% Mizar problem: t26_osafree,osafree,3111,5 
fof(t26_osafree, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) &  (v2_osalg_4(A) & l3_osalg_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] :  (m1_msualg_4(C, u1_struct_0(A), u3_msualg_1(A, k8_osafree(A, B)), u3_msualg_1(A, k8_osafree(A, B))) =>  (r8_pboole(u1_struct_0(A), C, k20_osafree(A, B)) <=>  ( (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (r2_hidden(F, k1_funct_1(B, D)) =>  ( (r3_orders_2(A, D, E) => r2_hidden(k4_tarski(k1_trees_4(k4_tarski(F, D)), k1_trees_4(k4_tarski(F, D))), k1_msualg_4(u1_struct_0(A), u3_msualg_1(A, k8_osafree(A, B)), u3_msualg_1(A, k8_osafree(A, B)), C, E)))  &  (! [G] :  ( (r2_hidden(k4_tarski(k1_trees_4(k4_tarski(F, D)), G), k1_msualg_4(u1_struct_0(A), u3_msualg_1(A, k8_osafree(A, B)), u3_msualg_1(A, k8_osafree(A, B)), C, E)) | r2_hidden(k4_tarski(G, k1_trees_4(k4_tarski(F, D))), k1_msualg_4(u1_struct_0(A), u3_msualg_1(A, k8_osafree(A, B)), u3_msualg_1(A, k8_osafree(A, B)), C, E)))  =>  (r3_orders_2(A, D, E) & G=k1_trees_4(k4_tarski(F, D))) ) ) ) ) ) ) ) ) )  &  (! [D] :  (m1_subset_1(D, u4_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u4_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, k3_msualg_1(A, D, k8_osafree(A, B))) =>  (! [G] :  (m1_subset_1(G, k3_msualg_1(A, E, k8_osafree(A, B))) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  (r2_hidden(k4_tarski(k3_funct_2(k3_msualg_1(A, D, k8_osafree(A, B)), k4_msualg_1(A, D, k8_osafree(A, B)), k5_msualg_1(A, D, k8_osafree(A, B)), F), k3_funct_2(k3_msualg_1(A, E, k8_osafree(A, B)), k4_msualg_1(A, E, k8_osafree(A, B)), k5_msualg_1(A, E, k8_osafree(A, B)), G)), k1_msualg_4(u1_struct_0(A), u3_msualg_1(A, k8_osafree(A, B)), u3_msualg_1(A, k8_osafree(A, B)), C, H)) <=>  (r1_osalg_1(A, D, E) &  (k3_finseq_1(k1_msualg_1(A, D))=k3_finseq_1(k1_msualg_1(A, E)) &  (r3_orders_2(A, k2_msualg_1(A, D), H) &  (r3_orders_2(A, k2_msualg_1(A, E), H) &  (? [I] :  (m2_finseq_2(I, u1_struct_0(A), k3_finseq_2(u1_struct_0(A))) &  (k4_finseq_1(I)=k4_finseq_1(F) &  (! [J] :  (v7_ordinal1(J) =>  (r2_tarski(J, k4_finseq_1(I)) => r2_hidden(k4_tarski(k1_funct_1(F, J), k1_funct_1(G, J)), k1_msualg_4(u1_struct_0(A), u3_msualg_1(A, k8_osafree(A, B)), u3_msualg_1(A, k8_osafree(A, B)), C, k7_partfun1(u1_struct_0(A), I, J)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(abstractness_v1_lang1, axiom,  (! [A] :  (l1_lang1(A) =>  (v1_lang1(A) => A=g1_lang1(u1_struct_0(A), u1_lang1(A))) ) ) ).
fof(abstractness_v3_msualg_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  & l3_msualg_1(B, A))  =>  (v3_msualg_1(B, A) => B=g3_msualg_1(A, u3_msualg_1(A, B), u4_msualg_1(A, B))) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(cc10_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v6_membered(A)) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc10_trees_3, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_trees_3(B, A) => v3_trees_3(B)) ) ) ) ).
fof(cc11_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_finseq_1(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_trees_3, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_trees_3(B, A)) )  =>  (! [C] :  (m1_subset_1(C, B) => v5_relat_1(C, A)) ) ) ) ).
fof(cc12_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) => v4_funct_1(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc12_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  ( ~ (v2_struct_0(A))  => v14_struct_0(A)) ) ) ).
fof(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(cc13_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finseq_1(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(cc14_finseq_1, axiom,  (! [A] :  (v4_finseq_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_finseq_1(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(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_trees_3, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_trees_3(A))  =>  (! [B] :  (m1_finseq_1(B, A) => v4_trees_3(B)) ) ) ) ).
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_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_trees_3, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v2_trees_3(A))  =>  (! [B] :  (m1_finseq_1(B, A) => v5_trees_3(B)) ) ) ) ).
fof(cc17_finseq_1, axiom,  (! [A] :  (m1_finseq_1(A, k4_ordinal1) => v6_valued_0(A)) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc17_trees_3, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v3_trees_3(A))  =>  (! [B] :  (m1_finseq_1(B, A) => v6_trees_3(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(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_dtconstr, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_trees_3(B, A))  =>  (! [C] :  (m1_finseq_1(C, B) => v6_trees_3(C)) ) ) ) ).
fof(cc1_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_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_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_4, 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] :  (m1_msualg_4(D, A, B, C) => v2_funcop_1(D)) ) ) ) ).
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_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc1_osalg_1, axiom,  (! [A] :  (l3_osalg_1(A) =>  (v4_osalg_1(A) =>  (v3_orders_2(A) &  (v4_orders_2(A) & v5_orders_2(A)) ) ) ) ) ).
fof(cc1_partfun1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_partfun1(C, 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_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc1_trees_3, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v1_trees_3(A) &  (v2_trees_3(A) & v3_trees_3(A)) ) ) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(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_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_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_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc2_partfun1, 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_partfun1(C, A)) ) ) ) ) ).
fof(cc2_pboole, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v3_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  =>  (v1_relat_1(B) &  ( ~ (v2_relat_1(B))  &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ) ) ).
fof(cc2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(B)) ) ) ) ).
fof(cc2_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc2_trees_3, axiom,  (! [A] :  (v2_trees_3(A) => v1_trees_3(A)) ) ).
fof(cc3_finseq_1, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, A) => v5_relat_1(B, A)) ) ) ).
fof(cc3_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ) ).
fof(cc3_funct_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_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc3_partfun1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v3_relat_2(A) & v8_relat_2(A)) )  =>  (v1_relat_1(A) & v1_relat_2(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_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc3_trees_3, axiom,  (! [A] :  (v1_trees_3(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_trees_3(B)) ) ) ) ).
fof(cc4_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_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_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_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, 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(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_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_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_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc5_trees_3, axiom,  (! [A] :  (v3_trees_3(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_trees_3(B)) ) ) ) ).
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_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_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(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_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
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(cc8_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_finseq_1(A)) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc8_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(cc9_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v1_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_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(commutativity_k1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_subset_1(B, k4_ordinal1))  => k1_nat_1(A, B)=k1_nat_1(B, A)) ) ).
fof(commutativity_k2_tarski, axiom,  (! [A, B] : k2_tarski(A, B)=k2_tarski(B, A)) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(commutativity_k2_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(A, B)=k2_xcmplx_0(B, A)) ) ).
fof(connectedness_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  =>  (r1_xxreal_0(A, B) | r1_xxreal_0(B, A)) ) ) ).
fof(d10_osafree, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_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] :  (m2_pboole(C, u4_struct_0(A), k3_relat_1(u1_msualg_1(A), k6_finseq_2(u1_struct_0(A), k5_osafree(A, B))), k3_relat_1(u2_msualg_1(A), k5_osafree(A, B))) =>  (C=k7_osafree(A, B) <=>  (! [D] :  (m1_subset_1(D, u4_struct_0(A)) => r2_funct_2(k1_funct_1(k3_relat_1(u1_msualg_1(A), k6_finseq_2(u1_struct_0(A), k5_osafree(A, B))), D), k1_funct_1(k3_relat_1(u2_msualg_1(A), k5_osafree(A, B)), D), k5_msualg_4(A, k3_relat_1(u1_msualg_1(A), k6_finseq_2(u1_struct_0(A), k5_osafree(A, B))), k3_relat_1(u2_msualg_1(A), k5_osafree(A, B)), C, D), k6_osafree(A, B, D))) ) ) ) ) ) ) ) ) ).
fof(d11_osafree, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_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))) ) ) )  => k8_osafree(A, B)=g3_msualg_1(A, k5_osafree(A, B), k7_osafree(A, B))) ) ) ) ).
fof(d11_relat_2, axiom,  (! [A] :  (v1_relat_1(A) =>  (v3_relat_2(A) <=> r3_relat_2(A, k1_relat_1(A))) ) ) ).
fof(d19_osafree, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_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] :  (m1_subset_1(C, u1_struct_0(k2_osafree(A, B))) => k17_osafree(A, B, C)=a_3_1_osafree(A, B, C)) ) ) ) ) ) ).
fof(d1_funct_2, axiom,  (! [A] :  (! [B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( ( ~ (B=k1_xboole_0)  =>  (v1_funct_2(C, A, B) <=> A=k1_relset_1(A, C)) )  &  (B=k1_xboole_0 =>  (v1_funct_2(C, A, B) <=> C=k1_xboole_0) ) ) ) ) ) ) ).
fof(d1_lang1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_lang1(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  ( (v1_relat_1(C) &  (v1_funct_1(C) & v1_finseq_1(C)) )  =>  (r1_lang1(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_lang1(A))) ) ) ) ) ) ) ).
fof(d1_tarski, axiom,  (! [A] :  (! [B] :  (B=k1_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=> C=A) ) ) ) ) ).
fof(d20_osafree, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_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] :  (m1_subset_1(C, u1_struct_0(k2_osafree(A, B))) =>  (! [D] :  (m2_finseq_1(D, k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A, B)), u1_struct_0(A)))) => k18_osafree(A, B, C, D)=a_4_0_osafree(A, B, C, D)) ) ) ) ) ) ) ) ).
