% Mizar problem: t32_ltlaxio4,ltlaxio4,2349,7 
fof(t32_ltlaxio4, conjecture,  (! [A] :  (m1_subset_1(A, k1_hilbert1) =>  (! [B] :  (m1_subset_1(B, k1_hilbert1) =>  (! [C] :  ( ( ~ (v2_ltlaxio3(C))  &  (v3_ltlaxio3(C) & m1_subset_1(C, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)))) )  =>  (! [D] :  (m3_ltlaxio4(D, C) =>  ~ ( (r2_tarski(k4_hilbert1(A, B), k2_relset_1(k1_hilbert1, k8_ltlaxio3(C))) &  (! [E] :  (m2_subset_1(E, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)), k11_ltlaxio4(C, D)) =>  ~ (r2_tarski(B, k2_relset_1(k1_hilbert1, k8_ltlaxio3(E)))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(cc10_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A))  => v3_card_1(A, 1)) ) ).
fof(cc10_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v6_membered(A)) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
fof(cc11_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_card_1(A))  =>  (! [B] :  (v3_card_1(B, A) =>  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(cc11_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_finseq_1(A)) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(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(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(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(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(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(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(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_card_1, axiom,  (! [A] :  (v1_card_1(A) => v3_ordinal1(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_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_hilbert1, axiom,  (! [A] :  (v5_hilbert1(A) =>  ( ~ (v1_xboole_0(A))  &  (v1_hilbert1(A) &  (v2_hilbert1(A) &  (v3_hilbert1(A) & v4_hilbert1(A)) ) ) ) ) ) ).
fof(cc1_jordan23, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_funct_1(A) & v1_finseq_1(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finseq_1(A) & v1_jordan23(A)) ) ) ) ) ).
fof(cc1_margrel1, axiom,  (! [A] :  (v1_xboole_0(A) => v2_card_3(A)) ) ).
fof(cc1_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v3_ordinal1(A) & v7_ordinal1(A)) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc1_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc1_trees_9, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) & v1_trees_1(A)) )  =>  ( ~ (v1_xboole_0(A))  &  (v1_trees_1(A) & v1_trees_2(A)) ) ) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_card_1(A)) ) ).
fof(cc2_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(cc2_finset_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_finset_1(B)) ) ) ) ).
fof(cc2_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_jordan23, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finseq_1(A) & v1_jordan23(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finseq_1(A) & v3_jordan23(A)) ) ) ) ) ).
fof(cc2_ltlaxio4, axiom,  (! [A] :  ( ( ~ (v2_ltlaxio3(A))  & m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))))  =>  (! [B] :  (m1_subset_1(B, k5_ltlaxio4(A)) =>  ~ (v2_ltlaxio3(B)) ) ) ) ) ).
fof(cc2_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc2_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_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc2_trees_9, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  (v1_trees_1(A) & v1_trees_2(A)) )  =>  ( ~ (v1_xboole_0(A))  &  (v1_trees_1(A) & v1_trees_9(A)) ) ) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc2_xxreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xxreal_0(A)) ) ).
fof(cc3_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_card_1(A)) ) ).
fof(cc3_finseq_1, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, A) => v5_relat_1(B, 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_hilbert1, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) => v1_finseq_1(A)) ) ).
fof(cc3_jordan23, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_xboole_0(A) &  (v1_funct_1(A) & v1_finseq_1(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finseq_1(A) & v2_jordan23(A)) ) ) ) ) ).
fof(cc3_ltlaxio4, axiom,  (! [A] :  ( ( ~ (v2_ltlaxio3(A))  & m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))))  =>  (! [B] :  (m1_subset_1(B, k8_ltlaxio4(A)) =>  ~ (v2_ltlaxio3(B)) ) ) ) ) ).
fof(cc3_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc3_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_xboole_0(C)) ) ) ) ).
fof(cc3_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc3_trees_9, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finset_1(A) & v3_trees_2(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_trees_2(A) & v2_trees_9(A)) ) ) ) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc3_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v2_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc4_card_1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v1_finset_1(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_jordan23, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_funct_1(A) & v1_finseq_1(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finseq_1(A) & v2_jordan23(A)) ) ) ) ) ).
fof(cc4_ltlaxio4, axiom,  (! [A] :  ( ( ~ (v2_ltlaxio3(A))  & m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))))  =>  (! [B] :  (m1_subset_1(B, k9_ltlaxio4(A)) =>  ~ (v2_ltlaxio3(B)) ) ) ) ) ).
fof(cc4_nat_1, axiom,  (! [A] :  ( (v7_ordinal1(A) & v8_ordinal1(A))  =>  (v7_ordinal1(A) &  ~ (v2_xxreal_0(A)) ) ) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(A)) ) ).
fof(cc4_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_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_trees_9, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_trees_2(A) & v2_trees_9(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_trees_2(A) & v3_trees_9(A)) ) ) ) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc4_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ) ).
fof(cc5_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_finset_1(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_ltlaxio4, axiom,  (! [A] :  ( ( ~ (v2_ltlaxio3(A))  & m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))))  =>  (! [B] :  (m1_subset_1(B, k9_ltlaxio4(A)) => v3_ltlaxio3(B)) ) ) ) ).
fof(cc5_nat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v8_ordinal1(A)) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc5_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc5_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v3_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) ) ) ) ).
fof(cc6_card_1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v1_finset_1(A))  => v7_ordinal1(A)) ) ).
fof(cc6_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ).
fof(cc6_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_finset_1(A)) ) ).
fof(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc6_ltlaxio4, axiom,  (! [A, B] :  ( ( ( ~ (v2_ltlaxio3(A))  & m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))))  & m3_ltlaxio4(B, A))  =>  (! [C] :  (m1_subset_1(C, k2_relset_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)), B)) =>  ~ (v2_ltlaxio3(C)) ) ) ) ) ).
fof(cc6_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc6_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ) ).
fof(cc7_card_1, axiom,  (! [A] :  (v3_card_1(A, k5_ordinal1) => v1_xboole_0(A)) ) ).
fof(cc7_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ) ).
fof(cc7_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finset_1(B)) ) ) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_ltlaxio4, axiom,  (! [A, B] :  ( ( ( ~ (v2_ltlaxio3(A))  &  (v3_ltlaxio3(A) & m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)))) )  & m3_ltlaxio4(B, A))  =>  (! [C] :  (m1_subset_1(C, k2_relset_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)), B)) => v3_ltlaxio3(C)) ) ) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_xxreal_0, axiom,  (! [A] :  ( (v8_ordinal1(A) & v1_xxreal_0(A))  =>  (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc8_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_card_1(A, k5_ordinal1)) ) ).
