% Mizar problem: t27_equation,equation,1090,5 
fof(t27_equation, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  ( (v4_msualg_1(B, A) & l3_msualg_1(B, A))  =>  (! [C] :  (C=a_2_0_equation(A, B) =>  (! [D] :  (m1_pralg_2(D, C, A) =>  ~ ( ( (! [E] :  (r2_hidden(E, C) => E=k1_funct_1(D, E)) )  &  (! [E] :  ( (v3_msualg_1(E, A) &  (v4_msualg_1(E, A) & m1_msualg_2(E, A, k14_pralg_2(C, A, D))) )  =>  (! [F] :  (m2_pboole(F, u1_struct_0(A), u3_msualg_1(A, E), u3_msualg_1(A, B)) =>  ~ (r2_msualg_3(A, E, B, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(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(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(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(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(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc15_struct_0, axiom,  (! [A] :  (l5_struct_0(A) =>  ( ( ~ (v11_struct_0(A))  & v14_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc16_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(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(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v5_ordinal1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc1_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc1_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_finset_1(A)) ) ).
fof(cc1_funcop_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_funcop_1(B)) ) ) ) ) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_partfun1(C, A) => v1_funct_2(C, A, B)) ) ) ) ).
fof(cc1_mssubfam, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v3_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  =>  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v2_finset_1(B)) ) ) ) ) ) ) ).
fof(cc1_msualg_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  &  (v4_msualg_1(B, A) & l3_msualg_1(B, A)) )  =>  (! [C] :  (m1_subset_1(C, k10_xtuple_0(u3_msualg_1(A, B))) =>  ~ (v1_xboole_0(C)) ) ) ) ) ).
fof(cc1_msualg_6, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (l3_msualg_1(B, A) =>  (v4_msualg_1(B, A) => v1_msualg_6(B, A)) ) ) ) ) ).
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_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(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_afinsq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v5_ordinal1(B) &  (v1_funct_1(B) &  (v1_finset_1(B) & v3_card_1(B, A)) ) ) )  =>  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_finset_1(B)) ) ) ) ) ) ) ) ).
fof(cc2_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(cc2_finset_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_finset_1(B)) ) ) ) ).
fof(cc2_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funcop_1(A)) ) ) ) ).
fof(cc2_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ) ).
fof(cc2_funct_2, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc2_mssubfam, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v2_finset_1(B)) ) ) )  =>  (! [C] :  (m3_pboole(C, A, B) => v2_finset_1(C)) ) ) ) ).
fof(cc2_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_msualg_9, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (m1_subset_1(C, u1_struct_0(A)) & m1_pralg_2(D, B, A)) )  =>  (! [E] :  (m1_subset_1(E, k1_funct_1(k10_pralg_2(B, A, D), C)) =>  (v1_relat_1(E) & v1_funct_1(E)) ) ) ) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc2_pboole, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v3_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  =>  (v1_relat_1(B) &  ( ~ (v2_relat_1(B))  &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ) ) ).
fof(cc2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(B)) ) ) ) ).
fof(cc2_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc3_afinsq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) &  (v1_finset_1(B) & v3_card_1(B, A)) ) ) ) )  =>  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) &  (v1_partfun1(B, A) &  (v1_finset_1(B) & v3_card_1(B, A)) ) ) ) ) ) ) ) ) ) ).
fof(cc3_finseq_1, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, A) => v5_relat_1(B, A)) ) ) ).
fof(cc3_finset_1, axiom,  (! [A, B] :  (v1_finset_1(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  (v1_funct_2(C, A, B) & v1_finset_1(C)) ) ) ) ) ) ) ).
fof(cc3_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ) ).
fof(cc3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_funct_1(B)) ) ) ) ).
fof(cc3_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc3_pboole, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) )  =>  (! [D] :  (m2_pboole(D, A, B, C) => v1_funcop_1(D)) ) ) ) ).
fof(cc3_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(A)) ) ) ).
fof(cc3_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_xboole_0(C)) ) ) ) ).
fof(cc3_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc4_finset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) => v1_finset_1(A)) ) ).
fof(cc4_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc4_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  (v1_funct_2(B, A, A) => v1_partfun1(B, A)) ) ) ) ).
fof(cc4_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(cc5_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_relat_1(A, k4_ordinal1) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) )  =>  (v1_relat_1(A) &  (v5_relat_1(A, k4_ordinal1) &  (v5_ordinal1(A) &  (v1_funct_1(A) &  (v1_finset_1(A) & v6_valued_0(A)) ) ) ) ) ) ) ).
fof(cc5_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) ) ) ).
fof(cc5_finset_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_zfmisc_1(A)) ) ) ).
fof(cc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc5_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A))) =>  (v1_funct_2(B, k2_zfmisc_1(A, A), A) => v1_partfun1(B, k2_zfmisc_1(A, A))) ) ) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc5_pboole, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  ( ~ (v1_xboole_0(B))  &  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ) ) ).
fof(cc5_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(cc6_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_afinsq_1(A)) ) ) ) ).
fof(cc6_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ).
fof(cc6_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_finset_1(A)) ) ).
fof(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc6_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(cc7_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) )  =>  (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) &  (v1_finset_1(A) & v1_afinsq_1(A)) ) ) ) ) ) ).
fof(cc7_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ) ).
fof(cc7_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finset_1(B)) ) ) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_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(cc8_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ) ) ).
fof(cc8_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_finseq_1(A)) ) ).
fof(cc8_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_finset_1(B)) ) ) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc8_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(cc9_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v1_finset_1(A) & v1_afinsq_1(A)) ) ) )  =>  (v1_relat_1(A) &  (v5_ordinal1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc9_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v1_finset_1(A)) ) ).
fof(cc9_finset_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_finset_1(A)) ) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(cc9_funct_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(d10_pralg_2, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  & l1_msualg_1(B))  =>  (! [C] :  (m1_pralg_2(C, A, B) =>  (! [D] :  ( (v1_relat_1(D) &  (v4_relat_1(D, u1_struct_0(B)) &  (v1_funct_1(D) & v1_partfun1(D, u1_struct_0(B))) ) )  =>  (D=k10_pralg_2(A, B, C) <=>  (! [E] :  (m1_subset_1(E, u1_struct_0(B)) => k1_funct_1(D, E)=k4_card_3(k9_pralg_2(A, B, E, C))) ) ) ) ) ) ) ) ) ) ).
fof(d10_xboole_0, axiom,  (! [A] :  (! [B] :  (A=B <=>  (r1_tarski(A, B) & r1_tarski(B, A)) ) ) ) ).
fof(d13_pboole, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (v2_relat_1(B) <=>  (! [C] :  ~ ( (r2_hidden(C, A) & v1_xboole_0(k1_funct_1(B, C))) ) ) ) ) ) ) ).
fof(d14_pralg_2, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  =>  (! [C] :  (m1_pralg_2(C, A, B) => k14_pralg_2(A, B, C)=g3_msualg_1(B, k10_pralg_2(A, B, C), k13_pralg_2(A, B, C))) ) ) ) ) ).
fof(d15_msualg_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (l3_msualg_1(B, A) =>  (! [C] :  (m3_pboole(C, u1_struct_0(A), u3_msualg_1(A, B)) =>  (v3_msualg_2(C, A, B) => k10_msualg_2(A, B, C)=g3_msualg_1(A, C, k4_msualg_2(A, B, C))) ) ) ) ) ) ) ).
fof(d17_msualg_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (l3_msualg_1(B, A) =>  (! [C] :  (m3_pboole(C, u1_struct_0(A), u3_msualg_1(A, B)) =>  (! [D] :  ( (v3_msualg_1(D, A) & m1_msualg_2(D, A, B))  =>  (D=k12_msualg_2(A, B, C) <=>  (m3_pboole(C, u1_struct_0(A), u3_msualg_1(A, D)) &  (! [E] :  (m1_msualg_2(E, A, B) =>  (m3_pboole(C, u1_struct_0(A), u3_msualg_1(A, E)) => m1_msualg_2(D, A, E)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d18_pboole, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) )  =>  (m3_pboole(C, A, B) <=> r2_pboole(A, C, B)) ) ) ) ) ) ).
fof(d18_relat_1, axiom,  (! [A] :  (! [B] :  (v1_relat_1(B) =>  (v4_relat_1(B, A) <=> r1_tarski(k9_xtuple_0(B), A)) ) ) ) ).
fof(d19_msualg_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (l3_msualg_1(B, A) =>  (! [C] :  (C=k14_msualg_2(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (v3_msualg_1(D, A) & m1_msualg_2(D, A, B)) ) ) ) ) ) ) ) ) ).
fof(d1_funct_2, axiom,  (! [A] :  (! [B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( ( ~ (B=k1_xboole_0)  =>  (v1_funct_2(C, A, B) <=> A=k1_relset_1(A, C)) )  &  (B=k1_xboole_0 =>  (v1_funct_2(C, A, B) <=> C=k1_xboole_0) ) ) ) ) ) ) ).
fof(d1_funct_4, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (C=k1_funct_4(A, B) <=>  (k9_xtuple_0(C)=k2_xboole_0(k9_xtuple_0(A), k9_xtuple_0(B)) &  (! [D] :  (r2_hidden(D, k2_xboole_0(k9_xtuple_0(A), k9_xtuple_0(B))) =>  ( (r2_hidden(D, k9_xtuple_0(B)) => k1_funct_1(C, D)=k1_funct_1(B, D))  &  ( ~ (r2_hidden(D, k9_xtuple_0(B)))  => k1_funct_1(C, D)=k1_funct_1(A, D)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_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)) => k1_msualg_1(A, B)=k3_funct_2(u4_struct_0(A), k3_finseq_2(u1_struct_0(A)), u1_msualg_1(A), B)) ) ) ) ).