fof(d21_osafree, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) &  (v2_osalg_4(A) & l3_osalg_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] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k4_dtconstr(k2_osafree(A, B)), k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A, B)), u1_struct_0(A)))) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A, B)), k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A, B)), u1_struct_0(A))))))) )  =>  (C=k19_osafree(A, B) <=>  ( (! [D] :  (m1_subset_1(D, u1_struct_0(k2_osafree(A, B))) =>  (r2_tarski(D, k6_dtconstr(k2_osafree(A, B))) => k1_funct_1(C, k2_trees_4(u1_struct_0(k2_osafree(A, B)), D))=k17_osafree(A, B, D)) ) )  &  (! [D] :  (m1_subset_1(D, u1_struct_0(k2_osafree(A, B))) =>  (! [E] :  (m1_trees_4(E, k5_trees_3(u1_struct_0(k2_osafree(A, B))), k4_dtconstr(k2_osafree(A, B))) =>  (r1_lang1(k2_osafree(A, B), D, k1_dtconstr(u1_struct_0(k2_osafree(A, B)), k5_trees_3(u1_struct_0(k2_osafree(A, B))), E)) => k1_funct_1(C, k8_trees_4(u1_struct_0(k2_osafree(A, B)), D, E))=k18_osafree(A, B, D, k11_lang1(k4_dtconstr(k2_osafree(A, B)), k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A, B)), u1_struct_0(A))), E, C))) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(d22_osafree, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) &  (v2_osalg_4(A) & l3_osalg_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] :  ( (v2_msualg_4(C, A, k8_osafree(A, B)) & m1_osalg_4(C, A, k8_osafree(A, B)))  =>  (C=k20_osafree(A, B) <=>  (! [D] :  (r2_tarski(D, u1_struct_0(A)) => k1_funct_1(C, D)=a_3_2_osafree(A, B, D)) ) ) ) ) ) ) ) ) ).
fof(d2_osalg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_osalg_1(A)) )  =>  (! [B] :  (m1_subset_1(B, u4_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u4_struct_0(A)) =>  (r1_osalg_1(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_osalg_1(A))) ) ) ) ) ) ) ).
fof(d2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (v1_relat_1(B) =>  (A=B <=>  (! [C] :  (! [D] :  (r2_hidden(k4_tarski(C, D), A) <=> r2_hidden(k4_tarski(C, D), B)) ) ) ) ) ) ) ) ).
fof(d3_lang1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_lang1(A))  => k2_lang1(A)=a_1_1_lang1(A)) ) ).
fof(d3_relat_2, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (r3_relat_2(A, B) <=>  (! [C] :  (! [D] :  ( (r2_hidden(C, B) &  (r2_hidden(D, B) & r2_hidden(k4_tarski(C, D), A)) )  => r2_hidden(k4_tarski(D, C), A)) ) ) ) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d4_finseq_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) )  =>  (m1_finseq_1(B, A) <=> r1_tarski(k10_xtuple_0(B), A)) ) ) ) ).
fof(d4_osafree, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_1(A)) ) ) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_xboole_0(k2_zfmisc_1(u4_struct_0(A), k1_tarski(u1_struct_0(A))), k3_card_3(k3_msafree(u1_struct_0(A), B))), k3_finseq_2(k2_xboole_0(k2_zfmisc_1(u4_struct_0(A), k1_tarski(u1_struct_0(A))), k3_card_3(k3_msafree(u1_struct_0(A), B))))))) =>  (C=k1_osafree(A, B) <=>  (! [D] :  (m1_subset_1(D, k2_xboole_0(k2_zfmisc_1(u4_struct_0(A), k1_tarski(u1_struct_0(A))), k3_card_3(k3_msafree(u1_struct_0(A), B)))) =>  (! [E] :  (m2_finseq_2(E, k2_xboole_0(k2_zfmisc_1(u4_struct_0(A), k1_tarski(u1_struct_0(A))), k3_card_3(k3_msafree(u1_struct_0(A), B))), k3_finseq_2(k2_xboole_0(k2_zfmisc_1(u4_struct_0(A), k1_tarski(u1_struct_0(A))), k3_card_3(k3_msafree(u1_struct_0(A), B))))) =>  (r2_hidden(k4_tarski(D, E), C) <=>  (r2_tarski(D, k2_zfmisc_1(u4_struct_0(A), k1_tarski(u1_struct_0(A)))) &  (! [F] :  (m1_subset_1(F, u4_struct_0(A)) =>  (k4_tarski(F, u1_struct_0(A))=D =>  (k3_finseq_1(E)=k3_finseq_1(k1_msualg_1(A, F)) &  (! [G] :  (r2_tarski(G, k4_finseq_1(E)) =>  ( (r2_tarski(k1_funct_1(E, G), k2_zfmisc_1(u4_struct_0(A), k1_tarski(u1_struct_0(A)))) =>  (! [H] :  (m1_subset_1(H, u4_struct_0(A)) =>  (k4_tarski(H, u1_struct_0(A))=k1_funct_1(E, G) => r3_orders_2(A, k2_msualg_1(A, H), k7_partfun1(u1_struct_0(A), k1_msualg_1(A, F), G))) ) ) )  &  ~ ( (r2_tarski(k1_funct_1(E, G), k3_card_3(k3_msafree(u1_struct_0(A), B))) &  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  ~ ( (r3_orders_2(A, H, k7_partfun1(u1_struct_0(A), k1_msualg_1(A, F), G)) & r2_tarski(k1_funct_1(E, G), k2_msafree(u1_struct_0(A), B, H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_trees_4, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) )  =>  (v6_trees_3(B) =>  (! [C] :  ( (v1_relat_1(C) &  (v1_funct_1(C) & v3_trees_2(C)) )  =>  (C=k4_trees_4(A, B) <=>  ( (? [D] :  ( (v1_relat_1(D) &  (v1_funct_1(D) &  (v1_finseq_1(D) & v6_trees_3(D)) ) )  &  (B=D & k9_xtuple_0(C)=k11_trees_3(k1_funct_6(D))) ) )  &  (k1_funct_1(C, k1_xboole_0)=A &  (! [D] :  (v7_ordinal1(D) =>  ( ~ (r1_xxreal_0(k3_finseq_1(B), D))  => k5_trees_2(C, k14_trees_3(D))=k1_funct_1(B, k1_nat_1(D, 1))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_osafree, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_1(A)) ) ) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) )  => k2_osafree(A, B)=g1_lang1(k2_xboole_0(k2_zfmisc_1(u4_struct_0(A), k1_tarski(u1_struct_0(A))), k3_card_3(k3_msafree(u1_struct_0(A), B))), k1_osafree(A, B))) ) ) ) ).
fof(d5_tarski, axiom,  (! [A] :  (! [B] : k4_tarski(A, B)=k2_tarski(k2_tarski(A, B), k1_tarski(A))) ) ).
fof(d6_dtconstr, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_dtconstr(A) &  (v3_dtconstr(A) & l1_lang1(A)) ) )  =>  (! [B] :  (m2_subset_1(B, u1_struct_0(A), k7_dtconstr(A)) =>  (! [C] :  (m1_trees_4(C, k5_trees_3(u1_struct_0(A)), k4_dtconstr(A)) =>  (m2_dtconstr(C, A, B) <=> r1_lang1(A, B, k1_dtconstr(u1_struct_0(A), k5_trees_3(u1_struct_0(A)), C))) ) ) ) ) ) ) ).
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(d6_osafree, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_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] :  (m1_subset_1(C, u4_struct_0(A)) => k3_osafree(A, B, C)=k4_tarski(C, u1_struct_0(A))) ) ) ) ) ) ).
fof(d7_osafree, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_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] :  (m1_subset_1(C, u1_struct_0(A)) => k4_osafree(A, B, C)=a_3_0_osafree(A, B, C)) ) ) ) ) ) ).
fof(d8_osafree, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_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] :  ( (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(A)) &  (v1_funct_1(C) &  (v1_partfun1(C, u1_struct_0(A)) & v11_osalg_1(C, A)) ) ) )  =>  (C=k5_osafree(A, B) <=>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) => k1_funct_1(C, D)=k4_osafree(A, B, D)) ) ) ) ) ) ) ) ) ).
fof(d9_osafree, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_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] :  (m1_subset_1(C, u4_struct_0(A)) =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k1_funct_1(k3_relat_1(u1_msualg_1(A), k6_finseq_2(u1_struct_0(A), k5_osafree(A, B))), C), k1_funct_1(k3_relat_1(u2_msualg_1(A), k5_osafree(A, B)), C)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k1_funct_1(k3_relat_1(u1_msualg_1(A), k6_finseq_2(u1_struct_0(A), k5_osafree(A, B))), C), k1_funct_1(k3_relat_1(u2_msualg_1(A), k5_osafree(A, B)), C))))) )  =>  (D=k6_osafree(A, B, C) <=>  (! [E] :  (m1_trees_4(E, k5_trees_3(u1_struct_0(k2_osafree(A, B))), k4_dtconstr(k2_osafree(A, B))) =>  (r1_lang1(k2_osafree(A, B), k3_osafree(A, B, C), k1_dtconstr(u1_struct_0(k2_osafree(A, B)), k5_trees_3(u1_struct_0(k2_osafree(A, B))), E)) => k1_funct_1(D, E)=k8_trees_4(u1_struct_0(k2_osafree(A, B)), k3_osafree(A, B, C), E)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_g1_lang1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k3_finseq_2(A)))) =>  (v1_lang1(g1_lang1(A, B)) & l1_lang1(g1_lang1(A, B))) ) ) ).
fof(dt_g3_msualg_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) )  & m2_pboole(C, u4_struct_0(A), k3_relat_1(u1_msualg_1(A), k6_finseq_2(u1_struct_0(A), B)), k3_relat_1(u2_msualg_1(A), B))) )  =>  (v3_msualg_1(g3_msualg_1(A, B, C), A) & l3_msualg_1(g3_msualg_1(A, B, C), A)) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k11_lang1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (m1_finseq_1(C, A) &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ) )  => m2_finseq_2(k11_lang1(A, B, C, D), B, k3_finseq_2(B))) ) ).
fof(dt_k11_trees_3, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  ( ~ (v1_xboole_0(k11_trees_3(A)))  & v1_trees_1(k11_trees_3(A))) ) ) ).
fof(dt_k13_finseq_1, axiom, $true).
fof(dt_k14_trees_3, axiom,  (! [A] :  (v7_ordinal1(A) => m2_finseq_1(k14_trees_3(A), k4_ordinal1)) ) ).
fof(dt_k15_trees_3, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(k15_trees_3(A)) &  (v1_funct_1(k15_trees_3(A)) & v1_finseq_1(k15_trees_3(A))) ) ) ) ).
fof(dt_k17_osafree, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_1(A)) ) ) )  &  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) ) )  & m1_subset_1(C, u1_struct_0(k2_osafree(A, B)))) )  => m1_subset_1(k17_osafree(A, B, C), k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A, B)), u1_struct_0(A))))) ) ).
fof(dt_k18_osafree, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_1(A)) ) ) )  &  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) ) )  &  (m1_subset_1(C, u1_struct_0(k2_osafree(A, B))) & m1_finseq_1(D, k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A, B)), u1_struct_0(A))))) ) )  => m1_subset_1(k18_osafree(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A, B)), u1_struct_0(A))))) ) ).
fof(dt_k19_osafree, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) &  (v2_osalg_4(A) & l3_osalg_1(A)) ) ) ) )  &  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) ) ) )  =>  (v1_funct_1(k19_osafree(A, B)) &  (v1_funct_2(k19_osafree(A, B), k4_dtconstr(k2_osafree(A, B)), k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A, B)), u1_struct_0(A)))) & m1_subset_1(k19_osafree(A, B), k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A, B)), k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A, B)), u1_struct_0(A))))))) ) ) ) ).
fof(dt_k1_card_1, axiom,  (! [A] : v1_card_1(k1_card_1(A))) ).
fof(dt_k1_dtconstr, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_trees_3(B, A) & m1_finseq_1(C, B)) )  => m2_finseq_1(k1_dtconstr(A, B, C), A)) ) ).