fof(cc8_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_finseq_1(A)) ) ).
fof(cc8_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_finset_1(B)) ) ) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc8_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) )  =>  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ) ).
fof(cc9_card_1, axiom,  (! [A] :  (v3_card_1(A, 1) =>  ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A)) ) ) ).
fof(cc9_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v1_finset_1(A)) ) ).
fof(cc9_finset_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_finset_1(A)) ) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(commutativity_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => k4_subset_1(A, B, C)=k4_subset_1(A, C, B)) ) ).
fof(connectedness_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  =>  (r1_xxreal_0(A, B) | r1_xxreal_0(B, A)) ) ) ).
fof(d10_ltlaxio3, axiom,  (! [A] :  (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) =>  (v2_ltlaxio3(A) <=> r8_ltlaxio1(k1_subset_1(k1_hilbert1), k1_ltlaxio1(k12_ltlaxio3(A)))) ) ) ).
fof(d10_ltlaxio4, axiom,  (! [A] :  (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) => k9_ltlaxio4(A)=a_1_6_ltlaxio4(A)) ) ).
fof(d11_ltlaxio4, axiom,  (! [A] :  (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) =>  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) &  (v1_funct_1(B) &  (v3_trees_2(B) & v3_trees_9(B)) ) ) )  =>  (m3_ltlaxio4(B, A) <=>  (k1_funct_1(B, k1_xboole_0)=A &  (! [C] :  (m1_trees_1(C, k9_xtuple_0(B)) =>  (! [D] :  (m1_subset_1(D, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) =>  (D=k3_trees_2(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)), B, C) => k2_trees_9(B, C)=o_1_7_ltlaxio4(D)) ) ) ) ) ) ) ) ) ) ) ).
fof(d12_ltlaxio4, axiom,  (! [A] :  (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) =>  (! [B] :  (m3_ltlaxio4(B, A) => k11_ltlaxio4(A, B)=a_2_0_ltlaxio4(A, B)) ) ) ) ).
fof(d17_ltlaxio1, axiom,  (! [A] :  (v2_ltlaxio1(A) <=>  (! [B] :  (m1_subset_1(B, k1_hilbert1) =>  (! [C] :  (m1_subset_1(C, k1_hilbert1) =>  ( (v1_ltlaxio1(B) => r2_tarski(B, A))  &  (r2_tarski(k3_hilbert1(k1_ltlaxio1(k2_ltlaxio1(B)), k2_ltlaxio1(k1_ltlaxio1(B))), A) &  (r2_tarski(k3_hilbert1(k2_ltlaxio1(k1_ltlaxio1(B)), k1_ltlaxio1(k2_ltlaxio1(B))), A) &  (r2_tarski(k3_hilbert1(k2_ltlaxio1(k3_hilbert1(B, C)), k3_hilbert1(k2_ltlaxio1(B), k2_ltlaxio1(C))), A) &  (r2_tarski(k3_hilbert1(k6_ltlaxio1(B), k4_ltlaxio1(B, k2_ltlaxio1(k6_ltlaxio1(B)))), A) &  (r2_tarski(k3_hilbert1(k4_hilbert1(B, C), k5_ltlaxio1(k2_ltlaxio1(C), k2_ltlaxio1(k4_ltlaxio1(B, k4_hilbert1(B, C))))), A) &  (r2_tarski(k3_hilbert1(k5_ltlaxio1(k2_ltlaxio1(C), k2_ltlaxio1(k4_ltlaxio1(B, k4_hilbert1(B, C)))), k4_hilbert1(B, C)), A) & r2_tarski(k3_hilbert1(k4_hilbert1(B, C), k2_ltlaxio1(k7_ltlaxio1(C))), A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_ltlaxio1, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) => k1_ltlaxio1(A)=k3_hilbert1(A, k2_hilbert1)) ) ).
fof(d1_ltlaxio2, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) =>  (! [B] :  (m1_subset_1(B, k1_hilbert1) => k1_ltlaxio2(A, B)=k5_ltlaxio1(B, k4_ltlaxio1(A, k4_hilbert1(A, B)))) ) ) ) ).
fof(d1_rlaffin3, axiom,  (! [A] :  (v1_finset_1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v1_funct_1(B) &  (v2_funct_1(B) & v1_finseq_1(B)) ) )  =>  (m1_rlaffin3(B, A) <=> k10_xtuple_0(B)=A) ) ) ) ) ).
fof(d1_xboole_0, axiom,  (! [A] :  (v1_xboole_0(A) <=>  (! [B] :  ~ (r2_hidden(B, A)) ) ) ) ).
fof(d2_ltlaxio1, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) => k2_ltlaxio1(A)=k4_hilbert1(k2_hilbert1, A)) ) ).
fof(d30_ltlaxio1, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(k1_hilbert1)) =>  (! [B] :  (m1_subset_1(B, k1_hilbert1) =>  (r8_ltlaxio1(A, B) <=>  (? [C] :  (m2_finseq_1(C, k1_hilbert1) &  (k1_funct_1(C, k3_finseq_1(C))=B &  (r1_xxreal_0(1, k3_finseq_1(C)) &  (! [D] :  (v7_ordinal1(D) =>  ( (r1_xxreal_0(1, D) & r1_xxreal_0(D, k3_finseq_1(C)))  => r7_ltlaxio1(D, C, A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_ltlaxio1, axiom, k3_ltlaxio1=k1_ltlaxio1(k2_hilbert1)).
fof(d3_ltlaxio4, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)))) => k3_ltlaxio4(A)=a_1_0_ltlaxio4(A)) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d4_ltlaxio1, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) =>  (! [B] :  (m1_subset_1(B, k1_hilbert1) => k4_ltlaxio1(A, B)=k1_ltlaxio1(k3_hilbert1(A, k1_ltlaxio1(B)))) ) ) ) ).
fof(d5_ltlaxio1, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) =>  (! [B] :  (m1_subset_1(B, k1_hilbert1) => k5_ltlaxio1(A, B)=k1_ltlaxio1(k4_ltlaxio1(k1_ltlaxio1(A), k1_ltlaxio1(B)))) ) ) ) ).
