% Mizar problem: t62_aofa_a01,aofa_a01,1843,7 
fof(t62_aofa_a01, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v16_aofa_a00(A) &  (v18_aofa_a00(A, 4, 1) & l6_aofa_a00(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] :  ( (v5_msafree4(C, A, B) &  (v6_msafree4(C, A, B) &  (v7_msafree4(C, A, B) &  (v8_msafree4(C, A, B) &  (v3_aofa_a00(C, A, B) &  (v1_aofa_a01(C, A) & l1_aofa_a00(C, A)) ) ) ) ) )  =>  (! [D] :  ( (v4_msualg_1(D, A) &  (v4_msafree4(D, A, C) &  (v17_aofa_a00(D, A) &  (v20_aofa_a00(D, 4, 1, A) & l3_msualg_1(D, A)) ) ) )  =>  (! [E] :  ( (v4_aofa_a01(E, A, B, C) & l4_aofa_a00(E, A, B, C))  =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (! [G] :  ( (v3_aofa_a01(G, A, B, C, u4_aofa_a00(A, B, C, E), F) & m1_msafree4(G, u1_struct_0(A), u4_aofa_a00(A, B, C, E), k1_msafree4(u1_struct_0(A), u4_aofa_a00(A, B, C, E), F)))  =>  (! [H] :  (m2_pboole(H, u1_struct_0(A), k1_aofa_a01(A, B, C), u3_msualg_1(A, D)) => k14_aofa_a00(A, B, C, D, F, k4_aofa_a01(A, C, u4_aofa_a00(A, B, C, E), F, G), H)=k1_funct_1(k2_msafree4(u1_struct_0(A), k1_aofa_a01(A, B, C), u3_msualg_1(A, D), H, F), G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A))  => v3_card_1(A, 1)) ) ).
fof(cc10_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v6_membered(A)) ) ).
fof(cc10_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_int_1(B)) ) ) ) ).
fof(cc10_msafree4, 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) &  (v5_msafree4(C, A, B) & l3_msualg_1(C, A)) )  & m1_subset_1(D, u1_struct_0(A))) ) )  =>  (! [E] :  (m1_subset_1(E, k1_funct_1(u3_msualg_1(A, C), D)) => v3_trees_2(E)) ) ) ) ).
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(cc10_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_valued_0(B)) ) ) ) ).
fof(cc10_xxreal_2, axiom,  (! [A] :  ( (v3_membered(A) & v1_xxreal_2(A))  =>  (v3_membered(A) & v3_xxreal_2(A)) ) ) ).
fof(cc11_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_card_1(A))  =>  (! [B] :  (v3_card_1(B, A) =>  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(cc11_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_finseq_1(A)) ) ).
fof(cc11_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v7_ordinal1(B)) ) ) ) ).
fof(cc11_msafree4, 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))) ) ) ) )  =>  (! [C] :  (l3_msualg_1(C, A) =>  (v5_msafree4(C, A, B) => v1_msafree1(C, A)) ) ) ) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc11_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_valued_0(B)) ) ) ) ).
fof(cc11_xxreal_2, axiom,  (! [A] :  ( (v3_membered(A) & v2_xxreal_2(A))  =>  (v3_membered(A) & v4_xxreal_2(A)) ) ) ).
fof(cc12_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) => v4_funct_1(A)) ) ).
fof(cc12_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v6_membered(A)) ) ).
fof(cc12_msafree4, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (m3_pboole(B, u1_struct_0(A), k4_equation(A)) &  (v4_msualg_1(C, A) &  (v9_msafree4(C, A, B) & l3_msualg_1(C, A)) ) ) )  =>  (! [D] :  (l3_msualg_1(D, A) =>  ( (v4_msualg_1(D, A) & v4_msafree4(D, A, C))  =>  (v4_msualg_1(D, A) & v9_msafree4(D, A, B)) ) ) ) ) ) ).
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(cc12_trees_3, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v1_trees_1(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_funct_2(C, A, B) & v3_trees_2(C)) ) ) ) ) ) ) ).
fof(cc12_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_valued_0(B)) ) ) ) ).
fof(cc12_xxreal_2, axiom,  (! [A] :  ( (v5_membered(A) & v5_xxreal_2(A))  =>  (v5_membered(A) & v1_finset_1(A)) ) ) ).
fof(cc13_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finseq_1(B)) ) ) ) ).
fof(cc13_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_membered(B)) ) ) ) ).
fof(cc13_msafree4, 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] :  (l3_msualg_1(C, A) =>  (v4_msafree4(C, A, B) =>  (v4_msafree4(C, A, B) & v9_msafree4(C, A, k5_msafree4(A, B))) ) ) ) ) ) ).
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(cc13_trees_3, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v4_trees_3(A) &  (v5_trees_3(A) & v6_trees_3(A)) ) ) ) ) ) ).
fof(cc13_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_valued_0(B)) ) ) ) ).
fof(cc13_xxreal_2, axiom,  (! [A] :  ( (v6_membered(A) & v4_xxreal_2(A))  =>  (v6_membered(A) &  (v1_finset_1(A) & v4_xxreal_2(A)) ) ) ) ).
fof(cc14_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_finseq_1(B)) ) ) ) ).
fof(cc14_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_membered(B)) ) ) ) ).
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(cc14_trees_3, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_trees_3(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v4_trees_3(A)) ) ) ) ).
fof(cc14_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_valued_0(B)) ) ) ) ).
fof(cc14_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) & v5_xxreal_2(A))  =>  (v2_membered(A) & v3_membered(A)) ) ) ).
fof(cc15_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v3_valued_0(A) & v7_valued_0(A)) ) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_funct_1(A) & v3_valued_0(A)) ) ) ) ) ).
fof(cc15_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_membered(B)) ) ) ) ).
fof(cc15_msafree4, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v1_xboole_0(A) &  (v3_rewrite1(A) & v4_rewrite1(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(cc15_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_valued_0(B)) ) ) ) ).
fof(cc15_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) & v1_xboole_0(A))  =>  (v2_membered(A) & v6_xxreal_2(A)) ) ) ).
fof(cc16_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finset_1(A) & v2_finseq_1(A)) ) ) ) ) ).
fof(cc16_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_membered(B)) ) ) ) ).
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(cc16_valued_0, axiom,  (! [A, B] :  (v1_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_valued_0(C)) ) ) ) ).
fof(cc16_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) & v1_xxreal_2(A))  =>  (v2_membered(A) &  ~ (v1_xboole_0(A)) ) ) ) ).
fof(cc17_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_membered(B)) ) ) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc17_valued_0, axiom,  (! [A, B] :  (v2_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v2_valued_0(C)) ) ) ) ).
fof(cc17_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) & v2_xxreal_2(A))  =>  (v2_membered(A) &  ~ (v1_xboole_0(A)) ) ) ) ).
fof(cc18_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_membered(B)) ) ) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc18_trees_3, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v6_trees_3(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ) ).
fof(cc18_valued_0, axiom,  (! [A, B] :  (v3_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v3_valued_0(C)) ) ) ) ).
fof(cc19_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v7_membered(A)) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc19_valued_0, axiom,  (! [A, B] :  (v4_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v4_valued_0(C)) ) ) ) ).
fof(cc1_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v5_ordinal1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc1_aofa_a00, 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))) ) ) ) )  =>  (! [C] :  (l1_aofa_a00(C, A) =>  ( (v5_msafree4(C, A, B) & v6_msafree4(C, A, B))  =>  (v4_msualg_1(C, A) & v5_msafree4(C, A, B)) ) ) ) ) ) ).
fof(cc1_card_1, axiom,  (! [A] :  (v1_card_1(A) => v3_ordinal1(A)) ) ).
fof(cc1_exchsort, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_exchsort(A)) ) ) ) ).
fof(cc1_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc1_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_finset_1(A)) ) ).
fof(cc1_funcop_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_funcop_1(B)) ) ) ) ) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_instalg1, 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, u4_struct_0(A))) )  =>  (! [D] :  (m1_subset_1(D, k3_msualg_1(A, C, k11_msafree(A, B))) => v6_trees_3(D)) ) ) ) ).
fof(cc1_int_1, axiom,  (! [A] :  (m1_subset_1(A, k4_numbers) => v1_int_1(A)) ) ).
fof(cc1_margrel1, axiom,  (! [A] :  (v1_xboole_0(A) => v2_card_3(A)) ) ).
fof(cc1_membered, axiom,  (! [A] :  (v6_membered(A) => v5_membered(A)) ) ).
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_msualg_9, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  ( (v4_msualg_1(B, A) & l3_msualg_1(B, A))  & m1_subset_1(C, u4_struct_0(A))) )  =>  (! [D] :  (m1_subset_1(D, k3_msualg_1(A, C, B)) => v1_finseq_1(D)) ) ) ) ).
fof(cc1_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v3_ordinal1(A) & v7_ordinal1(A)) ) ) ).
