% Mizar problem: t53_mesfunc5,mesfunc5,3724,5 
include('Axioms/SET010^0.ax').
thf(n0_type, type, np__0: $i).
thf(n1_type, type, np__1: $i).
thf(k12_supinf_2_type, type, k12_supinf_2: $i > $i > $i).
thf(k1_card_1_type, type, k1_card_1: $i > $i).
thf(k1_finseq_1_type, type, k1_finseq_1: $i > $i).
thf(k1_funct_1_type, type, k1_funct_1: $i > $i > $i).
thf(k1_nat_1_type, type, k1_nat_1: $i > $i > $i).
thf(k1_relset_1_type, type, k1_relset_1: $i > $i > $i).
thf(k1_supinf_2_type, type, k1_supinf_2: $i).
thf(k1_xboole_0_type, type, k1_xboole_0: $i).
thf(k1_xxreal_3_type, type, k1_xxreal_3: $i > $i > $i).
thf(k1_zfmisc_1_type, type, k1_zfmisc_1: $i > $i).
thf(k2_finseq_1_type, type, k2_finseq_1: $i > $i).
thf(k2_xcmplx_0_type, type, k2_xcmplx_0: $i > $i > $i).
thf(k2_zfmisc_1_type, type, k2_zfmisc_1: $i > $i > $i).
thf(k3_finseq_1_type, type, k3_finseq_1: $i > $i).
thf(k3_numbers_type, type, k3_numbers: $i).
thf(k3_supinf_2_type, type, k3_supinf_2: $i > $i > $i).
thf(k4_extreal1_type, type, k4_extreal1: $i > $i).
thf(k4_numbers_type, type, k4_numbers: $i).
thf(k4_ordinal1_type, type, k4_ordinal1: $i).
thf(k5_numbers_type, type, k5_numbers: $i).
thf(k5_ordinal1_type, type, k5_ordinal1: $i).
thf(k6_numbers_type, type, k6_numbers: $i).
thf(k8_nat_1_type, type, k8_nat_1: $i > $i > $i > $i).
thf(k9_xtuple_0_type, type, k9_xtuple_0: $i > $i).
thf(m1_finseq_1_type, type, m1_finseq_1: $i > $i > $o).
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(m2_finseq_1_type, type, m2_finseq_1: $i > $i > $o).
thf(r1_tarski_type, type, r1_tarski: $i > $i > $o).
thf(r1_xxreal_0_type, type, r1_xxreal_0: $i > $i > $o).
thf(r2_tarski_type, type, r2_tarski: $i > $i > $o).
thf(v10_ordinal1_type, type, v10_ordinal1: $i > $o).
thf(v1_card_1_type, type, v1_card_1: $i > $o).
thf(v1_finseq_1_type, type, v1_finseq_1: $i > $o).
thf(v1_finset_1_type, type, v1_finset_1: $i > $o).
thf(v1_funct_1_type, type, v1_funct_1: $i > $o).
thf(v1_funct_2_type, type, v1_funct_2: $i > $i > $i > $o).
thf(v1_int_1_type, type, v1_int_1: $i > $o).
thf(v1_membered_type, type, v1_membered: $i > $o).
thf(v1_ordinal1_type, type, v1_ordinal1: $i > $o).
thf(v1_partfun1_type, type, v1_partfun1: $i > $i > $o).
thf(v1_rat_1_type, type, v1_rat_1: $i > $o).
thf(v1_relat_1_type, type, v1_relat_1: $i > $o).
thf(v1_setfam_1_type, type, v1_setfam_1: $i > $o).
thf(v1_subset_1_type, type, v1_subset_1: $i > $i > $o).
thf(v1_valued_0_type, type, v1_valued_0: $i > $o).
thf(v1_xboole_0_type, type, v1_xboole_0: $i > $o).
thf(v1_xcmplx_0_type, type, v1_xcmplx_0: $i > $o).
thf(v1_xreal_0_type, type, v1_xreal_0: $i > $o).
thf(v1_xxreal_0_type, type, v1_xxreal_0: $i > $o).
thf(v1_xxreal_2_type, type, v1_xxreal_2: $i > $o).
thf(v1_zfmisc_1_type, type, v1_zfmisc_1: $i > $o).
thf(v2_finseq_1_type, type, v2_finseq_1: $i > $o).
thf(v2_finset_1_type, type, v2_finset_1: $i > $o).
thf(v2_funct_1_type, type, v2_funct_1: $i > $o).
thf(v2_int_1_type, type, v2_int_1: $i > $o).
thf(v2_membered_type, type, v2_membered: $i > $o).
thf(v2_ordinal1_type, type, v2_ordinal1: $i > $o).
thf(v2_valued_0_type, type, v2_valued_0: $i > $o).
thf(v2_xxreal_0_type, type, v2_xxreal_0: $i > $o).
thf(v2_xxreal_2_type, type, v2_xxreal_2: $i > $o).
thf(v3_card_1_type, type, v3_card_1: $i > $i > $o).
thf(v3_finseq_1_type, type, v3_finseq_1: $i > $o).
thf(v3_membered_type, type, v3_membered: $i > $o).
thf(v3_ordinal1_type, type, v3_ordinal1: $i > $o).
thf(v3_valued_0_type, type, v3_valued_0: $i > $o).
thf(v3_xxreal_0_type, type, v3_xxreal_0: $i > $o).
thf(v3_xxreal_2_type, type, v3_xxreal_2: $i > $o).
thf(v4_funct_1_type, type, v4_funct_1: $i > $o).
thf(v4_membered_type, type, v4_membered: $i > $o).
thf(v4_relat_1_type, type, v4_relat_1: $i > $i > $o).
thf(v4_valued_0_type, type, v4_valued_0: $i > $o).
thf(v4_xxreal_2_type, type, v4_xxreal_2: $i > $o).
thf(v5_finset_1_type, type, v5_finset_1: $i > $o).
thf(v5_membered_type, type, v5_membered: $i > $o).
thf(v5_ordinal1_type, type, v5_ordinal1: $i > $o).
thf(v5_relat_1_type, type, v5_relat_1: $i > $i > $o).
thf(v5_valued_0_type, type, v5_valued_0: $i > $o).
thf(v5_xxreal_2_type, type, v5_xxreal_2: $i > $o).
thf(v6_membered_type, type, v6_membered: $i > $o).
thf(v6_ordinal1_type, type, v6_ordinal1: $i > $o).
thf(v6_valued_0_type, type, v6_valued_0: $i > $o).
thf(v6_xxreal_2_type, type, v6_xxreal_2: $i > $o).
thf(v7_membered_type, type, v7_membered: $i > $o).
thf(v7_ordinal1_type, type, v7_ordinal1: $i > $o).
thf(v7_valued_0_type, type, v7_valued_0: $i > $o).
thf(v8_ordinal1_type, type, v8_ordinal1: $i > $o).
thf(v8_valued_0_type, type, v8_valued_0: $i > $o).
thf(v9_ordinal1_type, type, v9_ordinal1: $i > $o).
thf(antisymmetry_r2_hidden, axiom,  (! [A: $i, B: $i] :  ( ( (r2_hidden @ A)  @ B)  =>  ~ ( ( (r2_hidden @ B)  @ A) ) ) ) , file(hidden, r2_hidden)).
thf(asymmetry_r2_tarski, axiom,  (! [A: $i, B: $i] :  ( ( (r2_tarski @ A)  @ B)  =>  ~ ( ( (r2_tarski @ B)  @ A) ) ) ) , file(tarski, r2_tarski)).
thf(cc10_finseq_1, axiom,  (! [A: $i] :  ( (v3_finseq_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_finseq_1 @ B) ) ) ) ) , file(finseq_1, cc10_finseq_1)).
thf(cc10_membered, axiom,  (! [A: $i] :  ( (v5_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_int_1 @ B) ) ) ) ) , file(membered, cc10_membered)).
thf(cc10_ordinal1, axiom,  (! [A: $i] :  ( (v6_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v6_ordinal1 @ B) ) ) ) ) , file(ordinal1, cc10_ordinal1)).
thf(cc10_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_valued_0 @ B) ) ) ) ) , file(valued_0, cc10_valued_0)).
thf(cc10_xxreal_2, axiom,  (! [A: $i] :  ( ( (v3_membered @ A)  &  (v1_xxreal_2 @ A) )  =>  ( (v3_membered @ A)  &  (v3_xxreal_2 @ A) ) ) ) , file(xxreal_2, cc10_xxreal_2)).
thf(cc11_finseq_1, axiom,  (! [A: $i] :  ( (v3_finseq_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v3_finseq_1 @ B) ) ) ) ) , file(finseq_1, cc11_finseq_1)).
thf(cc11_membered, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v7_ordinal1 @ B) ) ) ) ) , file(membered, cc11_membered)).
thf(cc11_ordinal1, axiom,  (! [A: $i] :  ( (v8_ordinal1 @ A)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc11_ordinal1)).
thf(cc11_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v2_valued_0 @ B) ) ) ) ) , file(valued_0, cc11_valued_0)).
thf(cc11_xxreal_2, axiom,  (! [A: $i] :  ( ( (v3_membered @ A)  &  (v2_xxreal_2 @ A) )  =>  ( (v3_membered @ A)  &  (v4_xxreal_2 @ A) ) ) ) , file(xxreal_2, cc11_xxreal_2)).
thf(cc12_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  ( (v5_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) ) ) ) ) , file(finseq_1, cc12_finseq_1)).
thf(cc12_membered, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v6_membered @ A) ) ) , file(membered, cc12_membered)).
thf(cc12_ordinal1, axiom,  (! [A: $i] :  ( (v8_ordinal1 @ A)  =>  (v1_zfmisc_1 @ A) ) ) , file(ordinal1, cc12_ordinal1)).
thf(cc12_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v3_valued_0 @ B) ) ) ) ) , file(valued_0, cc12_valued_0)).