fof(d6_finseq_1, axiom,  (! [A] : k6_finseq_1(A)=k1_xboole_0) ).
fof(d6_ltlaxio1, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) => k6_ltlaxio1(A)=k1_ltlaxio1(k5_ltlaxio1(k1_ltlaxio1(A), k4_hilbert1(k3_ltlaxio1, k1_ltlaxio1(A))))) ) ).
fof(d6_ltlaxio4, axiom,  (! [A] :  (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) => k5_ltlaxio4(A)=a_1_2_ltlaxio4(A)) ) ).
fof(d7_ltlaxio1, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) => k7_ltlaxio1(A)=k1_ltlaxio1(k6_ltlaxio1(k1_ltlaxio1(A)))) ) ).
fof(d7_ltlaxio4, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)))) => k6_ltlaxio4(A)=k3_tarski(a_1_3_ltlaxio4(A))) ) ).
fof(d8_ltlaxio4, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(k1_hilbert1)) => k7_ltlaxio4(A)=a_1_4_ltlaxio4(A)) ) ).
fof(d9_ltlaxio3, axiom,  (! [A] :  (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) => k12_ltlaxio3(A)=k4_ltlaxio1(k7_partfun1(k1_hilbert1, k2_ltlaxio2(k8_ltlaxio3(A)), k3_finseq_1(k2_ltlaxio2(k8_ltlaxio3(A)))), k7_partfun1(k1_hilbert1, k2_ltlaxio2(k4_ltlaxio2(k9_ltlaxio3(A))), k3_finseq_1(k2_ltlaxio2(k4_ltlaxio2(k9_ltlaxio3(A))))))) ) ).
fof(d9_ltlaxio4, axiom,  (! [A] :  (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) => k8_ltlaxio4(A)=a_1_5_ltlaxio4(A)) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k11_ltlaxio4, axiom,  (! [A, B] :  ( (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) & m3_ltlaxio4(B, A))  =>  (v1_finset_1(k11_ltlaxio4(A, B)) & m1_subset_1(k11_ltlaxio4(A, B), k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))))) ) ) ).
fof(dt_k12_ltlaxio3, axiom,  (! [A] :  (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) => m1_subset_1(k12_ltlaxio3(A), k1_hilbert1)) ) ).
fof(dt_k13_ltlaxio1, axiom, m1_subset_1(k13_ltlaxio1, k1_zfmisc_1(k1_hilbert1))).
fof(dt_k1_card_1, axiom,  (! [A] : v1_card_1(k1_card_1(A))) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_hilbert1, axiom, $true).
fof(dt_k1_ltlaxio1, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) => m1_subset_1(k1_ltlaxio1(A), k1_hilbert1)) ) ).
fof(dt_k1_ltlaxio2, axiom,  (! [A, B] :  ( (m1_subset_1(A, k1_hilbert1) & m1_subset_1(B, k1_hilbert1))  => m1_subset_1(k1_ltlaxio2(A, B), k1_hilbert1)) ) ).
fof(dt_k1_ltlaxio3, 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_subset_1, axiom,  (! [A] : m1_subset_1(k1_subset_1(A), k1_zfmisc_1(A))) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_xtuple_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_hilbert1, axiom, m1_subset_1(k2_hilbert1, k1_hilbert1)).
fof(dt_k2_ltlaxio1, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) => m1_subset_1(k2_ltlaxio1(A), k1_hilbert1)) ) ).
fof(dt_k2_ltlaxio2, axiom,  (! [A] :  (m1_finseq_1(A, k1_hilbert1) => m2_finseq_1(k2_ltlaxio2(A), k1_hilbert1)) ) ).
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_trees_9, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_trees_2(A) & v3_trees_9(A)) ) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) )  =>  (v1_relat_1(k2_trees_9(A, B)) &  (v1_funct_1(k2_trees_9(A, B)) & v1_finseq_1(k2_trees_9(A, B))) ) ) ) ).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_xtuple_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_hilbert1, axiom,  (! [A, B] :  ( (m1_subset_1(A, k1_hilbert1) & m1_subset_1(B, k1_hilbert1))  => m1_subset_1(k3_hilbert1(A, B), k1_hilbert1)) ) ).
fof(dt_k3_ltlaxio1, axiom, m1_subset_1(k3_ltlaxio1, k1_hilbert1)).
fof(dt_k3_ltlaxio4, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)))) => m1_subset_1(k3_ltlaxio4(A), k1_zfmisc_1(k1_hilbert1))) ) ).
fof(dt_k3_tarski, axiom, $true).
fof(dt_k3_trees_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v3_trees_2(B)) ) )  & m1_subset_1(C, k9_xtuple_0(B))) )  => m1_subset_1(k3_trees_2(A, B, C), A)) ) ).
fof(dt_k4_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => m1_subset_1(k4_finseq_1(A), k1_zfmisc_1(k4_ordinal1))) ) ).
fof(dt_k4_hilbert1, axiom,  (! [A, B] :  ( (m1_subset_1(A, k1_hilbert1) & m1_subset_1(B, k1_hilbert1))  => m1_subset_1(k4_hilbert1(A, B), k1_hilbert1)) ) ).
fof(dt_k4_ltlaxio1, axiom,  (! [A, B] :  ( (m1_subset_1(A, k1_hilbert1) & m1_subset_1(B, k1_hilbert1))  => m1_subset_1(k4_ltlaxio1(A, B), k1_hilbert1)) ) ).
fof(dt_k4_ltlaxio2, axiom,  (! [A] :  (m1_finseq_1(A, k1_hilbert1) => m2_finseq_1(k4_ltlaxio2(A), k1_hilbert1)) ) ).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k5_ltlaxio1, axiom,  (! [A, B] :  ( (m1_subset_1(A, k1_hilbert1) & m1_subset_1(B, k1_hilbert1))  => m1_subset_1(k5_ltlaxio1(A, B), k1_hilbert1)) ) ).
fof(dt_k5_ltlaxio4, axiom,  (! [A] :  (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) =>  (v1_finset_1(k5_ltlaxio4(A)) & m1_subset_1(k5_ltlaxio4(A), k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))))) ) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k6_finseq_1, axiom,  (! [A] : m2_finseq_1(k6_finseq_1(A), A)) ).