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_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(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_trees_3, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v1_trees_3(A) &  (v2_trees_3(A) & v3_trees_3(A)) ) ) ) ).
fof(cc1_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v5_valued_0(A)) ) ) ).
fof(cc1_xreal_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xreal_0(A)) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc20_valued_0, axiom,  (! [A, B] :  (v5_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v5_valued_0(C)) ) ) ) ).
fof(cc21_valued_0, axiom,  (! [A, B] :  (v6_membered(B) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v6_valued_0(C)) ) ) ) ).
fof(cc22_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_zfmisc_1(A) & v2_valued_0(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) &  (v7_valued_0(A) & v8_valued_0(A)) ) ) ) ) ) ).
fof(cc23_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v7_valued_0(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v9_valued_0(A)) ) ) ) ) ).
fof(cc24_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v8_valued_0(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v10_valued_0(A)) ) ) ) ) ).
fof(cc28_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k2_numbers))  =>  (v1_relat_1(A) & v1_valued_0(A)) ) ) ).
fof(cc29_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k2_numbers)) ) ) ).
fof(cc2_afinsq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v5_ordinal1(B) &  (v1_funct_1(B) &  (v1_finset_1(B) & v3_card_1(B, A)) ) ) )  =>  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_finset_1(B)) ) ) ) ) ) ) ) ).
fof(cc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_card_1(A)) ) ).
fof(cc2_exchsort, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_exchsort(A)) ) ) ) ).
fof(cc2_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
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_instalg1, axiom,  (! [A] :  (l1_msualg_1(A) =>  ( ~ (v2_struct_0(A))  => v1_instalg1(A)) ) ) ).
fof(cc2_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_int_1(A)) ) ).
fof(cc2_membered, axiom,  (! [A] :  (v5_membered(A) => v4_membered(A)) ) ).
fof(cc2_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(k6_finseq_2(u1_struct_0(A), u3_msualg_1(A, B)))) =>  ~ (v1_xboole_0(C)) ) ) ) ) ).
fof(cc2_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
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_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(B)) ) ) ) ).
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_trees_3, axiom,  (! [A] :  (v2_trees_3(A) => v1_trees_3(A)) ) ).
fof(cc2_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v4_valued_0(A)) ) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc2_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) &  (v1_finset_1(A) &  ~ (v1_xboole_0(A)) ) )  =>  (v2_membered(A) &  ( ~ (v1_xboole_0(A))  &  (v1_xxreal_2(A) & v2_xxreal_2(A)) ) ) ) ) ).
fof(cc30_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k6_numbers))  =>  (v1_relat_1(A) & v2_valued_0(A)) ) ) ).
fof(cc31_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k6_numbers)) ) ) ).
fof(cc32_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k1_numbers))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc33_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k1_numbers)) ) ) ).
fof(cc34_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k3_numbers))  =>  (v1_relat_1(A) & v4_valued_0(A)) ) ) ).
fof(cc35_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k3_numbers)) ) ) ).
fof(cc36_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k4_numbers))  =>  (v1_relat_1(A) & v5_valued_0(A)) ) ) ).
fof(cc37_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k4_numbers)) ) ) ).
fof(cc38_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k4_ordinal1))  =>  (v1_relat_1(A) & v6_valued_0(A)) ) ) ).
fof(cc39_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k4_ordinal1)) ) ) ).
fof(cc3_afinsq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) &  (v1_finset_1(B) & v3_card_1(B, A)) ) ) ) )  =>  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v1_finset_1(B) & v3_card_1(B, A)) ) ) ) ) ) ) ) ) ) ).
fof(cc3_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_card_1(A)) ) ).
fof(cc3_exchsort, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_exchsort(A, k5_numbers)) ) ) ) ).
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_instalg1, axiom,  (! [A] :  (l1_msualg_1(A) =>  (v11_struct_0(A) => v1_instalg1(A)) ) ) ).
fof(cc3_int_1, axiom,  (! [A] :  (v1_int_1(A) => v1_xreal_0(A)) ) ).
fof(cc3_membered, axiom,  (! [A] :  (v4_membered(A) => v3_membered(A)) ) ).
fof(cc3_msafree4, 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))) ) ) )  & m3_pboole(C, u1_struct_0(A), u3_msualg_1(A, k11_msafree(A, B)))) )  =>  (! [E] :  (m1_subset_1(E, k1_funct_1(C, D)) =>  (v1_relat_1(E) & v1_funct_1(E)) ) ) ) ) ).
fof(cc3_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
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_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(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_trees_3, axiom,  (! [A] :  (v1_trees_3(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_trees_3(B)) ) ) ) ).
fof(cc3_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc3_xxreal_2, axiom,  (! [A] :  ( (v6_membered(A) &  ~ (v1_xboole_0(A)) )  =>  (v6_membered(A) &  ( ~ (v1_xboole_0(A))  & v1_xxreal_2(A)) ) ) ) ).
fof(cc40_valued_0, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k2_numbers)) ) ) ) ) ).
fof(cc41_valued_0, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v1_valued_0(B)) ) ) ) ) ).
fof(cc42_valued_0, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k6_numbers)) ) ) ) ) ).
fof(cc43_valued_0, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v2_valued_0(B)) ) ) ) ) ).
fof(cc44_valued_0, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k1_numbers)) ) ) ) ) ).
fof(cc45_valued_0, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v3_valued_0(B)) ) ) ) ) ).
fof(cc46_valued_0, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k3_numbers)) ) ) ) ) ).
fof(cc47_valued_0, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v4_valued_0(B)) ) ) ) ) ).
fof(cc48_valued_0, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k4_numbers)) ) ) ) ) ).
fof(cc49_valued_0, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_valued_0(B)) ) ) ) ) ).
fof(cc4_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_relat_1(A, k1_numbers) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) )  =>  (v1_relat_1(A) &  (v5_relat_1(A, k1_numbers) &  (v5_ordinal1(A) &  (v1_funct_1(A) &  (v1_finset_1(A) & v3_valued_0(A)) ) ) ) ) ) ) ).
fof(cc4_card_1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v1_finset_1(A)) ) ).
fof(cc4_exchsort, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_exchsort(A, 1)) ) ) ) ).
fof(cc4_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
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_instalg1, axiom,  (! [A] :  (l1_msualg_1(A) =>  ( (v2_struct_0(A) & v1_instalg1(A))  => v11_struct_0(A)) ) ) ).
fof(cc4_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v2_int_1(A)) ) ).
fof(cc4_membered, axiom,  (! [A] :  (v3_membered(A) => v2_membered(A)) ) ).
fof(cc4_msafree4, 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] :  (l3_msualg_1(C, A) =>  (v4_msafree4(C, A, B) => v4_msualg_1(C, A)) ) ) ) ) ).
fof(cc4_nat_1, axiom,  (! [A] :  ( (v7_ordinal1(A) & v8_ordinal1(A))  =>  (v7_ordinal1(A) &  ~ (v2_xxreal_0(A)) ) ) ) ).
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_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_1(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_trees_3, axiom,  (! [A] :  (v2_trees_3(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_trees_3(B)) ) ) ) ).
fof(cc4_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc4_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) & v5_xxreal_2(A))  =>  (v2_membered(A) &  (v3_xxreal_2(A) & v4_xxreal_2(A)) ) ) ) ).
fof(cc50_valued_0, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v5_relat_1(B, k4_ordinal1)) ) ) ) ) ).
fof(cc51_valued_0, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_relat_1(B) & v6_valued_0(B)) ) ) ) ) ).
fof(cc5_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_relat_1(A, k4_ordinal1) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) )  =>  (v1_relat_1(A) &  (v5_relat_1(A, k4_ordinal1) &  (v5_ordinal1(A) &  (v1_funct_1(A) &  (v1_finset_1(A) & v6_valued_0(A)) ) ) ) ) ) ) ).
fof(cc5_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_finset_1(A)) ) ).
fof(cc5_exchsort, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_exchsort(A) & v2_exchsort(A, k5_numbers)) ) )  =>  (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_exchsort(A)) ) ) ) ) ).
fof(cc5_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) ) ) ).
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_instalg1, axiom,  (! [A] :  (l1_msualg_1(A) =>  ( ( ~ (v11_struct_0(A))  & v1_instalg1(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc5_int_1, axiom,  (! [A] :  (v2_int_1(A) => v1_int_1(A)) ) ).
fof(cc5_membered, axiom,  (! [A] :  (v3_membered(A) => v1_membered(A)) ) ).
fof(cc5_msafree4, 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))) ) ) ) )  =>  (! [C] :  (l3_msualg_1(C, A) =>  ( (v5_msafree4(C, A, B) & v6_msafree4(C, A, B))  =>  (v4_msualg_1(C, A) & v5_msafree4(C, A, B)) ) ) ) ) ) ).
fof(cc5_nat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v8_ordinal1(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_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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc5_trees_3, axiom,  (! [A] :  (v3_trees_3(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_trees_3(B)) ) ) ) ).
fof(cc5_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v2_valued_0(A)) ) ) ).
fof(cc5_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) &  (v3_xxreal_2(A) & v4_xxreal_2(A)) )  =>  (v2_membered(A) & v5_xxreal_2(A)) ) ) ).
fof(cc6_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_afinsq_1(A)) ) ) ) ).
fof(cc6_aofa_a00, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  ( (v4_msualg_1(B, A) & l3_msualg_1(B, A))  & m1_subset_1(C, u4_struct_0(A))) )  =>  (! [D] :  (m1_subset_1(D, k3_msualg_1(A, C, B)) =>  (v1_relat_1(D) & v1_funct_1(D)) ) ) ) ) ).
fof(cc6_card_1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v1_finset_1(A))  => v7_ordinal1(A)) ) ).
fof(cc6_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ).