fof(d1_pralg_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (l3_msualg_1(B, A) =>  (! [C] :  (m1_subset_1(C, u4_struct_0(A)) => k1_pralg_3(A, B, C)=k1_funct_1(k5_msualg_1(A, C, B), k1_xboole_0)) ) ) ) ) ) ).
fof(d1_tarski, axiom,  (! [A] :  (! [B] :  (B=k1_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=> C=A) ) ) ) ) ).
fof(d1_xboole_0, axiom,  (! [A] :  (v1_xboole_0(A) <=>  (! [B] :  ~ (r2_hidden(B, A)) ) ) ) ).
fof(d21_pboole, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) )  =>  (r8_pboole(A, B, C) <=>  (! [D] :  (m1_subset_1(D, A) => k1_funct_1(B, D)=k1_funct_1(C, D)) ) ) ) ) ) ) ) ) ).
fof(d2_equation, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (l3_msualg_1(B, A) =>  (! [C] :  (m1_msualg_2(C, A, B) =>  (! [D] :  (D=k2_equation(A, B, C) <=>  (! [E] :  (r2_hidden(E, D) <=>  (? [F] :  ( (v3_msualg_1(F, A) & m1_msualg_2(F, A, B))  &  (E=F & m1_msualg_2(C, A, F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_msualg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (m1_subset_1(B, u4_struct_0(A)) => k2_msualg_1(A, B)=k3_funct_2(u4_struct_0(A), u1_struct_0(A), u2_msualg_1(A), B)) ) ) ) ).
fof(d2_partfun1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (v1_partfun1(B, A) <=> k1_relset_1(A, B)=A) ) ) ) ).
fof(d2_pboole, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) )  =>  (r2_pboole(A, B, C) <=>  (! [D] :  (r2_hidden(D, A) => r1_tarski(k1_funct_1(B, D), k1_funct_1(C, D))) ) ) ) ) ) ) ) ).
fof(d3_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (! [B] :  (m1_subset_1(B, k4_ordinal1) =>  (B=k3_finseq_1(A) <=> k2_finseq_1(B)=k9_xtuple_0(A)) ) ) ) ) ).
fof(d3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (B=k10_xtuple_0(A) <=>  (! [C] :  (r2_hidden(C, B) <=>  (? [D] :  (r2_hidden(D, k9_xtuple_0(A)) & C=k1_funct_1(A, D)) ) ) ) ) ) ) ) ).
fof(d3_msualg_1, axiom,  (! [A] :  (l1_struct_0(A) =>  (! [B] :  (l2_msualg_1(B, A) =>  (v4_msualg_1(B, A) <=> v2_relat_1(u3_msualg_1(A, B))) ) ) ) ) ).
fof(d3_msualg_3, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) )  =>  (! [D] :  (m2_pboole(D, A, B, C) =>  (v2_msualg_3(D, A, B, C) <=>  (! [E] :  (r2_tarski(E, A) => k10_xtuple_0(k1_funct_1(D, E))=k1_funct_1(C, E)) ) ) ) ) ) ) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d4_msualg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (m1_subset_1(B, u4_struct_0(A)) =>  (! [C] :  (l3_msualg_1(C, A) => k3_msualg_1(A, B, C)=k1_funct_1(k3_relat_1(u1_msualg_1(A), k6_finseq_2(u1_struct_0(A), u3_msualg_1(A, C))), B)) ) ) ) ) ) ).
fof(d5_card_3, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (B=k4_card_3(A) <=>  (! [C] :  (r2_hidden(C, B) <=>  (? [D] :  ( (v1_relat_1(D) & v1_funct_1(D))  &  (C=D &  (k9_xtuple_0(D)=k9_xtuple_0(A) &  (! [E] :  (r2_hidden(E, k9_xtuple_0(A)) => r2_tarski(k1_funct_1(D, E), k1_funct_1(A, E))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_finseq_2, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, k3_finseq_2(A)) &  (v1_funct_1(C) & v1_partfun1(C, k3_finseq_2(A))) ) )  =>  (C=k6_finseq_2(A, B) <=>  (! [D] :  (m2_finseq_2(D, A, k3_finseq_2(A)) => k1_funct_1(C, D)=k4_card_3(k3_relat_1(D, B))) ) ) ) ) ) ) ) ).
fof(d5_finset_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) )  =>  (v2_finset_1(B) <=>  (! [C] :  (r2_hidden(C, A) => v1_finset_1(k1_funct_1(B, C))) ) ) ) ) ) ).
fof(d5_msualg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (m1_subset_1(B, u4_struct_0(A)) =>  (! [C] :  (l3_msualg_1(C, A) => k4_msualg_1(A, B, C)=k1_funct_1(k3_relat_1(u2_msualg_1(A), u3_msualg_1(A, C)), B)) ) ) ) ) ) ).
fof(d5_msualg_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (l3_msualg_1(B, A) =>  (! [C] :  (m1_subset_1(C, u4_struct_0(A)) =>  (! [D] :  (m3_pboole(D, u1_struct_0(A), u3_msualg_1(A, B)) =>  (r1_msualg_2(A, B, C, D) <=> r1_tarski(k10_xtuple_0(k5_relat_1(k5_msualg_1(A, C, B), k1_funct_1(k3_relat_1(u1_msualg_1(A), k6_finseq_2(u1_struct_0(A), D)), C))), k1_funct_1(k3_relat_1(u2_msualg_1(A), D), C))) ) ) ) ) ) ) ) ) ).
fof(d5_pralg_2, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  & l1_msualg_1(B))  =>  (! [C] :  ( (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) )  =>  (m1_pralg_2(C, A, B) <=>  (! [D] :  (r2_hidden(D, A) =>  (v4_msualg_1(k1_funct_1(C, D), B) & l3_msualg_1(k1_funct_1(C, D), B)) ) ) ) ) ) ) ) ) ).
fof(d6_msualg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (m1_subset_1(B, u4_struct_0(A)) =>  (! [C] :  (l3_msualg_1(C, A) => k5_msualg_1(A, B, C)=k1_funct_1(u4_msualg_1(A, C), B)) ) ) ) ) ) ).
fof(d6_msualg_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (l3_msualg_1(B, A) =>  (! [C] :  (m3_pboole(C, u1_struct_0(A), u3_msualg_1(A, B)) =>  (v3_msualg_2(C, A, B) <=>  (! [D] :  (m1_subset_1(D, u4_struct_0(A)) => r1_msualg_2(A, B, D, C)) ) ) ) ) ) ) ) ) ).
fof(d6_msualg_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  ( (v4_msualg_1(B, A) & l3_msualg_1(B, A))  =>  (! [C] :  ( (v4_msualg_1(C, A) & l3_msualg_1(C, A))  =>  (! [D] :  (m1_subset_1(D, u4_struct_0(A)) =>  (! [E] :  (m2_pboole(E, u1_struct_0(A), u3_msualg_1(A, B), u3_msualg_1(A, C)) =>  (! [F] :  (m1_subset_1(F, k3_msualg_1(A, D, B)) =>  (! [G] :  (m1_subset_1(G, k3_msualg_1(A, D, C)) =>  (G=k5_msualg_3(A, B, C, D, E, F) <=>  (! [H] :  (v7_ordinal1(H) =>  (r2_tarski(H, k9_xtuple_0(F)) => k1_funct_1(G, H)=k1_funct_1(k1_msualg_3(u1_struct_0(A), u3_msualg_1(A, B), u3_msualg_1(A, C), E, k7_partfun1(u1_struct_0(A), k1_msualg_1(A, D), H)), k1_funct_1(F, H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_partfun1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  =>  (! [C] :  (r2_hidden(C, k9_xtuple_0(B)) => k7_partfun1(A, B, C)=k1_funct_1(B, C)) ) ) ) ) ).
fof(d7_msualg_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (l3_msualg_1(B, A) =>  (! [C] :  (l3_msualg_1(C, A) =>  (! [D] :  (m2_pboole(D, u1_struct_0(A), u3_msualg_1(A, B), u3_msualg_1(A, C)) =>  (r1_msualg_3(A, B, C, D) <=>  (! [E] :  (m1_subset_1(E, u4_struct_0(A)) =>  ( ~ (k3_msualg_1(A, E, B)=k1_xboole_0)  =>  (! [F] :  (m1_subset_1(F, k3_msualg_1(A, E, B)) => k1_funct_1(k1_msualg_3(u1_struct_0(A), u3_msualg_1(A, B), u3_msualg_1(A, C), D, k2_msualg_1(A, E)), k1_funct_1(k5_msualg_1(A, E, B), F))=k1_funct_1(k5_msualg_1(A, E, C), k5_msualg_3(A, B, C, E, D, F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d8_msualg_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (l3_msualg_1(B, A) =>  (! [C] :  (l3_msualg_1(C, A) =>  (! [D] :  (m2_pboole(D, u1_struct_0(A), u3_msualg_1(A, B), u3_msualg_1(A, C)) =>  (r2_msualg_3(A, B, C, D) <=>  (r1_msualg_3(A, B, C, D) & v2_msualg_3(D, u1_struct_0(A), u3_msualg_1(A, B), u3_msualg_1(A, C))) ) ) ) ) ) ) ) ) ) ).
fof(d9_msualg_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (l3_msualg_1(B, A) =>  (! [C] :  (l3_msualg_1(C, A) =>  (m1_msualg_2(C, A, B) <=>  (m3_pboole(u3_msualg_1(A, C), u1_struct_0(A), u3_msualg_1(A, B)) &  (! [D] :  (m3_pboole(D, u1_struct_0(A), u3_msualg_1(A, B)) =>  (r8_pboole(u1_struct_0(A), D, u3_msualg_1(A, C)) =>  (v3_msualg_2(D, A, B) & r8_pboole(u4_struct_0(A), u4_msualg_1(A, C), k4_msualg_2(A, B, D))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d9_pralg_2, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  & l1_msualg_1(B))  =>  (! [C] :  (m1_subset_1(C, u1_struct_0(B)) =>  (! [D] :  (m1_pralg_2(D, A, B) =>  (! [E] :  ( (v1_relat_1(E) &  (v4_relat_1(E, A) &  (v1_funct_1(E) & v1_partfun1(E, A)) ) )  =>  ( ( ~ (A=k1_xboole_0)  =>  (E=k9_pralg_2(A, B, C, D) <=>  (! [F] :  ~ ( (r2_tarski(F, A) &  (! [G] :  (l3_msualg_1(G, B) =>  ~ ( (G=k1_funct_1(D, F) & k1_funct_1(E, F)=k1_funct_1(u3_msualg_1(B, G), C)) ) ) ) ) ) ) ) )  &  (A=k1_xboole_0 =>  (E=k9_pralg_2(A, B, C, D) <=> E=k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ).