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_lang1, axiom, $true).
fof(dt_k1_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)))  => m2_finseq_2(k1_msualg_1(A, B), u1_struct_0(A), k3_finseq_2(u1_struct_0(A)))) ) ).
fof(dt_k1_msualg_4, 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)) ) )  &  (m1_msualg_4(D, A, B, C) & m1_subset_1(E, A)) ) ) )  => m1_subset_1(k1_msualg_4(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(k1_funct_1(B, E), k1_funct_1(C, E))))) ) ).
fof(dt_k1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_subset_1(B, k4_ordinal1))  => m1_subset_1(k1_nat_1(A, B), k4_ordinal1)) ) ).
fof(dt_k1_osafree, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_1(A)) ) ) )  &  (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) ) )  => m1_subset_1(k1_osafree(A, B), k1_zfmisc_1(k2_zfmisc_1(k2_xboole_0(k2_zfmisc_1(u4_struct_0(A), k1_tarski(u1_struct_0(A))), k3_card_3(k3_msafree(u1_struct_0(A), B))), k3_finseq_2(k2_xboole_0(k2_zfmisc_1(u4_struct_0(A), k1_tarski(u1_struct_0(A))), k3_card_3(k3_msafree(u1_struct_0(A), B)))))))) ) ).
fof(dt_k1_relat_1, axiom, $true).
fof(dt_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => m1_subset_1(k1_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_trees_4, axiom,  (! [A] :  (v1_relat_1(k1_trees_4(A)) &  (v1_funct_1(k1_trees_4(A)) & v3_trees_2(k1_trees_4(A))) ) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k20_osafree, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) &  (v2_osalg_4(A) & l3_osalg_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_msualg_4(k20_osafree(A, B), A, k8_osafree(A, B)) & m1_osalg_4(k20_osafree(A, B), A, k8_osafree(A, B))) ) ) ).
fof(dt_k2_card_3, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_relat_1(k2_card_3(A)) & v1_funct_1(k2_card_3(A))) ) ) ).
fof(dt_k2_lang1, axiom, $true).
fof(dt_k2_msafree, axiom, $true).
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_msualg_4, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (l3_msualg_1(B, A) &  ( (v2_msualg_4(C, A, B) & m1_msualg_4(C, u1_struct_0(A), u3_msualg_1(A, B), u3_msualg_1(A, B)))  & m1_subset_1(D, u1_struct_0(A))) ) )  =>  (v3_relat_2(k2_msualg_4(A, B, C, D)) &  (v8_relat_2(k2_msualg_4(A, B, C, D)) &  (v1_partfun1(k2_msualg_4(A, B, C, D), k1_funct_1(u3_msualg_1(A, B), D)) & m1_subset_1(k2_msualg_4(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(k1_funct_1(u3_msualg_1(A, B), D), k1_funct_1(u3_msualg_1(A, B), D))))) ) ) ) ) ).
fof(dt_k2_osafree, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_1(A)) ) ) )  &  (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) ) )  => l1_lang1(k2_osafree(A, B))) ) ).
fof(dt_k2_tarski, axiom, $true).
fof(dt_k2_trees_4, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => m1_subset_1(k2_trees_4(A, B), k5_trees_3(A))) ) ).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_xcmplx_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_card_3, axiom, $true).
fof(dt_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => m1_subset_1(k3_finseq_1(A), k4_ordinal1)) ) ).
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_msafree, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (v1_relat_1(k3_msafree(A, B)) & v1_funct_1(k3_msafree(A, 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_osafree, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_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))) )  => m1_subset_1(k3_osafree(A, B, C), u1_struct_0(k2_osafree(A, B)))) ) ).
fof(dt_k3_relat_1, axiom,  (! [A, B] : v1_relat_1(k3_relat_1(A, B))) ).
fof(dt_k4_dtconstr, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_lang1(A))  => m1_subset_1(k4_dtconstr(A), k1_zfmisc_1(k5_trees_3(u1_struct_0(A))))) ) ).
fof(dt_k4_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => m1_subset_1(k4_finseq_1(A), k1_zfmisc_1(k4_ordinal1))) ) ).
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_ordinal1, axiom, $true).
fof(dt_k4_osafree, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_1(A)) ) ) )  &  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) ) )  & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k4_osafree(A, B, C), k1_zfmisc_1(k4_dtconstr(k2_osafree(A, B))))) ) ).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k4_trees_4, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) )  =>  (v1_relat_1(k4_trees_4(A, B)) &  (v1_funct_1(k4_trees_4(A, B)) & v3_trees_2(k4_trees_4(A, B))) ) ) ) ).
fof(dt_k5_finseq_1, axiom, $true).
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_4, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  ( (v1_relat_1(B) &  (v4_relat_1(B, u4_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u4_struct_0(A))) ) )  &  ( (v1_relat_1(C) &  (v4_relat_1(C, u4_struct_0(A)) &  (v1_funct_1(C) & v1_partfun1(C, u4_struct_0(A))) ) )  &  (m2_pboole(D, u4_struct_0(A), B, C) & m1_subset_1(E, u4_struct_0(A))) ) ) )  =>  (v1_funct_1(k5_msualg_4(A, B, C, D, E)) &  (v1_funct_2(k5_msualg_4(A, B, C, D, E), k1_funct_1(B, E), k1_funct_1(C, E)) & m1_subset_1(k5_msualg_4(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(k1_funct_1(B, E), k1_funct_1(C, E))))) ) ) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_osafree, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_1(A)) ) ) )  &  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) ) ) )  =>  (v1_relat_1(k5_osafree(A, B)) &  (v4_relat_1(k5_osafree(A, B), u1_struct_0(A)) &  (v1_funct_1(k5_osafree(A, B)) &  (v1_partfun1(k5_osafree(A, B), u1_struct_0(A)) & v11_osalg_1(k5_osafree(A, B), A)) ) ) ) ) ) ).
fof(dt_k5_trees_2, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_trees_2(A)) )  & m1_finseq_1(B, k4_ordinal1))  =>  (v1_relat_1(k5_trees_2(A, B)) &  (v1_funct_1(k5_trees_2(A, B)) & v3_trees_2(k5_trees_2(A, B))) ) ) ) ).
fof(dt_k5_trees_3, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  => m1_trees_3(k5_trees_3(A), A)) ) ).
fof(dt_k6_dtconstr, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_dtconstr(A) & l1_lang1(A)) )  =>  ( ~ (v1_xboole_0(k6_dtconstr(A)))  & m1_subset_1(k6_dtconstr(A), k1_zfmisc_1(u1_struct_0(A)))) ) ) ).
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_osafree, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_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))) )  =>  (v1_funct_1(k6_osafree(A, B, C)) &  (v1_funct_2(k6_osafree(A, B, C), k1_funct_1(k3_relat_1(u1_msualg_1(A), k6_finseq_2(u1_struct_0(A), k5_osafree(A, B))), C), k1_funct_1(k3_relat_1(u2_msualg_1(A), k5_osafree(A, B)), C)) & m1_subset_1(k6_osafree(A, B, C), k1_zfmisc_1(k2_zfmisc_1(k1_funct_1(k3_relat_1(u1_msualg_1(A), k6_finseq_2(u1_struct_0(A), k5_osafree(A, B))), C), k1_funct_1(k3_relat_1(u2_msualg_1(A), k5_osafree(A, B)), C))))) ) ) ) ).
fof(dt_k7_dtconstr, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_dtconstr(A) & l1_lang1(A)) )  =>  ( ~ (v1_xboole_0(k7_dtconstr(A)))  & m1_subset_1(k7_dtconstr(A), k1_zfmisc_1(u1_struct_0(A)))) ) ) ).
fof(dt_k7_osafree, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_1(A)) ) ) )  &  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) ) ) )  => m2_pboole(k7_osafree(A, B), u4_struct_0(A), k3_relat_1(u1_msualg_1(A), k6_finseq_2(u1_struct_0(A), k5_osafree(A, B))), k3_relat_1(u2_msualg_1(A), k5_osafree(A, B)))) ) ).
fof(dt_k7_partfun1, axiom,  (! [A, B, C] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  => m1_subset_1(k7_partfun1(A, B, C), A)) ) ).
fof(dt_k8_dtconstr, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v1_dtconstr(A) & l1_lang1(A)) )  & m1_subset_1(B, k6_dtconstr(A)))  => m1_dtconstr(k8_dtconstr(A, B), u1_struct_0(A), k5_trees_3(u1_struct_0(A)), k4_dtconstr(A))) ) ).
fof(dt_k8_osafree, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_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))) ) ) ) )  =>  (v12_osalg_1(k8_osafree(A, B), A) & l3_msualg_1(k8_osafree(A, B), A)) ) ) ).
fof(dt_k8_trees_4, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) & m1_finseq_1(C, k5_trees_3(A))) )  => m1_subset_1(k8_trees_4(A, B, C), k5_trees_3(A))) ) ).
fof(dt_k9_dtconstr, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_dtconstr(A) &  (v3_dtconstr(A) & l1_lang1(A)) ) )  &  (m1_subset_1(B, k7_dtconstr(A)) & m2_dtconstr(C, A, B)) )  => m1_dtconstr(k9_dtconstr(A, B, C), u1_struct_0(A), k5_trees_3(u1_struct_0(A)), k4_dtconstr(A))) ) ).
fof(dt_k9_osafree, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_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))) )  => m2_subset_1(k9_osafree(A, B, C), u1_struct_0(k2_osafree(A, B)), k7_dtconstr(k2_osafree(A, B)))) ) ).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_l1_lang1, axiom,  (! [A] :  (l1_lang1(A) => l1_struct_0(A)) ) ).
fof(dt_l1_msualg_1, axiom,  (! [A] :  (l1_msualg_1(A) => l5_struct_0(A)) ) ).
fof(dt_l1_orders_2, axiom,  (! [A] :  (l1_orders_2(A) => l1_struct_0(A)) ) ).
fof(dt_l1_osalg_1, axiom,  (! [A] :  (l1_osalg_1(A) => l1_msualg_1(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_msualg_1, axiom, $true).
fof(dt_l2_osalg_1, axiom,  (! [A] :  (l2_osalg_1(A) =>  (l1_msualg_1(A) & l1_orders_2(A)) ) ) ).
