat_1(D, C), A, B)) ) ) ).
fof(fc4_mssubfam, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_funcop_1(B)) ) ) )  =>  (v1_relat_1(k2_funct_6(B)) &  (v4_relat_1(k2_funct_6(B), A) &  (v1_funct_1(k2_funct_6(B)) & v1_partfun1(k2_funct_6(B), A)) ) ) ) ) ).
fof(fc4_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  => v3_ordinal1(k9_xtuple_0(A))) ) ).
fof(fc4_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc5_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, B, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (v1_funct_1(k3_relat_1(D, C)) & v1_funct_2(k3_relat_1(D, C), A, B)) ) ) ).
fof(fc5_msafree1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(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))) ) ) ) )  => v4_msualg_1(k11_msafree(A, B), A)) ) ).
fof(fc5_ordinal1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  & v3_ordinal1(B))  =>  (v1_relat_1(k5_relat_1(A, B)) &  (v5_relat_1(k5_relat_1(A, B), k10_xtuple_0(A)) & v5_ordinal1(k5_relat_1(A, B))) ) ) ) ).
fof(fc5_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_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_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_funct_2, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(E) &  (v1_funct_2(E, B, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) ) ) )  =>  (v1_funct_1(k3_relat_1(D, E)) & v1_funct_2(k3_relat_1(D, E), A, C)) ) ) ).
fof(fc8_msafree1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(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))) ) ) ) )  =>  (v1_relat_1(u3_msualg_1(A, k11_msafree(A, B))) &  (v4_relat_1(u3_msualg_1(A, k11_msafree(A, B)), u1_struct_0(A)) &  (v1_funct_1(u3_msualg_1(A, k11_msafree(A, B))) &  (v1_partfun1(u3_msualg_1(A, k11_msafree(A, B)), u1_struct_0(A)) & v1_prob_2(u3_msualg_1(A, k11_msafree(A, B)))) ) ) ) ) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
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_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_funct_1(A, B)) & v1_funct_1(k1_funct_1(A, B))) ) ) ).
fof(fc9_msafree1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(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))) ) ) ) )  => v1_msafree1(k11_msafree(A, B), A)) ) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k2_zfmisc_1(B, C)))) => v1_relat_1(k10_xtuple_0(D))) ) ).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc1_extens_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (v4_msualg_1(B, A) & l3_msualg_1(B, A)) )  =>  (? [C] :  (m1_msafree(C, A, B) &  (v1_relat_1(C) &  (v2_relat_1(C) &  (v4_relat_1(C, u1_struct_0(A)) &  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  & v1_partfun1(C, u1_struct_0(A))) ) ) ) ) ) ) ) ) ).
fof(rc1_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ).
fof(rc1_funct_2, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(rc1_msafree1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v1_prob_2(B)) ) ) ) ) ) ).
fof(rc1_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, B) &  (v1_relat_1(C) &  (v3_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) &  (v1_partfun1(C, A) & v2_finset_1(C)) ) ) ) ) ) ) ) ) ).
fof(rc1_msualg_4, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v2_funcop_1(B)) ) ) ) ) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(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_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_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(rc25_struct_0, axiom,  (? [A] :  (l5_struct_0(A) &  ~ (v15_struct_0(A)) ) ) ).
fof(rc2_msafree1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  =>  (? [B] :  (l3_msualg_1(B, A) &  (v4_msualg_1(B, A) & v1_msafree1(B, A)) ) ) ) ) ).
fof(rc2_msualg_9, 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) & v2_finset_1(C)) ) ) ) ) ) ) ) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(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_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(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(rc4_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) ) ) ) ) ).
fof(rc4_ordinal1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v5_ordinal1(B)) ) ) ) ) ).
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_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(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_ordinal1, axiom,  (? [A] : v7_ordinal1(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(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc7_pboole, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, B) &  (v5_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, B)) ) ) ) ) ) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(redefinition_k1_msualg_3, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( (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)) ) )  &  (m2_pboole(D, A, B, C) & m1_subset_1(E, A)) ) ) )  => k1_msualg_3(A, B, C, D, E)=k1_funct_1(D, E)) ) ).
fof(redefinition_k1_partfun1, axiom,  (! [A, B, C, D, E, F] :  ( ( (v1_funct_1(E) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B))))  &  (v1_funct_1(F) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D)))) )  => k1_partfun1(A, B, C, D, E, F)=k3_relat_1(E, F)) ) ).
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_partfun1, axiom,  (! [A, B, C, D] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))  => k2_partfun1(A, B, C, D)=k5_relat_1(C, D)) ) ).
fof(redefinition_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => k2_relset_1(A, B)=k10_xtuple_0(B)) ) ).
fof(redefinition_k3_msualg_3, axiom,  (! [A, B, C, D, E, F] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  ( (v1_relat_1(C) &  (v2_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) )  &  ( (v1_relat_1(D) &  (v2_relat_1(D) &  (v4_relat_1(D, A) &  (v1_funct_1(D) & v1_partfun1(D, A)) ) ) )  &  (m2_pboole(E, A, B, C) & m2_pboole(F, A, C, D)) ) ) )  => k3_msualg_3(A, B, C, D, E, F)=k8_pboole(E, F)) ) ).
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(redefinition_r8_pboole, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) )  =>  (r8_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(reflexivity_r8_pboole, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) )  => r8_pboole(A, B, B)) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
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(symmetry_r8_pboole, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) )  =>  (r8_pboole(A, B, C) => r8_pboole(A, C, B)) ) ) ).
fof(t10_extens_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  ( (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))) ) ) )  => r8_pboole(u1_struct_0(A), k2_funct_6(k15_msafree(A, B)), B)) ) ) ) ).
fof(t13_funct_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_hidden(A, k9_xtuple_0(B)) => k1_funct_1(k3_relat_1(B, C), A)=k1_funct_1(C, k1_funct_1(B, A))) ) ) ) ) ) ).
fof(t13_mssubfam, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) &  (v1_partfun1(C, A) & v1_funcop_1(C)) ) ) )  =>  (! [D] :  ( (v1_relat_1(D) & v1_funct_1(D))  =>  ( (r2_hidden(B, A) & D=k1_funct_1(C, B))  => k1_funct_1(k2_funct_6(C), B)=k10_xtuple_0(D)) ) ) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_msualg_3, 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)) ) )  =>  (! [D] :  ( (v1_relat_1(D) &  (v4_relat_1(D, A) &  (v1_funct_1(D) & v1_partfun1(D, A)) ) )  =>  (! [E] :  (m2_pboole(E, A, B, C) =>  (! [F] :  (m2_pboole(F, A, C, D) =>  (k9_xtuple_0(k8_pboole(E, F))=A &  (! [G] :  (r2_tarski(G, A) => k1_funct_1(k8_pboole(E, F), G)=k3_relat_1(k1_funct_1(E, G), k1_funct_1(F, G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t49_funct_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_hidden(B, A) => k1_funct_1(k5_relat_1(C, A), B)=k1_funct_1(C, B)) ) ) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t9_extens_1, 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)) ) )  =>  (! [D] :  (m2_pboole(D, A, B, C) =>  (v2_msualg_3(D, A, B, C) <=> r6_pboole(A, k2_funct_6(D), C)) ) ) ) ) ) ) ) ).