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(cc6_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xcmplx_0(B)) ) ) ) ).
fof(cc6_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc6_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v5_relat_1(C, A)) ) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc6_trees_3, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_trees_3(A))  =>  (! [B] :  (m1_subset_1(B, A) =>  ( ~ (v1_xboole_0(B))  & v1_trees_1(B)) ) ) ) ) ).
fof(cc6_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v1_valued_0(A)) ) ) ).
fof(cc6_xxreal_2, axiom,  (! [A] :  ( (v3_membered(A) & v1_finset_1(A))  =>  (v3_membered(A) & v5_xxreal_2(A)) ) ) ).
fof(cc7_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) )  =>  (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) &  (v1_finset_1(A) & v1_afinsq_1(A)) ) ) ) ) ) ).
fof(cc7_aofa_a00, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v16_aofa_a00(A) &  (v18_aofa_a00(A, 4, 1) & l6_aofa_a00(A)) ) ) )  &  (v4_msualg_1(B, A) &  (v17_aofa_a00(B, A) &  (v20_aofa_a00(B, 4, 1, A) & l3_msualg_1(B, A)) ) ) )  =>  (! [C] :  (m1_subset_1(C, k1_funct_1(u3_msualg_1(A, B), 1)) => v1_int_1(C)) ) ) ) ).
fof(cc7_card_1, axiom,  (! [A] :  (v3_card_1(A, k5_ordinal1) => v1_xboole_0(A)) ) ).
fof(cc7_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v2_finseq_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_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xxreal_0(B)) ) ) ) ).
fof(cc7_msafree4, 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))) ) ) )  &  (v4_msualg_1(C, A) &  (v5_msafree4(C, A, B) & l3_msualg_1(C, A)) ) ) )  =>  (! [D] :  (m1_subset_1(D, k3_card_3(u3_msualg_1(A, C))) =>  (v1_relat_1(D) & v1_funct_1(D)) ) ) ) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(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(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc7_trees_3, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v2_trees_3(A))  =>  (! [B] :  (m1_subset_1(B, A) => v1_finset_1(B)) ) ) ) ).
fof(cc7_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v4_valued_0(A)) ) ) ).
fof(cc7_xxreal_2, axiom,  (! [A] :  ( (v5_membered(A) &  ( ~ (v1_xboole_0(A))  & v4_xxreal_2(A)) )  =>  (v5_membered(A) &  ( ~ (v1_xboole_0(A))  & v2_xxreal_2(A)) ) ) ) ).
fof(cc8_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ) ) ).
fof(cc8_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_card_1(A, k5_ordinal1)) ) ).
fof(cc8_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_finseq_1(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(cc8_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xreal_0(B)) ) ) ) ).
fof(cc8_msafree4, 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) &  (v5_msafree4(C, A, B) & l3_msualg_1(C, A)) )  & m1_subset_1(D, u1_struct_0(A))) ) )  =>  (! [E] :  (m1_subset_1(E, k1_funct_1(u3_msualg_1(A, C), D)) =>  (v1_relat_1(E) & v1_funct_1(E)) ) ) ) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc8_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v5_relat_1(B, A)) ) ) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc8_trees_3, axiom,  (! [A] :  (v3_trees_3(A) => v4_funct_1(A)) ) ).
fof(cc8_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc8_xxreal_2, axiom,  (! [A] :  ( (v5_membered(A) &  ( ~ (v1_xboole_0(A))  & v3_xxreal_2(A)) )  =>  (v5_membered(A) &  ( ~ (v1_xboole_0(A))  & v1_xxreal_2(A)) ) ) ) ).
fof(cc9_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v1_finset_1(A) & v1_afinsq_1(A)) ) ) )  =>  (v1_relat_1(A) &  (v5_ordinal1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc9_card_1, axiom,  (! [A] :  (v3_card_1(A, 1) =>  ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A)) ) ) ).
fof(cc9_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v1_finset_1(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_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_rat_1(B)) ) ) ) ).
fof(cc9_msafree4, 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))) ) ) )  &  (v4_msualg_1(C, A) &  (v5_msafree4(C, A, B) & l3_msualg_1(C, A)) ) ) )  =>  (! [D] :  (m1_subset_1(D, k3_card_3(u3_msualg_1(A, C))) => v3_trees_2(D)) ) ) ) ).
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(cc9_trees_3, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v3_trees_3(A))  =>  (! [B] :  (m1_subset_1(B, A) => v3_trees_2(B)) ) ) ) ).
fof(cc9_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v6_valued_0(A)) ) ) ).
fof(cc9_xxreal_2, axiom,  (! [A] :  (v6_membered(A) =>  (v6_membered(A) & v3_xxreal_2(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(d13_ordinal1, axiom, k5_ordinal1=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_aofa_a00, 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] :  ( (v5_msafree4(C, A, B) &  (v6_msafree4(C, A, B) &  (v7_msafree4(C, A, B) &  (v8_msafree4(C, A, B) & l3_msualg_1(C, A)) ) ) )  =>  (! [D] :  (l4_aofa_a00(D, A, B, C) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, k1_funct_1(u3_msualg_1(A, C), E)) =>  (m4_aofa_a00(F, A, B, C, D, E) <=> r2_tarski(F, k1_msafree4(u1_struct_0(A), u4_aofa_a00(A, B, C, D), E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_aofa_a01, 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] :  ( (v5_msafree4(C, A, B) &  (v6_msafree4(C, A, B) &  (v7_msafree4(C, A, B) & l3_msualg_1(C, A)) ) )  => k1_aofa_a01(A, B, C)=k13_msafree(A, B)) ) ) ) ) ) ).
fof(d2_msualg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (m1_subset_1(B, u4_struct_0(A)) => k2_msualg_1(A, B)=k3_funct_2(u4_struct_0(A), u1_struct_0(A), u2_msualg_1(A), B)) ) ) ) ).
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(d4_aofa_a01, 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] :  ( (v5_msafree4(C, A, B) &  (v6_msafree4(C, A, B) &  (v7_msafree4(C, A, B) & l3_msualg_1(C, A)) ) )  =>  (! [D] :  (m1_msafree(D, A, C) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, k1_msafree4(u1_struct_0(A), D, E)) =>  (v3_aofa_a01(F, A, B, C, D, E) <=> r2_tarski(F, k1_msafree4(u1_struct_0(A), k1_aofa_a01(A, B, C), E))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_msualg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (m1_subset_1(B, u4_struct_0(A)) =>  (! [C] :  (l3_msualg_1(C, A) => k3_msualg_1(A, B, C)=k1_funct_1(k3_relat_1(u1_msualg_1(A), k6_finseq_2(u1_struct_0(A), u3_msualg_1(A, C))), B)) ) ) ) ) ) ).
fof(d5_msualg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (m1_subset_1(B, u4_struct_0(A)) =>  (! [C] :  (l3_msualg_1(C, A) => k4_msualg_1(A, B, C)=k1_funct_1(k3_relat_1(u2_msualg_1(A), u3_msualg_1(A, C)), B)) ) ) ) ) ) ).
fof(d6_msualg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (m1_subset_1(B, u4_struct_0(A)) =>  (! [C] :  (l3_msualg_1(C, A) => k5_msualg_1(A, B, C)=k1_funct_1(u4_msualg_1(A, C), B)) ) ) ) ) ) ).
fof(d7_aofa_a01, axiom,  (! [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] :  ( (v2_relat_1(C) & m1_msafree(C, A, B))  =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_msafree4(E, u1_struct_0(A), C, k1_msafree4(u1_struct_0(A), C, D)) => k4_aofa_a01(A, B, C, D, E)=E) ) ) ) ) ) ) ) ) ) ).
fof(d7_msualg_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (l3_msualg_1(B, A) =>  (! [C] :  (l3_msualg_1(C, A) =>  (! [D] :  (m2_pboole(D, u1_struct_0(A), u3_msualg_1(A, B), u3_msualg_1(A, C)) =>  (r1_msualg_3(A, B, C, D) <=>  (! [E] :  (m1_subset_1(E, u4_struct_0(A)) =>  ( ~ (k3_msualg_1(A, E, B)=k1_xboole_0)  =>  (! [F] :  (m1_subset_1(F, k3_msualg_1(A, E, B)) => k1_funct_1(k1_msualg_3(u1_struct_0(A), u3_msualg_1(A, B), u3_msualg_1(A, C), D, k2_msualg_1(A, E)), k1_funct_1(k5_msualg_1(A, E, B), F))=k1_funct_1(k5_msualg_1(A, E, C), k5_msualg_3(A, B, C, E, D, F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_finseq_1, axiom, $true).