thf(cc12_xxreal_2, axiom,  (! [A: $i] :  ( ( (v5_membered @ A)  &  (v5_xxreal_2 @ A) )  =>  ( (v5_membered @ A)  &  (v1_finset_1 @ A) ) ) ) , file(xxreal_2, cc12_xxreal_2)).
thf(cc13_finseq_1, axiom,  (! [A: $i] :  ( ( (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) ) ) ) ) ) , file(finseq_1, cc13_finseq_1)).
thf(cc13_membered, axiom,  (! [A: $i] :  ( (v1_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_membered @ B) ) ) ) ) , file(membered, cc13_membered)).
thf(cc13_ordinal1, axiom,  (! [A: $i] :  ( ~ ( (v1_zfmisc_1 @ A) )  =>  ~ ( (v8_ordinal1 @ A) ) ) ) , file(ordinal1, cc13_ordinal1)).
thf(cc13_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( (v5_relat_1 @ B)  @ k3_numbers) ) ) ) ) , file(valued_0, cc13_valued_0)).
thf(cc13_xxreal_2, axiom,  (! [A: $i] :  ( ( (v6_membered @ A)  &  (v4_xxreal_2 @ A) )  =>  ( (v6_membered @ A)  &  ( (v1_finset_1 @ A)  &  (v4_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, cc13_xxreal_2)).
thf(cc14_membered, axiom,  (! [A: $i] :  ( (v2_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v2_membered @ B) ) ) ) ) , file(membered, cc14_membered)).
thf(cc14_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  ~ ( (v10_ordinal1 @ A) ) ) ) , file(ordinal1, cc14_ordinal1)).
thf(cc14_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( (v5_relat_1 @ B)  @ k4_numbers) ) ) ) ) , file(valued_0, cc14_valued_0)).
thf(cc14_xxreal_2, axiom,  (! [A: $i] :  ( ( (v2_membered @ A)  &  (v5_xxreal_2 @ A) )  =>  ( (v2_membered @ A)  &  (v3_membered @ A) ) ) ) , file(xxreal_2, cc14_xxreal_2)).
thf(cc15_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v3_membered @ B) ) ) ) ) , file(membered, cc15_membered)).
thf(cc15_ordinal1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v9_ordinal1 @ A) ) ) ) , file(ordinal1, cc15_ordinal1)).
thf(cc15_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v4_valued_0 @ B) ) ) ) ) , file(valued_0, cc15_valued_0)).
thf(cc15_xxreal_2, axiom,  (! [A: $i] :  ( ( (v2_membered @ A)  &  (v1_xboole_0 @ A) )  =>  ( (v2_membered @ A)  &  (v6_xxreal_2 @ A) ) ) ) , file(xxreal_2, cc15_xxreal_2)).
thf(cc16_membered, axiom,  (! [A: $i] :  ( (v4_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v4_membered @ B) ) ) ) ) , file(membered, cc16_membered)).
thf(cc16_ordinal1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v10_ordinal1 @ A) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  ~ ( (v8_ordinal1 @ B) ) ) ) ) ) , file(ordinal1, cc16_ordinal1)).
thf(cc16_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v1_valued_0 @ C) ) ) ) ) , file(valued_0, cc16_valued_0)).
thf(cc16_xxreal_2, axiom,  (! [A: $i] :  ( ( (v2_membered @ A)  &  (v1_xxreal_2 @ A) )  =>  ( (v2_membered @ A)  &  ~ ( (v1_xboole_0 @ A) ) ) ) ) , file(xxreal_2, cc16_xxreal_2)).
thf(cc17_membered, axiom,  (! [A: $i] :  ( (v5_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v5_membered @ B) ) ) ) ) , file(membered, cc17_membered)).
thf(cc17_ordinal1, axiom,  (! [A: $i] :  ( ~ ( (v10_ordinal1 @ A) )  =>  (v1_setfam_1 @ A) ) ) , file(ordinal1, cc17_ordinal1)).
thf(cc17_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v2_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v2_valued_0 @ C) ) ) ) ) , file(valued_0, cc17_valued_0)).
thf(cc17_xxreal_2, axiom,  (! [A: $i] :  ( ( (v2_membered @ A)  &  (v2_xxreal_2 @ A) )  =>  ( (v2_membered @ A)  &  ~ ( (v1_xboole_0 @ A) ) ) ) ) , file(xxreal_2, cc17_xxreal_2)).
thf(cc18_membered, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v6_membered @ B) ) ) ) ) , file(membered, cc18_membered)).
thf(cc18_ordinal1, axiom,  (! [A: $i] :  ( (v10_ordinal1 @ A)  =>  ~ ( (v1_setfam_1 @ A) ) ) ) , file(ordinal1, cc18_ordinal1)).
thf(cc18_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v3_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v3_valued_0 @ C) ) ) ) ) , file(valued_0, cc18_valued_0)).
thf(cc19_membered, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v7_membered @ A) ) ) , file(membered, cc19_membered)).
thf(cc19_ordinal1, axiom,  (! [A: $i] :  ( (v1_setfam_1 @ A)  =>  ~ ( (v10_ordinal1 @ A) ) ) ) , file(ordinal1, cc19_ordinal1)).
thf(cc19_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v4_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v5_relat_1 @ C)  @ k3_numbers) ) ) ) ) , file(valued_0, cc19_valued_0)).
thf(cc1_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_xboole_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v1_finseq_1 @ A) ) ) ) , file(finseq_1, cc1_finseq_1)).
thf(cc1_finset_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_finset_1 @ A) ) ) , file(finset_1, cc1_finset_1)).
thf(cc1_int_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_numbers)  =>  (v1_int_1 @ A) ) ) , file(int_1, cc1_int_1)).
thf(cc1_membered, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  (v5_membered @ A) ) ) , file(membered, cc1_membered)).
thf(cc1_nat_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v3_ordinal1 @ A)  &  (v7_ordinal1 @ A) ) ) ) , file(nat_1, cc1_nat_1)).
thf(cc1_ordinal1, axiom,  (! [A: $i] :  ( (v3_ordinal1 @ A)  =>  ( (v1_ordinal1 @ A)  &  (v2_ordinal1 @ A) ) ) ) , file(ordinal1, cc1_ordinal1)).
thf(cc1_partfun1, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v1_partfun1 @ C)  @ A) ) ) ) ) , file(partfun1, cc1_partfun1)).
thf(cc1_rat_1, axiom,  (! [A: $i] :  ( (v1_rat_1 @ A)  =>  (v1_xreal_0 @ A) ) ) , file(rat_1, cc1_rat_1)).
thf(cc1_relset_1, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v1_relat_1 @ C) ) ) ) , file(relset_1, cc1_relset_1)).
thf(cc1_subset_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_xboole_0 @ B) ) ) ) ) , file(subset_1, cc1_subset_1)).
thf(cc1_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) ) ) ) , file(valued_0, cc1_valued_0)).
thf(cc1_xcmplx_0, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, cc1_xcmplx_0)).
thf(cc1_xxreal_0, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k6_numbers)  =>  (v1_xxreal_0 @ A) ) ) , file(xxreal_0, cc1_xxreal_0)).
thf(cc1_xxreal_3, axiom,  (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  ( ~ ( (v3_xxreal_0 @ A) )  &  ~ ( (v1_xreal_0 @ A) ) ) )  =>  ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) ) ) ) , file(xxreal_3, cc1_xxreal_3)).
thf(cc20_ordinal1, axiom,  (! [A: $i] :  ( ~ ( (v1_setfam_1 @ A) )  =>  (v10_ordinal1 @ A) ) ) , file(ordinal1, cc20_ordinal1)).
thf(cc20_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v5_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v5_relat_1 @ C)  @ k4_numbers) ) ) ) ) , file(valued_0, cc20_valued_0)).
thf(cc21_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v6_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v4_valued_0 @ C) ) ) ) ) , file(valued_0, cc21_valued_0)).
thf(cc22_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_zfmisc_1 @ A)  &  (v2_valued_0 @ A) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  ( (v5_valued_0 @ A)  &  (v6_valued_0 @ A) ) ) ) ) ) ) , file(valued_0, cc22_valued_0)).
thf(cc23_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v5_valued_0 @ A) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v7_valued_0 @ A) ) ) ) ) ) , file(valued_0, cc23_valued_0)).
thf(cc24_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v6_valued_0 @ A) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v8_valued_0 @ A) ) ) ) ) ) , file(valued_0, cc24_valued_0)).
thf(cc29_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k6_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) ) ) ) , file(valued_0, cc29_valued_0)).
thf(cc2_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) ) ) , file(finseq_1, cc2_finseq_1)).
thf(cc2_finset_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_finset_1 @ B) ) ) ) ) , file(finset_1, cc2_finset_1)).
thf(cc2_int_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_int_1 @ A) ) ) , file(int_1, cc2_int_1)).
thf(cc2_membered, axiom,  (! [A: $i] :  ( (v5_membered @ A)  =>  (v4_membered @ A) ) ) , file(membered, cc2_membered)).
thf(cc2_nat_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  ~ ( (v3_xxreal_0 @ A) ) ) ) , file(nat_1, cc2_nat_1)).
thf(cc2_ordinal1, axiom,  (! [A: $i] :  ( ( (v1_ordinal1 @ A)  &  (v2_ordinal1 @ A) )  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc2_ordinal1)).
thf(cc2_partfun1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_xboole_0 @ B) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ~ ( ( (v1_partfun1 @ C)  @ A) ) ) ) ) ) , file(partfun1, cc2_partfun1)).
thf(cc2_rat_1, axiom,  (! [A: $i] :  ( (v1_int_1 @ A)  =>  (v1_rat_1 @ A) ) ) , file(rat_1, cc2_rat_1)).
thf(cc2_relset_1, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v5_relat_1 @ C)  @ B) ) ) ) ) , file(relset_1, cc2_relset_1)).
thf(cc2_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( ~ ( ( (v1_subset_1 @ B)  @ A) )  =>  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) ) , file(subset_1, cc2_subset_1)).