fof(dt_k6_ltlaxio1, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) => m1_subset_1(k6_ltlaxio1(A), k1_hilbert1)) ) ).
fof(dt_k6_ltlaxio4, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)))) => m1_subset_1(k6_ltlaxio4(A), k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))))) ) ).
fof(dt_k7_ltlaxio1, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) => m1_subset_1(k7_ltlaxio1(A), k1_hilbert1)) ) ).
fof(dt_k7_ltlaxio4, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(k1_hilbert1)) => m1_subset_1(k7_ltlaxio4(A), k1_zfmisc_1(k1_hilbert1))) ) ).
fof(dt_k7_partfun1, axiom,  (! [A, B, C] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  => m1_subset_1(k7_partfun1(A, B, C), A)) ) ).
fof(dt_k8_ltlaxio3, axiom,  (! [A] :  (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) =>  (v2_funct_1(k8_ltlaxio3(A)) & m2_finseq_1(k8_ltlaxio3(A), k1_hilbert1)) ) ) ).
fof(dt_k8_ltlaxio4, axiom,  (! [A] :  (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) =>  ( ~ (v1_xboole_0(k8_ltlaxio4(A)))  &  (v1_finset_1(k8_ltlaxio4(A)) & m1_subset_1(k8_ltlaxio4(A), k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))))) ) ) ) ).
fof(dt_k9_ltlaxio3, axiom,  (! [A] :  (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) =>  (v2_funct_1(k9_ltlaxio3(A)) & m2_finseq_1(k9_ltlaxio3(A), k1_hilbert1)) ) ) ).
fof(dt_k9_ltlaxio4, axiom,  (! [A] :  (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) =>  (v1_finset_1(k9_ltlaxio4(A)) & m1_subset_1(k9_ltlaxio4(A), k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))))) ) ) ).
fof(dt_k9_xtuple_0, axiom, $true).
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_rlaffin3, axiom,  (! [A] :  (v1_finset_1(A) =>  (! [B] :  (m1_rlaffin3(B, A) =>  (v1_relat_1(B) &  (v1_funct_1(B) &  (v2_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m1_trees_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_trees_1(A))  =>  (! [B] :  (m1_trees_1(B, A) => m2_finseq_1(B, k4_ordinal1)) ) ) ) ).
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_ltlaxio4, axiom,  (! [A, B] :  ( (v1_finset_1(B) & m1_subset_1(B, k1_zfmisc_1(A)))  =>  (! [C] :  (m2_ltlaxio4(C, A, B) =>  (v2_funct_1(C) & m2_finseq_1(C, A)) ) ) ) ) ).
fof(dt_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) => m1_subset_1(C, A)) ) ) ) ).
fof(dt_m3_ltlaxio4, axiom,  (! [A] :  (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) =>  (! [B] :  (m3_ltlaxio4(B, A) =>  (v1_relat_1(B) &  (v5_relat_1(B, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) &  (v1_funct_1(B) &  (v3_trees_2(B) & v3_trees_9(B)) ) ) ) ) ) ) ) ).
fof(dt_o_1_7_ltlaxio4, axiom,  (! [A] :  (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) => m2_ltlaxio4(o_1_7_ltlaxio4(A), k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)), k9_ltlaxio4(A))) ) ).
fof(dt_o_2_2_ltlaxio4, axiom,  (! [A, B] :  ( ( ( ~ (v2_ltlaxio3(A))  &  (v3_ltlaxio3(A) & m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)))) )  & m3_ltlaxio4(B, A))  => m2_ltlaxio4(o_2_2_ltlaxio4(A, B), k1_hilbert1, k3_ltlaxio4(k11_ltlaxio4(A, B)))) ) ).
fof(dt_o_2_3_ltlaxio4, axiom,  (! [A, B] :  ( ( ( ~ (v2_ltlaxio3(A))  &  (v3_ltlaxio3(A) & m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)))) )  & m2_subset_1(B, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)), k8_ltlaxio4(A)))  => m2_ltlaxio4(o_2_3_ltlaxio4(A, B), k1_hilbert1, k3_ltlaxio4(k5_ltlaxio4(B)))) ) ).
fof(existence_m1_finseq_1, axiom,  (! [A] :  (? [B] : m1_finseq_1(B, A)) ) ).
fof(existence_m1_rlaffin3, axiom,  (! [A] :  (v1_finset_1(A) =>  (? [B] : m1_rlaffin3(B, A)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m1_trees_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_trees_1(A))  =>  (? [B] : m1_trees_1(B, A)) ) ) ).
fof(existence_m2_finseq_1, axiom,  (! [A] :  (? [B] : m2_finseq_1(B, A)) ) ).
fof(existence_m2_ltlaxio4, axiom,  (! [A, B] :  ( (v1_finset_1(B) & m1_subset_1(B, k1_zfmisc_1(A)))  =>  (? [C] : m2_ltlaxio4(C, A, B)) ) ) ).
fof(existence_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (? [C] : m2_subset_1(C, A, B)) ) ) ).
fof(existence_m3_ltlaxio4, axiom,  (! [A] :  (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) =>  (? [B] : m3_ltlaxio4(B, A)) ) ) ).
fof(fc10_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ( ~ (v1_finset_1(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc10_ltlaxio4, axiom,  (! [A, B] :  ( ( ( ~ (v2_ltlaxio3(A))  & m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))))  & m3_ltlaxio4(B, A))  =>  ( ~ (v1_xboole_0(k11_ltlaxio4(A, B)))  & v1_finset_1(k11_ltlaxio4(A, B))) ) ) ).
fof(fc10_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_ordinal1(A))  =>  ~ (v10_ordinal1(k10_xtuple_0(A))) ) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc11_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  ~ (v9_ordinal1(A)) )  => v10_ordinal1(k10_xtuple_0(A))) ) ).
fof(fc12_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k1_zfmisc_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(fc13_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_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_subset_1, axiom,  (! [A] : v1_xboole_0(k1_subset_1(A))) ).
fof(fc14_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(B, A))) ) ) ).
fof(fc14_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v1_finset_1(k2_zfmisc_1(A, B))) ) ).
fof(fc17_card_1, axiom,  (! [A, B] :  ( (v1_card_1(A) &  (v1_relat_1(B) &  (v1_funct_1(B) & v3_card_1(B, A)) ) )  => v3_card_1(k9_xtuple_0(B), A)) ) ).