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_l3_osalg_1, axiom,  (! [A] :  (l3_osalg_1(A) =>  (l1_osalg_1(A) & l2_osalg_1(A)) ) ) ).
fof(dt_l5_struct_0, axiom,  (! [A] :  (l5_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_m1_dtconstr, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  & m1_trees_3(B, A))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(C, k1_zfmisc_1(B))) ) )  =>  (! [D] :  (m1_dtconstr(D, A, B, C) => m1_subset_1(D, B)) ) ) ) ).
fof(dt_m1_finseq_1, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, A) =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ).
fof(dt_m1_finseq_2, axiom, $true).
fof(dt_m1_msualg_4, 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] :  (m1_msualg_4(D, A, B, C) =>  (v1_relat_1(D) &  (v4_relat_1(D, A) &  (v1_funct_1(D) & v1_partfun1(D, A)) ) ) ) ) ) ) ).
fof(dt_m1_osalg_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_1(A)) ) ) )  &  (v12_osalg_1(B, A) & l3_msualg_1(B, A)) )  =>  (! [C] :  (m1_osalg_4(C, A, B) => m1_msualg_4(C, u1_struct_0(A), u3_msualg_1(A, B), u3_msualg_1(A, B))) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m1_trees_3, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_trees_3(B, A) =>  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(dt_m1_trees_4, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, k1_zfmisc_1(A)))  =>  (! [C] :  (m1_trees_4(C, A, B) => m2_finseq_1(C, A)) ) ) ) ).
fof(dt_m2_dtconstr, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_dtconstr(A) &  (v3_dtconstr(A) & l1_lang1(A)) ) )  & m1_subset_1(B, k7_dtconstr(A)))  =>  (! [C] :  (m2_dtconstr(C, A, B) => m1_trees_4(C, k5_trees_3(u1_struct_0(A)), k4_dtconstr(A))) ) ) ) ).
fof(dt_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) =>  (v1_funct_1(B) &  (v1_finseq_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A)))) ) ) ) ) ).
fof(dt_m2_finseq_2, axiom,  (! [A, B] :  (m1_finseq_2(B, A) =>  (! [C] :  (m2_finseq_2(C, A, B) => m2_finseq_1(C, A)) ) ) ) ).
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_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) => m1_subset_1(C, A)) ) ) ) ).
fof(dt_u1_lang1, axiom,  (! [A] :  (l1_lang1(A) => m1_subset_1(u1_lang1(A), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), k3_finseq_2(u1_struct_0(A)))))) ) ).
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_osalg_1, axiom,  (! [A] :  (l1_osalg_1(A) =>  (v3_relat_2(u1_osalg_1(A)) &  (v8_relat_2(u1_osalg_1(A)) &  (v1_partfun1(u1_osalg_1(A), u4_struct_0(A)) & m1_subset_1(u1_osalg_1(A), k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(A), u4_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_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_lang1, axiom,  (? [A] : l1_lang1(A)) ).
fof(existence_l1_msualg_1, axiom,  (? [A] : l1_msualg_1(A)) ).
fof(existence_l1_orders_2, axiom,  (? [A] : l1_orders_2(A)) ).
fof(existence_l1_osalg_1, axiom,  (? [A] : l1_osalg_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_l2_osalg_1, axiom,  (? [A] : l2_osalg_1(A)) ).
fof(existence_l3_msualg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  =>  (? [B] : l3_msualg_1(B, A)) ) ) ).
fof(existence_l3_osalg_1, axiom,  (? [A] : l3_osalg_1(A)) ).
fof(existence_l5_struct_0, axiom,  (? [A] : l5_struct_0(A)) ).
fof(existence_m1_dtconstr, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  & m1_trees_3(B, A))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(C, k1_zfmisc_1(B))) ) )  =>  (? [D] : m1_dtconstr(D, A, B, C)) ) ) ).
fof(existence_m1_finseq_1, axiom,  (! [A] :  (? [B] : m1_finseq_1(B, A)) ) ).
fof(existence_m1_finseq_2, axiom,  (! [A] :  (? [B] : m1_finseq_2(B, A)) ) ).
fof(existence_m1_msualg_4, 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] : m1_msualg_4(D, A, B, C)) ) ) ).
fof(existence_m1_osalg_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_1(A)) ) ) )  &  (v12_osalg_1(B, A) & l3_msualg_1(B, A)) )  =>  (? [C] : m1_osalg_4(C, A, B)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m1_trees_3, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] : m1_trees_3(B, A)) ) ) ).
fof(existence_m1_trees_4, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, k1_zfmisc_1(A)))  =>  (? [C] : m1_trees_4(C, A, B)) ) ) ).
fof(existence_m2_dtconstr, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_dtconstr(A) &  (v3_dtconstr(A) & l1_lang1(A)) ) )  & m1_subset_1(B, k7_dtconstr(A)))  =>  (? [C] : m2_dtconstr(C, A, B)) ) ) ).
fof(existence_m2_finseq_1, axiom,  (! [A] :  (? [B] : m2_finseq_1(B, A)) ) ).
fof(existence_m2_finseq_2, axiom,  (! [A, B] :  (m1_finseq_2(B, A) =>  (? [C] : m2_finseq_2(C, A, B)) ) ) ).
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_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (? [C] : m2_subset_1(C, A, B)) ) ) ).
fof(fc10_funcop_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k3_relat_1(B, A)) & v1_funcop_1(k3_relat_1(B, A))) ) ) ).
fof(fc10_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(fc10_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc11_funct_1, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) )  & m1_subset_1(B, k9_xtuple_0(A)))  =>  ~ (v1_xboole_0(k1_funct_1(A, B))) ) ) ).
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(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_trees_3, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) & v1_trees_1(A)) )  => v5_trees_3(k5_finseq_1(A))) ) ).
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_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  => v4_funct_1(k1_tarski(A))) ) ).
fof(fc14_struct_0, axiom,  (! [A] :  ( ( ~ (v11_struct_0(A))  & l5_struct_0(A))  =>  ~ (v1_xboole_0(u4_struct_0(A))) ) ) ).
fof(fc15_funct_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  => v4_funct_1(k2_tarski(A, B))) ) ).
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(fc15_trees_3, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_trees_2(A)) )  =>  ( ~ (v1_xboole_0(k5_finseq_1(A)))  & v6_trees_3(k5_finseq_1(A))) ) ) ).
fof(fc16_finseq_1, axiom,  (! [A] :  ( (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) )  => v3_finseq_1(k1_tarski(A))) ) ).
fof(fc17_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => v3_finseq_1(k9_xtuple_0(A))) ) ).
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(fc18_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  => v3_finseq_1(k9_xtuple_0(A))) ) ).
fof(fc18_funct_1, axiom,  (! [A] :  ( ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  ~ (v1_zfmisc_1(k9_xtuple_0(A))) ) ) ).
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_finseq_1, axiom,  (! [A, B] :  ( (v3_finseq_1(A) & v3_finseq_1(B))  => v3_finseq_1(k2_xboole_0(A, B))) ) ).
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_dtconstr, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k3_finseq_2(A)))))  =>  ( ~ (v2_struct_0(g1_lang1(A, B)))  & v1_lang1(g1_lang1(A, B))) ) ) ).
fof(fc1_funct_1, axiom,  (! [A, B] : v1_funct_1(k1_tarski(k4_tarski(A, B)))) ).
fof(fc1_msafree, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (v1_relat_1(k2_card_3(B)) &  (v4_relat_1(k2_card_3(B), A) & v1_funct_1(k2_card_3(B))) ) ) ) ).
fof(fc1_msualg_1, axiom,  (! [A, B] :  ( (l1_struct_0(A) &  (v4_msualg_1(B, A) & l2_msualg_1(B, A)) )  =>  (v1_relat_1(u3_msualg_1(A, B)) &  (v2_relat_1(u3_msualg_1(A, B)) &  (v4_relat_1(u3_msualg_1(A, B), u1_struct_0(A)) &  (v1_funct_1(u3_msualg_1(A, B)) & v1_partfun1(u3_msualg_1(A, B), u1_struct_0(A))) ) ) ) ) ) ).
fof(fc1_msualg_3, 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))) )  => v4_funct_1(k3_msualg_1(A, C, B))) ) ).
fof(fc1_msualg_4, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_finseq_1(B, A) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) )  =>  (v1_relat_1(k3_relat_1(B, C)) &  (v4_relat_1(k3_relat_1(B, C), k4_finseq_1(B)) & v1_funct_1(k3_relat_1(B, C))) ) ) ) ).
fof(fc1_osafree, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_1(A)) ) ) )  &  (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) ) )  =>  ( ~ (v2_struct_0(k2_osafree(A, B)))  & v1_lang1(k2_osafree(A, B))) ) ) ).
fof(fc1_osalg_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  & m1_finseq_1(C, A))  =>  (v1_relat_1(k3_relat_1(C, B)) & v1_finseq_1(k3_relat_1(C, B))) ) ) ).
fof(fc1_pboole, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_relat_1(D) &  (v4_relat_1(D, B) &  (v1_funct_1(D) & v1_partfun1(D, B)) ) ) ) )  =>  (v1_relat_1(k3_relat_1(C, D)) &  (v4_relat_1(k3_relat_1(C, D), A) &  (v1_funct_1(k3_relat_1(C, D)) & v1_partfun1(k3_relat_1(C, D), A)) ) ) ) ) ).
fof(fc1_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  &  (v1_relat_1(C) & v4_relat_1(C, A)) )  => v4_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc1_xtuple_0, axiom,  (! [A, B] : v1_xtuple_0(k4_tarski(A, B))) ).
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(fc23_finseq_1, axiom,  (! [A] :  ~ (v1_xboole_0(k5_finseq_1(A))) ) ).
fof(fc23_trees_3, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v1_trees_1(A))  &  ( ~ (v1_xboole_0(B))  & v1_trees_1(B)) )  =>  ( ~ (v1_xboole_0(k2_xboole_0(A, B)))  & v1_trees_1(k2_xboole_0(A, B))) ) ) ).
fof(fc24_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k9_xtuple_0(A))) ) ).
fof(fc24_trees_3, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finseq_1(A) & v5_trees_3(A)) ) )  =>  ( ~ (v1_xboole_0(k11_trees_3(A)))  &  (v1_finset_1(k11_trees_3(A)) & v1_trees_1(k11_trees_3(A))) ) ) ) ).
fof(fc25_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc27_trees_3, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, k5_trees_3(A)))  => v1_finset_1(k9_xtuple_0(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_dtconstr, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_dtconstr(A) & l1_lang1(A)) )  =>  ~ (v1_xboole_0(k4_dtconstr(A))) ) ) ).
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_msafree, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (v1_relat_1(k2_card_3(B)) &  (v1_funct_1(k2_card_3(B)) & v1_partfun1(k2_card_3(B), A)) ) ) ) ).
fof(fc2_msualg_4, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_finseq_1(B, A) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) )  =>  (v1_relat_1(k3_relat_1(B, C)) &  (v4_relat_1(k3_relat_1(B, C), k4_finseq_1(B)) &  (v1_funct_1(k3_relat_1(B, C)) & v1_partfun1(k3_relat_1(B, C), k4_finseq_1(B))) ) ) ) ) ).
fof(fc2_osafree, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_1(A)) ) ) )  &  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) ) ) )  =>  (v1_dtconstr(k2_osafree(A, B)) &  (v2_dtconstr(k2_osafree(A, B)) & v3_dtconstr(k2_osafree(A, B))) ) ) ) ).