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_k14_aofa_a00, axiom,  (! [A, B, C, D, E, F, G] :  ( ( ( ~ (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) &  (v5_msafree4(C, A, B) & l3_msualg_1(C, A)) )  &  ( (v4_msualg_1(D, A) &  (v4_msafree4(D, A, C) & l3_msualg_1(D, A)) )  &  (m1_subset_1(E, u1_struct_0(A)) &  (m1_subset_1(F, k1_funct_1(u3_msualg_1(A, C), E)) &  (v1_relat_1(G) &  (v1_funct_1(G) & v1_funcop_1(G)) ) ) ) ) ) ) )  => m1_subset_1(k14_aofa_a00(A, B, C, D, E, F, G), k1_funct_1(u3_msualg_1(A, D), E))) ) ).
fof(dt_k1_aofa_a01, 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))) ) ) )  &  (v5_msafree4(C, A, B) &  (v6_msafree4(C, A, B) &  (v7_msafree4(C, A, B) & l3_msualg_1(C, A)) ) ) ) )  =>  (v2_relat_1(k1_aofa_a01(A, B, C)) & m1_msafree(k1_aofa_a01(A, B, C), A, C)) ) ) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_funct_6, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_funct_6(A)) & v1_funct_1(k1_funct_6(A))) ) ) ).
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_msafree4, 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, A))  => m1_subset_1(k1_msafree4(A, B, C), k10_xtuple_0(B))) ) ).
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_numbers, axiom, $true).
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_msafree4, 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)) ) )  & m2_pboole(D, A, B, C)) )  =>  (v1_funct_1(k2_msafree4(A, B, C, D, E)) &  (v1_funct_2(k2_msafree4(A, B, C, D, E), k1_funct_1(B, E), k1_funct_1(C, E)) & m1_subset_1(k2_msafree4(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(k1_funct_1(B, E), k1_funct_1(C, E))))) ) ) ) ).
fof(dt_k2_msualg_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  & m1_subset_1(B, u4_struct_0(A)))  => m1_subset_1(k2_msualg_1(A, B), u1_struct_0(A))) ) ).
fof(dt_k2_numbers, axiom, $true).
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_zfmisc_1, axiom, $true).
fof(dt_k3_card_3, axiom, $true).
fof(dt_k3_finseq_2, axiom,  (! [A] : m1_finseq_2(k3_finseq_2(A), A)) ).
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_msualg_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (m1_subset_1(B, u4_struct_0(A)) & l3_msualg_1(C, A)) )  => m1_subset_1(k3_msualg_1(A, B, C), k10_xtuple_0(k6_finseq_2(u1_struct_0(A), u3_msualg_1(A, C))))) ) ).
fof(dt_k3_numbers, axiom, $true).
fof(dt_k3_relat_1, axiom,  (! [A, B] : v1_relat_1(k3_relat_1(A, B))) ).
fof(dt_k4_aofa_a01, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  ( (v4_msualg_1(B, A) & l3_msualg_1(B, A))  &  ( (v2_relat_1(C) & m1_msafree(C, A, B))  &  (m1_subset_1(D, u1_struct_0(A)) & m1_subset_1(E, k1_msafree4(u1_struct_0(A), C, D))) ) ) )  => m1_subset_1(k4_aofa_a01(A, B, C, D, E), k1_funct_1(u3_msualg_1(A, B), D))) ) ).
fof(dt_k4_equation, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (v1_relat_1(k4_equation(A)) &  (v4_relat_1(k4_equation(A), u1_struct_0(A)) &  (v1_funct_1(k4_equation(A)) & v1_partfun1(k4_equation(A), u1_struct_0(A))) ) ) ) ) ).
fof(dt_k4_msualg_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (m1_subset_1(B, u4_struct_0(A)) & l3_msualg_1(C, A)) )  => m1_subset_1(k4_msualg_1(A, B, C), k10_xtuple_0(u3_msualg_1(A, C)))) ) ).
fof(dt_k4_numbers, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k5_msafree4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  & l3_msualg_1(B, A))  => m3_pboole(k5_msafree4(A, B), u1_struct_0(A), k4_equation(A))) ) ).
fof(dt_k5_msualg_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (m1_subset_1(B, u4_struct_0(A)) & l3_msualg_1(C, A)) )  =>  (v1_funct_1(k5_msualg_1(A, B, C)) &  (v1_funct_2(k5_msualg_1(A, B, C), k3_msualg_1(A, B, C), k4_msualg_1(A, B, C)) & m1_subset_1(k5_msualg_1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(k3_msualg_1(A, B, C), k4_msualg_1(A, B, C))))) ) ) ) ).
fof(dt_k5_msualg_3, axiom,  (! [A, B, C, D, E, F] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (l3_msualg_1(B, A) &  (l3_msualg_1(C, A) &  (m1_subset_1(D, u4_struct_0(A)) &  (m2_pboole(E, u1_struct_0(A), u3_msualg_1(A, B), u3_msualg_1(A, C)) & m1_subset_1(F, k3_msualg_1(A, D, B))) ) ) ) )  => m1_subset_1(k5_msualg_3(A, B, C, D, E, F), k3_msualg_1(A, D, C))) ) ).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
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_k6_finseq_2, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (v1_relat_1(k6_finseq_2(A, B)) &  (v4_relat_1(k6_finseq_2(A, B), k3_finseq_2(A)) &  (v1_funct_1(k6_finseq_2(A, B)) & v1_partfun1(k6_finseq_2(A, B), k3_finseq_2(A))) ) ) ) ) ).
fof(dt_k6_numbers, axiom, $true).
fof(dt_l1_aofa_a00, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (l1_aofa_a00(B, A) => l3_msualg_1(B, A)) ) ) ) ).
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_l4_aofa_a00, axiom, $true).
fof(dt_l5_aofa_a00, axiom,  (! [A] :  (l5_aofa_a00(A) => l1_msualg_1(A)) ) ).
fof(dt_l5_struct_0, axiom,  (! [A] :  (l5_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_l6_aofa_a00, axiom,  (! [A] :  (l6_aofa_a00(A) => l5_aofa_a00(A)) ) ).
fof(dt_m1_finseq_2, axiom, $true).
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_msafree4, axiom,  (! [A, B, C] :  ( ( (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, k10_xtuple_0(B)))  =>  (! [D] :  (m1_msafree4(D, A, B, C) => m1_subset_1(D, k3_card_3(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_m4_aofa_a00, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (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))) ) ) )  &  ( (v5_msafree4(C, A, B) &  (v6_msafree4(C, A, B) &  (v7_msafree4(C, A, B) &  (v8_msafree4(C, A, B) & l3_msualg_1(C, A)) ) ) )  &  (l4_aofa_a00(D, A, B, C) & m1_subset_1(E, u1_struct_0(A))) ) ) )  =>  (! [F] :  (m4_aofa_a00(F, A, B, C, D, E) => m1_subset_1(F, k1_funct_1(u3_msualg_1(A, C), E))) ) ) ) ).
fof(dt_u1_msualg_1, axiom,  (! [A] :  (l1_msualg_1(A) =>  (v1_funct_1(u1_msualg_1(A)) &  (v1_funct_2(u1_msualg_1(A), u4_struct_0(A), k3_finseq_2(u1_struct_0(A))) & m1_subset_1(u1_msualg_1(A), k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(A), k3_finseq_2(u1_struct_0(A)))))) ) ) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u2_msualg_1, axiom,  (! [A] :  (l1_msualg_1(A) =>  (v1_funct_1(u2_msualg_1(A)) &  (v1_funct_2(u2_msualg_1(A), u4_struct_0(A), u1_struct_0(A)) & m1_subset_1(u2_msualg_1(A), k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(A), u1_struct_0(A))))) ) ) ) ).