fof(fc17_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  => v3_finseq_1(k9_xtuple_0(A))) ) ).
fof(fc17_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v1_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc17_funct_1, axiom,  (! [A, B, C] :  ( (v4_funct_1(A) &  (v1_relat_1(C) &  (v5_relat_1(C, A) & v1_funct_1(C)) ) )  =>  (v1_relat_1(k1_funct_1(C, B)) & v1_funct_1(k1_funct_1(C, B))) ) ) ).
fof(fc18_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  => v3_finseq_1(k9_xtuple_0(A))) ) ).
fof(fc18_funct_1, axiom,  (! [A] :  ( ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  ~ (v1_zfmisc_1(k9_xtuple_0(A))) ) ) ).
fof(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(fc1_card_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v1_xboole_0(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc1_hilbert1, axiom, v5_hilbert1(k1_hilbert1)).
fof(fc1_ltlaxio1, axiom, v2_ltlaxio1(k13_ltlaxio1)).
fof(fc1_ltlaxio3, axiom,  (! [A] :  ~ (v1_xboole_0(k1_ltlaxio3(A))) ) ).
fof(fc1_ltlaxio4, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)))))  =>  ~ (v1_xboole_0(k3_ltlaxio4(A))) ) ) ).
fof(fc1_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  &  (v1_relat_1(C) & v4_relat_1(C, A)) )  => v4_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc22_finset_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_finset_1(A))  => v1_finset_1(k10_xtuple_0(A))) ) ).
fof(fc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v8_ordinal1(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc2_hilbert1, axiom, v4_funct_1(k1_hilbert1)).
fof(fc2_ltlaxio1, axiom,  ~ (v1_xboole_0(k13_ltlaxio1)) ).
fof(fc2_ltlaxio3, axiom,  (! [A] :  (v1_finset_1(A) => v1_finset_1(k1_ltlaxio3(A))) ) ).
fof(fc2_ltlaxio4, axiom,  (! [A] :  ( (v1_finset_1(A) & m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)))))  => v1_finset_1(k3_ltlaxio4(A))) ) ).
fof(fc2_trees_2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_trees_2(A)) )  =>  ( ~ (v1_xboole_0(k9_xtuple_0(A)))  & v1_trees_1(k9_xtuple_0(A))) ) ) ).
fof(fc2_trees_9, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_trees_2(A) & v2_trees_9(A)) ) )  => v1_trees_2(k9_xtuple_0(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(fc34_finset_1, axiom,  (! [A] :  ( (v1_finset_1(A) & v5_finset_1(A))  => v1_finset_1(k3_tarski(A))) ) ).
fof(fc35_finset_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) )  => v1_finset_1(k1_funct_1(A, B))) ) ).
fof(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(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_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v1_xboole_0(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc3_ltlaxio4, axiom,  (! [A] :  ( ( ~ (v2_ltlaxio3(A))  & m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))))  =>  ( ~ (v1_xboole_0(k5_ltlaxio4(A)))  & v1_finset_1(k5_ltlaxio4(A))) ) ) ).
fof(fc3_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) => v3_ordinal1(k3_tarski(A))) ) ).
fof(fc3_trees_9, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_trees_2(A) & v3_trees_9(A)) ) )  => v1_trees_9(k9_xtuple_0(A))) ) ).
fof(fc4_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v8_ordinal1(k1_card_1(A)))  & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc4_ltlaxio4, axiom,  (! [A] :  ( (v1_finset_1(A) & m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)))))  => v1_finset_1(k6_ltlaxio4(A))) ) ).
fof(fc4_ordinal1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v5_ordinal1(A)) )  => v3_ordinal1(k9_xtuple_0(A))) ) ).
fof(fc4_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  &  (v1_relat_1(C) & v5_relat_1(C, A)) )  => v5_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc4_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A))) ) ).
fof(fc5_finseq_1, axiom,  (! [A] : v1_xboole_0(k6_finseq_1(A))) ).
fof(fc5_ltlaxio4, axiom,  (! [A] :  ( (v1_finset_1(A) & m1_subset_1(A, k1_zfmisc_1(k1_hilbert1)))  => v1_finset_1(k7_ltlaxio4(A))) ) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc5_xtuple_0, axiom,  (! [A] :  (v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A))) ) ).
fof(fc6_card_1, axiom, v1_card_1(k4_ordinal1)).
fof(fc6_ltlaxio4, axiom,  (! [A] :  ( ( ~ (v2_ltlaxio3(A))  & m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))))  =>  ( ~ (v1_xboole_0(k9_ltlaxio4(A)))  & v1_finset_1(k9_ltlaxio4(A))) ) ) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc7_card_1, axiom, v2_card_1(k4_ordinal1)).
fof(fc7_ltlaxio4, axiom,  (! [A, B] :  ( (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) & m3_ltlaxio4(B, A))  =>  ( ~ (v1_xboole_0(k10_xtuple_0(B)))  & v1_finset_1(k10_xtuple_0(B))) ) ) ).
fof(fc8_card_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A))) ) ) ).
fof(fc8_ltlaxio4, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_ltlaxio3(A))  &  (v3_ltlaxio3(A) & m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)))) )  &  (m3_ltlaxio4(B, A) & m1_subset_1(C, k9_xtuple_0(B))) )  =>  ( ~ (v2_ltlaxio3(k1_funct_1(B, C)))  & v3_ltlaxio3(k1_funct_1(B, C))) ) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C))) => v1_relat_1(k9_xtuple_0(D))) ) ).
fof(fc9_card_1, axiom,  ~ (v1_finset_1(k4_ordinal1)) ).