thf(cc2_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) ) ) ) , file(valued_0, cc2_valued_0)).
thf(cc2_xreal_0, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_xreal_0 @ A) ) ) , file(xreal_0, cc2_xreal_0)).
thf(cc2_xxreal_0, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_xxreal_0 @ A) ) ) , file(xxreal_0, cc2_xxreal_0)).
thf(cc2_xxreal_2, axiom,  (! [A: $i] :  ( ( (v2_membered @ A)  &  ( (v1_finset_1 @ A)  &  ~ ( (v1_xboole_0 @ A) ) ) )  =>  ( (v2_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_xxreal_2 @ A)  &  (v2_xxreal_2 @ A) ) ) ) ) ) , file(xxreal_2, cc2_xxreal_2)).
thf(cc2_xxreal_3, axiom,  (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  ( ~ ( (v2_xxreal_0 @ A) )  &  ~ ( (v1_xreal_0 @ A) ) ) )  =>  ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) ) ) ) , file(xxreal_3, cc2_xxreal_3)).
thf(cc31_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_ordinal1) )  =>  ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, cc31_valued_0)).
thf(cc3_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_finseq_1 @ B)  @ A)  =>  ( (v5_relat_1 @ B)  @ A) ) ) ) , file(finseq_1, cc3_finseq_1)).
thf(cc3_finset_1, axiom,  (! [A: $i, B: $i] :  ( (v1_finset_1 @ A)  =>  (! [C: $i] :  ( ( (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) ) ) ) ) ) ) ) , file(finset_1, cc3_finset_1)).
thf(cc3_int_1, axiom,  (! [A: $i] :  ( (v1_int_1 @ A)  =>  (v1_xreal_0 @ A) ) ) , file(int_1, cc3_int_1)).
thf(cc3_membered, axiom,  (! [A: $i] :  ( (v4_membered @ A)  =>  (v3_membered @ A) ) ) , file(membered, cc3_membered)).
thf(cc3_nat_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v7_ordinal1 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) ) ) ) , file(nat_1, cc3_nat_1)).
thf(cc3_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc3_ordinal1)).
thf(cc3_relset_1, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v1_xboole_0 @ C) ) ) ) ) , file(relset_1, cc3_relset_1)).
thf(cc3_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( (v1_xboole_0 @ B)  =>  ( (v1_subset_1 @ B)  @ A) ) ) ) ) ) , file(subset_1, cc3_subset_1)).
thf(cc3_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc3_valued_0)).
thf(cc3_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v1_xcmplx_0 @ A) ) ) , file(xreal_0, cc3_xreal_0)).
thf(cc3_xxreal_0, axiom,  (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) )  =>  ( ~ ( (v8_ordinal1 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc3_xxreal_0)).
thf(cc3_xxreal_2, axiom,  (! [A: $i] :  ( ( (v6_membered @ A)  &  ~ ( (v1_xboole_0 @ A) ) )  =>  ( (v6_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, cc3_xxreal_2)).
thf(cc4_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_xboole_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v1_finseq_1 @ A) ) ) ) , file(finseq_1, cc4_finseq_1)).
thf(cc4_finset_1, axiom,  (! [A: $i] :  ( (v1_zfmisc_1 @ A)  =>  (v1_finset_1 @ A) ) ) , file(finset_1, cc4_finset_1)).
thf(cc4_int_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v2_int_1 @ A) ) ) , file(int_1, cc4_int_1)).
thf(cc4_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (v2_membered @ A) ) ) , file(membered, cc4_membered)).
thf(cc4_nat_1, axiom,  (! [A: $i] :  ( ( (v7_ordinal1 @ A)  &  (v8_ordinal1 @ A) )  =>  ( (v7_ordinal1 @ A)  &  ~ ( (v2_xxreal_0 @ A) ) ) ) ) , file(nat_1, cc4_nat_1)).
thf(cc4_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v5_ordinal1 @ A) ) ) , file(ordinal1, cc4_ordinal1)).
thf(cc4_relset_1, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ A) ) )  =>  (v1_xboole_0 @ C) ) ) ) ) , file(relset_1, cc4_relset_1)).
thf(cc4_subset_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ~ ( ( (v1_subset_1 @ B)  @ A) ) ) ) ) ) , file(subset_1, cc4_subset_1)).
thf(cc4_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc4_valued_0)).
thf(cc4_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v1_xxreal_0 @ A) ) ) , file(xreal_0, cc4_xreal_0)).
thf(cc4_xxreal_0, axiom,  (! [A: $i] :  ( ( ~ ( (v8_ordinal1 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) ) )  =>  ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) ) ) ) , file(xxreal_0, cc4_xxreal_0)).
thf(cc4_xxreal_2, axiom,  (! [A: $i] :  ( ( (v2_membered @ A)  &  (v5_xxreal_2 @ A) )  =>  ( (v2_membered @ A)  &  ( (v3_xxreal_2 @ A)  &  (v4_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, cc4_xxreal_2)).
thf(cc5_finseq_1, axiom,  (! [A: $i] :  ( ( (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) ) ) ) ) ) , file(finseq_1, cc5_finseq_1)).
thf(cc5_finset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_finset_1 @ A) )  =>  ~ ( (v1_zfmisc_1 @ A) ) ) ) , file(finset_1, cc5_finset_1)).
thf(cc5_int_1, axiom,  (! [A: $i] :  ( (v2_int_1 @ A)  =>  (v1_int_1 @ A) ) ) , file(int_1, cc5_int_1)).
thf(cc5_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (v1_membered @ A) ) ) , file(membered, cc5_membered)).
thf(cc5_nat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v8_ordinal1 @ A) ) ) , file(nat_1, cc5_nat_1)).
thf(cc5_ordinal1, axiom,  (! [A: $i] :  ( (v3_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v3_ordinal1 @ B) ) ) ) ) , file(ordinal1, cc5_ordinal1)).
thf(cc5_subset_1, axiom,  (! [A: $i] :  ( (v1_zfmisc_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_zfmisc_1 @ B) ) ) ) ) , file(subset_1, cc5_subset_1)).
thf(cc5_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) ) ) ) , file(valued_0, cc5_valued_0)).
thf(cc5_xxreal_0, axiom,  (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) )  =>  ( ~ ( (v8_ordinal1 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v2_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc5_xxreal_0)).
thf(cc5_xxreal_2, axiom,  (! [A: $i] :  ( ( (v2_membered @ A)  &  ( (v3_xxreal_2 @ A)  &  (v4_xxreal_2 @ A) ) )  =>  ( (v2_membered @ A)  &  (v5_xxreal_2 @ A) ) ) ) , file(xxreal_2, cc5_xxreal_2)).
thf(cc6_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) , file(finseq_1, cc6_finseq_1)).
thf(cc6_finset_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v5_finset_1 @ A) ) ) , file(finset_1, cc6_finset_1)).
thf(cc6_membered, axiom,  (! [A: $i] :  ( (v1_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xcmplx_0 @ B) ) ) ) ) , file(membered, cc6_membered)).
thf(cc6_nat_1, axiom,  (! [A: $i] :  ( ~ ( (v8_ordinal1 @ A) )  =>  ~ ( (v1_xboole_0 @ A) ) ) ) , file(nat_1, cc6_nat_1)).
thf(cc6_ordinal1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc6_ordinal1)).
thf(cc6_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) ) ) ) , file(valued_0, cc6_valued_0)).
thf(cc6_xxreal_0, axiom,  (! [A: $i] :  ( ( ~ ( (v8_ordinal1 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v2_xxreal_0 @ A) ) ) )  =>  ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) ) ) ) , file(xxreal_0, cc6_xxreal_0)).
thf(cc6_xxreal_2, axiom,  (! [A: $i] :  ( ( (v3_membered @ A)  &  (v1_finset_1 @ A) )  =>  ( (v3_membered @ A)  &  (v5_xxreal_2 @ A) ) ) ) , file(xxreal_2, cc6_xxreal_2)).
thf(cc7_finseq_1, axiom,  (! [A: $i] :  ( ( (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) ) ) ) ) ) , file(finseq_1, cc7_finseq_1)).
thf(cc7_finset_1, axiom,  (! [A: $i] :  ( (v5_finset_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_finset_1 @ B) ) ) ) ) , file(finset_1, cc7_finset_1)).
thf(cc7_membered, axiom,  (! [A: $i] :  ( (v2_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xxreal_0 @ B) ) ) ) ) , file(membered, cc7_membered)).
thf(cc7_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc7_ordinal1)).
thf(cc7_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) ) ) ) , file(valued_0, cc7_valued_0)).
thf(cc7_xxreal_0, axiom,  (! [A: $i] :  ( ( (v8_ordinal1 @ A)  &  (v1_xxreal_0 @ A) )  =>  ( (v1_xxreal_0 @ A)  &  ( ~ ( (v2_xxreal_0 @ A) )  &  ~ ( (v3_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc7_xxreal_0)).
thf(cc7_xxreal_2, axiom,  (! [A: $i] :  ( ( (v5_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v4_xxreal_2 @ A) ) )  =>  ( (v5_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v2_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, cc7_xxreal_2)).
thf(cc8_finseq_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v3_finseq_1 @ A) ) ) , file(finseq_1, cc8_finseq_1)).
thf(cc8_finset_1, axiom,  (! [A: $i] :  ( (v5_finset_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v5_finset_1 @ B) ) ) ) ) , file(finset_1, cc8_finset_1)).
thf(cc8_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xreal_0 @ B) ) ) ) ) , file(membered, cc8_membered)).
thf(cc8_ordinal1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc8_ordinal1)).
thf(cc8_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc8_valued_0)).
thf(cc8_xxreal_0, axiom,  (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  ( ~ ( (v2_xxreal_0 @ A) )  &  ~ ( (v3_xxreal_0 @ A) ) ) )  =>  ( (v8_ordinal1 @ A)  &  (v1_xxreal_0 @ A) ) ) ) , file(xxreal_0, cc8_xxreal_0)).