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_trees_2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_trees_2(A)) )  =>  ( ~ (v1_xboole_0(k9_xtuple_0(A)))  & v1_trees_1(k9_xtuple_0(A))) ) ) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(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(fc32_finseq_1, axiom,  (! [A] : v3_card_1(k5_finseq_1(A), 1)) ).
fof(fc35_finseq_1, axiom, v4_finseq_1(k1_tarski(k1_xboole_0))).
fof(fc36_finseq_1, axiom,  (! [A, B] :  ( (v4_finseq_1(A) & v4_finseq_1(B))  => v4_finseq_1(k2_xboole_0(A, B))) ) ).
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_dtconstr, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_dtconstr(A) & l1_lang1(A)) )  =>  ~ (v1_xboole_0(k4_dtconstr(A))) ) ) ).
fof(fc3_msafree, axiom,  (! [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(k2_card_3(B)) &  (v2_relat_1(k2_card_3(B)) & v1_funct_1(k2_card_3(B))) ) ) ) ).
fof(fc3_osafree, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_1(A)) ) ) )  &  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) ) )  & m1_subset_1(C, u1_struct_0(A))) )  =>  ~ (v1_xboole_0(k4_osafree(A, B, C))) ) ) ).
fof(fc3_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_relat_1(B))  => v1_relat_1(k2_xboole_0(A, B))) ) ).
fof(fc3_trees_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v3_trees_2(B)) ) )  & m1_subset_1(C, k9_xtuple_0(B))) )  =>  (v1_relat_1(k5_trees_2(B, C)) &  (v5_relat_1(k5_trees_2(B, C), A) &  (v1_funct_1(k5_trees_2(B, C)) & v3_trees_2(k5_trees_2(B, C))) ) ) ) ) ).
fof(fc3_xboole_0, axiom,  (! [A, B] :  ~ (v1_xboole_0(k2_tarski(A, B))) ) ).
fof(fc4_msafree, axiom,  (! [A, B] :  ( ( ~ (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)) ) ) ) )  =>  ~ (v1_xboole_0(k3_card_3(B))) ) ) ).
fof(fc4_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  => v3_ordinal1(k9_xtuple_0(A))) ) ).
fof(fc4_osafree, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_1(A)) ) ) )  &  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) ) ) )  =>  (v1_relat_1(k5_osafree(A, B)) &  (v2_relat_1(k5_osafree(A, B)) &  (v4_relat_1(k5_osafree(A, B), u1_struct_0(A)) &  (v1_funct_1(k5_osafree(A, B)) &  (v1_partfun1(k5_osafree(A, B), u1_struct_0(A)) & v11_osalg_1(k5_osafree(A, B), A)) ) ) ) ) ) ) ).
fof(fc4_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  &  (v1_relat_1(C) & v5_relat_1(C, A)) )  => v5_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc4_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc5_osafree, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_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))) ) ) ) )  =>  (v3_msualg_1(k8_osafree(A, B), A) &  (v4_msualg_1(k8_osafree(A, B), A) & v12_osalg_1(k8_osafree(A, B), A)) ) ) ) ).
fof(fc5_relat_1, axiom,  (! [A, B] : v1_relat_1(k1_tarski(k4_tarski(A, B)))) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc5_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc61_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => v6_valued_0(k5_finseq_1(A))) ) ).
fof(fc65_finseq_1, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_valued_0(k5_finseq_1(A))) ) ).
fof(fc66_finseq_1, axiom,  (! [A] :  (v1_xxreal_0(A) => v2_valued_0(k5_finseq_1(A))) ) ).
fof(fc67_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(k2_card_3(A)) &  (v1_funct_1(k2_card_3(A)) & v1_finseq_1(k2_card_3(A))) ) ) ) ).
fof(fc6_finseq_1, axiom,  (! [A] :  (v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A))) ) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc6_osafree, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_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))) )  =>  ~ (v1_xboole_0(k3_msualg_1(A, C, k8_osafree(A, B)))) ) ) ).
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(fc7_finseq_1, axiom,  (! [A] : v1_finseq_1(k5_finseq_1(A))) ).
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_relat_1, axiom,  (! [A, B, C, D] : v1_relat_1(k2_tarski(k4_tarski(A, B), k4_tarski(C, D)))) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_relat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  =>  ~ (v1_xboole_0(k9_xtuple_0(A))) ) ) ).
fof(fc8_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C))) => v1_relat_1(k9_xtuple_0(D))) ) ).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_funct_1(A, B)) & v1_funct_1(k1_funct_1(A, B))) ) ) ).
fof(fc9_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(fc9_trees_3, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_trees_1(A))  =>  ( ~ (v1_xboole_0(k5_finseq_1(A)))  & v4_trees_3(k5_finseq_1(A))) ) ) ).
fof(fraenkel_a_1_1_lang1, axiom,  (! [A, B] :  ( ( ~ (v2_struct_0(B))  & l1_lang1(B))  =>  (r2_hidden(A, a_1_1_lang1(B)) <=>  (? [C] :  (m1_subset_1(C, u1_struct_0(B)) &  (A=C &  (? [D] :  ( (v1_relat_1(D) &  (v1_funct_1(D) & v1_finseq_1(D)) )  & r1_lang1(B, C, D)) ) ) ) ) ) ) ) ).
fof(fraenkel_a_2_1_osafree, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v4_osalg_1(B) &  (v5_osalg_1(B) &  (v2_osalg_4(B) & l3_osalg_1(B)) ) ) ) )  &  (v1_relat_1(C) &  (v2_relat_1(C) &  (v4_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) & v1_partfun1(C, u1_struct_0(B))) ) ) ) )  =>  (r2_hidden(A, a_2_1_osafree(B, C)) <=>  (? [D] :  (m1_subset_1(D, u1_struct_0(k2_osafree(B, C))) &  (A=D &  (? [E] :  ( (v1_relat_1(E) &  (v1_funct_1(E) & v1_finseq_1(E)) )  & r1_lang1(k2_osafree(B, C), D, E)) ) ) ) ) ) ) ) ).
fof(fraenkel_a_3_0_osafree, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v4_osalg_1(B) &  (v5_osalg_1(B) & l3_osalg_1(B)) ) ) )  &  ( (v1_relat_1(C) &  (v2_relat_1(C) &  (v4_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) & v1_partfun1(C, u1_struct_0(B))) ) ) )  & m1_subset_1(D, u1_struct_0(B))) )  =>  (r2_hidden(A, a_3_0_osafree(B, C, D)) <=>  (? [E] :  (m1_dtconstr(E, u1_struct_0(k2_osafree(B, C)), k5_trees_3(u1_struct_0(k2_osafree(B, C))), k4_dtconstr(k2_osafree(B, C))) &  (A=E &  ~ ( ( (! [F] :  (m1_subset_1(F, u1_struct_0(B)) =>  (! [G] :  ~ ( (r3_orders_2(B, F, D) &  (r2_hidden(G, k1_funct_1(C, F)) & E=k1_trees_4(k4_tarski(G, F))) ) ) ) ) )  &  (! [F] :  (m1_subset_1(F, u4_struct_0(B)) =>  ~ ( (k4_tarski(F, u1_struct_0(B))=k1_funct_1(E, k1_xboole_0) & r3_orders_2(B, k2_msualg_1(B, F), D)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_3_10_osafree, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v4_osalg_1(B) &  (v5_osalg_1(B) &  (v2_osalg_4(B) & l3_osalg_1(B)) ) ) ) )  &  ( (v1_relat_1(C) &  (v2_relat_1(C) &  (v4_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) & v1_partfun1(C, u1_struct_0(B))) ) ) )  & m1_subset_1(D, u1_struct_0(B))) )  =>  (r2_hidden(A, a_3_10_osafree(B, C, D)) <=>  (? [E] :  (m1_dtconstr(E, u1_struct_0(k2_osafree(B, C)), k5_trees_3(u1_struct_0(k2_osafree(B, C))), k4_dtconstr(k2_osafree(B, C))) &  (A=E &  ~ ( ( (! [F] :  (m1_subset_1(F, u1_struct_0(B)) =>  (! [G] :  ~ ( (r3_orders_2(B, F, D) &  (r2_hidden(G, k1_funct_1(C, F)) & E=k1_trees_4(k4_tarski(G, F))) ) ) ) ) )  &  (! [F] :  (m1_subset_1(F, u4_struct_0(B)) =>  ~ ( (k4_tarski(F, u1_struct_0(B))=k1_funct_1(E, k1_xboole_0) & r3_orders_2(B, k2_msualg_1(B, F), D)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_3_11_osafree, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v4_osalg_1(B) &  (v5_osalg_1(B) &  (v2_osalg_4(B) & l3_osalg_1(B)) ) ) ) )  &  ( (v1_relat_1(C) &  (v2_relat_1(C) &  (v4_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) & v1_partfun1(C, u1_struct_0(B))) ) ) )  & m1_subset_1(D, u1_struct_0(B))) )  =>  (r2_hidden(A, a_3_11_osafree(B, C, D)) <=>  (? [E, F] :  ( (m1_dtconstr(E, u1_struct_0(k2_osafree(B, C)), k5_trees_3(u1_struct_0(k2_osafree(B, C))), k4_dtconstr(k2_osafree(B, C))) & m1_dtconstr(F, u1_struct_0(k2_osafree(B, C)), k5_trees_3(u1_struct_0(k2_osafree(B, C))), k4_dtconstr(k2_osafree(B, C))))  &  (A=k4_tarski(E, F) & r2_hidden(k4_tarski(E, D), k3_funct_2(k4_dtconstr(k2_osafree(B, C)), k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(B, C)), u1_struct_0(B))), k19_osafree(B, C), F))) ) ) ) ) ) ).