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_msualg_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (l3_msualg_1(B, A) & m3_pboole(C, u1_struct_0(A), u3_msualg_1(A, B))) )  =>  (v3_msualg_1(k10_msualg_2(A, B, C), A) & m1_msualg_2(k10_msualg_2(A, B, C), A, B)) ) ) ).
fof(dt_k10_pralg_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  & l1_msualg_1(B))  & m1_pralg_2(C, A, B))  =>  (v1_relat_1(k10_pralg_2(A, B, C)) &  (v4_relat_1(k10_pralg_2(A, B, C), u1_struct_0(B)) &  (v1_funct_1(k10_pralg_2(A, B, C)) & v1_partfun1(k10_pralg_2(A, B, C), u1_struct_0(B))) ) ) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k12_msualg_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (l3_msualg_1(B, A) & m3_pboole(C, u1_struct_0(A), u3_msualg_1(A, B))) )  =>  (v3_msualg_1(k12_msualg_2(A, B, C), A) & m1_msualg_2(k12_msualg_2(A, B, C), A, B)) ) ) ).
fof(dt_k13_finseq_1, axiom, $true).
fof(dt_k13_pralg_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  & m1_pralg_2(C, A, B))  => m2_pboole(k13_pralg_2(A, B, C), u4_struct_0(B), k3_relat_1(u1_msualg_1(B), k6_finseq_2(u1_struct_0(B), k10_pralg_2(A, B, C))), k3_relat_1(u2_msualg_1(B), k10_pralg_2(A, B, C)))) ) ).
fof(dt_k14_msualg_2, axiom, $true).
fof(dt_k14_pralg_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  & m1_pralg_2(C, A, B))  => l3_msualg_1(k14_pralg_2(A, B, C), B)) ) ).
fof(dt_k1_card_1, axiom,  (! [A] : v1_card_1(k1_card_1(A))) ).
fof(dt_k1_finseq_1, axiom, $true).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_funct_2, axiom, $true).
fof(dt_k1_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k1_funct_4(A, B)) & v1_funct_1(k1_funct_4(A, B))) ) ) ).
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_3, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  ( (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) )  &  (m2_pboole(D, A, B, C) & m1_subset_1(E, A)) ) ) )  =>  (v1_funct_1(k1_msualg_3(A, B, C, D, E)) &  (v1_funct_2(k1_msualg_3(A, B, C, D, E), k1_funct_1(B, E), k1_funct_1(C, E)) & m1_subset_1(k1_msualg_3(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(k1_funct_1(B, E), k1_funct_1(C, E))))) ) ) ) ).
fof(dt_k1_pralg_3, axiom, $true).
fof(dt_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => m1_subset_1(k1_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_equation, axiom, $true).
fof(dt_k2_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => m1_subset_1(k2_finseq_1(A), k1_zfmisc_1(k4_ordinal1))) ) ).
fof(dt_k2_funcop_1, 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_partfun1, axiom,  (! [A, B, C, D] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))  =>  (v1_funct_1(k2_partfun1(A, B, C, D)) & m1_subset_1(k2_partfun1(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ).
fof(dt_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => m1_subset_1(k2_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_zfmisc_1, 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_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_relat_1, axiom,  (! [A, B] : v1_relat_1(k3_relat_1(A, B))) ).
fof(dt_k3_tarski, axiom, $true).
fof(dt_k4_card_3, axiom, $true).
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_msualg_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (l3_msualg_1(B, A) & m3_pboole(C, u1_struct_0(A), u3_msualg_1(A, B))) )  => m2_pboole(k4_msualg_2(A, B, C), u4_struct_0(A), k3_relat_1(u1_msualg_1(A), k6_finseq_2(u1_struct_0(A), C)), k3_relat_1(u2_msualg_1(A), C))) ) ).
fof(dt_k4_ordinal1, 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_3, axiom,  (! [A, B, C, D, E, F] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (l3_msualg_1(B, A) &  (l3_msualg_1(C, A) &  (m1_subset_1(D, u4_struct_0(A)) &  (m2_pboole(E, u1_struct_0(A), u3_msualg_1(A, B), u3_msualg_1(A, C)) & m1_subset_1(F, k3_msualg_1(A, D, B))) ) ) ) )  => m1_subset_1(k5_msualg_3(A, B, C, D, E, F), k3_msualg_1(A, D, C))) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_pralg_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v2_struct_0(B))  & l1_msualg_1(B))  &  (m1_pralg_2(C, A, B) & m1_subset_1(D, A)) ) )  =>  (v4_msualg_1(k5_pralg_2(A, B, C, D), B) & l3_msualg_1(k5_pralg_2(A, B, C, D), B)) ) ) ).
fof(dt_k5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k5_relat_1(A, B))) ) ).
fof(dt_k6_finseq_2, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (v1_relat_1(k6_finseq_2(A, B)) &  (v4_relat_1(k6_finseq_2(A, B), k3_finseq_2(A)) &  (v1_funct_1(k6_finseq_2(A, B)) & v1_partfun1(k6_finseq_2(A, B), k3_finseq_2(A))) ) ) ) ) ).
fof(dt_k7_funcop_1, axiom,  (! [A, B] :  (v1_funct_1(k7_funcop_1(A, B)) &  (v1_funct_2(k7_funcop_1(A, B), A, k1_tarski(B)) & m1_subset_1(k7_funcop_1(A, B), k1_zfmisc_1(k2_zfmisc_1(A, k1_tarski(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_k9_funct_6, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_relat_1(k9_funct_6(A)) &  (v1_funct_1(k9_funct_6(A)) & v1_funcop_1(k9_funct_6(A))) ) ) ) ).
fof(dt_k9_pralg_2, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  & l1_msualg_1(B))  &  (m1_subset_1(C, u1_struct_0(B)) & m1_pralg_2(D, A, B)) )  =>  (v1_relat_1(k9_pralg_2(A, B, C, D)) &  (v4_relat_1(k9_pralg_2(A, B, C, D), A) &  (v1_funct_1(k9_pralg_2(A, B, C, D)) & v1_partfun1(k9_pralg_2(A, B, C, D), A)) ) ) ) ) ).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_l1_msualg_1, axiom,  (! [A] :  (l1_msualg_1(A) => l5_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_msualg_1, axiom, $true).
fof(dt_l3_msualg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  =>  (! [B] :  (l3_msualg_1(B, A) => l2_msualg_1(B, A)) ) ) ) ).
fof(dt_l5_struct_0, axiom,  (! [A] :  (l5_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_m1_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_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  & l3_msualg_1(B, A))  =>  (! [C] :  (m1_msualg_2(C, A, B) => l3_msualg_1(C, A)) ) ) ) ).
fof(dt_m1_pralg_2, axiom,  (! [A, B] :  ( ( ~ (v2_struct_0(B))  & l1_msualg_1(B))  =>  (! [C] :  (m1_pralg_2(C, A, B) =>  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
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_m3_pboole, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  (m3_pboole(C, A, B) =>  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) ) ) ) ).
fof(dt_o_2_1_equation, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (v4_msualg_1(B, A) & l3_msualg_1(B, A)) )  =>  (v2_relat_1(o_2_1_equation(A, B)) &  (v2_finset_1(o_2_1_equation(A, B)) & m3_pboole(o_2_1_equation(A, B), u1_struct_0(A), u3_msualg_1(A, B))) ) ) ) ).
fof(dt_o_2_2_equation, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (v4_msualg_1(B, A) & l3_msualg_1(B, A)) )  =>  (v3_msualg_1(o_2_2_equation(A, B), A) &  (v4_msualg_1(o_2_2_equation(A, B), A) &  (v3_msafree2(o_2_2_equation(A, B), A) & m1_msualg_2(o_2_2_equation(A, B), A, B)) ) ) ) ) ).
fof(dt_u1_msualg_1, axiom,  (! [A] :  (l1_msualg_1(A) =>  (v1_funct_1(u1_msualg_1(A)) &  (v1_funct_2(u1_msualg_1(A), u4_struct_0(A), k3_finseq_2(u1_struct_0(A))) & m1_subset_1(u1_msualg_1(A), k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(A), k3_finseq_2(u1_struct_0(A)))))) ) ) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u2_msualg_1, axiom,  (! [A] :  (l1_msualg_1(A) =>  (v1_funct_1(u2_msualg_1(A)) &  (v1_funct_2(u2_msualg_1(A), u4_struct_0(A), u1_struct_0(A)) & m1_subset_1(u2_msualg_1(A), k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(A), u1_struct_0(A))))) ) ) ) ).
fof(dt_u3_msualg_1, axiom,  (! [A, B] :  ( (l1_struct_0(A) & l2_msualg_1(B, A))  =>  (v1_relat_1(u3_msualg_1(A, B)) &  (v4_relat_1(u3_msualg_1(A, B), u1_struct_0(A)) &  (v1_funct_1(u3_msualg_1(A, B)) & v1_partfun1(u3_msualg_1(A, B), u1_struct_0(A))) ) ) ) ) ).