thf(cc8_xxreal_2, axiom,  (! [A: $i] :  ( ( (v5_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v3_xxreal_2 @ A) ) )  =>  ( (v5_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, cc8_xxreal_2)).
thf(cc9_finseq_1, axiom,  (! [A: $i] :  ( (v3_finseq_1 @ A)  =>  (v4_funct_1 @ A) ) ) , file(finseq_1, cc9_finseq_1)).
thf(cc9_finset_1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v2_finset_1 @ A) ) ) ) , file(finset_1, cc9_finset_1)).
thf(cc9_membered, axiom,  (! [A: $i] :  ( (v4_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_rat_1 @ B) ) ) ) ) , file(membered, cc9_membered)).
thf(cc9_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v6_ordinal1 @ A) ) ) , file(ordinal1, cc9_ordinal1)).
thf(cc9_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_xboole_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, cc9_valued_0)).
thf(cc9_xxreal_2, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  ( (v6_membered @ A)  &  (v3_xxreal_2 @ A) ) ) ) , file(xxreal_2, cc9_xxreal_2)).
thf(commutativity_k1_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( (m1_subset_1 @ B)  @ k4_ordinal1) )  =>  ( ( (k1_nat_1 @ A)  @ B)  =  ( (k1_nat_1 @ B)  @ A) ) ) ) , file(nat_1, k1_nat_1)).
thf(commutativity_k1_xxreal_3, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v1_xxreal_0 @ B) )  =>  ( ( (k1_xxreal_3 @ A)  @ B)  =  ( (k1_xxreal_3 @ B)  @ A) ) ) ) , file(xxreal_3, k1_xxreal_3)).
thf(commutativity_k2_xcmplx_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( ( (k2_xcmplx_0 @ A)  @ B)  =  ( (k2_xcmplx_0 @ B)  @ A) ) ) ) , file(xcmplx_0, k2_xcmplx_0)).
thf(commutativity_k3_supinf_2, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k6_numbers)  &  ( (m1_subset_1 @ B)  @ k6_numbers) )  =>  ( ( (k3_supinf_2 @ A)  @ B)  =  ( (k3_supinf_2 @ B)  @ A) ) ) ) , file(supinf_2, k3_supinf_2)).
thf(connectedness_r1_xxreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v1_xxreal_0 @ B) )  =>  ( ( (r1_xxreal_0 @ A)  @ B)  |  ( (r1_xxreal_0 @ B)  @ A) ) ) ) , file(xxreal_0, r1_xxreal_0)).
thf(d12_ordinal1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  <=>  ( (r2_hidden @ A)  @ k4_ordinal1) ) ) , file(ordinal1, d12_ordinal1)).
thf(d1_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (k1_finseq_1 @ A)  =  ( ( (replSep1 @  (^ [B: $i] :  (v7_ordinal1 @ B) ) )  @  (^ [B: $i] : B) )  @  (^ [B: $i] :  ( ( (r1_xxreal_0 @ np__1)  @ B)  &  ( (r1_xxreal_0 @ B)  @ A) ) ) ) ) ) ) , file(finseq_1, d1_finseq_1)).
thf(d2_extreal1, axiom,  (! [A: $i] :  ( ( (m2_finseq_1 @ A)  @ k6_numbers)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ k6_numbers)  =>  ( (B =  (k4_extreal1 @ A) )  <=>  (? [C: $i] :  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ k4_ordinal1)  @ k6_numbers)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ k6_numbers) ) ) ) )  &  ( (B =  ( (k12_supinf_2 @ C)  @  (k3_finseq_1 @ A) ) )  &  ( ( ( (k12_supinf_2 @ C)  @ k5_numbers)  = k1_supinf_2)  &  (! [D: $i] :  ( (v7_ordinal1 @ D)  =>  ( ~ ( ( (r1_xxreal_0 @  (k3_finseq_1 @ A) )  @ D) )  =>  ( ( (k12_supinf_2 @ C)  @  ( (k1_nat_1 @ D)  @ np__1) )  =  ( (k3_supinf_2 @  ( (k12_supinf_2 @ C)  @ D) )  @  ( (k12_supinf_2 @ A)  @  ( (k1_nat_1 @ D)  @ np__1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(extreal1, d2_extreal1)).
thf(d2_xboole_0, axiom,  (k1_xboole_0 =  (eps @  (^ [A: $i] :  (v1_xboole_0 @ A) ) ) ) , file(xboole_0, d2_xboole_0)).
thf(d3_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ k4_ordinal1)  =>  ( (B =  (k3_finseq_1 @ A) )  <=>  ( (k2_finseq_1 @ B)  =  (k9_xtuple_0 @ A) ) ) ) ) ) ) , file(finseq_1, d3_finseq_1)).
thf(dt_k12_supinf_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_valued_0 @ A) ) )  =>  ( (m1_subset_1 @  ( (k12_supinf_2 @ A)  @ B) )  @ k6_numbers) ) ) , file(supinf_2, k12_supinf_2)).
thf(dt_k1_card_1, axiom,  (! [A: $i] :  (v1_card_1 @  (k1_card_1 @ A) ) ) , file(card_1, k1_card_1)).
thf(dt_k1_finseq_1, axiom, $true, file(finseq_1, k1_finseq_1)).
thf(dt_k1_funct_1, axiom, $true, file(funct_1, k1_funct_1)).
thf(dt_k1_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( (m1_subset_1 @ B)  @ k4_ordinal1) )  =>  ( (m1_subset_1 @  ( (k1_nat_1 @ A)  @ B) )  @ k4_ordinal1) ) ) , file(nat_1, k1_nat_1)).
thf(dt_k1_relset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  ( (m1_subset_1 @  ( (k1_relset_1 @ A)  @ B) )  @  (k1_zfmisc_1 @ A) ) ) ) , file(relset_1, k1_relset_1)).
thf(dt_k1_supinf_2, axiom,  ( (m1_subset_1 @ k1_supinf_2)  @ k6_numbers) , file(supinf_2, k1_supinf_2)).
thf(dt_k1_xboole_0, axiom, $true, file(xboole_0, k1_xboole_0)).
thf(dt_k1_xxreal_3, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v1_xxreal_0 @ B) )  =>  (v1_xxreal_0 @  ( (k1_xxreal_3 @ A)  @ B) ) ) ) , file(xxreal_3, k1_xxreal_3)).
thf(dt_k1_zfmisc_1, axiom, $true, file(zfmisc_1, k1_zfmisc_1)).
thf(dt_k2_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (m1_subset_1 @  (k2_finseq_1 @ A) )  @  (k1_zfmisc_1 @ k4_ordinal1) ) ) ) , file(finseq_1, k2_finseq_1)).
thf(dt_k2_xcmplx_0, axiom, $true, file(xcmplx_0, k2_xcmplx_0)).
thf(dt_k2_zfmisc_1, axiom, $true, file(zfmisc_1, k2_zfmisc_1)).
thf(dt_k3_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (m1_subset_1 @  (k3_finseq_1 @ A) )  @ k4_ordinal1) ) ) , file(finseq_1, k3_finseq_1)).
thf(dt_k3_numbers, axiom, $true, file(numbers, k3_numbers)).
thf(dt_k3_supinf_2, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k6_numbers)  &  ( (m1_subset_1 @ B)  @ k6_numbers) )  =>  ( (m1_subset_1 @  ( (k3_supinf_2 @ A)  @ B) )  @ k6_numbers) ) ) , file(supinf_2, k3_supinf_2)).
thf(dt_k4_extreal1, axiom,  (! [A: $i] :  ( ( (m1_finseq_1 @ A)  @ k6_numbers)  =>  ( (m1_subset_1 @  (k4_extreal1 @ A) )  @ k6_numbers) ) ) , file(extreal1, k4_extreal1)).
thf(dt_k4_numbers, axiom, $true, file(numbers, k4_numbers)).
thf(dt_k4_ordinal1, axiom, $true, file(ordinal1, k4_ordinal1)).
thf(dt_k5_numbers, axiom,  ( (m1_subset_1 @ k5_numbers)  @ k4_ordinal1) , file(numbers, k5_numbers)).
thf(dt_k5_ordinal1, axiom, $true, file(ordinal1, k5_ordinal1)).
thf(dt_k6_numbers, axiom, $true, file(numbers, k6_numbers)).
thf(dt_k8_nat_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ k4_ordinal1)  @ A)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ A) ) ) ) )  &  (v7_ordinal1 @ C) )  =>  ( (m1_subset_1 @  ( ( (k8_nat_1 @ A)  @ B)  @ C) )  @ A) ) ) , file(nat_1, k8_nat_1)).
thf(dt_k9_xtuple_0, axiom, $true, file(xtuple_0, k9_xtuple_0)).
thf(dt_m1_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_finseq_1 @ B)  @ A)  =>  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) ) ) ) ) , file(finseq_1, m1_finseq_1)).
thf(dt_m1_subset_1, axiom, $true, file(subset_1, m1_subset_1)).
thf(dt_m2_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (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) ) ) ) ) ) ) ) , file(finseq_1, m2_finseq_1)).
thf(existence_m1_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m1_finseq_1 @ B)  @ A) ) ) , file(finseq_1, m1_finseq_1)).
thf(existence_m1_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m1_subset_1 @ B)  @ A) ) ) , file(subset_1, m1_subset_1)).
thf(existence_m2_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m2_finseq_1 @ B)  @ A) ) ) , file(finseq_1, m2_finseq_1)).
thf(fc10_subset_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  ~ ( (v1_xboole_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) , file(subset_1, fc10_subset_1)).
thf(fc10_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v2_xxreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc10_xreal_0)).