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(dt_u4_aofa_a00, 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))) ) ) )  &  ( (v5_msafree4(C, A, B) &  (v6_msafree4(C, A, B) &  (v7_msafree4(C, A, B) &  (v8_msafree4(C, A, B) & l3_msualg_1(C, A)) ) ) )  & l4_aofa_a00(D, A, B, C)) ) )  =>  (v2_relat_1(u4_aofa_a00(A, B, C, D)) & m1_msafree(u4_aofa_a00(A, B, C, D), A, C)) ) ) ).
fof(dt_u4_msualg_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  & l3_msualg_1(B, A))  => m2_pboole(u4_msualg_1(A, B), u4_struct_0(A), k3_relat_1(u1_msualg_1(A), k6_finseq_2(u1_struct_0(A), u3_msualg_1(A, B))), k3_relat_1(u2_msualg_1(A), u3_msualg_1(A, B)))) ) ).
fof(dt_u4_struct_0, axiom, $true).
fof(existence_l1_aofa_a00, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (? [B] : l1_aofa_a00(B, 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_l4_aofa_a00, 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))) ) ) )  &  (v5_msafree4(C, A, B) &  (v6_msafree4(C, A, B) &  (v7_msafree4(C, A, B) &  (v8_msafree4(C, A, B) & l3_msualg_1(C, A)) ) ) ) ) )  =>  (? [D] : l4_aofa_a00(D, A, B, C)) ) ) ).
fof(existence_l5_aofa_a00, axiom,  (? [A] : l5_aofa_a00(A)) ).
fof(existence_l5_struct_0, axiom,  (? [A] : l5_struct_0(A)) ).
fof(existence_l6_aofa_a00, axiom,  (? [A] : l6_aofa_a00(A)) ).
fof(existence_m1_finseq_2, axiom,  (! [A] :  (? [B] : m1_finseq_2(B, 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_msafree4, axiom,  (! [A, B, C] :  ( ( (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, k10_xtuple_0(B)))  =>  (? [D] : m1_msafree4(D, A, B, C)) ) ) ).
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(existence_m4_aofa_a00, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (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))) ) ) )  &  ( (v5_msafree4(C, A, B) &  (v6_msafree4(C, A, B) &  (v7_msafree4(C, A, B) &  (v8_msafree4(C, A, B) & l3_msualg_1(C, A)) ) ) )  &  (l4_aofa_a00(D, A, B, C) & m1_subset_1(E, u1_struct_0(A))) ) ) )  =>  (? [F] : m4_aofa_a00(F, A, B, C, D, E)) ) ) ).
fof(fc100_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v7_valued_0(A)) ) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v7_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc101_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v10_valued_0(A)) ) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v10_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc102_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v8_valued_0(A)) ) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v8_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc103_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v9_valued_0(A)) ) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v9_valued_0(k5_relat_1(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_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) )  => v1_setfam_1(k10_xtuple_0(A))) ) ).
fof(fc10_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_ordinal1(A))  =>  ~ (v10_ordinal1(k10_xtuple_0(A))) ) ) ).
fof(fc11_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  ~ (v9_ordinal1(A)) )  => v10_ordinal1(k10_xtuple_0(A))) ) ).
fof(fc11_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc11_xxreal_2, axiom,  ( ~ (v3_xxreal_2(k1_numbers))  &  ~ (v4_xxreal_2(k1_numbers)) ) ).
fof(fc12_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k1_zfmisc_1(A))) ) ) ).
fof(fc12_finseq_1, axiom,  (! [A] :  ~ (v1_xboole_0(k13_finseq_1(A))) ) ).
fof(fc12_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) )  => v1_zfmisc_1(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(fc12_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(B))  =>  (v1_xboole_0(k3_relat_1(A, B)) & v1_relat_1(k3_relat_1(A, B))) ) ) ).
fof(fc12_xxreal_2, axiom, v6_xxreal_2(k6_numbers)).
fof(fc13_aofa_a00, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v18_aofa_a00(A, 4, 1) & l6_aofa_a00(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_xboole_0(k1_funct_1(B, 1))) ) ) ).
fof(fc13_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(A, B))) ) ) ).
fof(fc13_finseq_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v2_finseq_1(k5_relat_1(A, B))) ) ) ).
fof(fc13_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ~ (v1_zfmisc_1(k10_xtuple_0(A))) ) ) ).
fof(fc13_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(B))  =>  (v1_xboole_0(k3_relat_1(B, A)) & v1_relat_1(k3_relat_1(B, A))) ) ) ).
fof(fc13_struct_0, axiom,  (! [A] :  ( (v11_struct_0(A) & l5_struct_0(A))  => v1_xboole_0(u4_struct_0(A))) ) ).
fof(fc14_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(B, 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(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(fc14_struct_0, axiom,  (! [A] :  ( ( ~ (v11_struct_0(A))  & l5_struct_0(A))  =>  ~ (v1_xboole_0(u4_struct_0(A))) ) ) ).
fof(fc15_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_relat_1(B) & v2_relat_1(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v2_relat_1(k3_relat_1(A, B))) ) ) ).
fof(fc16_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_xboole_0(B))  =>  (v1_xboole_0(k5_relat_1(A, B)) & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc17_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v1_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc17_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v3_funct_1(k5_relat_1(A, B))) ) ) ).
fof(fc17_funct_1, axiom,  (! [A, B, C] :  ( (v4_funct_1(A) &  (v1_relat_1(C) &  (v5_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_1(C, B)) & v1_funct_1(k1_funct_1(C, B))) ) ) ).
fof(fc17_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_xboole_0(k5_relat_1(A, B)) & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc17_xxreal_2, axiom, v6_xxreal_2(k1_numbers)).
fof(fc18_trees_3, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finseq_1(A) & v6_trees_3(A)) ) )  =>  (v1_relat_1(k1_funct_6(A)) &  (v1_funct_1(k1_funct_6(A)) &  (v1_finseq_1(k1_funct_6(A)) & v4_trees_3(k1_funct_6(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(fc19_struct_0, axiom,  (! [A, B] :  ( (v1_card_1(A) &  (v13_struct_0(B, A) & l1_struct_0(B)) )  => v3_card_1(u1_struct_0(B), A)) ) ).
fof(fc1_membered, axiom, v1_membered(k2_numbers)).
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_numbers, axiom,  ~ (v1_xboole_0(k1_numbers)) ).
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_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_valued_0(A))  => v1_membered(k10_xtuple_0(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc20_finset_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finset_1(B)) ) )  =>  (v1_relat_1(k3_relat_1(B, A)) & v1_finset_1(k3_relat_1(B, A))) ) ) ).
fof(fc20_struct_0, axiom,  (! [A] :  ( (v15_struct_0(A) & l5_struct_0(A))  => v1_zfmisc_1(u4_struct_0(A))) ) ).
fof(fc21_struct_0, axiom,  (! [A] :  ( ( ~ (v15_struct_0(A))  & l5_struct_0(A))  =>  ~ (v1_zfmisc_1(u4_struct_0(A))) ) ) ).
fof(fc21_trees_3, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (v1_relat_1(C) &  (v5_relat_1(C, A) &  (v1_funct_1(C) & v3_trees_2(C)) ) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ) )  =>  (v1_relat_1(k3_relat_1(C, D)) & v3_trees_2(k3_relat_1(C, D))) ) ) ).
fof(fc22_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_finset_1(A))  => v1_finset_1(k10_xtuple_0(A))) ) ).
fof(fc23_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v3_relat_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v3_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc25_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc26_finset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v1_finset_1(B))  =>  (v1_relat_1(k5_relat_1(B, A)) & v1_finset_1(k5_relat_1(B, A))) ) ) ).
fof(fc26_relat_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(C) & v5_relat_1(C, B))  =>  (v1_relat_1(k5_relat_1(C, A)) & v5_relat_1(k5_relat_1(C, A), B)) ) ) ).
fof(fc27_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k5_relat_1(B, A)) & v1_finset_1(k5_relat_1(B, A))) ) ) ).
fof(fc27_relat_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(C) & v4_relat_1(C, B))  =>  (v1_relat_1(k5_relat_1(C, A)) &  (v4_relat_1(k5_relat_1(C, A), A) & v4_relat_1(k5_relat_1(C, A), B)) ) ) ) ).
fof(fc29_relat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  =>  (v1_relat_1(k3_relat_1(C, B)) & v5_relat_1(k3_relat_1(C, B), A)) ) ) ).
fof(fc2_afinsq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) )  & v7_ordinal1(B))  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_finset_1(k5_relat_1(A, B))) ) ) ).
fof(fc2_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v1_funct_1(k3_relat_1(A, B))) ) ) ).
fof(fc2_instalg1, 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))) ) ).
fof(fc2_membered, axiom, v2_membered(k6_numbers)).
fof(fc2_msafree4, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v6_trees_3(A)) )  => v3_trees_3(k10_xtuple_0(A))) ) ).
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_numbers, axiom,  ~ (v1_xboole_0(k2_numbers)) ).
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(fc2_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_valued_0(A))  => v2_membered(k10_xtuple_0(A))) ) ).
fof(fc30_relat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  =>  (v1_relat_1(k3_relat_1(B, C)) & v4_relat_1(k3_relat_1(B, C), A)) ) ) ).
fof(fc31_finseq_1, axiom,  (! [A] : v4_funct_1(k13_finseq_1(A))) ).
fof(fc31_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v5_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc33_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v2_relat_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v2_relat_1(k5_relat_1(A, B))) ) ) ).