fof(dt_u4_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_msualg_1, axiom,  (? [A] : l1_msualg_1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_msualg_1, axiom,  (! [A] :  (l1_struct_0(A) =>  (? [B] : l2_msualg_1(B, A)) ) ) ).
fof(existence_l3_msualg_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_msualg_1(A))  =>  (? [B] : l3_msualg_1(B, A)) ) ) ).
fof(existence_l5_struct_0, axiom,  (? [A] : l5_struct_0(A)) ).
fof(existence_m1_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_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  & l3_msualg_1(B, A))  =>  (? [C] : m1_msualg_2(C, A, B)) ) ) ).
fof(existence_m1_pralg_2, axiom,  (! [A, B] :  ( ( ~ (v2_struct_0(B))  & l1_msualg_1(B))  =>  (? [C] : m1_pralg_2(C, A, B)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
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_m3_pboole, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (? [C] : m3_pboole(C, A, B)) ) ) ).
fof(fc10_funcop_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k3_relat_1(B, A)) & v1_funcop_1(k3_relat_1(B, A))) ) ) ).
fof(fc10_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_funct_2, axiom,  (! [A, B] : v4_funct_1(k1_funct_2(A, B))) ).
fof(fc10_msualg_2, 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))  &  (v2_relat_1(C) & m3_pboole(C, u1_struct_0(A), u3_msualg_1(A, B))) ) )  =>  (v3_msualg_1(k12_msualg_2(A, B, C), A) & v4_msualg_1(k12_msualg_2(A, B, C), 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_relset_1, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v1_relat_1(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(k9_xtuple_0(A)))) )  =>  ( ~ (v1_xboole_0(k5_relat_1(A, B)))  & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc11_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => v2_relat_1(k2_funcop_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_msualg_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  & l3_msualg_1(B, A))  =>  ~ (v1_xboole_0(k14_msualg_2(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(fc13_finseq_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v2_finseq_1(k5_relat_1(A, B))) ) ) ).
fof(fc13_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ~ (v1_zfmisc_1(k10_xtuple_0(A))) ) ) ).
fof(fc13_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(B))  =>  (v1_xboole_0(k3_relat_1(B, A)) & v1_relat_1(k3_relat_1(B, A))) ) ) ).
fof(fc13_struct_0, axiom,  (! [A] :  ( (v11_struct_0(A) & l5_struct_0(A))  => v1_xboole_0(u4_struct_0(A))) ) ).
fof(fc14_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v1_finset_1(k2_zfmisc_1(A, B))) ) ).
fof(fc14_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_funcop_1(k5_relat_1(A, B))) ) ) ).
fof(fc14_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_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_finseq_1(k1_finseq_1(A))) ) ).
fof(fc15_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v1_funct_1(B))  => v1_funcop_1(k2_funcop_1(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(fc16_finseq_1, axiom,  (! [A] :  ( (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) )  => v3_finseq_1(k1_tarski(A))) ) ).
fof(fc16_funcop_1, axiom,  (! [A, B] : v3_funct_1(k2_funcop_1(A, B))) ).
fof(fc16_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_xboole_0(B))  =>  (v1_xboole_0(k5_relat_1(A, B)) & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc17_afinsq_1, axiom,  (! [A, B] :  (v7_ordinal1(A) =>  (v5_ordinal1(k2_funcop_1(A, B)) & v1_finset_1(k2_funcop_1(A, B))) ) ) ).
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_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v1_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc17_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v3_funct_1(k5_relat_1(A, B))) ) ) ).
fof(fc17_funct_1, axiom,  (! [A, B, C] :  ( (v4_funct_1(A) &  (v1_relat_1(C) &  (v5_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_1(C, B)) & v1_funct_1(k1_funct_1(C, B))) ) ) ).
fof(fc17_relat_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_xboole_0(k5_relat_1(A, B)) & v1_relat_1(k5_relat_1(A, B))) ) ) ).
fof(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_funcop_1, axiom,  (! [A, B] : v4_relat_1(k2_funcop_1(A, B), 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(fc19_finseq_1, axiom,  (! [A, B] :  ( (v3_finseq_1(A) & v3_finseq_1(B))  => v3_finseq_1(k2_xboole_0(A, B))) ) ).
fof(fc19_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_finset_1(A))  => v1_finset_1(k9_xtuple_0(A))) ) ).
fof(fc19_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v3_relat_1(A) & v1_funct_1(A)) )  => v1_xboole_0(k1_funct_1(A, B))) ) ).
fof(fc19_struct_0, axiom,  (! [A, B] :  ( (v1_card_1(A) &  (v13_struct_0(B, A) & l1_struct_0(B)) )  => v3_card_1(u1_struct_0(B), A)) ) ).
fof(fc1_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) )  => v7_ordinal1(k9_xtuple_0(A))) ) ).
fof(fc1_equation, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (l3_msualg_1(B, A) & m1_msualg_2(C, A, B)) )  =>  ~ (v1_xboole_0(k2_equation(A, B, C))) ) ) ).
fof(fc1_finseq_1, axiom,  (! [A] :  ( (v7_ordinal1(A) & v8_ordinal1(A))  => v1_xboole_0(k1_finseq_1(A))) ) ).
fof(fc1_finset_1, axiom,  (! [A] : v1_finset_1(k1_tarski(A))) ).
fof(fc1_funcop_1, axiom,  (! [A, B] :  (v1_relat_1(k2_funcop_1(A, B)) & v1_funct_1(k2_funcop_1(A, B))) ) ).
fof(fc1_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  ~ (v1_xboole_0(k1_funct_2(A, B))) ) ) ).
fof(fc1_msualg_1, axiom,  (! [A, B] :  ( (l1_struct_0(A) &  (v4_msualg_1(B, A) & l2_msualg_1(B, A)) )  =>  (v1_relat_1(u3_msualg_1(A, B)) &  (v2_relat_1(u3_msualg_1(A, B)) &  (v4_relat_1(u3_msualg_1(A, B), u1_struct_0(A)) &  (v1_funct_1(u3_msualg_1(A, B)) & v1_partfun1(u3_msualg_1(A, B), u1_struct_0(A))) ) ) ) ) ) ).
fof(fc1_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_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_pralg_3, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  & m1_pralg_2(C, A, B))  => v4_msualg_1(k14_pralg_2(A, B, C), B)) ) ).
fof(fc1_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  &  (v1_relat_1(C) & v4_relat_1(C, A)) )  => v4_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc20_finset_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finset_1(B)) ) )  =>  (v1_relat_1(k3_relat_1(B, A)) & v1_finset_1(k3_relat_1(B, A))) ) ) ).
fof(fc20_struct_0, axiom,  (! [A] :  ( (v15_struct_0(A) & l5_struct_0(A))  => v1_zfmisc_1(u4_struct_0(A))) ) ).
fof(fc21_funcop_1, axiom,  (! [A, B] :  (v1_relat_1(k2_funcop_1(A, B)) &  (v4_relat_1(k2_funcop_1(A, B), A) &  (v1_funct_1(k2_funcop_1(A, B)) & v1_partfun1(k2_funcop_1(A, B), A)) ) ) ) ).
fof(fc21_struct_0, axiom,  (! [A] :  ( ( ~ (v15_struct_0(A))  & l5_struct_0(A))  =>  ~ (v1_zfmisc_1(u4_struct_0(A))) ) ) ).
fof(fc22_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_finset_1(A))  => v1_finset_1(k10_xtuple_0(A))) ) ).
fof(fc23_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_subset_1(C, B))  => v5_relat_1(k2_funcop_1(A, C), B)) ) ).
fof(fc23_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v3_relat_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v3_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc24_finset_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finset_1(B)) ) )  =>  (v1_relat_1(k1_funct_4(A, B)) &  (v1_funct_1(k1_funct_4(A, B)) & v1_finset_1(k1_funct_4(A, B))) ) ) ) ).
fof(fc24_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k9_xtuple_0(A))) ) ).
fof(fc25_relat_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) & v1_relat_1(A))  => v1_zfmisc_1(k10_xtuple_0(A))) ) ).
fof(fc26_finset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v1_finset_1(B))  =>  (v1_relat_1(k5_relat_1(B, A)) & v1_finset_1(k5_relat_1(B, A))) ) ) ).
fof(fc26_relat_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(C) & v5_relat_1(C, B))  =>  (v1_relat_1(k5_relat_1(C, A)) & v5_relat_1(k5_relat_1(C, A), B)) ) ) ).
fof(fc27_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) &  (v1_relat_1(B) & v1_funct_1(B)) )  =>  (v1_relat_1(k5_relat_1(B, A)) & v1_finset_1(k5_relat_1(B, A))) ) ) ).
fof(fc27_relat_1, axiom,  (! [A, B, C] :  ( (v1_relat_1(C) & v4_relat_1(C, B))  =>  (v1_relat_1(k5_relat_1(C, A)) &  (v4_relat_1(k5_relat_1(C, A), A) & v4_relat_1(k5_relat_1(C, A), B)) ) ) ) ).
fof(fc29_relat_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  =>  (v1_relat_1(k3_relat_1(C, B)) & v5_relat_1(k3_relat_1(C, B), A)) ) ) ).
fof(fc2_afinsq_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) )  & v7_ordinal1(B))  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_finset_1(k5_relat_1(A, B))) ) ) ).
fof(fc2_equation, 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))  &  (v2_relat_1(C) &  (v2_finset_1(C) & m3_pboole(C, u1_struct_0(A), u3_msualg_1(A, B))) ) ) )  =>  (v3_msualg_1(k12_msualg_2(A, B, C), A) & v3_msafree2(k12_msualg_2(A, B, C), A)) ) ) ).
fof(fc2_finseq_1, axiom,  (! [A] :  ( (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) )  =>  ~ (v1_xboole_0(k1_finseq_1(A))) ) ) ).