thf(fc10_xxreal_3, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) )  &  ( (v1_xxreal_0 @ B)  &  ~ ( (v3_xxreal_0 @ B) ) ) )  =>  ( (v1_xxreal_0 @  ( (k1_xxreal_3 @ A)  @ B) )  &  (v2_xxreal_0 @  ( (k1_xxreal_3 @ A)  @ B) ) ) ) ) , file(xxreal_3, fc10_xxreal_3)).
thf(fc11_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v2_xxreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc11_xreal_0)).
thf(fc11_xxreal_3, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) )  &  ( (v1_xxreal_0 @ B)  &  ~ ( (v3_xxreal_0 @ B) ) ) )  =>  ( (v1_xxreal_0 @  ( (k1_xxreal_3 @ B)  @ A) )  &  (v2_xxreal_0 @  ( (k1_xxreal_3 @ B)  @ A) ) ) ) ) , file(xxreal_3, fc11_xxreal_3)).
thf(fc12_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v2_xxreal_0 @  ( (k2_xcmplx_0 @ B)  @ A) ) ) ) , file(xreal_0, fc12_xreal_0)).
thf(fc12_xxreal_2, axiom,  (v6_xxreal_2 @ k6_numbers) , file(xxreal_2, fc12_xxreal_2)).
thf(fc12_xxreal_3, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) )  &  ( (v1_xxreal_0 @ B)  &  ~ ( (v2_xxreal_0 @ B) ) ) )  =>  ( (v1_xxreal_0 @  ( (k1_xxreal_3 @ A)  @ B) )  &  (v3_xxreal_0 @  ( (k1_xxreal_3 @ A)  @ B) ) ) ) ) , file(xxreal_3, fc12_xxreal_3)).
thf(fc13_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v3_xxreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc13_xreal_0)).
thf(fc13_xxreal_3, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) )  &  ( (v1_xxreal_0 @ B)  &  ~ ( (v2_xxreal_0 @ B) ) ) )  =>  ( (v1_xxreal_0 @  ( (k1_xxreal_3 @ B)  @ A) )  &  (v3_xxreal_0 @  ( (k1_xxreal_3 @ B)  @ A) ) ) ) ) , file(xxreal_3, fc13_xxreal_3)).
thf(fc14_finset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_finset_1 @ A)  &  (v1_finset_1 @ B) )  =>  (v1_finset_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(finset_1, fc14_finset_1)).
thf(fc14_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v3_xxreal_0 @  ( (k2_xcmplx_0 @ B)  @ A) ) ) ) , file(xreal_0, fc14_xreal_0)).
thf(fc17_finset_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  (v1_finset_1 @  (k1_zfmisc_1 @ A) ) ) ) , file(finset_1, fc17_finset_1)).
thf(fc19_finset_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_finset_1 @ A) )  =>  (v1_finset_1 @  (k9_xtuple_0 @ A) ) ) ) , file(finset_1, fc19_finset_1)).
thf(fc1_finseq_1, axiom,  (! [A: $i] :  ( ( (v7_ordinal1 @ A)  &  (v8_ordinal1 @ A) )  =>  (v1_xboole_0 @  (k1_finseq_1 @ A) ) ) ) , file(finseq_1, fc1_finseq_1)).
thf(fc1_int_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_int_1 @ A)  &  (v1_int_1 @ B) )  =>  (v1_int_1 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(int_1, fc1_int_1)).
thf(fc1_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  (v7_ordinal1 @ B) )  =>  (v7_ordinal1 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(nat_1, fc1_nat_1)).
thf(fc1_subset_1, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  (k1_zfmisc_1 @ A) ) ) ) , file(subset_1, fc1_subset_1)).
thf(fc2_finseq_1, axiom,  (! [A: $i] :  ( ( (v7_ordinal1 @ A)  &  ~ ( (v8_ordinal1 @ A) ) )  =>  ~ ( (v1_xboole_0 @  (k1_finseq_1 @ A) ) ) ) ) , file(finseq_1, fc2_finseq_1)).
thf(fc2_membered, axiom,  (v2_membered @ k6_numbers) , file(membered, fc2_membered)).
thf(fc2_rat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_rat_1 @ A)  &  (v1_rat_1 @ B) )  =>  (v1_rat_1 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(rat_1, fc2_rat_1)).
thf(fc2_xcmplx_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  (v1_xcmplx_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(xcmplx_0, fc2_xcmplx_0)).
thf(fc2_xxreal_3, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  ( (v1_xxreal_0 @  ( (k1_xxreal_3 @ A)  @ B) )  &  (v1_xreal_0 @  ( (k1_xxreal_3 @ A)  @ B) ) ) ) ) , file(xxreal_3, fc2_xxreal_3)).
thf(fc30_finseq_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v3_finseq_1 @ A)  &  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) ) )  =>  (v1_finseq_1 @  ( (k1_funct_1 @ B)  @ C) ) ) ) , file(finseq_1, fc30_finseq_1)).
thf(fc31_finset_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  (v5_finset_1 @  (k1_zfmisc_1 @ A) ) ) ) , file(finset_1, fc31_finset_1)).
thf(fc35_finset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finset_1 @ A) ) )  =>  (v1_finset_1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(finset_1, fc35_finset_1)).
thf(fc3_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_finset_1 @  (k1_finseq_1 @ A) ) ) ) , file(finseq_1, fc3_finseq_1)).
thf(fc3_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( (v7_ordinal1 @ B)  &  ~ ( (v8_ordinal1 @ B) ) ) )  =>  ~ ( (v8_ordinal1 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) ) , file(nat_1, fc3_nat_1)).
thf(fc3_numbers, axiom,  ~ ( (v1_xboole_0 @ k3_numbers) ) , file(numbers, fc3_numbers)).
thf(fc43_xxreal_3, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  (v7_ordinal1 @ B) )  =>  ( (v7_ordinal1 @  ( (k1_xxreal_3 @ A)  @ B) )  &  (v1_xxreal_0 @  ( (k1_xxreal_3 @ A)  @ B) ) ) ) ) , file(xxreal_3, fc43_xxreal_3)).
thf(fc46_xxreal_3, axiom,  (! [A: $i] :  ( (v2_int_1 @ A)  =>  ( (v7_ordinal1 @  ( (k1_xxreal_3 @ A)  @ np__1) )  &  (v1_xxreal_0 @  ( (k1_xxreal_3 @ A)  @ np__1) ) ) ) ) , file(xxreal_3, fc46_xxreal_3)).
thf(fc4_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v3_card_1 @  (k1_finseq_1 @ A) )  @ A) ) ) , file(finseq_1, fc4_finseq_1)).
thf(fc4_membered, axiom,  (v4_membered @ k3_numbers) , file(membered, fc4_membered)).
thf(fc4_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( (v7_ordinal1 @ B)  &  ~ ( (v8_ordinal1 @ B) ) ) )  =>  ~ ( (v8_ordinal1 @  ( (k2_xcmplx_0 @ B)  @ A) ) ) ) ) , file(nat_1, fc4_nat_1)).
thf(fc4_numbers, axiom,  ~ ( (v1_xboole_0 @ k4_numbers) ) , file(numbers, fc4_numbers)).
thf(fc4_ordinal1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v5_ordinal1 @ A) ) )  =>  (v3_ordinal1 @  (k9_xtuple_0 @ A) ) ) ) , file(ordinal1, fc4_ordinal1)).
thf(fc4_xxreal_3, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  ( (v1_xxreal_0 @ B)  &  ~ ( (v1_xreal_0 @ B) ) ) )  =>  ~ ( (v1_xreal_0 @  ( (k1_xxreal_3 @ A)  @ B) ) ) ) ) , file(xxreal_3, fc4_xxreal_3)).
thf(fc57_membered, axiom,  (v7_membered @ k3_numbers) , file(membered, fc57_membered)).
thf(fc58_membered, axiom,  (v7_membered @ k4_numbers) , file(membered, fc58_membered)).
thf(fc59_membered, axiom,  (v7_membered @ k4_ordinal1) , file(membered, fc59_membered)).
thf(fc5_membered, axiom,  (v5_membered @ k4_numbers) , file(membered, fc5_membered)).
thf(fc5_numbers, axiom,  ~ ( (v1_xboole_0 @ k6_numbers) ) , file(numbers, fc5_numbers)).
thf(fc5_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  (v1_xreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc5_xreal_0)).
thf(fc5_xxreal_3, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_xxreal_0 @ A)  &  ( (v2_xxreal_0 @ A)  &  ~ ( (v1_xreal_0 @ A) ) ) )  &  ( (v1_xxreal_0 @ B)  &  ( (v2_xxreal_0 @ B)  &  ~ ( (v1_xreal_0 @ B) ) ) ) )  =>  ( (v1_xxreal_0 @  ( (k1_xxreal_3 @ A)  @ B) )  &  ~ ( (v1_xreal_0 @  ( (k1_xxreal_3 @ A)  @ B) ) ) ) ) ) , file(xxreal_3, fc5_xxreal_3)).
thf(fc61_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  (v1_xcmplx_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc61_valued_0)).
thf(fc62_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_valued_0 @ A) ) )  =>  (v1_xxreal_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc62_valued_0)).
thf(fc63_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_valued_0 @ A) ) )  =>  (v1_xreal_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc63_valued_0)).
thf(fc64_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k3_numbers)  &  (v1_funct_1 @ A) ) )  =>  (v1_rat_1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc64_valued_0)).
thf(fc65_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k4_numbers)  &  (v1_funct_1 @ A) ) )  =>  (v1_int_1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc65_valued_0)).
thf(fc66_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v4_valued_0 @ A) ) )  =>  (v7_ordinal1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc66_valued_0)).
thf(fc6_membered, axiom,  (v6_membered @ k4_ordinal1) , file(membered, fc6_membered)).
thf(fc6_numbers, axiom,  ~ ( (v1_finset_1 @ k4_numbers) ) , file(numbers, fc6_numbers)).
thf(fc6_ordinal1, axiom,  ( ~ ( (v1_xboole_0 @ k4_ordinal1) )  &  (v3_ordinal1 @ k4_ordinal1) ) , file(ordinal1, fc6_ordinal1)).