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(fc36_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_finset_1(A))  => v5_finset_1(k10_xtuple_0(A))) ) ).
fof(fc37_finseq_1, axiom,  (! [A] : v4_finseq_1(k13_finseq_1(A))) ).
fof(fc39_finseq_1, axiom,  (! [A, B, C] :  ( (v4_finseq_1(A) &  (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) ) )  => v1_finseq_1(k1_funct_1(B, C))) ) ).
fof(fc3_aofa_a01, 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))) ) ) )  &  (v5_msafree4(C, A, B) &  (v6_msafree4(C, A, B) &  (v7_msafree4(C, A, B) & l3_msualg_1(C, A)) ) ) ) )  =>  (v2_relat_1(k1_aofa_a01(A, B, C)) & v2_aofa_a01(k1_aofa_a01(A, B, C), A, B, C)) ) ) ).
fof(fc3_membered, axiom, v3_membered(k1_numbers)).
fof(fc3_msafree4, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_finset_1(A) & v1_funcop_1(A)) ) )  =>  (v1_relat_1(k1_funct_6(A)) &  (v1_funct_1(k1_funct_6(A)) & v2_finset_1(k1_funct_6(A))) ) ) ) ).
fof(fc3_numbers, axiom,  ~ (v1_xboole_0(k3_numbers)) ).
fof(fc3_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  => v3_membered(k10_xtuple_0(A))) ) ).
fof(fc43_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_valued_0(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc44_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v2_valued_0(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v2_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc45_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v3_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc46_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v4_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc47_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v5_valued_0(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v5_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc48_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v6_valued_0(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v6_valued_0(k5_relat_1(A, B))) ) ) ).
fof(fc4_aofa_a01, 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))) ) ) )  &  ( (v5_msafree4(C, A, B) &  (v6_msafree4(C, A, B) &  (v7_msafree4(C, A, B) &  (v8_msafree4(C, A, B) & l3_msualg_1(C, A)) ) ) )  &  (v4_aofa_a01(D, A, B, C) & l4_aofa_a00(D, A, B, C)) ) ) )  =>  (v2_relat_1(u4_aofa_a00(A, B, C, D)) & v2_aofa_a01(u4_aofa_a00(A, B, C, D), A, B, C)) ) ) ).
fof(fc4_membered, axiom, v4_membered(k3_numbers)).
fof(fc4_numbers, axiom,  ~ (v1_xboole_0(k4_numbers)) ).
fof(fc4_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  => v4_membered(k10_xtuple_0(A))) ) ).
fof(fc55_membered, axiom, v7_membered(k2_numbers)).
fof(fc55_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_relat_1(B) & v1_valued_0(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v1_valued_0(k3_relat_1(A, B))) ) ) ).
fof(fc56_membered, axiom, v7_membered(k1_numbers)).
fof(fc56_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_relat_1(B) & v2_valued_0(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v2_valued_0(k3_relat_1(A, B))) ) ) ).
fof(fc57_membered, axiom, v7_membered(k3_numbers)).
fof(fc57_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_relat_1(B) & v3_valued_0(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v3_valued_0(k3_relat_1(A, B))) ) ) ).
fof(fc58_membered, axiom, v7_membered(k4_numbers)).
fof(fc58_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_relat_1(B) & v4_valued_0(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v4_valued_0(k3_relat_1(A, B))) ) ) ).
fof(fc59_membered, axiom, v7_membered(k4_ordinal1)).
fof(fc59_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_relat_1(B) & v5_valued_0(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v5_valued_0(k3_relat_1(A, B))) ) ) ).
fof(fc5_margrel1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v2_card_3(B))  =>  (v1_relat_1(k5_relat_1(A, B)) & v2_margrel1(k5_relat_1(A, B))) ) ) ).
fof(fc5_membered, axiom, v5_membered(k4_numbers)).
fof(fc5_numbers, axiom,  ~ (v1_xboole_0(k6_numbers)) ).
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_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_valued_0(A))  => v5_membered(k10_xtuple_0(A))) ) ).
fof(fc5_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc60_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_relat_1(B) & v6_valued_0(B)) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v6_valued_0(k3_relat_1(A, B))) ) ) ).
fof(fc61_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_valued_0(A)) )  => v1_xcmplx_0(k1_funct_1(A, B))) ) ).
fof(fc62_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_valued_0(A)) )  => v1_xxreal_0(k1_funct_1(A, B))) ) ).
fof(fc63_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_valued_0(A)) )  => v1_xreal_0(k1_funct_1(A, B))) ) ).
fof(fc64_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v4_valued_0(A)) )  => v1_rat_1(k1_funct_1(A, B))) ) ).
fof(fc65_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_valued_0(A)) )  => v1_int_1(k1_funct_1(A, B))) ) ).
fof(fc66_valued_0, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v6_valued_0(A)) )  => v7_ordinal1(k1_funct_1(A, B))) ) ).
fof(fc6_aofa_000, axiom,  (! [A, B] : v1_freealg(k2_zfmisc_1(A, B))) ).
fof(fc6_card_1, axiom, v1_card_1(k4_ordinal1)).
fof(fc6_membered, axiom, v6_membered(k4_ordinal1)).
fof(fc6_numbers, axiom,  ~ (v1_finset_1(k4_numbers)) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc6_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v6_valued_0(A))  => v6_membered(k10_xtuple_0(A))) ) ).
fof(fc7_card_1, axiom, v2_card_1(k4_ordinal1)).
fof(fc7_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v2_funct_1(B)) ) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v2_funct_1(k3_relat_1(A, B))) ) ) ).
fof(fc7_msafree4, axiom,  (! [A, B, C, D] :  ( ( (v1_relat_1(B) &  (v2_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)) ) ) )  & m2_pboole(D, A, B, C)) )  =>  (v1_relat_1(k2_funct_6(D)) &  (v2_relat_1(k2_funct_6(D)) & v1_funct_1(k2_funct_6(D))) ) ) ) ).
fof(fc7_numbers, axiom,  ~ (v1_finset_1(k3_numbers)) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc85_valued_0, axiom,  (! [A, B] :  (v1_membered(B) => v1_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc86_valued_0, axiom,  (! [A, B] :  (v2_membered(B) => v2_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc87_valued_0, axiom,  (! [A, B] :  (v3_membered(B) => v3_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc88_valued_0, axiom,  (! [A, B] :  (v4_membered(B) => v4_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc89_valued_0, axiom,  (! [A, B] :  (v5_membered(B) => v5_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc8_aofa_a00, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  & l3_msualg_1(B, A))  => v1_funcop_1(u4_msualg_1(A, B))) ) ).
fof(fc8_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_funct_1(k5_relat_1(A, B))) ) ) ).
fof(fc8_nat_1, axiom,  (! [A, B, C] :  ( ( (v1_funct_1(A) &  (v1_funct_2(A, k4_ordinal1, k4_ordinal1) & m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k4_ordinal1)))) )  &  ( ~ (v1_xboole_0(B))  &  (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, B)))) ) ) )  =>  (v1_relat_1(k3_relat_1(A, C)) &  (v4_relat_1(k3_relat_1(A, C), k4_ordinal1) &  (v5_relat_1(k3_relat_1(A, C), B) & v1_funct_1(k3_relat_1(A, C))) ) ) ) ) ).
fof(fc8_numbers, axiom,  ~ (v1_finset_1(k1_numbers)) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc90_valued_0, axiom,  (! [A, B] :  (v6_membered(B) => v6_valued_0(k2_zfmisc_1(A, B))) ) ).
fof(fc91_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v7_valued_0(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v2_valued_0(B) & v7_valued_0(B)) ) ) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v7_valued_0(k3_relat_1(A, B))) ) ) ).
fof(fc92_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v9_valued_0(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v2_valued_0(B) & v9_valued_0(B)) ) ) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v9_valued_0(k3_relat_1(A, B))) ) ) ).
fof(fc93_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v8_valued_0(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v2_valued_0(B) & v8_valued_0(B)) ) ) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v7_valued_0(k3_relat_1(A, B))) ) ) ).
fof(fc94_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v10_valued_0(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v2_valued_0(B) & v10_valued_0(B)) ) ) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v9_valued_0(k3_relat_1(A, B))) ) ) ).
fof(fc95_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v8_valued_0(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v2_valued_0(B) & v7_valued_0(B)) ) ) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v8_valued_0(k3_relat_1(A, B))) ) ) ).
fof(fc96_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v8_valued_0(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v2_valued_0(B) & v7_valued_0(B)) ) ) )  =>  (v1_relat_1(k3_relat_1(B, A)) & v8_valued_0(k3_relat_1(B, A))) ) ) ).
fof(fc97_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v10_valued_0(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v2_valued_0(B) & v9_valued_0(B)) ) ) )  =>  (v1_relat_1(k3_relat_1(A, B)) & v10_valued_0(k3_relat_1(A, B))) ) ) ).
fof(fc98_valued_0, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v10_valued_0(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) &  (v2_valued_0(B) & v9_valued_0(B)) ) ) )  =>  (v1_relat_1(k3_relat_1(B, A)) & v10_valued_0(k3_relat_1(B, A))) ) ) ).
fof(fc9_card_1, axiom,  ~ (v1_finset_1(k4_ordinal1)) ).