fof(fc2_funcop_1, axiom,  (! [A] : v1_xboole_0(k2_funcop_1(k1_xboole_0, 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_funct_2, axiom,  (! [A] :  ~ (v1_xboole_0(k1_funct_2(A, 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_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_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc30_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v5_finset_1(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(fc31_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v5_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc33_finset_1, axiom,  (! [A, B] :  ( (v5_finset_1(A) & v5_finset_1(B))  => v5_finset_1(k2_xboole_0(A, B))) ) ).
fof(fc33_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v2_relat_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v2_relat_1(k5_relat_1(A, B))) ) ) ).
fof(fc34_finset_1, axiom,  (! [A] :  ( (v1_finset_1(A) & v5_finset_1(A))  => v1_finset_1(k3_tarski(A))) ) ).
fof(fc35_finseq_1, axiom, v4_finseq_1(k1_tarski(k1_xboole_0))).
fof(fc35_finset_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) )  => v1_finset_1(k1_funct_1(A, B))) ) ).
fof(fc36_finseq_1, axiom,  (! [A, B] :  ( (v4_finseq_1(A) & v4_finseq_1(B))  => v4_finseq_1(k2_xboole_0(A, B))) ) ).
fof(fc36_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v2_finset_1(A))  => v5_finset_1(k10_xtuple_0(A))) ) ).
fof(fc37_finseq_1, axiom,  (! [A] : v4_finseq_1(k13_finseq_1(A))) ).
fof(fc39_finseq_1, axiom,  (! [A, B, C] :  ( (v4_finseq_1(A) &  (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) ) )  => v1_finseq_1(k1_funct_1(B, C))) ) ).
fof(fc3_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_finset_1(k1_finseq_1(A))) ) ).
fof(fc3_funcop_1, axiom,  (! [A, B] :  (v1_xboole_0(B) => v1_xboole_0(k2_funcop_1(B, A))) ) ).
fof(fc3_funct_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & v1_xboole_0(B))  => v1_xboole_0(k1_funct_2(A, B))) ) ).
fof(fc3_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) => v3_ordinal1(k3_tarski(A))) ) ).
fof(fc3_pralg_3, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, u4_struct_0(A)) & m1_pralg_2(D, B, A)) ) )  =>  (v1_relat_1(k1_pralg_3(A, k14_pralg_2(B, A, D), C)) & v1_funct_1(k1_pralg_3(A, k14_pralg_2(B, A, D), 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(fc4_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_card_1(k1_finseq_1(A), A)) ) ).
fof(fc4_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  ~ (v1_xboole_0(k2_funcop_1(B, A))) ) ) ).
fof(fc4_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, A) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, A)))) ) )  =>  (v1_funct_1(k3_relat_1(D, C)) & v1_funct_2(k3_relat_1(D, C), A, B)) ) ) ).
fof(fc4_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  => v3_ordinal1(k9_xtuple_0(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(fc5_funcop_1, axiom,  (! [A] : v3_relat_1(k2_funcop_1(A, k1_xboole_0))) ).
fof(fc5_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, B, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (v1_funct_1(k3_relat_1(D, C)) & v1_funct_2(k3_relat_1(D, C), A, B)) ) ) ).
fof(fc5_ordinal1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  & v3_ordinal1(B))  =>  (v1_relat_1(k5_relat_1(A, B)) &  (v5_relat_1(k5_relat_1(A, B), k10_xtuple_0(A)) & v5_ordinal1(k5_relat_1(A, B))) ) ) ) ).
fof(fc5_pralg_2, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  & l1_msualg_1(B))  &  (m1_subset_1(C, u1_struct_0(B)) & m1_pralg_2(D, A, B)) )  =>  (v1_relat_1(k9_pralg_2(A, B, C, D)) &  (v2_relat_1(k9_pralg_2(A, B, C, D)) &  (v4_relat_1(k9_pralg_2(A, B, C, D), A) &  (v1_funct_1(k9_pralg_2(A, B, C, D)) & v1_partfun1(k9_pralg_2(A, B, C, D), A)) ) ) ) ) ) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc6_msualg_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (v4_msualg_1(B, A) & l3_msualg_1(B, A)) )  =>  (v3_msualg_1(g3_msualg_1(A, u3_msualg_1(A, B), u4_msualg_1(A, B)), A) & v4_msualg_1(g3_msualg_1(A, u3_msualg_1(A, B), u4_msualg_1(A, B)), A)) ) ) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc6_pralg_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  & l1_msualg_1(B))  & m1_pralg_2(C, A, B))  =>  (v1_relat_1(k10_pralg_2(A, B, C)) &  (v2_relat_1(k10_pralg_2(A, B, C)) &  (v4_relat_1(k10_pralg_2(A, B, C), u1_struct_0(B)) &  (v1_funct_1(k10_pralg_2(A, B, C)) & v1_partfun1(k10_pralg_2(A, B, C), u1_struct_0(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_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_pralg_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  & m1_pralg_2(C, A, B))  => v3_msualg_1(k14_pralg_2(A, B, C), B)) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_funct_1(k5_relat_1(A, B))) ) ) ).
fof(fc8_funct_2, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(E) &  (v1_funct_2(E, B, C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) ) ) )  =>  (v1_funct_1(k3_relat_1(D, E)) & v1_funct_2(k3_relat_1(D, E), A, C)) ) ) ).
fof(fc8_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_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v1_finset_1(k2_xboole_0(A, B))) ) ).
fof(fc9_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k1_funct_1(A, B)) & v1_funct_1(k1_funct_1(A, B))) ) ) ).
fof(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(fraenkel_a_2_0_equation, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  &  (v4_msualg_1(C, B) & l3_msualg_1(C, B)) )  =>  (r2_hidden(A, a_2_0_equation(B, C)) <=>  (? [D] :  (m1_subset_1(D, k14_msualg_2(B, C)) &  (A=D &  (? [E] :  ( (v3_msualg_1(E, B) &  (v4_msualg_1(E, B) &  (v3_msafree2(E, B) & m1_msualg_2(E, B, C)) ) )  & E=D) ) ) ) ) ) ) ) ).
fof(fraenkel_a_3_0_equation, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  &  ( ~ (v1_xboole_0(C))  & m1_pralg_2(D, C, B)) )  =>  (r2_hidden(A, a_3_0_equation(B, C, D)) <=>  (? [E, F] :  ( (m1_subset_1(E, C) & m1_subset_1(F, u1_struct_0(B)))  & A=k1_funct_1(u3_msualg_1(B, k5_pralg_2(C, B, D, E)), F)) ) ) ) ) ).
fof(fraenkel_a_3_1_pralg_3, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(B))  &  ( ( ~ (v2_struct_0(C))  &  ( ~ (v11_struct_0(C))  & l1_msualg_1(C)) )  & m1_pralg_2(D, B, C)) )  =>  (r2_hidden(A, a_3_1_pralg_3(B, C, D)) <=>  (? [E, F] :  ( (m1_subset_1(E, B) & m1_subset_1(F, u1_struct_0(C)))  & A=k1_funct_1(u3_msualg_1(C, k5_pralg_2(B, C, D, E)), F)) ) ) ) ) ).
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_k1_funct_4, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_funct_1(A))  &  (v1_relat_1(B) & v1_funct_1(B)) )  => k1_funct_4(A, A)=A) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(ie1_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) )  => k1_card_1(A)=k9_xtuple_0(A)) ) ).
fof(ie1_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (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)))) )  & m1_subset_1(D, A)) ) )  => k7_partfun1(B, C, D)=k3_funct_2(A, B, C, D)) ) ).
fof(ie2_afinsq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) )  => k9_xtuple_0(A)=k1_card_1(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_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) ) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_finseq_1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc14_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  (v2_funct_1(A) &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(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_afinsq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) & v1_finset_1(B)) ) ) ) ) ) ).
fof(rc1_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A))) &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ).
fof(rc1_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_finset_1(A)) ) ).
fof(rc1_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_funct_2, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(rc1_mssubfam, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (? [C] :  (m3_pboole(C, A, B) &  (v1_relat_1(C) &  (v3_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) &  (v1_partfun1(C, A) & v2_finset_1(C)) ) ) ) ) ) ) ) ) ).
fof(rc1_msualg_4, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v2_funcop_1(B)) ) ) ) ) ) ).
fof(rc1_msualg_6, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (? [B] :  (l3_msualg_1(B, A) & v4_msualg_1(B, A)) ) ) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_pboole, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc23_struct_0, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (l1_struct_0(B) & v13_struct_0(B, A)) ) ) ) ).
fof(rc25_struct_0, axiom,  (? [A] :  (l5_struct_0(A) &  ~ (v15_struct_0(A)) ) ) ).
fof(rc2_afinsq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) &  (v1_xboole_0(B) & v1_finset_1(B)) ) ) ) ) ) ) ).
fof(rc2_equation, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (v4_msualg_1(B, A) & l3_msualg_1(B, A)) )  =>  (? [C] :  (m1_msualg_2(C, A, B) &  (v3_msualg_1(C, A) &  (v4_msualg_1(C, A) & v3_msafree2(C, 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_finset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_finset_1(B)) ) ) ).
fof(rc2_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_funct_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_msualg_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  & l3_msualg_1(B, A))  =>  (? [C] :  (m1_msualg_2(C, A, B) & v3_msualg_1(C, A)) ) ) ) ).
fof(rc2_msualg_9, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  =>  (? [C] :  (m3_pboole(C, A, B) &  (v1_relat_1(C) &  (v2_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) &  (v1_partfun1(C, A) & v2_finset_1(C)) ) ) ) ) ) ) ) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_pboole, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v3_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc3_afinsq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v5_ordinal1(B) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  & v1_finset_1(B)) ) ) ) ) ) ) ) ).
fof(rc3_equation, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (v1_msualg_6(B, A) & l3_msualg_1(B, A)) )  =>  (? [C] :  (m1_msualg_2(C, A, B) & v1_msualg_6(C, 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_finset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc3_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) &  (v3_funct_1(C) &  (v1_partfun1(C, A) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ) ) ) ).