thf(fc6_xxreal_3, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_xxreal_0 @ A)  &  ( (v3_xxreal_0 @ A)  &  ~ ( (v1_xreal_0 @ A) ) ) )  &  ( (v1_xxreal_0 @ B)  &  ( (v3_xxreal_0 @ B)  &  ~ ( (v1_xreal_0 @ B) ) ) ) )  =>  ( (v1_xxreal_0 @  ( (k1_xxreal_3 @ A)  @ B) )  &  ~ ( (v1_xreal_0 @  ( (k1_xxreal_3 @ A)  @ B) ) ) ) ) ) , file(xxreal_3, fc6_xxreal_3)).
thf(fc7_int_1, axiom,  (! [A: $i] :  ( (v2_int_1 @ A)  =>  (v7_ordinal1 @  ( (k2_xcmplx_0 @ A)  @ np__1) ) ) ) , file(int_1, fc7_int_1)).
thf(fc7_numbers, axiom,  ~ ( (v1_finset_1 @ k3_numbers) ) , file(numbers, fc7_numbers)).
thf(fc7_xxreal_3, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_xxreal_0 @ A)  &  ( (v3_xxreal_0 @ A)  &  ~ ( (v1_xreal_0 @ A) ) ) )  &  ( (v1_xxreal_0 @ B)  &  ( (v2_xxreal_0 @ B)  &  ~ ( (v1_xreal_0 @ B) ) ) ) )  =>  ( (v8_ordinal1 @  ( (k1_xxreal_3 @ A)  @ B) )  &  (v1_xxreal_0 @  ( (k1_xxreal_3 @ A)  @ B) ) ) ) ) , file(xxreal_3, fc7_xxreal_3)).
thf(fc85_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_membered @ B)  =>  (v1_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc85_valued_0)).
thf(fc86_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v2_membered @ B)  =>  (v2_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc86_valued_0)).
thf(fc87_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v3_membered @ B)  =>  (v3_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc87_valued_0)).
thf(fc88_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v4_membered @ B)  =>  ( (v5_relat_1 @  ( (k2_zfmisc_1 @ A)  @ B) )  @ k3_numbers) ) ) , file(valued_0, fc88_valued_0)).
thf(fc89_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v5_membered @ B)  =>  ( (v5_relat_1 @  ( (k2_zfmisc_1 @ A)  @ B) )  @ k4_numbers) ) ) , file(valued_0, fc89_valued_0)).
thf(fc8_int_1, axiom,  (! [A: $i, B: $i] :  ( ( (v2_int_1 @ A)  &  ( (v7_ordinal1 @ B)  &  ~ ( (v8_ordinal1 @ B) ) ) )  =>  (v7_ordinal1 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(int_1, fc8_int_1)).
thf(fc8_ordinal1, axiom,  (v7_ordinal1 @ k5_ordinal1) , file(ordinal1, fc8_ordinal1)).
thf(fc8_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) )  @ C) ) )  =>  (v1_relat_1 @  (k9_xtuple_0 @ D) ) ) ) , file(relset_1, fc8_relset_1)).
thf(fc8_xxreal_3, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_xxreal_0 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) )  &  ( (v1_xxreal_0 @ B)  &  ~ ( (v3_xxreal_0 @ B) ) ) )  =>  ( (v1_xxreal_0 @  ( (k1_xxreal_3 @ A)  @ B) )  &  ~ ( (v3_xxreal_0 @  ( (k1_xxreal_3 @ A)  @ B) ) ) ) ) ) , file(xxreal_3, fc8_xxreal_3)).
thf(fc90_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v6_membered @ B)  =>  (v4_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc90_valued_0)).
thf(fc9_ordinal1, axiom,  (v8_ordinal1 @ k5_ordinal1) , file(ordinal1, fc9_ordinal1)).
thf(fc9_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v3_xxreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc9_xreal_0)).
thf(fc9_xxreal_3, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_xxreal_0 @ A)  &  ~ ( (v2_xxreal_0 @ A) ) )  &  ( (v1_xxreal_0 @ B)  &  ~ ( (v2_xxreal_0 @ B) ) ) )  =>  ( (v1_xxreal_0 @  ( (k1_xxreal_3 @ A)  @ B) )  &  ~ ( (v2_xxreal_0 @  ( (k1_xxreal_3 @ A)  @ B) ) ) ) ) ) , file(xxreal_3, fc9_xxreal_3)).
thf(ie1_xxreal_3, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v1_xreal_0 @ A)  &  ( (v1_xreal_0 @ B)  &  ( (v1_xcmplx_0 @ C)  &  (v1_xcmplx_0 @ D) ) ) )  =>  ( ( (A = C)  &  (B = D) )  =>  ( ( (k1_xxreal_3 @ A)  @ B)  =  ( (k2_xcmplx_0 @ C)  @ D) ) ) ) ) , file(xxreal_3, ie1_xxreal_3)).
thf(projectivity_k1_card_1, axiom,  (! [A: $i] :  ( (k1_card_1 @  (k1_card_1 @ A) )  =  (k1_card_1 @ A) ) ) , file(card_1, k1_card_1)).
thf(projectivity_k3_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (k3_finseq_1 @  (k3_finseq_1 @ A) )  =  (k3_finseq_1 @ A) ) ) ) , file(finseq_1, k3_finseq_1)).
thf(rc10_finset_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finset_1 @ A) ) ) ) ) , file(finset_1, rc10_finset_1)).
thf(rc10_ordinal1, axiom,  (? [A: $i] :  (v8_ordinal1 @ A) ) , file(ordinal1, rc10_ordinal1)).
thf(rc11_finseq_1, axiom,  (? [A: $i] :  ( (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) ) ) ) ) ) ) ) , file(finseq_1, rc11_finseq_1)).
thf(rc11_ordinal1, axiom,  (? [A: $i] :  ~ ( (v8_ordinal1 @ A) ) ) , file(ordinal1, rc11_ordinal1)).
thf(rc12_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (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) ) ) ) ) ) ) ) ) ) ) , file(finseq_1, rc12_finseq_1)).
thf(rc12_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v10_ordinal1 @ A) ) ) ) , file(ordinal1, rc12_ordinal1)).
thf(rc13_finseq_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k4_ordinal1)  &  ( (v1_funct_1 @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_finset_1 @ A)  &  ( (v4_valued_0 @ A)  &  ( (v1_finseq_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) ) ) ) ) , file(finseq_1, rc13_finseq_1)).
thf(rc13_ordinal1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  (v9_ordinal1 @ A) ) ) , file(ordinal1, rc13_ordinal1)).
thf(rc14_ordinal1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ~ ( (v9_ordinal1 @ A) ) ) ) , file(ordinal1, rc14_ordinal1)).
thf(rc1_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (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) ) ) ) ) ) , file(finseq_1, rc1_finseq_1)).
thf(rc1_finset_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_finset_1 @ A) ) ) , file(finset_1, rc1_finset_1)).
thf(rc1_int_1, axiom,  (? [A: $i] :  ( (v1_xxreal_0 @ A)  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xreal_0 @ A)  &  (v1_int_1 @ A) ) ) ) ) , file(int_1, rc1_int_1)).
thf(rc1_membered, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v6_membered @ A) ) ) , file(membered, rc1_membered)).
thf(rc1_nat_1, axiom,  (? [A: $i] :  (v7_ordinal1 @ A) ) , file(nat_1, rc1_nat_1)).
thf(rc1_ordinal1, axiom,  (? [A: $i] :  ( (v1_ordinal1 @ A)  &  (v2_ordinal1 @ A) ) ) , file(ordinal1, rc1_ordinal1)).
thf(rc1_partfun1, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( ( (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) ) ) ) ) ) ) , file(partfun1, rc1_partfun1)).
thf(rc1_rat_1, axiom,  (? [A: $i] :  ( (v1_xxreal_0 @ A)  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xreal_0 @ A)  &  (v1_rat_1 @ A) ) ) ) ) , file(rat_1, rc1_rat_1)).
thf(rc1_relset_1, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( ( (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) ) ) ) ) ) ) , file(relset_1, rc1_relset_1)).
thf(rc1_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) , file(subset_1, rc1_subset_1)).
thf(rc1_valued_0, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, rc1_valued_0)).
thf(rc1_xcmplx_0, axiom,  (? [A: $i] :  (v1_xcmplx_0 @ A) ) , file(xcmplx_0, rc1_xcmplx_0)).
thf(rc1_xreal_0, axiom,  (? [A: $i] :  (v1_xreal_0 @ A) ) , file(xreal_0, rc1_xreal_0)).
thf(rc1_xxreal_0, axiom,  (? [A: $i] :  (v1_xxreal_0 @ A) ) , file(xxreal_0, rc1_xxreal_0)).
thf(rc1_xxreal_2, axiom,  (? [A: $i] :  ( (v1_membered @ A)  &  ( (v2_membered @ A)  &  ( (v3_membered @ A)  &  ( (v4_membered @ A)  &  ( (v5_membered @ A)  &  ( (v6_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_xxreal_2 @ A)  &  (v2_xxreal_2 @ A) ) ) ) ) ) ) ) ) ) , file(xxreal_2, rc1_xxreal_2)).
thf(rc1_xxreal_3, axiom,  (? [A: $i] :  ( (v1_xxreal_0 @ A)  &  ( (v2_xxreal_0 @ A)  &  ~ ( (v1_xreal_0 @ A) ) ) ) ) , file(xxreal_3, rc1_xxreal_3)).
thf(rc2_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (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) ) ) ) ) ) ) ) ) , file(finseq_1, rc2_finseq_1)).
thf(rc2_finset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  (v1_finset_1 @ B) ) ) ) , file(finset_1, rc2_finset_1)).
thf(rc2_int_1, axiom,  (? [A: $i] :  (v1_int_1 @ A) ) , file(int_1, rc2_int_1)).