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_nat_1, axiom,  (! [A, B, C] :  ( ( (v1_funct_1(A) &  (v1_funct_2(A, k4_ordinal1, k4_ordinal1) & m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k4_ordinal1)))) )  &  ( ~ (v1_xboole_0(B))  &  (v1_funct_1(C) &  (v1_funct_2(C, k4_ordinal1, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, B)))) ) ) )  =>  (v1_relat_1(k3_relat_1(A, C)) & v1_partfun1(k3_relat_1(A, C), k4_ordinal1)) ) ) ).
fof(fc9_numbers, axiom,  ~ (v1_finset_1(k2_numbers)) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_relat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  =>  ~ (v1_xboole_0(k10_xtuple_0(A))) ) ) ).
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_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_card_1(B)) ) ) ) ).
fof(rc10_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v3_card_1(B, A) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ).
fof(rc10_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) ) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_finseq_1(A)) ) ).
fof(rc11_msafree4, 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_xboole_0(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))) ) ) ) ) ) ) ) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc14_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v2_funct_1(A) &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(rc16_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v6_valued_0(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ) ).
fof(rc1_afinsq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_finset_1(B)) ) ) ) ) ) ).
fof(rc1_aofa_a01, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v16_aofa_a00(A) &  (v18_aofa_a00(A, 4, 1) & l6_aofa_a00(A)) ) ) )  =>  (? [B] :  (l3_msualg_1(B, A) &  (v4_msualg_1(B, A) & v1_aofa_a01(B, A)) ) ) ) ) ).
fof(rc1_card_1, axiom,  (? [A] : v1_card_1(A)) ).
fof(rc1_exchsort, axiom,  (! [A, B, C] :  (v3_ordinal1(A) =>  (? [D] :  (v1_relat_1(D) &  (v4_relat_1(D, C) &  (v5_relat_1(D, B) &  (v5_ordinal1(D) &  (v1_funct_1(D) &  (v1_xboole_0(D) &  (v1_finset_1(D) &  (v1_exchsort(D) &  (v2_exchsort(D, A) & v2_exchsort(D, k5_numbers)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A))) &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ).
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_instalg1, axiom,  (? [A] :  (l1_msualg_1(A) &  ( ~ (v2_struct_0(A))  &  ~ (v11_struct_0(A)) ) ) ) ).
fof(rc1_int_1, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v1_xcmplx_0(A) &  (v1_xreal_0(A) & v1_int_1(A)) ) ) ) ).
fof(rc1_margrel1, axiom,  (? [A] :  (v4_finseq_1(A) & v2_card_3(A)) ) ).
fof(rc1_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc1_nat_1, axiom,  (? [A] : v7_ordinal1(A)) ).
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_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(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_trees_3, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_trees_3(A) & v2_trees_3(A)) ) ) ) ).
fof(rc1_valued_0, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v6_valued_0(A)) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc1_xxreal_2, axiom,  (? [A] :  (v1_membered(A) &  (v2_membered(A) &  (v3_membered(A) &  (v4_membered(A) &  (v5_membered(A) &  (v6_membered(A) &  ( ~ (v1_xboole_0(A))  &  (v1_xxreal_2(A) & v2_xxreal_2(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(rc23_struct_0, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (l1_struct_0(B) & v13_struct_0(B, A)) ) ) ) ).
fof(rc25_struct_0, axiom,  (? [A] :  (l5_struct_0(A) &  ~ (v15_struct_0(A)) ) ) ).
fof(rc2_afinsq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) &  (v1_xboole_0(B) & v1_finset_1(B)) ) ) ) ) ) ) ).
fof(rc2_aofa_a01, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v16_aofa_a00(A) &  (v18_aofa_a00(A, 4, 1) & l6_aofa_a00(A)) ) ) )  &  (v4_msualg_1(B, A) &  (v1_aofa_a01(B, A) & l3_msualg_1(B, A)) ) )  =>  (? [C] :  (l3_msualg_1(C, A) &  (v4_msualg_1(C, A) &  (v4_msafree4(C, A, B) &  (v9_msafree4(C, A, k5_msafree4(A, B)) & v17_aofa_a00(C, A)) ) ) ) ) ) ) ).
fof(rc2_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v1_finset_1(A) & v1_card_1(A)) ) ) ) ) ).
fof(rc2_exchsort, axiom,  (! [A, B, C] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  =>  (? [D] :  (v1_relat_1(D) &  (v4_relat_1(D, A) &  (v5_relat_1(D, C) &  (v5_relat_1(D, k4_numbers) &  (v1_funct_1(D) &  (v1_valued_0(D) &  (v3_valued_0(D) &  (v6_valued_0(D) &  (v1_finset_1(D) &  (v1_exchsort(D) & v2_exchsort(D, B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) & v1_finseq_1(B)) ) ) ) ) ) ).
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_int_1, axiom,  (? [A] : v1_int_1(A)) ).
fof(rc2_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(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_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) & v8_ordinal1(A)) ) ).
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_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_trees_3, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) & v3_trees_3(A)) ) ) ).
fof(rc2_valued_0, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v4_valued_0(A) &  (v5_valued_0(A) & v6_valued_0(A)) ) ) ) ) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_xxreal_2, axiom,  (? [A] :  (v6_membered(A) &  (v1_finset_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ).
fof(rc3_afinsq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  & v1_finset_1(B)) ) ) ) ) ) ) ) ).
fof(rc3_aofa_a00, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (? [B] :  (l1_aofa_a00(B, A) &  (v4_msualg_1(B, A) & v1_msafree1(B, A)) ) ) ) ) ).
fof(rc3_aofa_a01, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v16_aofa_a00(A) &  (v18_aofa_a00(A, 4, 1) & l6_aofa_a00(A)) ) ) )  &  (v4_msualg_1(B, A) &  (v1_aofa_a01(B, A) & l3_msualg_1(B, A)) ) )  =>  (? [C] :  (l3_msualg_1(C, A) &  (v4_msualg_1(C, A) &  (v4_msafree4(C, A, B) &  (v9_msafree4(C, A, k5_msafree4(A, B)) &  (v17_aofa_a00(C, A) & v20_aofa_a00(C, 4, 1, A)) ) ) ) ) ) ) ) ).
fof(rc3_card_1, axiom,  (? [A] :  ~ (v1_finset_1(A)) ) ).
fof(rc3_exchsort, axiom,  (! [A] :  (v3_ordinal1(A) =>  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, k4_numbers) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_valued_0(B) &  (v3_valued_0(B) &  (v6_valued_0(B) &  (v1_finset_1(B) &  (v1_exchsort(B) & v2_exchsort(B, A)) ) ) ) ) ) ) ) ) ) ) ) ).
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_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) &  (v3_funct_1(C) &  (v1_partfun1(C, A) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ) ) ) ).
fof(rc3_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ).
fof(rc3_int_1, axiom,  (? [A] : v2_int_1(A)) ).
fof(rc3_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v6_membered(A) & v7_membered(A)) ) ) ).
fof(rc3_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(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(rc3_relat_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(rc3_valued_0, axiom,  (? [A] :  (m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, k4_ordinal1))) &  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v5_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_partfun1(A, k4_ordinal1) &  (v1_funct_2(A, k4_ordinal1, k4_ordinal1) &  (v1_valued_0(A) &  (v2_valued_0(A) &  (v3_valued_0(A) &  (v4_valued_0(A) &  (v5_valued_0(A) &  (v6_valued_0(A) & v7_valued_0(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc3_xxreal_2, axiom,  (? [A] :  (v1_membered(A) &  (v2_membered(A) &  (v3_membered(A) &  (v4_membered(A) &  (v5_membered(A) &  (v6_membered(A) &  ( ~ (v1_xboole_0(A))  &  (v1_xxreal_2(A) & v5_xxreal_2(A)) ) ) ) ) ) ) ) ) ).
fof(rc4_afinsq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (? [B] :  (v1_relat_1(B) &  (v5_ordinal1(B) &  (v1_funct_1(B) &  (v1_finset_1(B) & v3_card_1(B, A)) ) ) ) ) ) ) ).
fof(rc4_aofa_a01, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v16_aofa_a00(A) &  (v18_aofa_a00(A, 4, 1) & l6_aofa_a00(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))) ) ) ) )  =>  (? [C] :  (l1_aofa_a00(C, A) &  (v4_msualg_1(C, A) &  (v5_msafree4(C, A, B) &  (v6_msafree4(C, A, B) &  (v7_msafree4(C, A, B) &  (v8_msafree4(C, A, B) &  (v3_aofa_a00(C, A, B) &  (v1_msafree1(C, A) & v1_aofa_a01(C, A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc4_card_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc4_exchsort, axiom,  (! [A, B] :  ( (v3_ordinal1(A) &  ~ (v1_xboole_0(B)) )  =>  (? [C] :  (v1_relat_1(C) &  (v5_relat_1(C, B) &  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  &  (v1_finset_1(C) &  (v1_exchsort(C) & v2_exchsort(C, A)) ) ) ) ) ) ) ) ) ).