fof(rc3_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ).
fof(rc3_msualg_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (v4_msualg_1(B, A) & l3_msualg_1(B, A)) )  =>  (? [C] :  (m1_msualg_2(C, A, B) &  (v3_msualg_1(C, A) & v4_msualg_1(C, A)) ) ) ) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_pboole, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) ) ) ) ).
fof(rc3_relat_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc4_afinsq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (? [B] :  (v1_relat_1(B) &  (v5_ordinal1(B) &  (v1_funct_1(B) &  (v1_finset_1(B) & v3_card_1(B, A)) ) ) ) ) ) ) ).
fof(rc4_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ).
fof(rc4_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(rc4_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) ) ) ) ) ).
fof(rc4_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v2_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(rc4_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(rc5_afinsq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v5_ordinal1(A) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) & v6_valued_0(A)) ) ) ) ) ) ).
fof(rc5_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_pboole, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) ) )  =>  (? [C] :  (m3_pboole(C, A, B) &  (v1_relat_1(C) &  (v2_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) ) ) ) ) ).
fof(rc5_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc6_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(rc6_finset_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ).
fof(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(rc6_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_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc7_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v2_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ) ).
fof(rc7_finset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (? [C] :  ( ~ (v1_xboole_0(C))  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ) ) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc7_pboole, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, B) &  (v5_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, B)) ) ) ) ) ) ) ).
fof(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_finset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_zfmisc_1(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_finseq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ).
fof(rc9_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) & v5_finset_1(A)) ) ) ).
fof(rc9_funct_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v2_relat_1(B) &  (v4_relat_1(B, A) & v1_funct_1(B)) ) ) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rd1_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(C, A))  => k1_funct_1(k2_funcop_1(A, B), C)=B) ) ).
fof(rd2_funcop_1, axiom,  (! [A, B] : k9_xtuple_0(k2_funcop_1(A, B))=A) ).
fof(rd4_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => k5_relat_1(A, k9_xtuple_0(A))=A) ) ).
fof(rd5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => k5_relat_1(k5_relat_1(A, B), B)=k5_relat_1(A, B)) ) ).
fof(rd8_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k5_relat_1(B, A)=B) ) ).
fof(redefinition_k1_msualg_3, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  ( (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) )  &  (m2_pboole(D, A, B, C) & m1_subset_1(E, A)) ) ) )  => k1_msualg_3(A, B, C, D, E)=k1_funct_1(D, E)) ) ).
fof(redefinition_k1_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_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) => k2_finseq_1(A)=k1_finseq_1(A)) ) ).
fof(redefinition_k2_partfun1, axiom,  (! [A, B, C, D] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))  => k2_partfun1(A, B, C, D)=k5_relat_1(C, D)) ) ).
fof(redefinition_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => k2_relset_1(A, B)=k10_xtuple_0(B)) ) ).
fof(redefinition_k3_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_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_pralg_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v2_struct_0(B))  & l1_msualg_1(B))  &  (m1_pralg_2(C, A, B) & m1_subset_1(D, A)) ) )  => k5_pralg_2(A, B, C, D)=k1_funct_1(C, D)) ) ).
fof(redefinition_k7_funcop_1, axiom,  (! [A, B] : k7_funcop_1(A, B)=k2_funcop_1(A, 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_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_r8_pboole, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) )  =>  (r8_pboole(A, B, C) <=> B=C) ) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(reflexivity_r2_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_r2_pboole, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) )  => r2_pboole(A, B, B)) ) ).
fof(reflexivity_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(s1_mssubfam__e16_33__equation, axiom,  (! [A, B, C, D, E, F, G] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  ( (v4_msualg_1(B, A) & l3_msualg_1(B, A))  &  ( ~ (v1_xboole_0(D))  &  (m1_pralg_2(E, C, A) &  (m1_pralg_2(F, D, A) &  (v3_msualg_1(G, A) &  (v4_msualg_1(G, A) & m1_msualg_2(G, A, k14_pralg_2(C, A, E))) ) ) ) ) ) )  =>  ( (! [H] :  (r2_hidden(H, u1_struct_0(A)) =>  (! [I] :  ~ ( (r2_hidden(I, k1_funct_1(u3_msualg_1(A, G), H)) &  (! [J] :  ~ ( (r2_hidden(J, k1_funct_1(u3_msualg_1(A, B), H)) &  (? [K] :  (m1_subset_1(K, u1_struct_0(A)) &  (? [L] :  (m1_subset_1(L, k1_funct_1(k10_pralg_2(D, A, F), K)) &  (? [M] :  ( (v3_msualg_1(M, A) &  (v4_msualg_1(M, A) &  (v3_msafree2(M, A) & m1_msualg_2(M, A, B)) ) )  &  (K=H &  (L=I &  ( (! [N] :  ( (v3_msualg_1(N, A) &  (v4_msualg_1(N, A) &  (v3_msafree2(N, A) & m1_msualg_2(N, A, B)) ) )  =>  (m1_msualg_2(M, A, N) => k1_funct_1(L, M)=k1_funct_1(L, N)) ) )  & J=k1_funct_1(L, M)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [H] :  (m2_pboole(H, u1_struct_0(A), u3_msualg_1(A, G), u3_msualg_1(A, B)) &  (! [I] :  ~ ( (r2_hidden(I, u1_struct_0(A)) &  (! [J] :  ( (v1_funct_1(J) &  (v1_funct_2(J, k1_funct_1(u3_msualg_1(A, G), I), k1_funct_1(u3_msualg_1(A, B), I)) & m1_subset_1(J, k1_zfmisc_1(k2_zfmisc_1(k1_funct_1(u3_msualg_1(A, G), I), k1_funct_1(u3_msualg_1(A, B), I))))) )  =>  ~ ( (J=k1_funct_1(H, I) &  (! [O] :  (r2_hidden(O, k1_funct_1(u3_msualg_1(A, G), I)) =>  (? [P] :  (m1_subset_1(P, u1_struct_0(A)) &  (? [Q] :  (m1_subset_1(Q, k1_funct_1(k10_pralg_2(D, A, F), P)) &  (? [R] :  ( (v3_msualg_1(R, A) &  (v4_msualg_1(R, A) &  (v3_msafree2(R, A) & m1_msualg_2(R, A, B)) ) )  &  (P=I &  (Q=O &  ( (! [S] :  ( (v3_msualg_1(S, A) &  (v4_msualg_1(S, A) &  (v3_msafree2(S, A) & m1_msualg_2(S, A, B)) ) )  =>  (m1_msualg_2(R, A, S) => k1_funct_1(Q, R)=k1_funct_1(Q, S)) ) )  & k1_funct_1(J, O)=k1_funct_1(Q, R)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(s1_xboole_0__e1_33_4__equation, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  (v4_msualg_1(B, A) & l3_msualg_1(B, A)) )  =>  (? [C] :  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, k2_equation(A, B, o_2_2_equation(A, B))) &  (? [E] :  ( (v3_msualg_1(E, A) &  (v4_msualg_1(E, A) & m1_msualg_2(E, A, B)) )  &  (D=E & v3_msafree2(E, A)) ) ) ) ) ) ) ) ) ).
fof(s1_xboole_0__e32_33__equation, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  ( (v4_msualg_1(B, A) & l3_msualg_1(B, A))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(D, u1_struct_0(A))) ) )  =>  (? [F] :  (! [G] :  (r2_hidden(G, F) <=>  (r2_hidden(G, C) &  (? [H] :  (m1_msualg_2(H, A, B) &  (H=G & r2_hidden(E, k1_funct_1(u3_msualg_1(A, H), D))) ) ) ) ) ) ) ) ) ).