thf(rc2_membered, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v6_membered @ A) ) ) , file(membered, rc2_membered)).
thf(rc2_nat_1, axiom,  (? [A: $i] :  ( (v7_ordinal1 @ A)  &  (v8_ordinal1 @ A) ) ) , file(nat_1, rc2_nat_1)).
thf(rc2_ordinal1, axiom,  (? [A: $i] :  (v3_ordinal1 @ A) ) , file(ordinal1, rc2_ordinal1)).
thf(rc2_rat_1, axiom,  (? [A: $i] :  (v1_rat_1 @ A) ) , file(rat_1, rc2_rat_1)).
thf(rc2_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  (v1_xboole_0 @ B) ) ) ) , file(subset_1, rc2_subset_1)).
thf(rc2_xcmplx_0, axiom,  (? [A: $i] :  (v1_xcmplx_0 @ A) ) , file(xcmplx_0, rc2_xcmplx_0)).
thf(rc2_xreal_0, axiom,  (? [A: $i] :  (v1_xreal_0 @ A) ) , file(xreal_0, rc2_xreal_0)).
thf(rc2_xxreal_0, axiom,  (? [A: $i] :  (v1_xxreal_0 @ A) ) , file(xxreal_0, rc2_xxreal_0)).
thf(rc2_xxreal_2, axiom,  (? [A: $i] :  ( (v6_membered @ A)  &  ( (v1_finset_1 @ A)  &  ~ ( (v1_xboole_0 @ A) ) ) ) ) , file(xxreal_2, rc2_xxreal_2)).
thf(rc2_xxreal_3, axiom,  (? [A: $i] :  ( (v1_xxreal_0 @ A)  &  ( (v3_xxreal_0 @ A)  &  ~ ( (v1_xreal_0 @ A) ) ) ) ) , file(xxreal_3, rc2_xxreal_3)).
thf(rc3_finseq_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) , file(finseq_1, rc3_finseq_1)).
thf(rc3_finset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_finset_1 @ B) ) ) ) ) ) , file(finset_1, rc3_finset_1)).
thf(rc3_int_1, axiom,  (? [A: $i] :  (v2_int_1 @ A) ) , file(int_1, rc3_int_1)).
thf(rc3_membered, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v6_membered @ A)  &  (v7_membered @ A) ) ) ) , file(membered, rc3_membered)).
thf(rc3_nat_1, axiom,  (? [A: $i] :  ( (v7_ordinal1 @ A)  &  ~ ( (v8_ordinal1 @ A) ) ) ) , file(nat_1, rc3_nat_1)).
thf(rc3_ordinal1, axiom,  (? [A: $i] :  (v3_ordinal1 @ A) ) , file(ordinal1, rc3_ordinal1)).
thf(rc3_partfun1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  (? [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( ( (v5_relat_1 @ C)  @ B)  &  ( (v1_funct_1 @ C)  &  ~ ( (v1_xboole_0 @ C) ) ) ) ) ) ) ) ) ) , file(partfun1, rc3_partfun1)).
thf(rc3_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( ( (v1_subset_1 @ B)  @ A) ) ) ) ) , file(subset_1, rc3_subset_1)).
thf(rc3_valued_0, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ k4_ordinal1) ) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k4_ordinal1)  &  ( ( (v5_relat_1 @ A)  @ k4_ordinal1)  &  ( (v1_funct_1 @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_partfun1 @ A)  @ k4_ordinal1)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k4_ordinal1)  &  ( (v1_valued_0 @ A)  &  ( (v2_valued_0 @ A)  &  ( (v3_valued_0 @ A)  &  ( (v4_valued_0 @ A)  &  (v5_valued_0 @ A) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(valued_0, rc3_valued_0)).
thf(rc3_xcmplx_0, axiom,  (? [A: $i] :  ( (v8_ordinal1 @ A)  &  (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, rc3_xcmplx_0)).
thf(rc3_xreal_0, axiom,  (? [A: $i] :  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc3_xreal_0)).
thf(rc3_xxreal_0, axiom,  (? [A: $i] :  ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) ) ) , file(xxreal_0, rc3_xxreal_0)).
thf(rc3_xxreal_2, axiom,  (? [A: $i] :  ( (v1_membered @ A)  &  ( (v2_membered @ A)  &  ( (v3_membered @ A)  &  ( (v4_membered @ A)  &  ( (v5_membered @ A)  &  ( (v6_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_xxreal_2 @ A)  &  (v5_xxreal_2 @ A) ) ) ) ) ) ) ) ) ) , file(xxreal_2, rc3_xxreal_2)).
thf(rc4_finseq_1, axiom,  (? [A: $i] :  ( (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) ) ) ) ) ) ) ) , file(finseq_1, rc4_finseq_1)).
thf(rc4_finset_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) ) ) , file(finset_1, rc4_finset_1)).
thf(rc4_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  (v3_ordinal1 @ A) ) ) ) ) , file(ordinal1, rc4_ordinal1)).
thf(rc4_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( (v1_subset_1 @ B)  @ A) ) ) ) ) , file(subset_1, rc4_subset_1)).
thf(rc4_xcmplx_0, axiom,  (? [A: $i] :  ( ~ ( (v8_ordinal1 @ A) )  &  (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, rc4_xcmplx_0)).
thf(rc4_xreal_0, axiom,  (? [A: $i] :  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc4_xreal_0)).
thf(rc4_xxreal_0, axiom,  (? [A: $i] :  ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) ) ) , file(xxreal_0, rc4_xxreal_0)).
thf(rc4_xxreal_2, axiom,  (? [A: $i] :  ( (v2_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v6_xxreal_2 @ A) ) ) ) , file(xxreal_2, rc4_xxreal_2)).
thf(rc5_nat_1, axiom,  (? [A: $i] :  ( ( (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) ) ) ) ) ) ) ) ) ) ) ) , file(nat_1, rc5_nat_1)).
thf(rc5_ordinal1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  (v5_ordinal1 @ B) ) ) ) ) ) , file(ordinal1, rc5_ordinal1)).
thf(rc5_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_zfmisc_1 @ B) ) ) ) ) ) , file(subset_1, rc5_subset_1)).
thf(rc5_xcmplx_0, axiom,  (? [A: $i] :  ( ~ ( (v8_ordinal1 @ A) )  &  (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, rc5_xcmplx_0)).
thf(rc5_xreal_0, axiom,  (? [A: $i] :  ( (v8_ordinal1 @ A)  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc5_xreal_0)).
thf(rc5_xxreal_0, axiom,  (? [A: $i] :  ( (v8_ordinal1 @ A)  &  (v1_xxreal_0 @ A) ) ) , file(xxreal_0, rc5_xxreal_0)).
thf(rc5_xxreal_2, axiom,  (? [A: $i] :  ( (v2_membered @ A)  &  ( (v1_xxreal_2 @ A)  &  ( (v2_xxreal_2 @ A)  &  (v6_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, rc5_xxreal_2)).
thf(rc6_finseq_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (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) ) ) ) ) ) ) ) ) ) ) ) , file(finseq_1, rc6_finseq_1)).
thf(rc6_finset_1, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( ( (v5_relat_1 @ C)  @ B)  &  ( (v1_funct_1 @ C)  &  (v1_finset_1 @ C) ) ) ) ) ) ) , file(finset_1, rc6_finset_1)).
thf(rc6_ordinal1, axiom,  (? [A: $i] :  (v7_ordinal1 @ A) ) , file(ordinal1, rc6_ordinal1)).
thf(rc6_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_zfmisc_1 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( (v1_zfmisc_1 @ B) ) ) ) ) ) , file(subset_1, rc6_subset_1)).
thf(rc6_valued_0, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  (v4_valued_0 @ B) ) ) ) ) ) ) , file(valued_0, rc6_valued_0)).
thf(rc6_xxreal_2, axiom,  (? [A: $i] :  ( (v2_membered @ A)  &  ( ~ ( (v1_xxreal_2 @ A) )  &  ( (v2_xxreal_2 @ A)  &  (v6_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, rc6_xxreal_2)).
thf(rc7_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (? [B: $i] :  ( (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) ) ) ) ) ) ) ) ) ) , file(finseq_1, rc7_finseq_1)).
thf(rc7_finset_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  (? [C: $i] :  ( ~ ( (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) ) ) ) ) ) ) ) ) , file(finset_1, rc7_finset_1)).
thf(rc7_ordinal1, axiom,  (? [A: $i] :  (v7_ordinal1 @ A) ) , file(ordinal1, rc7_ordinal1)).
thf(rc7_xxreal_2, axiom,  (? [A: $i] :  ( (v2_membered @ A)  &  ( (v1_xxreal_2 @ A)  &  ( ~ ( (v2_xxreal_2 @ A) )  &  (v6_xxreal_2 @ A) ) ) ) ) , file(xxreal_2, rc7_xxreal_2)).
thf(rc8_finseq_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v3_finseq_1 @ A) ) ) , file(finseq_1, rc8_finseq_1)).
thf(rc8_finset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_zfmisc_1 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( ~ ( (v1_zfmisc_1 @ B) )  &  (v1_finset_1 @ B) ) ) ) ) ) , file(finset_1, rc8_finset_1)).
thf(rc8_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v7_ordinal1 @ A) ) ) , file(ordinal1, rc8_ordinal1)).
thf(rc8_xxreal_2, axiom,  (? [A: $i] :  ( (v2_membered @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xxreal_2 @ A) )  &  ( ~ ( (v2_xxreal_2 @ A) )  &  (v6_xxreal_2 @ A) ) ) ) ) ) , file(xxreal_2, rc8_xxreal_2)).
thf(rc9_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (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) ) ) ) ) ) ) ) ) , file(finseq_1, rc9_finseq_1)).
thf(rc9_finset_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_finset_1 @ A)  &  (v5_finset_1 @ A) ) ) ) , file(finset_1, rc9_finset_1)).