fof(fraenkel_a_3_12_osafree, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v4_osalg_1(B) &  (v5_osalg_1(B) &  (v2_osalg_4(B) & l3_osalg_1(B)) ) ) ) )  &  ( (v1_relat_1(C) &  (v2_relat_1(C) &  (v4_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) & v1_partfun1(C, u1_struct_0(B))) ) ) )  & m2_subset_1(D, u1_struct_0(k2_osafree(B, C)), k6_dtconstr(k2_osafree(B, C)))) )  =>  (r2_hidden(A, a_3_12_osafree(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, u1_struct_0(B)) &  (A=k4_tarski(k8_dtconstr(k2_osafree(B, C), D), E) &  (? [F] :  (m1_subset_1(F, u1_struct_0(B)) &  (? [G] :  (r2_tarski(G, k1_funct_1(C, F)) &  (D=k4_tarski(G, F) & r3_orders_2(B, F, E)) ) ) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_3_1_osafree, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v4_osalg_1(B) &  (v5_osalg_1(B) & l3_osalg_1(B)) ) ) )  &  ( (v1_relat_1(C) &  (v2_relat_1(C) &  (v4_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) & v1_partfun1(C, u1_struct_0(B))) ) ) )  & m1_subset_1(D, u1_struct_0(k2_osafree(B, C)))) )  =>  (r2_hidden(A, a_3_1_osafree(B, C, D)) <=>  (? [E] :  (m1_subset_1(E, u1_struct_0(B)) &  (A=k4_tarski(k2_trees_4(u1_struct_0(k2_osafree(B, C)), D), E) &  (? [F] :  (m1_subset_1(F, u1_struct_0(B)) &  (? [G] :  (r2_tarski(G, k1_funct_1(C, F)) &  (D=k4_tarski(G, F) & r3_orders_2(B, F, E)) ) ) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_3_2_osafree, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v4_osalg_1(B) &  (v5_osalg_1(B) &  (v2_osalg_4(B) & l3_osalg_1(B)) ) ) ) )  &  (v1_relat_1(C) &  (v2_relat_1(C) &  (v4_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) & v1_partfun1(C, u1_struct_0(B))) ) ) ) )  =>  (r2_hidden(A, a_3_2_osafree(B, C, D)) <=>  (? [E, F] :  ( (m1_dtconstr(E, u1_struct_0(k2_osafree(B, C)), k5_trees_3(u1_struct_0(k2_osafree(B, C))), k4_dtconstr(k2_osafree(B, C))) & m1_dtconstr(F, u1_struct_0(k2_osafree(B, C)), k5_trees_3(u1_struct_0(k2_osafree(B, C))), k4_dtconstr(k2_osafree(B, C))))  &  (A=k4_tarski(E, F) & r2_hidden(k4_tarski(E, D), k3_funct_2(k4_dtconstr(k2_osafree(B, C)), k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(B, C)), u1_struct_0(B))), k19_osafree(B, C), F))) ) ) ) ) ) ).
fof(fraenkel_a_4_0_osafree, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v4_osalg_1(B) &  (v5_osalg_1(B) & l3_osalg_1(B)) ) ) )  &  ( (v1_relat_1(C) &  (v2_relat_1(C) &  (v4_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) & v1_partfun1(C, u1_struct_0(B))) ) ) )  &  (m1_subset_1(D, u1_struct_0(k2_osafree(B, C))) & m2_finseq_1(E, k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(B, C)), u1_struct_0(B))))) ) )  =>  (r2_hidden(A, a_4_0_osafree(B, C, D, E)) <=>  (? [F, G, H] :  ( (m1_subset_1(F, u4_struct_0(B)) &  (m1_subset_1(G, k3_msualg_1(B, F, k8_osafree(B, C))) & m1_subset_1(H, u1_struct_0(B))) )  &  (A=k4_tarski(k3_funct_2(k3_msualg_1(B, F, k8_osafree(B, C)), k4_msualg_1(B, F, k8_osafree(B, C)), k5_msualg_1(B, F, k8_osafree(B, C)), G), H) &  ( (? [I] :  (m1_subset_1(I, u4_struct_0(B)) &  (D=k4_tarski(I, u1_struct_0(B)) &  (r1_osalg_1(B, I, F) &  (k3_finseq_1(k1_msualg_1(B, I))=k3_finseq_1(k1_msualg_1(B, F)) &  (r3_orders_2(B, k2_msualg_1(B, I), H) & r3_orders_2(B, k2_msualg_1(B, F), H)) ) ) ) ) )  &  (? [I] :  (m2_finseq_2(I, u1_struct_0(B), k3_finseq_2(u1_struct_0(B))) &  (k4_finseq_1(I)=k4_finseq_1(E) &  (! [J] :  (v7_ordinal1(J) =>  (r2_tarski(J, k4_finseq_1(E)) => r2_hidden(k4_tarski(k1_funct_1(G, J), k7_partfun1(u1_struct_0(B), I, J)), k1_funct_1(E, J))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_4_4_osafree, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v4_osalg_1(B) &  (v5_osalg_1(B) &  (v2_osalg_4(B) & l3_osalg_1(B)) ) ) ) )  &  ( (v1_relat_1(C) &  (v2_relat_1(C) &  (v4_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) & v1_partfun1(C, u1_struct_0(B))) ) ) )  &  (m1_subset_1(D, u4_struct_0(B)) & m2_finseq_1(E, k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(B, C)), u1_struct_0(B))))) ) )  =>  (r2_hidden(A, a_4_4_osafree(B, C, D, E)) <=>  (? [F, G, H] :  ( (m1_subset_1(F, u4_struct_0(B)) &  (m1_subset_1(G, k3_msualg_1(B, F, k8_osafree(B, C))) & m1_subset_1(H, u1_struct_0(B))) )  &  (A=k4_tarski(k3_funct_2(k3_msualg_1(B, F, k8_osafree(B, C)), k4_msualg_1(B, F, k8_osafree(B, C)), k5_msualg_1(B, F, k8_osafree(B, C)), G), H) &  ( (? [I] :  (m1_subset_1(I, u4_struct_0(B)) &  (k9_osafree(B, C, D)=k4_tarski(I, u1_struct_0(B)) &  (r1_osalg_1(B, I, F) &  (k3_finseq_1(k1_msualg_1(B, I))=k3_finseq_1(k1_msualg_1(B, F)) &  (r3_orders_2(B, k2_msualg_1(B, I), H) & r3_orders_2(B, k2_msualg_1(B, F), H)) ) ) ) ) )  &  (? [I] :  (m2_finseq_2(I, u1_struct_0(B), k3_finseq_2(u1_struct_0(B))) &  (k4_finseq_1(I)=k4_finseq_1(E) &  (! [J] :  (v7_ordinal1(J) =>  (r2_tarski(J, k4_finseq_1(E)) => r2_hidden(k4_tarski(k1_funct_1(G, J), k7_partfun1(u1_struct_0(B), I, J)), k1_funct_1(E, J))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_4_5_osafree, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  &  (v4_osalg_1(B) &  (v5_osalg_1(B) &  (v2_osalg_4(B) & l3_osalg_1(B)) ) ) ) )  &  ( (v1_relat_1(C) &  (v2_relat_1(C) &  (v4_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) & v1_partfun1(C, u1_struct_0(B))) ) ) )  &  (m2_finseq_2(D, u1_struct_0(B), k3_finseq_2(u1_struct_0(B))) & v7_ordinal1(E)) ) )  =>  (r2_hidden(A, a_4_5_osafree(B, C, D, E)) <=>  (? [F, G] :  ( (m1_dtconstr(F, u1_struct_0(k2_osafree(B, C)), k5_trees_3(u1_struct_0(k2_osafree(B, C))), k4_dtconstr(k2_osafree(B, C))) & m1_dtconstr(G, u1_struct_0(k2_osafree(B, C)), k5_trees_3(u1_struct_0(k2_osafree(B, C))), k4_dtconstr(k2_osafree(B, C))))  &  (A=k4_tarski(F, G) & r2_hidden(k4_tarski(F, k7_partfun1(u1_struct_0(B), D, E)), k3_funct_2(k4_dtconstr(k2_osafree(B, C)), k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(B, C)), u1_struct_0(B))), k19_osafree(B, C), G))) ) ) ) ) ) ).
fof(free_g1_lang1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k3_finseq_2(A)))) =>  (! [C, D] :  (g1_lang1(A, B)=g1_lang1(C, D) =>  (A=C & B=D) ) ) ) ) ).
fof(free_g3_msualg_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u1_struct_0(A))) ) )  & m2_pboole(C, u4_struct_0(A), k3_relat_1(u1_msualg_1(A), k6_finseq_2(u1_struct_0(A), B)), k3_relat_1(u2_msualg_1(A), B))) )  =>  (! [D, E, F] :  (g3_msualg_1(A, B, C)=g3_msualg_1(D, E, F) =>  (A=D &  (B=E & C=F) ) ) ) ) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(projectivity_k1_card_1, axiom,  (! [A] : k1_card_1(k1_card_1(A))=k1_card_1(A)) ).
fof(projectivity_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k3_finseq_1(k3_finseq_1(A))=k3_finseq_1(A)) ) ).
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_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc10_osalg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) & l1_orders_2(A)) ) ) )  =>  (? [B] :  ( ~ (v1_xboole_0(B))  &  (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  (v1_funct_1(B) &  (v1_partfun1(B, u1_struct_0(A)) & v11_osalg_1(B, A)) ) ) ) ) ) ) ) ).
fof(rc11_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_finseq_1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc11_osalg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) & l1_orders_2(A)) ) ) )  =>  (? [B] :  ( ~ (v1_xboole_0(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)) & v11_osalg_1(B, 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(rc12_osalg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_1(A)) ) ) )  =>  (? [B] :  (l3_msualg_1(B, A) &  (v3_msualg_1(B, A) &  (v4_msualg_1(B, A) & v12_osalg_1(B, 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(rc15_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v2_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ).
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_dtconstr, axiom,  (? [A] :  (l1_lang1(A) &  ( ~ (v2_struct_0(A))  &  (v1_lang1(A) &  (v1_dtconstr(A) &  (v2_dtconstr(A) & v3_dtconstr(A)) ) ) ) ) ) ).
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_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_msualg_4, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v2_funcop_1(B)) ) ) ) ) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_osalg_4, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) & l1_orders_2(A)) ) ) )  =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, u1_struct_0(A)) &  ( ~ (v1_xboole_0(B))  &  (v1_funct_1(B) &  (v1_partfun1(B, u1_struct_0(A)) &  (v2_funcop_1(B) & v11_osalg_1(B, A)) ) ) ) ) ) ) ) ) ).
fof(rc1_partfun1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ) ).
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_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(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_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_0(A)) ).
fof(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(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_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_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_msualg_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  & l3_msualg_1(B, A))  =>  (? [C] :  (m1_msualg_4(C, u1_struct_0(A), u3_msualg_1(A, B), u3_msualg_1(A, B)) &  ( ~ (v1_xboole_0(C))  &  (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(A)) &  (v1_funct_1(C) &  (v1_partfun1(C, u1_struct_0(A)) &  (v2_funcop_1(C) & v2_msualg_4(C, A, B)) ) ) ) ) ) ) ) ) ) ).
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_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_trees_3, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) & v3_trees_3(A)) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc3_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_finseq_1(B, A) &  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_xboole_0(B) &  (v1_finset_1(B) & v1_finseq_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_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_osalg_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_1(A)) ) ) )  &  (v12_osalg_1(B, A) & l3_msualg_1(B, A)) )  =>  (? [C] :  (m1_osalg_4(C, A, B) &  (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(A)) &  ( ~ (v1_xboole_0(C))  &  (v1_funct_1(C) &  (v1_partfun1(C, u1_struct_0(A)) &  (v2_funcop_1(C) & v2_msualg_4(C, A, B)) ) ) ) ) ) ) ) ) ) ).
fof(rc3_partfun1, 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) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) &  ~ (v1_xboole_0(C)) ) ) ) ) ) ) ) ) ).