fof(rc4_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(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_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_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(rc4_margrel1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  & v2_margrel1(A)) ) ) ) ).
fof(rc4_nat_1, axiom,  (? [A] :  (m1_subset_1(A, k1_zfmisc_1(k1_numbers)) &  ( ~ (v1_xboole_0(A))  & v3_ordinal1(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(rc4_valued_0, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A))) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v3_funct_1(B) & v1_funct_2(B, k4_ordinal1, A)) ) ) ) ) ) ) ) ).
fof(rc4_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_xxreal_2, axiom,  (? [A] :  (v2_membered(A) &  ( ~ (v1_xboole_0(A))  & v6_xxreal_2(A)) ) ) ).
fof(rc5_afinsq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) & v6_valued_0(A)) ) ) ) ) ) ).
fof(rc5_aofa_000, axiom,  (? [A] :  ( ~ (v1_finset_1(A))  & v1_freealg(A)) ) ).
fof(rc5_aofa_a01, 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))) ) ) )  &  (v5_msafree4(C, A, B) &  (v6_msafree4(C, A, B) &  (v7_msafree4(C, A, B) & l3_msualg_1(C, A)) ) ) ) )  =>  (? [D] :  (m1_msafree(D, A, C) &  ( ~ (v1_xboole_0(D))  &  (v1_relat_1(D) &  (v2_relat_1(D) &  ( ~ (v3_relat_1(D))  &  (v4_relat_1(D, u1_struct_0(A)) &  (v1_funct_1(D) &  (v1_partfun1(D, u1_struct_0(A)) & v2_aofa_a01(D, A, B, C)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc5_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  & v1_card_1(A)) ) ) ) ) ) ).
fof(rc5_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v3_finseq_1(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_nat_1, axiom,  (? [A] :  (m1_subset_1(A, k4_ordinal1) &  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v1_xreal_0(A) &  (v1_finset_1(A) & v1_card_1(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(rc5_trees_2, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v3_trees_2(A)) ) ) ).
fof(rc5_trees_3, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) &  (v2_finseq_1(A) &  (v4_trees_3(A) & v5_trees_3(A)) ) ) ) ) ) ) ) ) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc5_xxreal_2, axiom,  (? [A] :  (v2_membered(A) &  (v1_xxreal_2(A) &  (v2_xxreal_2(A) & v6_xxreal_2(A)) ) ) ) ).
fof(rc6_aofa_a01, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (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))) ) ) )  &  ( (v5_msafree4(C, A, B) &  (v6_msafree4(C, A, B) &  (v7_msafree4(C, A, B) & l3_msualg_1(C, A)) ) )  &  ( (v2_aofa_a01(D, A, B, C) & m1_msafree(D, A, C))  & m1_subset_1(E, u1_struct_0(A))) ) ) )  =>  (? [F] :  (m1_subset_1(F, k1_msafree4(u1_struct_0(A), D, E)) & v3_aofa_a01(F, A, B, C, D, E)) ) ) ) ).
fof(rc6_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_finset_1(B)) ) ) ) ) ).
fof(rc6_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(rc6_finset_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ).
fof(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_trees_2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v3_trees_2(B)) ) ) ) ) ) ).
fof(rc6_trees_3, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) &  (v2_finseq_1(A) & v6_trees_3(A)) ) ) ) ) ) ) ) ).
fof(rc6_valued_0, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v6_valued_0(B)) ) ) ) ) ) ).
fof(rc6_xxreal_2, axiom,  (? [A] :  (v2_membered(A) &  ( ~ (v1_xxreal_2(A))  &  (v2_xxreal_2(A) & v6_xxreal_2(A)) ) ) ) ).
fof(rc7_aofa_a01, 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))) ) ) )  &  (v5_msafree4(C, A, B) &  (v6_msafree4(C, A, B) &  (v7_msafree4(C, A, B) &  (v8_msafree4(C, A, B) & l3_msualg_1(C, A)) ) ) ) ) )  =>  (? [D] :  (l4_aofa_a00(D, A, B, C) & v4_aofa_a01(D, A, B, C)) ) ) ) ).
fof(rc7_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] : v3_card_1(B, A)) ) ) ).
fof(rc7_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ) ).
fof(rc7_finset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (? [C] :  ( ~ (v1_xboole_0(C))  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ) ) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(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(rc7_trees_2, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finset_1(A) & v3_trees_2(A)) ) ) ) ).
fof(rc7_trees_3, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v4_trees_3(A) & v5_trees_3(A)) ) ) ) ) ).
fof(rc7_xxreal_2, axiom,  (? [A] :  (v2_membered(A) &  (v1_xxreal_2(A) &  ( ~ (v2_xxreal_2(A))  & v6_xxreal_2(A)) ) ) ) ).
fof(rc8_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (v1_relat_1(B) &  (v1_funct_1(B) & v3_card_1(B, 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(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc8_trees_2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) & v3_trees_2(B)) ) ) ) ) ) ) ).
fof(rc8_trees_3, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  & v6_trees_3(A)) ) ) ) ).
fof(rc8_xxreal_2, axiom,  (? [A] :  (v2_membered(A) &  ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xxreal_2(A))  &  ( ~ (v2_xxreal_2(A))  & v6_xxreal_2(A)) ) ) ) ) ).
fof(rc9_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v3_card_1(B, 1)) ) ) ) ).
fof(rc9_finseq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_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(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_trees_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_relat_1(C) &  ~ (v1_xboole_0(C)) ) ) ) ) ) ).
fof(rd5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => k5_relat_1(k5_relat_1(A, B), B)=k5_relat_1(A, B)) ) ).
fof(rd8_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k5_relat_1(B, A)=B) ) ).
fof(redefinition_k1_msafree4, 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, A))  => k1_msafree4(A, B, C)=k1_funct_1(B, C)) ) ).
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_k2_msafree4, 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)) ) )  & m2_pboole(D, A, B, C)) )  => k2_msafree4(A, B, C, D, E)=k1_funct_1(D, E)) ) ).
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_k3_finseq_2, axiom,  (! [A] : k3_finseq_2(A)=k13_finseq_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_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_m1_msafree4, axiom,  (! [A, B, C] :  ( ( (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, k10_xtuple_0(B)))  =>  (! [D] :  (m1_msafree4(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(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_pzfmisc1, 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)) ) ) )  => r1_pzfmisc1(A, B, B)) ) ).
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(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(spc4_boole, axiom,  ~ (v1_xboole_0(4)) ).
fof(spc4_numerals, axiom,  (v2_xxreal_0(4) & m1_subset_1(4, k4_ordinal1)) ).
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(t17_mssubfam, 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) & v1_funcop_1(D)) ) ) )  =>  ( (r1_pzfmisc1(A, B, C) & m2_pboole(D, A, B, C))  =>  (r6_pboole(A, k1_funct_6(D), B) & r2_pboole(A, k2_funct_6(D), C)) ) ) ) ) ) ) ) ) ).
fof(t19_extens_1, axiom,  (! [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] :  ( (v4_msualg_1(C, A) & l3_msualg_1(C, A))  =>  (! [D] :  (m1_msafree(D, A, B) =>  (! [E] :  (m2_pboole(E, u1_struct_0(A), u3_msualg_1(A, B), u3_msualg_1(A, C)) =>  (! [F] :  (m2_pboole(F, u1_struct_0(A), u3_msualg_1(A, B), u3_msualg_1(A, C)) =>  ( (r1_msualg_3(A, B, C, E) &  (r1_msualg_3(A, B, C, F) & r8_pboole(u1_struct_0(A), k1_msafree(u1_struct_0(A), u3_msualg_1(A, B), u3_msualg_1(A, C), D, E), k1_msafree(u1_struct_0(A), u3_msualg_1(A, B), u3_msualg_1(A, C), D, F))) )  => r8_pboole(u1_struct_0(A), E, F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t21_msafree4, 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) &  (v2_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) )  => r1_pzfmisc1(A, B, C)) ) ) ) ) ).
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(t46_msafree4, 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) &  (v5_msafree4(C, A, B) &  (v8_msafree4(C, A, B) & l3_msualg_1(C, A)) ) )  =>  (! [D] :  ( (v4_msualg_1(D, A) &  (v4_msafree4(D, A, C) & l3_msualg_1(D, A)) )  =>  (! [E] :  (m1_msafree(E, A, C) =>  (r8_pboole(u1_struct_0(A), E, k13_msafree(A, B)) =>  (! [F] :  (m2_pboole(F, u1_struct_0(A), E, u3_msualg_1(A, D)) =>  (? [G] :  (m2_pboole(G, u1_struct_0(A), u3_msualg_1(A, C), u3_msualg_1(A, D)) &  (r1_msualg_3(A, C, D, G) & r8_pboole(u1_struct_0(A), F, k1_msafree(u1_struct_0(A), u3_msualg_1(A, C), u3_msualg_1(A, D), E, G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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)) ) ) ) ) ).