thf(rc9_ordinal1, axiom,  (? [A: $i] :  (v8_ordinal1 @ A) ) , file(ordinal1, rc9_ordinal1)).
thf(redefinition_k12_supinf_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_valued_0 @ A) ) )  =>  ( ( (k12_supinf_2 @ A)  @ B)  =  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(supinf_2, k12_supinf_2)).
thf(redefinition_k1_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( (m1_subset_1 @ B)  @ k4_ordinal1) )  =>  ( ( (k1_nat_1 @ A)  @ B)  =  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(nat_1, k1_nat_1)).
thf(redefinition_k1_relset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  ( ( (k1_relset_1 @ A)  @ B)  =  (k9_xtuple_0 @ B) ) ) ) , file(relset_1, k1_relset_1)).
thf(redefinition_k1_supinf_2, axiom,  (k1_supinf_2 = k5_ordinal1) , file(supinf_2, k1_supinf_2)).
thf(redefinition_k2_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (k2_finseq_1 @ A)  =  (k1_finseq_1 @ A) ) ) ) , file(finseq_1, k2_finseq_1)).
thf(redefinition_k3_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (k3_finseq_1 @ A)  =  (k1_card_1 @ A) ) ) ) , file(finseq_1, k3_finseq_1)).
thf(redefinition_k3_supinf_2, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k6_numbers)  &  ( (m1_subset_1 @ B)  @ k6_numbers) )  =>  ( ( (k3_supinf_2 @ A)  @ B)  =  ( (k1_xxreal_3 @ A)  @ B) ) ) ) , file(supinf_2, k3_supinf_2)).
thf(redefinition_k5_numbers, axiom,  (k5_numbers = k5_ordinal1) , file(numbers, k5_numbers)).
thf(redefinition_k8_nat_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ k4_ordinal1)  @ A)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ A) ) ) ) )  &  (v7_ordinal1 @ C) )  =>  ( ( ( (k8_nat_1 @ A)  @ B)  @ C)  =  ( (k1_funct_1 @ B)  @ C) ) ) ) , file(nat_1, k8_nat_1)).
thf(redefinition_m2_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m2_finseq_1 @ B)  @ A)  <=>  ( (m1_finseq_1 @ B)  @ A) ) ) ) , file(finseq_1, m2_finseq_1)).
thf(redefinition_r2_tarski, axiom,  (! [A: $i, B: $i] :  ( ( (r2_tarski @ A)  @ B)  <=>  ( (r2_hidden @ A)  @ B) ) ) , file(tarski, r2_tarski)).
thf(reflexivity_r1_tarski, axiom,  (! [A: $i, B: $i] :  ( (r1_tarski @ A)  @ A) ) , file(tarski, r1_tarski)).
thf(reflexivity_r1_xxreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v1_xxreal_0 @ B) )  =>  ( (r1_xxreal_0 @ A)  @ A) ) ) , file(xxreal_0, r1_xxreal_0)).
thf(rqLessOrEqual__r1_xxreal_0__r0_r0, axiom,  ( (r1_xxreal_0 @ np__0)  @ np__0) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_r0)).
thf(rqLessOrEqual__r1_xxreal_0__r0_r1, axiom,  ( (r1_xxreal_0 @ np__0)  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r0, axiom,  ~ ( ( (r1_xxreal_0 @ np__1)  @ np__0) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r0)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r1, axiom,  ( (r1_xxreal_0 @ np__1)  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r1)).
thf(rqRealAdd__k2_xcmplx_0__r0_r0_r0, axiom,  ( ( (k2_xcmplx_0 @ np__0)  @ np__0)  = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r0_r0)).
thf(rqRealAdd__k2_xcmplx_0__r0_r1_r1, axiom,  ( ( (k2_xcmplx_0 @ np__0)  @ np__1)  = np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r1_r1)).
thf(rqRealAdd__k2_xcmplx_0__r1_r0_r1, axiom,  ( ( (k2_xcmplx_0 @ np__1)  @ np__0)  = np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r0_r1)).
thf(spc0_boole, axiom,  (v1_xboole_0 @ np__0) , file(boole, spc0_boole)).
thf(spc0_numerals, axiom,  ( (m1_subset_1 @ np__0)  @ k4_ordinal1) , file(numerals, spc0_numerals)).
thf(spc1_boole, axiom,  ~ ( (v1_xboole_0 @ np__1) ) , file(boole, spc1_boole)).
thf(spc1_numerals, axiom,  ( (v2_xxreal_0 @ np__1)  &  ( (m1_subset_1 @ np__1)  @ k4_ordinal1) ) , file(numerals, spc1_numerals)).
thf(spc6_arithm, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_xcmplx_0 @ A)  &  ( (v1_xcmplx_0 @ B)  &  (v1_xcmplx_0 @ C) ) )  =>  ( ( (k2_xcmplx_0 @  ( (k2_xcmplx_0 @ A)  @ B) )  @ C)  =  ( (k2_xcmplx_0 @ A)  @  ( (k2_xcmplx_0 @ B)  @ C) ) ) ) ) , file(arithm, spc6_arithm)).
thf(t11_nat_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  ( (r1_xxreal_0 @ A)  @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) ) ) , file(nat_1, t11_nat_1)).
thf(t13_nat_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  ( ~ ( ( (r1_xxreal_0 @  ( (k1_nat_1 @ B)  @ np__1) )  @ A) )  <=>  ( (r1_xxreal_0 @ A)  @ B) ) ) ) ) ) , file(nat_1, t13_nat_1)).
thf(t1_arithm, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( ( (k2_xcmplx_0 @ A)  @ k5_numbers)  = A) ) ) , file(arithm, t1_arithm)).
thf(t1_numerals, axiom,  ( (m1_subset_1 @ k1_xboole_0)  @ k4_ordinal1) , file(numerals, t1_numerals)).
thf(t1_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( ( (r1_xxreal_0 @ A)  @ B)  &  (v2_xxreal_0 @ A) )  =>  (v2_xxreal_0 @ B) ) ) ) ) ) , file(real, t1_real)).
thf(t1_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (r2_tarski @ A)  @ B)  =>  ( (m1_subset_1 @ A)  @ B) ) ) ) , file(subset, t1_subset)).
thf(t2_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( ( (r1_xxreal_0 @ A)  @ B)  &  (v3_xxreal_0 @ B) )  =>  (v3_xxreal_0 @ A) ) ) ) ) ) , file(real, t2_real)).
thf(t2_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ A)  @ B)  =>  ( (v1_xboole_0 @ B)  |  ( (r2_tarski @ A)  @ B) ) ) ) ) , file(subset, t2_subset)).
thf(t3_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ( (r1_xxreal_0 @ A)  @ B)  &  ( ~ ( (v3_xxreal_0 @ A) )  &  (v3_xxreal_0 @ B) ) ) ) ) ) ) ) , file(real, t3_real)).
thf(t3_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ B) )  <=>  ( (r1_tarski @ A)  @ B) ) ) ) , file(subset, t3_subset)).
thf(t4_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ( (r1_xxreal_0 @ A)  @ B)  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v2_xxreal_0 @ A) ) ) ) ) ) ) ) , file(real, t4_real)).
thf(t4_subset, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( ( (r2_tarski @ A)  @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ C) ) )  =>  ( (m1_subset_1 @ A)  @ C) ) ) ) ) , file(subset, t4_subset)).
thf(t5_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (r1_xxreal_0 @ A)  @ B)  =>  ( (v8_ordinal1 @ B)  |  ( (v3_xxreal_0 @ A)  |  (v2_xxreal_0 @ B) ) ) ) ) ) ) ) , file(real, t5_real)).
thf(t5_subset, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ~ ( ( ( (r2_tarski @ A)  @ B)  &  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ C) )  &  (v1_xboole_0 @ C) ) ) ) ) ) ) , file(subset, t5_subset)).
thf(t6_boole, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (A = k1_xboole_0) ) ) , file(boole, t6_boole)).
thf(t6_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (r1_xxreal_0 @ A)  @ B)  =>  ( (v8_ordinal1 @ A)  |  ( (v2_xxreal_0 @ B)  |  (v3_xxreal_0 @ A) ) ) ) ) ) ) ) , file(real, t6_real)).
thf(t7_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( ( (r2_tarski @ A)  @ B)  &  (v1_xboole_0 @ B) ) ) ) ) , file(boole, t7_boole)).
thf(t7_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ~ ( ( (r1_xxreal_0 @ A)  @ B) )  &  ( ~ ( (v2_xxreal_0 @ A) )  &  ~ ( (v3_xxreal_0 @ B) ) ) ) ) ) ) ) ) , file(real, t7_real)).
thf(t8_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( (v1_xboole_0 @ A)  &  ( ~ ( (A = B) )  &  (v1_xboole_0 @ B) ) ) ) ) ) , file(boole, t8_boole)).
thf(t8_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ~ ( ( (r1_xxreal_0 @ A)  @ B) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  ~ ( (v2_xxreal_0 @ A) ) ) ) ) ) ) ) ) , file(real, t8_real)).
thf(s2_nat_1, axiom,  (! [A: $i > $o] :  ( ( (A @ k5_numbers)  &  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  ( (A @ B)  =>  (A @  ( (k1_nat_1 @ B)  @ np__1) ) ) ) ) )  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  (A @ B) ) ) ) ) , file(nat_1, s2_nat_1)).
thf(t53_mesfunc5, conjecture,  (! [A: $i] :  ( ( (m2_finseq_1 @ A)  @ k6_numbers)  =>  ( (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  ( ( (r2_tarski @ B)  @  ( (k1_relset_1 @ k4_ordinal1)  @ A) )  =>  ( (r1_xxreal_0 @ k5_numbers)  @  ( (k12_supinf_2 @ A)  @ B) ) ) ) )  =>  ( (r1_xxreal_0 @ k5_numbers)  @  (k4_extreal1 @ A) ) ) ) ) , file(mesfunc5, t53_mesfunc5)).