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_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k2_zfmisc_1(B, C)))) => v1_relat_1(k10_xtuple_0(D))) ) ).
fof(fraenkel_a_1_0_ltlaxio4, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)))) =>  (r2_hidden(A, a_1_0_ltlaxio4(B)) <=>  (? [C] :  (m1_subset_1(C, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) &  (A=k12_ltlaxio3(C) & r2_tarski(C, B)) ) ) ) ) ) ).
fof(fraenkel_a_1_2_ltlaxio4, axiom,  (! [A, B] :  (m1_subset_1(B, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) =>  (r2_hidden(A, a_1_2_ltlaxio4(B)) <=>  (? [C] :  ( ( ~ (v2_ltlaxio3(C))  & m1_subset_1(C, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))))  &  (A=C & r1_ltlaxio4(B, C)) ) ) ) ) ) ).
fof(fraenkel_a_1_3_ltlaxio4, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)))) =>  (r2_hidden(A, a_1_3_ltlaxio4(B)) <=>  (? [C] :  (m1_subset_1(C, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) &  (A=k5_ltlaxio4(C) & r2_tarski(C, B)) ) ) ) ) ) ).
fof(fraenkel_a_1_4_ltlaxio4, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_hilbert1)) =>  (r2_hidden(A, a_1_4_ltlaxio4(B)) <=>  (? [C, D] :  ( (m1_subset_1(C, k1_hilbert1) & m1_subset_1(D, k1_hilbert1))  &  (A=k1_ltlaxio2(C, D) & r2_tarski(k4_hilbert1(C, D), B)) ) ) ) ) ) ).
fof(fraenkel_a_1_5_ltlaxio4, axiom,  (! [A, B] :  (m1_subset_1(B, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) =>  (r2_hidden(A, a_1_5_ltlaxio4(B)) <=>  (? [C] :  (m1_subset_1(C, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) &  (A=C &  (k2_relset_1(k1_hilbert1, k8_ltlaxio3(C))=k7_ltlaxio4(k2_relset_1(k1_hilbert1, k8_ltlaxio3(B))) & k2_relset_1(k1_hilbert1, k9_ltlaxio3(C))=k7_ltlaxio4(k2_relset_1(k1_hilbert1, k9_ltlaxio3(B)))) ) ) ) ) ) ) ).
fof(fraenkel_a_1_6_ltlaxio4, axiom,  (! [A, B] :  (m1_subset_1(B, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) =>  (r2_hidden(A, a_1_6_ltlaxio4(B)) <=>  (? [C] :  (m1_subset_1(C, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) &  (A=C & r2_tarski(C, k6_ltlaxio4(k8_ltlaxio4(B)))) ) ) ) ) ) ).
fof(fraenkel_a_2_0_ltlaxio4, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) & m3_ltlaxio4(C, B))  =>  (r2_hidden(A, a_2_0_ltlaxio4(B, C)) <=>  (? [D] :  (m1_trees_1(D, k9_xtuple_0(C)) &  (A=k3_trees_2(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)), C, D) &  ~ (D=k1_xboole_0) ) ) ) ) ) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(idempotence_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => k4_subset_1(A, B, B)=B) ) ).
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_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_card_1(B)) ) ) ) ).
fof(rc10_finseq_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v3_card_1(B, A) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ).
fof(rc10_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) ) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_finseq_1(A)) ) ).
fof(rc11_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_card_1, axiom,  (? [A] : v1_card_1(A)) ).
fof(rc1_finseq_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1, A))) &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ).
fof(rc1_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_finset_1(A)) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_hilbert1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v5_hilbert1(A)) ) ).
fof(rc1_jordan23, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  ( ~ (v1_xboole_0(A))  &  (v1_funct_1(A) &  (v1_finset_1(A) &  (v1_finseq_1(A) &  (v2_finseq_1(A) & v2_jordan23(A)) ) ) ) ) ) ) ) ).
fof(rc1_ltlaxio3, axiom,  (? [A] :  (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) &  ( ~ (v2_ltlaxio3(A))  & v3_ltlaxio3(A)) ) ) ).
fof(rc1_margrel1, axiom,  (? [A] :  (v4_finseq_1(A) & v2_card_3(A)) ) ).
fof(rc1_nat_1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_trees_2, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_trees_1(A) & v1_trees_2(A)) ) ) ).
fof(rc1_trees_9, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_zfmisc_1(A) &  (v1_funct_1(A) & v3_trees_2(A)) ) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc2_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v1_finset_1(A) & v1_card_1(A)) ) ) ) ) ).
fof(rc2_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_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) & v8_ordinal1(A)) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_trees_9, axiom,  (? [A] :  (v1_relat_1(A) &  ( ~ (v1_zfmisc_1(A))  &  (v1_funct_1(A) &  (v1_finset_1(A) & v3_trees_2(A)) ) ) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc3_card_1, axiom,  (? [A] :  ~ (v1_finset_1(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_jordan23, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  ( ~ (v1_xboole_0(A))  &  (v1_funct_1(A) &  (v2_funct_1(A) &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ) ).
fof(rc3_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc3_trees_9, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_trees_1(A))  =>  (? [B] :  (m1_subset_1(B, A) &  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, k4_ordinal1) &  (v1_xboole_0(B) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc3_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ).
fof(rc4_card_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(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_ordinal1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v5_ordinal1(B)) ) ) ) ) ).
fof(rc4_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
fof(rc4_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ).
fof(rc5_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  & v1_card_1(A)) ) ) ) ) ) ).
fof(rc5_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v3_finseq_1(A)) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc5_nat_1, axiom,  (? [A] :  (m1_subset_1(A, k4_ordinal1) &  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v1_xreal_0(A) &  (v1_finset_1(A) & v1_card_1(A)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc5_trees_2, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v3_trees_2(A)) ) ) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc5_xxreal_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ).
fof(rc6_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_finset_1(B)) ) ) ) ) ).
fof(rc6_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k4_ordinal1) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(rc6_finset_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ).
fof(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc6_trees_2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v3_trees_2(B)) ) ) ) ) ) ).
fof(rc7_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] : v3_card_1(B, 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_trees_2, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_finset_1(A) & v3_trees_2(A)) ) ) ) ).
fof(rc8_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (v1_relat_1(B) &  (v1_funct_1(B) & v3_card_1(B, A)) ) ) ) ) ).
fof(rc8_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(rc8_trees_2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) & v3_trees_2(B)) ) ) ) ) ) ) ).
fof(rc9_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v3_card_1(B, 1)) ) ) ) ).
fof(rc9_finseq_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k4_ordinal1) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ).
fof(rc9_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) & v5_finset_1(A)) ) ) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_trees_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  ~ (v1_xboole_0(C)) ) ) ) ) ) ).
fof(rd1_card_1, axiom,  (! [A] :  (v1_card_1(A) => k1_card_1(A)=A) ) ).
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_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_trees_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v3_trees_2(B)) ) )  & m1_subset_1(C, k9_xtuple_0(B))) )  => k3_trees_2(A, B, C)=k1_funct_1(B, C)) ) ).