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_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc4_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_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_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_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
fof(rc4_trees_3, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_trees_3(B, A) &  (v4_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_finset_1(B) & v3_trees_3(B)) ) ) ) ) ) ) ).
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_msualg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  =>  (? [B] :  (l3_msualg_1(B, A) & v3_msualg_1(B, A)) ) ) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_osalg_1, axiom,  (? [A] :  (l1_osalg_1(A) &  ( ~ (v2_struct_0(A))  &  ~ (v11_struct_0(A)) ) ) ) ).
fof(rc5_osalg_4, axiom,  (? [A] :  (l1_orders_2(A) &  ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) & v2_osalg_4(A)) ) ) ) ) ) ).
fof(rc5_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(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(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_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_msualg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  =>  (? [B] :  (l3_msualg_1(B, A) &  (v3_msualg_1(B, A) & v4_msualg_1(B, A)) ) ) ) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_osalg_4, axiom,  (? [A] :  (l3_osalg_1(A) &  ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v14_struct_0(A) &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) &  (v4_osalg_1(A) &  (v5_osalg_1(A) & v2_osalg_4(A)) ) ) ) ) ) ) ) ) ) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(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(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_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(rc8_finseq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_finseq_1(B, A) &  (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(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(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_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(redefinition_k11_lang1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (m1_finseq_1(C, A) &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ) )  => k11_lang1(A, B, C, D)=k3_relat_1(C, D)) ) ).
fof(redefinition_k14_trees_3, axiom,  (! [A] :  (v7_ordinal1(A) => k14_trees_3(A)=k5_finseq_1(A)) ) ).
fof(redefinition_k1_dtconstr, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_trees_3(B, A) & m1_finseq_1(C, B)) )  => k1_dtconstr(A, B, C)=k15_trees_3(C)) ) ).
fof(redefinition_k1_msualg_4, 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)) ) )  &  (m1_msualg_4(D, A, B, C) & m1_subset_1(E, A)) ) ) )  => k1_msualg_4(A, B, C, D, E)=k1_funct_1(D, E)) ) ).
fof(redefinition_k1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & m1_subset_1(B, k4_ordinal1))  => k1_nat_1(A, B)=k2_xcmplx_0(A, B)) ) ).
fof(redefinition_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k1_relset_1(A, B)=k9_xtuple_0(B)) ) ).
fof(redefinition_k2_msualg_4, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (l3_msualg_1(B, A) &  ( (v2_msualg_4(C, A, B) & m1_msualg_4(C, u1_struct_0(A), u3_msualg_1(A, B), u3_msualg_1(A, B)))  & m1_subset_1(D, u1_struct_0(A))) ) )  => k2_msualg_4(A, B, C, D)=k1_funct_1(C, D)) ) ).
fof(redefinition_k2_trees_4, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => k2_trees_4(A, B)=k1_trees_4(B)) ) ).
fof(redefinition_k3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k3_finseq_1(A)=k1_card_1(A)) ) ).
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_k3_msafree, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  => k3_msafree(A, B)=k2_card_3(B)) ) ).
fof(redefinition_k4_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => k4_finseq_1(A)=k9_xtuple_0(A)) ) ).
fof(redefinition_k5_msualg_4, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  ( (v1_relat_1(B) &  (v4_relat_1(B, u4_struct_0(A)) &  (v1_funct_1(B) & v1_partfun1(B, u4_struct_0(A))) ) )  &  ( (v1_relat_1(C) &  (v4_relat_1(C, u4_struct_0(A)) &  (v1_funct_1(C) & v1_partfun1(C, u4_struct_0(A))) ) )  &  (m2_pboole(D, u4_struct_0(A), B, C) & m1_subset_1(E, u4_struct_0(A))) ) ) )  => k5_msualg_4(A, B, C, D, E)=k1_funct_1(D, E)) ) ).
fof(redefinition_k6_dtconstr, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v1_dtconstr(A) & l1_lang1(A)) )  => k6_dtconstr(A)=k1_lang1(A)) ) ).
fof(redefinition_k7_dtconstr, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_dtconstr(A) & l1_lang1(A)) )  => k7_dtconstr(A)=k2_lang1(A)) ) ).
fof(redefinition_k8_dtconstr, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v1_dtconstr(A) & l1_lang1(A)) )  & m1_subset_1(B, k6_dtconstr(A)))  => k8_dtconstr(A, B)=k1_trees_4(B)) ) ).
fof(redefinition_k8_trees_4, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) & m1_finseq_1(C, k5_trees_3(A))) )  => k8_trees_4(A, B, C)=k4_trees_4(B, C)) ) ).
fof(redefinition_k9_dtconstr, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_dtconstr(A) &  (v3_dtconstr(A) & l1_lang1(A)) ) )  &  (m1_subset_1(B, k7_dtconstr(A)) & m2_dtconstr(C, A, B)) )  => k9_dtconstr(A, B, C)=k4_trees_4(B, C)) ) ).
fof(redefinition_k9_osafree, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_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))) )  => k9_osafree(A, B, C)=k3_osafree(A, B, C)) ) ).
fof(redefinition_m1_dtconstr, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v1_xboole_0(B))  & m1_trees_3(B, A))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(C, k1_zfmisc_1(B))) ) )  =>  (! [D] :  (m1_dtconstr(D, A, B, C) <=> m1_subset_1(D, C)) ) ) ) ).
fof(redefinition_m1_trees_4, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, k1_zfmisc_1(A)))  =>  (! [C] :  (m1_trees_4(C, A, B) <=> m1_finseq_1(C, B)) ) ) ) ).
fof(redefinition_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) <=> m1_finseq_1(B, A)) ) ) ).
fof(redefinition_m2_finseq_2, axiom,  (! [A, B] :  (m1_finseq_2(B, A) =>  (! [C] :  (m2_finseq_2(C, A, B) <=> m1_subset_1(C, B)) ) ) ) ).
fof(redefinition_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) ) ) ) ).
fof(redefinition_r2_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (r2_funct_2(A, B, C, D) <=> C=D) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(redefinition_r3_orders_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) & l1_orders_2(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  =>  (r3_orders_2(A, B, C) <=> r1_orders_2(A, B, C)) ) ) ).
fof(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_osalg_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_osalg_1(A)) )  &  (m1_subset_1(B, u4_struct_0(A)) & m1_subset_1(C, u4_struct_0(A))) )  => r1_osalg_1(A, B, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(reflexivity_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => r1_xxreal_0(A, A)) ) ).
fof(reflexivity_r2_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  => r2_funct_2(A, B, C, C)) ) ).
fof(reflexivity_r3_orders_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) & l1_orders_2(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => r3_orders_2(A, B, B)) ) ).
fof(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(s7_dtconstr__e7_57_1__osafree, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) &  (v2_osalg_4(A) & l3_osalg_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_msualg_4(C, u1_struct_0(A), u3_msualg_1(A, k8_osafree(A, B)), u3_msualg_1(A, k8_osafree(A, B))) & m1_msualg_4(D, u1_struct_0(A), u3_msualg_1(A, k8_osafree(A, B)), u3_msualg_1(A, k8_osafree(A, B)))) ) )  =>  ( ( (! [E] :  (m1_subset_1(E, u1_struct_0(k2_osafree(A, B))) =>  (r2_tarski(E, k1_lang1(k2_osafree(A, B))) =>  (! [F] :  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  (r2_hidden(k4_tarski(k2_trees_4(u1_struct_0(k2_osafree(A, B)), E), F), k1_msualg_4(u1_struct_0(A), u3_msualg_1(A, k8_osafree(A, B)), u3_msualg_1(A, k8_osafree(A, B)), C, G)) <=> r2_hidden(k4_tarski(k2_trees_4(u1_struct_0(k2_osafree(A, B)), E), F), k1_msualg_4(u1_struct_0(A), u3_msualg_1(A, k8_osafree(A, B)), u3_msualg_1(A, k8_osafree(A, B)), D, G))) ) ) ) ) ) )  &  (! [E] :  (m1_subset_1(E, u1_struct_0(k2_osafree(A, B))) =>  (! [H] :  (m1_trees_4(H, k5_trees_3(u1_struct_0(k2_osafree(A, B))), k4_dtconstr(k2_osafree(A, B))) =>  ( (r1_lang1(k2_osafree(A, B), E, k1_dtconstr(u1_struct_0(k2_osafree(A, B)), k5_trees_3(u1_struct_0(k2_osafree(A, B))), H)) &  (! [I] :  ( (v1_relat_1(I) &  (v5_relat_1(I, u1_struct_0(k2_osafree(A, B))) &  (v1_funct_1(I) & v3_trees_2(I)) ) )  =>  (r2_tarski(I, k10_xtuple_0(H)) =>  (! [J] :  (! [K] :  (m1_subset_1(K, u1_struct_0(A)) =>  (r2_hidden(k4_tarski(I, J), k1_msualg_4(u1_struct_0(A), u3_msualg_1(A, k8_osafree(A, B)), u3_msualg_1(A, k8_osafree(A, B)), C, K)) <=> r2_hidden(k4_tarski(I, J), k1_msualg_4(u1_struct_0(A), u3_msualg_1(A, k8_osafree(A, B)), u3_msualg_1(A, k8_osafree(A, B)), D, K))) ) ) ) ) ) ) )  =>  (! [L] :  (! [M] :  (m1_subset_1(M, u1_struct_0(A)) =>  (r2_hidden(k4_tarski(k8_trees_4(u1_struct_0(k2_osafree(A, B)), E, H), L), k1_msualg_4(u1_struct_0(A), u3_msualg_1(A, k8_osafree(A, B)), u3_msualg_1(A, k8_osafree(A, B)), C, M)) <=> r2_hidden(k4_tarski(k8_trees_4(u1_struct_0(k2_osafree(A, B)), E, H), L), k1_msualg_4(u1_struct_0(A), u3_msualg_1(A, k8_osafree(A, B)), u3_msualg_1(A, k8_osafree(A, B)), D, M))) ) ) ) ) ) ) ) ) )  =>  (! [E] :  ( (v1_relat_1(E) &  (v5_relat_1(E, u1_struct_0(k2_osafree(A, B))) &  (v1_funct_1(E) & v3_trees_2(E)) ) )  =>  (r2_tarski(E, k4_dtconstr(k2_osafree(A, B))) =>  (! [N] :  (! [O] :  (m1_subset_1(O, u1_struct_0(A)) =>  (r2_hidden(k4_tarski(E, N), k1_msualg_4(u1_struct_0(A), u3_msualg_1(A, k8_osafree(A, B)), u3_msualg_1(A, k8_osafree(A, B)), C, O)) <=> r2_hidden(k4_tarski(E, N), k1_msualg_4(u1_struct_0(A), u3_msualg_1(A, k8_osafree(A, B)), u3_msualg_1(A, k8_osafree(A, B)), D, O))) ) ) ) ) ) ) ) ) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(symmetry_r1_osalg_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_osalg_1(A)) )  &  (m1_subset_1(B, u4_struct_0(A)) & m1_subset_1(C, u4_struct_0(A))) )  =>  (r1_osalg_1(A, B, C) => r1_osalg_1(A, C, B)) ) ) ).