fof(s2_pboole__e6_33__equation, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  ( (v4_msualg_1(B, A) & l3_msualg_1(B, A))  &  ( ~ (v1_xboole_0(C))  & m1_pralg_2(D, C, A)) ) )  =>  (? [E] :  ( (v1_relat_1(E) &  (v4_relat_1(E, u1_struct_0(A)) &  (v1_funct_1(E) & v1_partfun1(E, u1_struct_0(A))) ) )  &  (! [F] :  (r2_hidden(F, u1_struct_0(A)) =>  (! [G] :  (r2_hidden(G, k1_funct_1(E, F)) <=>  (r2_hidden(G, k1_funct_1(k10_pralg_2(C, A, D), F)) &  (? [H] :  (m1_subset_1(H, u1_struct_0(A)) &  (? [I] :  (m1_subset_1(I, k1_funct_1(k10_pralg_2(C, A, D), H)) &  (? [J] :  ( (v3_msualg_1(J, A) &  (v4_msualg_1(J, A) &  (v3_msafree2(J, A) & m1_msualg_2(J, A, B)) ) )  &  (H=F &  (I=G &  (! [K] :  ( (v3_msualg_1(K, A) &  (v4_msualg_1(K, A) &  (v3_msafree2(K, A) & m1_msualg_2(K, A, B)) ) )  =>  (m1_msualg_2(J, A, K) => k1_funct_1(I, J)=k1_funct_1(I, K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(s3_funct_2__e4_33_7_1_2__equation, axiom,  (! [A, B, C, D, E, F, G, H, I] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  ( (v4_msualg_1(B, A) & l3_msualg_1(B, A))  &  (m1_pralg_2(D, C, A) &  ( (v3_msualg_1(E, A) &  (v4_msualg_1(E, A) & m1_msualg_2(E, A, k14_pralg_2(C, A, D))) )  &  (m2_pboole(F, u1_struct_0(A), u3_msualg_1(A, E), u3_msualg_1(A, B)) &  (m1_subset_1(G, u4_struct_0(A)) &  (m1_subset_1(H, k3_msualg_1(A, G, E)) &  ( ~ (v1_xboole_0(I))  & v1_finset_1(I)) ) ) ) ) ) ) )  =>  ( (! [J] :  (m1_subset_1(J, I) =>  (? [K] :  (m1_subset_1(K, k14_msualg_2(A, B)) &  (? [L] :  ( (v1_relat_1(L) & v1_funct_1(L))  &  (? [M] :  ( (v3_msualg_1(M, A) &  (v4_msualg_1(M, A) &  (v3_msafree2(M, A) & m1_msualg_2(M, A, B)) ) )  &  (L=k1_funct_1(H, J) &  ( (! [N] :  ( (v3_msualg_1(N, A) &  (v4_msualg_1(N, A) &  (v3_msafree2(N, A) & m1_msualg_2(N, A, B)) ) )  =>  (m1_msualg_2(M, A, N) => k1_funct_1(L, M)=k1_funct_1(L, N)) ) )  &  (k1_funct_1(k1_funct_1(F, k1_funct_1(k1_msualg_1(A, G), J)), L)=k1_funct_1(L, M) & K=M) ) ) ) ) ) ) ) ) ) )  =>  (? [J] :  ( (v1_funct_1(J) &  (v1_funct_2(J, I, k14_msualg_2(A, B)) & m1_subset_1(J, k1_zfmisc_1(k2_zfmisc_1(I, k14_msualg_2(A, B))))) )  &  (! [K] :  (m1_subset_1(K, I) =>  (? [O] :  ( (v1_relat_1(O) & v1_funct_1(O))  &  (? [P] :  ( (v3_msualg_1(P, A) &  (v4_msualg_1(P, A) &  (v3_msafree2(P, A) & m1_msualg_2(P, A, B)) ) )  &  (O=k1_funct_1(H, K) &  ( (! [Q] :  ( (v3_msualg_1(Q, A) &  (v4_msualg_1(Q, A) &  (v3_msafree2(Q, A) & m1_msualg_2(Q, A, B)) ) )  =>  (m1_msualg_2(P, A, Q) => k1_funct_1(O, P)=k1_funct_1(O, Q)) ) )  &  (k1_funct_1(k1_funct_1(F, k1_funct_1(k1_msualg_1(A, G), K)), O)=k1_funct_1(O, P) & k3_funct_2(I, k14_msualg_2(A, B), J, K)=P) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(s3_funct_2__e7_33_3_1_1_2__equation, axiom,  (! [A, B, C, D, E, F, G] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  ( (v4_msualg_1(B, A) & l3_msualg_1(B, A))  &  ( ~ (v1_xboole_0(C))  &  (m1_pralg_2(D, C, A) &  (m1_subset_1(E, u4_struct_0(A)) &  (m1_subset_1(F, k3_msualg_1(A, E, k14_pralg_2(C, A, D))) &  ( ~ (v1_xboole_0(G))  & v1_finset_1(G)) ) ) ) ) ) )  =>  ( (! [H] :  (m1_subset_1(H, G) =>  (? [I] :  (m1_subset_1(I, k14_msualg_2(A, B)) &  (? [J] :  ( (v1_relat_1(J) & v1_funct_1(J))  &  (? [K] :  ( (v3_msualg_1(K, A) &  (v4_msualg_1(K, A) &  (v3_msafree2(K, A) & m1_msualg_2(K, A, B)) ) )  &  (J=k1_funct_1(F, H) &  ( (! [L] :  ( (v3_msualg_1(L, A) &  (v4_msualg_1(L, A) &  (v3_msafree2(L, A) & m1_msualg_2(L, A, B)) ) )  =>  (m1_msualg_2(K, A, L) => k1_funct_1(J, K)=k1_funct_1(J, L)) ) )  & I=K) ) ) ) ) ) ) ) ) )  =>  (? [H] :  ( (v1_funct_1(H) &  (v1_funct_2(H, G, k14_msualg_2(A, B)) & m1_subset_1(H, k1_zfmisc_1(k2_zfmisc_1(G, k14_msualg_2(A, B))))) )  &  (! [I] :  (m1_subset_1(I, G) =>  (? [M] :  ( (v1_relat_1(M) & v1_funct_1(M))  &  (? [N] :  ( (v3_msualg_1(N, A) &  (v4_msualg_1(N, A) &  (v3_msafree2(N, A) & m1_msualg_2(N, A, B)) ) )  &  (M=k1_funct_1(F, I) &  ( (! [O] :  ( (v3_msualg_1(O, A) &  (v4_msualg_1(O, A) &  (v3_msafree2(O, A) & m1_msualg_2(O, A, B)) ) )  =>  (m1_msualg_2(N, A, O) => k1_funct_1(M, N)=k1_funct_1(M, O)) ) )  & k3_funct_2(G, k14_msualg_2(A, B), H, I)=N) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(s3_pboole__e9_33_4__equation, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  &  ( (v4_msualg_1(B, A) & l3_msualg_1(B, A))  &  ~ (v1_xboole_0(C)) ) )  =>  ( (! [E] :  ~ ( (r2_hidden(E, C) &  (! [F] :  ~ ( (? [G] :  (m1_msualg_2(G, A, B) &  (? [H] :  (E=G &  (r2_tarski(H, k1_funct_1(u3_msualg_1(A, G), D)) & F=H) ) ) ) ) ) ) ) ) )  =>  (? [E] :  ( (v1_relat_1(E) &  (v4_relat_1(E, C) &  (v1_funct_1(E) & v1_partfun1(E, C)) ) )  &  (! [F] :  (r2_hidden(F, C) =>  (? [I] :  (m1_msualg_2(I, A, B) &  (? [J] :  (F=I &  (r2_tarski(J, k1_funct_1(u3_msualg_1(A, I), D)) & k1_funct_1(E, F)=J) ) ) ) ) ) ) ) ) ) ) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
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(t11_funct_4, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  ( ~ (r2_hidden(C, k9_xtuple_0(B)))  => k1_funct_1(k1_funct_4(A, B), C)=k1_funct_1(A, C)) ) ) ) ) ) ).
fof(t11_pralg_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (l3_msualg_1(B, A) =>  (! [C] :  (l3_msualg_1(C, A) =>  (! [D] :  (m1_subset_1(D, u4_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, k3_msualg_1(A, D, B)) =>  ( (E=k1_xboole_0 & k1_msualg_1(A, D)=k1_xboole_0)  =>  (k3_msualg_1(A, D, B)=k1_xboole_0 |  (k3_msualg_1(A, D, C)=k1_xboole_0 |  (! [F] :  (m2_pboole(F, u1_struct_0(A), u3_msualg_1(A, B), u3_msualg_1(A, C)) => k5_msualg_3(A, B, C, D, F, E)=k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t12_xboole_1, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) => k2_xboole_0(A, B)=B) ) ) ).
fof(t13_funct_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_hidden(A, k9_xtuple_0(B)) => k1_funct_1(k3_relat_1(B, C), A)=k1_funct_1(C, k1_funct_1(B, A))) ) ) ) ) ) ).
fof(t13_funct_4, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (! [C] :  (r2_hidden(C, k9_xtuple_0(B)) => k1_funct_1(k1_funct_4(A, B), C)=k1_funct_1(B, C)) ) ) ) ) ) ).
fof(t14_pralg_3, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  =>  (! [C] :  (m1_pralg_2(C, A, B) =>  (! [D] :  (m1_subset_1(D, u4_struct_0(B)) =>  (! [E] :  (m1_subset_1(E, k3_msualg_1(B, D, k14_pralg_2(A, B, C))) => r2_tarski(E, k1_funct_2(k1_relset_1(k4_ordinal1, k1_msualg_1(B, D)), k1_funct_2(A, k3_tarski(a_3_1_pralg_3(A, B, C)))))) ) ) ) ) ) ) ) ) ) ).
fof(t15_funct_2, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  =>  (! [E] :  ( (v1_relat_1(E) & v1_funct_1(E))  =>  (r2_hidden(C, A) =>  (B=k1_xboole_0 | k1_funct_1(k3_relat_1(D, E), C)=k1_funct_1(E, k1_funct_1(D, C))) ) ) ) ) ) ) ) ) ).
fof(t18_equation, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (l3_msualg_1(B, A) =>  (! [C] :  (m1_msualg_2(C, A, B) =>  (! [D] :  (m1_subset_1(D, u4_struct_0(A)) =>  (! [E] :  (r2_tarski(E, k3_msualg_1(A, D, C)) => r2_tarski(E, k3_msualg_1(A, D, B))) ) ) ) ) ) ) ) ) ) ).
fof(t18_msualg_9, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  ( (v4_msualg_1(B, A) & l3_msualg_1(B, A))  =>  (! [C] :  (m1_subset_1(C, u4_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, k3_msualg_1(A, C, B)) => r2_tarski(k3_funct_2(k3_msualg_1(A, C, B), k4_msualg_1(A, C, B), k5_msualg_1(A, C, B), D), k1_funct_1(u3_msualg_1(A, B), k2_msualg_1(A, C)))) ) ) ) ) ) ) ) ).
fof(t19_equation, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (l3_msualg_1(B, A) =>  (! [C] :  (m1_msualg_2(C, A, B) =>  (! [D] :  (m1_subset_1(D, u4_struct_0(A)) =>  (! [E] :  (r2_tarski(E, k3_msualg_1(A, D, C)) => k1_funct_1(k5_msualg_1(A, D, C), E)=k1_funct_1(k5_msualg_1(A, D, B), E)) ) ) ) ) ) ) ) ) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t1_tarski, axiom, $true).