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_k4_subset_1, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))  => k4_subset_1(A, B, C)=k2_xboole_0(B, C)) ) ).
fof(redefinition_k8_ltlaxio3, axiom,  (! [A] :  (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) => k8_ltlaxio3(A)=k1_xtuple_0(A)) ) ).
fof(redefinition_k9_ltlaxio3, axiom,  (! [A] :  (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) => k9_ltlaxio3(A)=k2_xtuple_0(A)) ) ).
fof(redefinition_m1_trees_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_trees_1(A))  =>  (! [B] :  (m1_trees_1(B, A) <=> m1_subset_1(B, A)) ) ) ) ).
fof(redefinition_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) <=> m1_finseq_1(B, A)) ) ) ).
fof(redefinition_m2_ltlaxio4, axiom,  (! [A, B] :  ( (v1_finset_1(B) & m1_subset_1(B, k1_zfmisc_1(A)))  =>  (! [C] :  (m2_ltlaxio4(C, A, B) <=> m1_rlaffin3(C, B)) ) ) ) ).
fof(redefinition_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) ) ) ) ).
fof(redefinition_r1_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (r1_relset_1(A, B, C, D) <=> r1_tarski(C, D)) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => r1_relset_1(A, B, C, C)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(reflexivity_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => r1_xxreal_0(A, A)) ) ).
fof(rqLessOrEqual__r1_xxreal_0__r0_r0, axiom, r1_xxreal_0(0, 0)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r1, axiom, r1_xxreal_0(0, 1)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r0, axiom,  ~ (r1_xxreal_0(1, 0)) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_r1, axiom, r1_xxreal_0(1, 1)).
fof(spc0_boole, axiom, v1_xboole_0(0)).
fof(spc0_numerals, axiom, m1_subset_1(0, k4_ordinal1)).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(t10_ltlaxio4, axiom,  (! [A] :  (m1_subset_1(A, k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)))) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)))) => k3_ltlaxio4(k4_subset_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)), A, B))=k4_subset_1(k1_hilbert1, k3_ltlaxio4(A), k3_ltlaxio4(B))) ) ) ) ).
fof(t12_xboole_1, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) => k2_xboole_0(A, B)=B) ) ) ).
fof(t17_ltlaxio4, axiom,  (! [A] :  ( ( ~ (v2_ltlaxio3(A))  & m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))))  =>  (! [B] :  (m2_finseq_1(B, k1_hilbert1) =>  (k2_relset_1(k1_hilbert1, B)=k3_ltlaxio4(k5_ltlaxio4(A)) => r8_ltlaxio1(k1_subset_1(k1_hilbert1), k3_hilbert1(k12_ltlaxio3(A), k1_ltlaxio1(k7_partfun1(k1_hilbert1, k2_ltlaxio2(k4_ltlaxio2(B)), k3_finseq_1(k2_ltlaxio2(k4_ltlaxio2(B)))))))) ) ) ) ) ).
fof(t18_ltlaxio4, axiom,  (! [A] :  (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) =>  (! [B] :  (m2_subset_1(B, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)), k8_ltlaxio4(A)) => r8_ltlaxio1(k1_subset_1(k1_hilbert1), k3_hilbert1(k12_ltlaxio3(A), k2_ltlaxio1(k12_ltlaxio3(B))))) ) ) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v2_xxreal_0(A))  => v2_xxreal_0(B)) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t22_trees_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_trees_1(A))  =>  (r2_tarski(k1_xboole_0, A) & r2_tarski(k6_finseq_1(k4_ordinal1), A)) ) ) ).
fof(t28_ltlaxio3, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) =>  (! [B] :  (m1_subset_1(B, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) =>  (r2_tarski(A, k2_relset_1(k1_hilbert1, k8_ltlaxio3(B))) => r8_ltlaxio1(k1_subset_1(k1_hilbert1), k3_hilbert1(k12_ltlaxio3(B), A))) ) ) ) ) ).
fof(t28_ltlaxio4, axiom,  (! [A] :  (m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) =>  (! [B] :  (m1_subset_1(B, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) =>  (! [C] :  (m1_subset_1(C, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) =>  (! [D] :  (m3_ltlaxio4(D, A) =>  ( (r2_tarski(C, k2_relset_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)), D)) & r2_tarski(B, k8_ltlaxio4(C)))  => r1_relset_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1), k5_ltlaxio4(B), k11_ltlaxio4(A, D))) ) ) ) ) ) ) ) ) ).
fof(t29_ltlaxio3, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) =>  (! [B] :  (m1_subset_1(B, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1))) =>  (r2_tarski(A, k2_relset_1(k1_hilbert1, k9_ltlaxio3(B))) => r8_ltlaxio1(k1_subset_1(k1_hilbert1), k3_hilbert1(k12_ltlaxio3(B), k1_ltlaxio1(A)))) ) ) ) ) ).
fof(t29_ltlaxio4, axiom,  (! [A] :  ( ( ~ (v2_ltlaxio3(A))  &  (v3_ltlaxio3(A) & m1_subset_1(A, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)))) )  =>  (! [B] :  (m3_ltlaxio4(B, A) =>  (! [C] :  (m2_finseq_1(C, k1_hilbert1) =>  (k2_relset_1(k1_hilbert1, C)=k3_ltlaxio4(k11_ltlaxio4(A, B)) => r8_ltlaxio1(k1_subset_1(k1_hilbert1), k3_hilbert1(k1_ltlaxio1(k7_partfun1(k1_hilbert1, k2_ltlaxio2(k4_ltlaxio2(C)), k3_finseq_1(k2_ltlaxio2(k4_ltlaxio2(C))))), k2_ltlaxio1(k1_ltlaxio1(k7_partfun1(k1_hilbert1, k2_ltlaxio2(k4_ltlaxio2(C)), k3_finseq_1(k2_ltlaxio2(k4_ltlaxio2(C))))))))) ) ) ) ) ) ) ).
fof(t2_partfun2, axiom,  (! [A] :  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  ( (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B, C))))  =>  (r2_tarski(A, k2_relset_1(C, D)) <=>  (? [E] :  (m1_subset_1(E, B) &  (r2_tarski(E, k1_relset_1(B, D)) & A=k7_partfun1(C, D, E)) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v3_xxreal_0(B))  => v3_xxreal_0(A)) ) ) ) ) ).