fof(symmetry_r2_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (r2_funct_2(A, B, C, D) => r2_funct_2(A, B, D, C)) ) ) ).
fof(symmetry_r8_pboole, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) )  =>  (r8_pboole(A, B, C) => r8_pboole(A, C, B)) ) ) ).
fof(t10_osafree, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_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] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (r2_tarski(E, k1_funct_1(B, C)) =>  (m1_dtconstr(k1_trees_4(k4_tarski(E, C)), u1_struct_0(k2_osafree(A, B)), k5_trees_3(u1_struct_0(k2_osafree(A, B))), k4_dtconstr(k2_osafree(A, B))) &  ( (! [F] :  ~ (k4_tarski(F, u1_struct_0(A))=k1_funct_1(k1_trees_4(k4_tarski(E, C)), k1_xboole_0)) )  &  ( (r2_tarski(k1_trees_4(k4_tarski(E, C)), k1_funct_1(u3_msualg_1(A, k8_osafree(A, B)), D)) => r3_orders_2(A, C, D))  &  (r3_orders_2(A, C, D) => r2_tarski(k1_trees_4(k4_tarski(E, C)), k1_funct_1(u3_msualg_1(A, k8_osafree(A, B)), D))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t11_osafree, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_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] :  (m1_dtconstr(C, u1_struct_0(k2_osafree(A, B)), k5_trees_3(u1_struct_0(k2_osafree(A, B))), k4_dtconstr(k2_osafree(A, B))) =>  (! [D] :  (m1_subset_1(D, u4_struct_0(A)) =>  (k1_funct_1(C, k1_xboole_0)=k4_tarski(D, u1_struct_0(A)) =>  ( (? [E] :  (m2_dtconstr(E, k2_osafree(A, B), k9_osafree(A, B, D)) &  (C=k9_dtconstr(k2_osafree(A, B), k9_osafree(A, B, D), E) &  (r1_lang1(k2_osafree(A, B), k9_osafree(A, B, D), k1_dtconstr(u1_struct_0(k2_osafree(A, B)), k5_trees_3(u1_struct_0(k2_osafree(A, B))), E)) &  (r2_tarski(E, k3_msualg_1(A, D, k8_osafree(A, B))) & C=k1_funct_1(k5_msualg_1(A, D, k8_osafree(A, B)), E)) ) ) ) )  &  ( (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  ~ (C=k1_trees_4(k4_tarski(F, E))) ) ) )  &  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (r2_tarski(C, k1_funct_1(u3_msualg_1(A, k8_osafree(A, B)), E)) <=> r3_orders_2(A, k2_msualg_1(A, D), E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t12_funct_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_hidden(A, k9_xtuple_0(k3_relat_1(B, C))) => k1_funct_1(k3_relat_1(B, C), A)=k1_funct_1(C, k1_funct_1(B, A))) ) ) ) ) ) ).
fof(t12_orders_1, axiom,  (! [A] :  (! [B] :  ( (v1_partfun1(B, A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))))  => k1_relat_1(B)=A) ) ) ).
fof(t12_osafree, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_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] :  (m1_subset_1(C, u1_struct_0(k2_osafree(A, B))) =>  (! [D] :  (m1_trees_4(D, k5_trees_3(u1_struct_0(k2_osafree(A, B))), k4_dtconstr(k2_osafree(A, B))) =>  (r1_lang1(k2_osafree(A, B), C, k1_dtconstr(u1_struct_0(k2_osafree(A, B)), k5_trees_3(u1_struct_0(k2_osafree(A, B))), D)) =>  (r2_tarski(C, k7_dtconstr(k2_osafree(A, B))) &  (r2_tarski(k8_trees_4(u1_struct_0(k2_osafree(A, B)), C, D), k4_dtconstr(k2_osafree(A, B))) &  (? [E] :  (m1_subset_1(E, u4_struct_0(A)) &  (C=k4_tarski(E, u1_struct_0(A)) &  (r2_tarski(D, k3_msualg_1(A, E, k8_osafree(A, B))) &  (k8_trees_4(u1_struct_0(k2_osafree(A, B)), C, D)=k1_funct_1(k5_msualg_1(A, E, k8_osafree(A, B)), D) &  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (r2_tarski(k8_trees_4(u1_struct_0(k2_osafree(A, B)), C, D), k1_funct_1(u3_msualg_1(A, k8_osafree(A, B)), F)) <=> r3_orders_2(A, k2_msualg_1(A, E), F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_osafree, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_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] :  (m1_subset_1(C, u4_struct_0(A)) =>  (! [D] :  ( (v1_relat_1(D) &  (v1_funct_1(D) & v1_finseq_1(D)) )  =>  (r2_tarski(D, k3_msualg_1(A, C, k8_osafree(A, B))) <=>  (m1_trees_4(D, k5_trees_3(u1_struct_0(k2_osafree(A, B))), k4_dtconstr(k2_osafree(A, B))) & r1_lang1(k2_osafree(A, B), k9_osafree(A, B, C), k15_trees_3(D))) ) ) ) ) ) ) ) ) ) ).
fof(t15_trees_4, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_relat_1(C) &  (v1_funct_1(C) &  (v1_finseq_1(C) & v6_trees_3(C)) ) )  =>  (! [D] :  ( (v1_relat_1(D) &  (v1_funct_1(D) &  (v1_finseq_1(D) & v6_trees_3(D)) ) )  =>  (k4_trees_4(A, C)=k4_trees_4(B, D) =>  (A=B & C=D) ) ) ) ) ) ) ) ).
fof(t17_trees_4, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_relat_1(C) &  (v1_funct_1(C) & v1_finseq_1(C)) )  =>  ( (k1_trees_4(A)=k4_trees_4(B, C) & v6_trees_3(C))  =>  (A=B & C=k1_xboole_0) ) ) ) ) ) ).
fof(t19_osafree, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) &  (v2_osalg_4(A) & l3_osalg_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] :  (m1_dtconstr(C, u1_struct_0(k2_osafree(A, B)), k5_trees_3(u1_struct_0(k2_osafree(A, B))), k4_dtconstr(k2_osafree(A, B))) =>  ( (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r2_tarski(C, k1_funct_1(u3_msualg_1(A, k8_osafree(A, B)), D)) <=> r2_hidden(k4_tarski(C, D), k3_funct_2(k4_dtconstr(k2_osafree(A, B)), k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A, B)), u1_struct_0(A))), k19_osafree(A, B), C))) ) )  &  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_dtconstr(E, u1_struct_0(k2_osafree(A, B)), k5_trees_3(u1_struct_0(k2_osafree(A, B))), k4_dtconstr(k2_osafree(A, B))) =>  (r2_hidden(k4_tarski(E, D), k3_funct_2(k4_dtconstr(k2_osafree(A, B)), k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A, B)), u1_struct_0(A))), k19_osafree(A, B), C)) => r2_hidden(k4_tarski(C, D), k3_funct_2(k4_dtconstr(k2_osafree(A, B)), k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A, B)), u1_struct_0(A))), k19_osafree(A, B), E))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_domain_1, axiom,  (! [A] :  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  ~ ( (r2_tarski(A, k2_zfmisc_1(B, C)) &  (! [D] :  (m1_subset_1(D, B) =>  (! [E] :  (m1_subset_1(E, C) =>  ~ (A=k4_tarski(D, E)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t1_xtuple_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (k4_tarski(A, B)=k4_tarski(C, D) =>  (A=C & B=D) ) ) ) ) ) ).
fof(t21_osafree, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) &  (v2_osalg_4(A) & l3_osalg_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] :  (m1_dtconstr(C, u1_struct_0(k2_osafree(A, B)), k5_trees_3(u1_struct_0(k2_osafree(A, B))), k4_dtconstr(k2_osafree(A, B))) =>  (! [D] :  (m1_dtconstr(D, u1_struct_0(k2_osafree(A, B)), k5_trees_3(u1_struct_0(k2_osafree(A, B))), k4_dtconstr(k2_osafree(A, B))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  ( (r3_orders_2(A, E, F) &  (r2_tarski(C, k1_funct_1(u3_msualg_1(A, k8_osafree(A, B)), E)) & r2_tarski(D, k1_funct_1(u3_msualg_1(A, k8_osafree(A, B)), E))) )  =>  (r2_hidden(k4_tarski(D, E), k3_funct_2(k4_dtconstr(k2_osafree(A, B)), k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A, B)), u1_struct_0(A))), k19_osafree(A, B), C)) <=> r2_hidden(k4_tarski(D, F), k3_funct_2(k4_dtconstr(k2_osafree(A, B)), k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A, B)), u1_struct_0(A))), k19_osafree(A, B), C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t29_finseq_2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) )  =>  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  ( (r1_tarski(k10_xtuple_0(A), k9_xtuple_0(C)) & B=k3_relat_1(A, C))  => k3_finseq_1(B)=k3_finseq_1(A)) ) ) ) ) ) ) ).
fof(t29_finseq_3, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (! [B] :  ( (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) )  =>  (k3_finseq_1(A)=k3_finseq_1(B) <=> k1_relset_1(k4_ordinal1, A)=k1_relset_1(k4_ordinal1, B)) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t2_tarski, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_hidden(C, A) <=> r2_hidden(C, B)) )  => A=B) ) ) ).
fof(t3_funct_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (r2_hidden(A, k9_xtuple_0(B)) => r2_tarski(k1_funct_1(B, A), k10_xtuple_0(B))) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_osafree, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  &  (v4_osalg_1(A) &  (v5_osalg_1(A) & l3_osalg_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] :  (r2_tarski(C, k6_dtconstr(k2_osafree(A, B))) <=>  (? [D] :  (m1_subset_1(D, u1_struct_0(A)) &  (? [E] :  (r2_tarski(E, k1_funct_1(B, D)) & C=k4_tarski(E, D)) ) ) ) ) ) ) ) ) ) ).
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(t6_msualg_3, 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) =>  (! [D] :  ( (v1_relat_1(D) & v1_funct_1(D))  =>  (r2_tarski(D, k3_msualg_1(A, B, C)) =>  (k9_xtuple_0(D)=k4_finseq_1(k1_msualg_1(A, B)) &  (! [E] :  (r2_tarski(E, k9_xtuple_0(k3_relat_1(k1_msualg_1(A, B), u3_msualg_1(A, C)))) => r2_tarski(k1_funct_1(D, E), k1_funct_1(k3_relat_1(k1_msualg_1(A, B), u3_msualg_1(A, C)), E))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t87_zfmisc_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (r2_hidden(k4_tarski(C, D), k2_zfmisc_1(A, B)) <=>  (r2_hidden(C, A) & r2_hidden(D, B)) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