fof(t20_equation, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  =>  (! [C] :  (m1_pralg_2(C, A, B) =>  (! [D] :  (m1_msualg_2(D, B, k14_pralg_2(A, B, C)) =>  (! [E] :  (m1_subset_1(E, u4_struct_0(B)) =>  (! [F] :  (r2_hidden(F, k3_msualg_1(B, E, D)) =>  ( (v1_relat_1(k1_funct_1(k5_msualg_1(B, E, D), F)) & v1_funct_1(k1_funct_1(k5_msualg_1(B, E, D), F)))  &  (v1_relat_1(k1_funct_1(k5_msualg_1(B, E, k14_pralg_2(A, B, C)), F)) & v1_funct_1(k1_funct_1(k5_msualg_1(B, E, k14_pralg_2(A, B, C)), F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t20_pralg_3, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  =>  (! [C] :  (m1_pralg_2(C, A, B) =>  (! [D] :  (m1_subset_1(D, A) =>  (! [E] :  (m1_subset_1(E, u4_struct_0(B)) =>  ( ~ (k1_msualg_1(B, E)=k1_xboole_0)  =>  (! [F] :  ( (v4_msualg_1(F, B) & l3_msualg_1(F, B))  =>  (! [G] :  (m1_subset_1(G, k3_msualg_1(B, E, k14_pralg_2(A, B, C))) => m1_subset_1(k1_funct_1(k9_funct_6(G), D), k3_msualg_1(B, E, k5_pralg_2(A, B, C, D)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t21_pralg_3, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  =>  (! [C] :  (m1_pralg_2(C, A, B) =>  (! [D] :  (m1_subset_1(D, A) =>  (! [E] :  (m1_subset_1(E, u4_struct_0(B)) =>  (! [F] :  (m1_subset_1(F, k3_msualg_1(B, E, k14_pralg_2(A, B, C))) =>  (! [G] :  (r2_tarski(G, k1_relset_1(k4_ordinal1, k1_msualg_1(B, E))) =>  (! [H] :  ( (v1_relat_1(H) & v1_funct_1(H))  =>  (H=k1_funct_1(F, G) => k1_funct_1(k1_funct_1(k9_funct_6(F), D), G)=k1_funct_1(H, D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t22_pralg_3, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  =>  (! [C] :  (m1_pralg_2(C, A, B) =>  (! [D] :  (m1_subset_1(D, u4_struct_0(B)) =>  ( ~ (k1_msualg_1(B, D)=k1_xboole_0)  =>  (! [E] :  (m1_subset_1(E, k3_msualg_1(B, D, k14_pralg_2(A, B, C))) =>  (! [F] :  (m1_subset_1(F, A) =>  (! [G] :  ( (v1_relat_1(G) & v1_funct_1(G))  =>  (G=k3_funct_2(k3_msualg_1(B, D, k14_pralg_2(A, B, C)), k4_msualg_1(B, D, k14_pralg_2(A, B, C)), k5_msualg_1(B, D, k14_pralg_2(A, B, C)), E) => k1_funct_1(G, F)=k1_funct_1(k5_msualg_1(B, D, k5_pralg_2(A, B, C, F)), k1_funct_1(k9_funct_6(E), F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t25_equation, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  & v1_finset_1(B))  =>  (! [C] :  ( (v4_msualg_1(C, A) & l3_msualg_1(C, A))  =>  (! [D] :  (m1_pralg_2(D, B, A) =>  ~ ( ( (! [E] :  (m1_subset_1(E, B) =>  (? [F] :  ( (v3_msualg_1(F, A) &  (v4_msualg_1(F, A) &  (v3_msafree2(F, A) & m1_msualg_2(F, A, C)) ) )  & F=k5_pralg_2(B, A, D, E)) ) ) )  &  (! [E] :  ( (v3_msualg_1(E, A) &  (v4_msualg_1(E, A) &  (v3_msafree2(E, A) & m1_msualg_2(E, A, C)) ) )  =>  ~ ( (! [F] :  (m1_subset_1(F, B) => m1_msualg_2(k5_pralg_2(B, A, D, F), A, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t26_equation, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  ( (v4_msualg_1(B, A) & l3_msualg_1(B, A))  =>  (! [C] :  ( (v3_msualg_1(C, A) &  (v4_msualg_1(C, A) &  (v3_msafree2(C, A) & m1_msualg_2(C, A, B)) ) )  =>  (! [D] :  ( (v3_msualg_1(D, A) &  (v4_msualg_1(D, A) &  (v3_msafree2(D, A) & m1_msualg_2(D, A, B)) ) )  =>  (? [E] :  ( (v3_msualg_1(E, A) &  (v4_msualg_1(E, A) &  (v3_msafree2(E, A) & m1_msualg_2(E, A, B)) ) )  &  (m1_msualg_2(C, A, E) & m1_msualg_2(D, A, E)) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  ( (k9_xtuple_0(A)=k9_xtuple_0(B) &  (! [C] :  (r2_hidden(C, k9_xtuple_0(A)) => k1_funct_1(A, C)=k1_funct_1(B, C)) ) )  => A=B) ) ) ) ) ).
fof(t2_msualg_6, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (l3_msualg_1(B, A) =>  (! [C] :  (m1_subset_1(C, u4_struct_0(A)) =>  (! [D] :  ( (v1_relat_1(D) & v1_funct_1(D))  =>  (r2_tarski(D, k3_msualg_1(A, C, B)) =>  (k9_xtuple_0(D)=k4_finseq_1(k1_msualg_1(A, C)) &  (! [E] :  (r2_tarski(E, k4_finseq_1(k1_msualg_1(A, C))) => r2_tarski(k1_funct_1(D, E), k1_funct_1(u3_msualg_1(A, B), k7_partfun1(u1_struct_0(A), k1_msualg_1(A, C), E)))) ) ) ) ) ) ) ) ) ) ) ) ).
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_equation, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (! [D] :  (! [E] :  ( (v1_relat_1(E) & v1_funct_1(E))  =>  ( (r2_tarski(E, k1_funct_2(A, k1_funct_2(B, C))) & r2_tarski(D, B))  =>  (k9_xtuple_0(k1_funct_1(k9_funct_6(E), D))=A & r1_tarski(k10_xtuple_0(k1_funct_1(k9_funct_6(E), D)), C)) ) ) ) ) ) ) ) ) ) ).
fof(t3_pralg_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (l3_msualg_1(B, A) =>  (! [C] :  (m1_subset_1(C, u4_struct_0(A)) =>  (k3_msualg_1(A, C, B)=k4_card_3(k3_relat_1(k1_msualg_1(A, C), u3_msualg_1(A, B))) &  (k9_xtuple_0(k3_relat_1(k1_msualg_1(A, C), u3_msualg_1(A, B)))=k9_xtuple_0(k1_msualg_1(A, C)) & k4_msualg_1(A, C, B)=k1_funct_1(u3_msualg_1(A, B), k2_msualg_1(A, C))) ) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t40_zfmisc_1, axiom,  (! [A] :  (! [B] :  (r2_hidden(A, B) => k2_xboole_0(k1_tarski(A), B)=B) ) ) ).
fof(t47_funct_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_hidden(B, k9_xtuple_0(k5_relat_1(C, A))) => k1_funct_1(k5_relat_1(C, A), B)=k1_funct_1(C, B)) ) ) ) ) ).
fof(t4_partfun1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_relat_1(C) &  (v5_relat_1(C, B) & v1_funct_1(C)) )  =>  (r2_hidden(A, k9_xtuple_0(C)) => r2_tarski(k1_funct_1(C, A), B)) ) ) ) ) ).
fof(t4_pralg_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (l3_msualg_1(B, A) =>  (! [C] :  (m1_subset_1(C, u4_struct_0(A)) =>  (k1_msualg_1(A, C)=k1_xboole_0 => k3_msualg_1(A, C, B)=k1_tarski(k1_xboole_0)) ) ) ) ) ) ) ).
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(t57_relat_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (v1_relat_1(C) =>  (r2_hidden(B, k9_xtuple_0(k5_relat_1(C, A))) <=>  (r2_hidden(B, A) & r2_hidden(B, k9_xtuple_0(C))) ) ) ) ) ) ).
fof(t5_msualg_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (l3_msualg_1(B, A) =>  (! [C] :  (l3_msualg_1(C, A) =>  (g3_msualg_1(A, u3_msualg_1(A, B), u4_msualg_1(A, B))=g3_msualg_1(A, u3_msualg_1(A, C), u4_msualg_1(A, C)) => m1_msualg_2(B, 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_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v11_struct_0(A))  & l1_msualg_1(A)) )  =>  (! [B] :  (l3_msualg_1(B, A) =>  (! [C] :  (l3_msualg_1(C, A) =>  (! [D] :  (l3_msualg_1(D, A) =>  ( (m1_msualg_2(B, A, C) & m1_msualg_2(C, A, D))  => m1_msualg_2(B, A, D)) ) ) ) ) ) ) ) ) ).
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(t7_funcop_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (r2_hidden(B, A) => k1_funct_1(k2_funcop_1(A, C), B)=C) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t92_funct_2, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  =>  (r2_tarski(C, k1_funct_2(A, B)) =>  (k9_xtuple_0(C)=A & r1_tarski(k10_xtuple_0(C), B)) ) ) ) ) ) ).
fof(t9_card_3, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (r2_tarski(B, k4_card_3(A)) <=>  (k9_xtuple_0(B)=k9_xtuple_0(A) &  (! [C] :  (r2_hidden(C, k9_xtuple_0(A)) => r2_tarski(k1_funct_1(B, C), k1_funct_1(A, C))) ) ) ) ) ) ) ) ).
fof(t9_pralg_3, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  ( ~ (v11_struct_0(B))  & l1_msualg_1(B)) )  =>  (! [C] :  (m1_subset_1(C, A) =>  (! [D] :  (m1_pralg_2(D, A, B) =>  (! [E] :  (m1_subset_1(E, u4_struct_0(B)) =>  (k1_msualg_1(B, E)=k1_xboole_0 => k1_funct_1(k1_pralg_3(B, k14_pralg_2(A, B, D), E), C)=k1_pralg_3(B, k5_pralg_2(A, B, D, C), E)) ) ) ) ) ) ) ) ) ) ) ).