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(t30_ltlaxio2, axiom,  (! [A] :  (m2_finseq_1(A, k1_hilbert1) =>  (! [B] :  (m2_finseq_1(B, k1_hilbert1) =>  (r1_tarski(k2_relset_1(k1_hilbert1, A), k2_relset_1(k1_hilbert1, B)) => v1_ltlaxio1(k3_hilbert1(k1_ltlaxio1(k7_partfun1(k1_hilbert1, k2_ltlaxio2(k4_ltlaxio2(A)), k3_finseq_1(k2_ltlaxio2(k4_ltlaxio2(A))))), k1_ltlaxio1(k7_partfun1(k1_hilbert1, k2_ltlaxio2(k4_ltlaxio2(B)), k3_finseq_1(k2_ltlaxio2(k4_ltlaxio2(B)))))))) ) ) ) ) ).
fof(t31_ltlaxio4, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) =>  (! [B] :  (m1_subset_1(B, k1_hilbert1) =>  (! [C] :  ( ( ~ (v2_ltlaxio3(C))  &  (v3_ltlaxio3(C) & m1_subset_1(C, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)))) )  =>  (! [D] :  (m3_ltlaxio4(D, C) =>  ( (r2_tarski(k4_hilbert1(A, B), k2_relset_1(k1_hilbert1, k8_ltlaxio3(C))) &  (! [E] :  (m2_subset_1(E, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)), k11_ltlaxio4(C, D)) =>  ~ (r2_tarski(B, k2_relset_1(k1_hilbert1, k8_ltlaxio3(E)))) ) ) )  =>  (! [E] :  (m2_subset_1(E, k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1), k1_ltlaxio3(k1_hilbert1)), k11_ltlaxio4(C, D)) =>  (r2_tarski(B, k2_relset_1(k1_hilbert1, k9_ltlaxio3(E))) & r2_tarski(k4_hilbert1(A, B), k2_relset_1(k1_hilbert1, k8_ltlaxio3(E)))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_funct_1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  (r2_hidden(A, k9_xtuple_0(B)) => r2_tarski(k1_funct_1(B, A), k10_xtuple_0(B))) ) ) ) ).
fof(t3_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v3_xxreal_0(A))  & v3_xxreal_0(B)) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t42_ltlaxio1, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_hilbert1)) =>  ( (r2_tarski(A, k13_ltlaxio1) | r2_tarski(A, B))  => r8_ltlaxio1(B, A)) ) ) ) ) ).
fof(t43_ltlaxio1, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) =>  (! [B] :  (m1_subset_1(B, k1_hilbert1) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k1_hilbert1)) =>  ( (r8_ltlaxio1(C, A) & r8_ltlaxio1(C, k3_hilbert1(A, B)))  => r8_ltlaxio1(C, B)) ) ) ) ) ) ) ).
fof(t44_ltlaxio1, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_hilbert1)) =>  (r8_ltlaxio1(B, A) => r8_ltlaxio1(B, k2_ltlaxio1(A))) ) ) ) ) ).
fof(t45_ltlaxio1, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) =>  (! [B] :  (m1_subset_1(B, k1_hilbert1) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k1_hilbert1)) =>  ( (r8_ltlaxio1(C, k3_hilbert1(A, B)) & r8_ltlaxio1(C, k3_hilbert1(A, k2_ltlaxio1(A))))  => r8_ltlaxio1(C, k3_hilbert1(A, k6_ltlaxio1(B)))) ) ) ) ) ) ) ).
fof(t47_ltlaxio1, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) =>  (! [B] :  (m1_subset_1(B, k1_hilbert1) =>  (! [C] :  (m1_subset_1(C, k1_hilbert1) =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(k1_hilbert1)) =>  ( (r8_ltlaxio1(D, k3_hilbert1(A, B)) & r8_ltlaxio1(D, k3_hilbert1(B, C)))  => r8_ltlaxio1(D, k3_hilbert1(A, C))) ) ) ) ) ) ) ) ) ).
fof(t4_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v2_xxreal_0(B))  & v2_xxreal_0(A)) ) ) ) ) ) ) ).
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(t52_ltlaxio2, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) =>  (! [B] :  (m1_subset_1(B, k1_hilbert1) =>  (! [C] :  (m1_subset_1(C, k1_hilbert1) =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(k1_hilbert1)) =>  ( (r8_ltlaxio1(D, k3_hilbert1(A, B)) & r8_ltlaxio1(D, k3_hilbert1(A, C)))  => r8_ltlaxio1(D, k3_hilbert1(A, k4_ltlaxio1(B, C)))) ) ) ) ) ) ) ) ) ).
fof(t55_ltlaxio2, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) =>  (! [B] :  (m1_subset_1(B, k1_hilbert1) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k1_hilbert1)) =>  (r8_ltlaxio1(C, k3_hilbert1(A, k4_ltlaxio1(B, k1_ltlaxio1(B)))) => r8_ltlaxio1(C, k1_ltlaxio1(A))) ) ) ) ) ) ) ).
fof(t57_ltlaxio2, axiom,  (! [A] :  (m1_subset_1(A, k1_hilbert1) =>  (! [B] :  (m2_finseq_1(B, k1_hilbert1) =>  ( (! [C] :  (v7_ordinal1(C) =>  (r2_tarski(C, k4_finseq_1(B)) => r8_ltlaxio1(k1_subset_1(k1_hilbert1), k3_hilbert1(k7_partfun1(k1_hilbert1, B, C), A))) ) )  => r8_ltlaxio1(k1_subset_1(k1_hilbert1), k3_hilbert1(k1_ltlaxio1(k7_partfun1(k1_hilbert1, k2_ltlaxio2(k4_ltlaxio2(B)), k3_finseq_1(k2_ltlaxio2(k4_ltlaxio2(B))))), A))) ) ) ) ) ).
fof(t5_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(B) |  (v3_xxreal_0(A) | v2_xxreal_0(B)) ) ) ) ) ) ) ).
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_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(A) |  (v2_xxreal_0(B) | v3_xxreal_0(A)) ) ) ) ) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(B)) ) ) ) ) ) ) ) ).
fof(t7_xboole_1, axiom,  (! [A] :  (! [B] : r1_tarski(A, k2_xboole_0(A, B))) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v3_xxreal_0(B))  &  ~ (v2_xxreal_0(A)) ) ) ) ) ) ) ) ).
