% Mizar problem: s2_scmpds_8,scmpds_8,581,12 
include('Axioms/SET010^0.ax').
thf(n0_type, type, np__0: $i).
thf(n1_type, type, np__1: $i).
thf(n2_type, type, np__2: $i).
thf(n3_type, type, np__3: $i).
thf(f1_s2_scmpds_8_type, type, f1_s2_scmpds_8: $i > $i).
thf(f2_s2_scmpds_8_type, type, f2_s2_scmpds_8: $i).
thf(f3_s2_scmpds_8_type, type, f3_s2_scmpds_8: $i).
thf(f4_s2_scmpds_8_type, type, f4_s2_scmpds_8: $i).
thf(f5_s2_scmpds_8_type, type, f5_s2_scmpds_8: $i).
thf(f6_s2_scmpds_8_type, type, f6_s2_scmpds_8: $i).
thf(g1_extpro_1_type, type, g1_extpro_1: $i > $i > $i > $i > $i > $i > $i > $i).
thf(k10_compos_1_type, type, k10_compos_1: $i > $i > $i).
thf(k10_xtuple_0_type, type, k10_xtuple_0: $i > $i).
thf(k16_funcop_1_type, type, k16_funcop_1: $i > $i > $i).
thf(k17_scmpds_2_type, type, k17_scmpds_2: $i > $i > $i).
thf(k1_card_1_type, type, k1_card_1: $i > $i).
thf(k1_funct_1_type, type, k1_funct_1: $i > $i > $i).
thf(k1_funct_2_type, type, k1_funct_2: $i > $i > $i).
thf(k1_funct_4_type, type, k1_funct_4: $i > $i > $i).
thf(k1_nat_1_type, type, k1_nat_1: $i > $i > $i).
thf(k1_numbers_type, type, k1_numbers: $i).
thf(k1_ordinal1_type, type, k1_ordinal1: $i > $i).
thf(k1_ordinal4_type, type, k1_ordinal4: $i > $i > $i).
thf(k1_scmpds_2_type, type, k1_scmpds_2: $i).
thf(k1_scmpds_8_type, type, k1_scmpds_8: $i > $i > $i > $i).
thf(k1_tarski_type, type, k1_tarski: $i > $i).
thf(k1_xboole_0_type, type, k1_xboole_0: $i).
thf(k1_zfmisc_1_type, type, k1_zfmisc_1: $i > $i).
thf(k2_compos_1_type, type, k2_compos_1: $i > $i).
thf(k2_extpro_1_type, type, k2_extpro_1: $i > $i > $i > $i > $i).
thf(k2_funcop_1_type, type, k2_funcop_1: $i > $i > $i).
thf(k2_memstr_0_type, type, k2_memstr_0: $i > $i > $i).
thf(k2_nat_1_type, type, k2_nat_1: $i > $i > $i).
thf(k2_scmpds_2_type, type, k2_scmpds_2: $i > $i > $i).
thf(k2_scmpds_4_type, type, k2_scmpds_4: $i > $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_afinsq_1_type, type, k3_afinsq_1: $i > $i).
thf(k3_compos_1_type, type, k3_compos_1: $i > $i > $i > $i).
thf(k3_extpro_1_type, type, k3_extpro_1: $i > $i > $i > $i > $i).
thf(k3_funct_2_type, type, k3_funct_2: $i > $i > $i > $i > $i).
thf(k3_numbers_type, type, k3_numbers: $i).
thf(k3_relat_1_type, type, k3_relat_1: $i > $i > $i).
thf(k3_scmpds_2_type, type, k3_scmpds_2: $i > $i).
thf(k3_scmpds_4_type, type, k3_scmpds_4: $i > $i > $i).
thf(k3_xcmplx_0_type, type, k3_xcmplx_0: $i > $i > $i).
thf(k4_card_1_type, type, k4_card_1: $i > $i).
thf(k4_card_3_type, type, k4_card_3: $i > $i).
thf(k4_compos_1_type, type, k4_compos_1: $i > $i).
thf(k4_extpro_1_type, type, k4_extpro_1: $i > $i > $i > $i > $i).
thf(k4_numbers_type, type, k4_numbers: $i).
thf(k4_ordinal1_type, type, k4_ordinal1: $i).
thf(k4_struct_0_type, type, k4_struct_0: $i > $i).
thf(k4_xcmplx_0_type, type, k4_xcmplx_0: $i > $i).
thf(k5_card_1_type, type, k5_card_1: $i > $i).
thf(k5_extpro_1_type, type, k5_extpro_1: $i > $i > $i > $i > $i > $i).
thf(k5_memstr_0_type, type, k5_memstr_0: $i > $i > $i > $i).
thf(k5_numbers_type, type, k5_numbers: $i).
thf(k5_relat_1_type, type, k5_relat_1: $i > $i > $i).
thf(k61_valued_1_type, type, k61_valued_1: $i > $i > $i).
thf(k6_compos_0_type, type, k6_compos_0: $i > $i).
thf(k6_extpro_1_type, type, k6_extpro_1: $i > $i > $i > $i > $i).
thf(k6_memstr_0_type, type, k6_memstr_0: $i > $i > $i > $i).
thf(k6_numbers_type, type, k6_numbers: $i).
thf(k6_scmpds_4_type, type, k6_scmpds_4: $i > $i > $i > $i).
thf(k6_xcmplx_0_type, type, k6_xcmplx_0: $i > $i > $i).
thf(k7_funcop_1_type, type, k7_funcop_1: $i > $i > $i).
thf(k7_memstr_0_type, type, k7_memstr_0: $i > $i > $i > $i).
thf(k7_partfun1_type, type, k7_partfun1: $i > $i > $i > $i).
thf(k8_extpro_1_type, type, k8_extpro_1: $i > $i > $i > $i > $i).
thf(k8_memstr_0_type, type, k8_memstr_0: $i > $i > $i > $i).
thf(k8_struct_0_type, type, k8_struct_0: $i > $i).
thf(k9_scmpds_2_type, type, k9_scmpds_2: $i > $i > $i > $i).
thf(k9_xtuple_0_type, type, k9_xtuple_0: $i > $i).
thf(u1_compos_1_type, type, u1_compos_1: $i > $i).
thf(u1_extpro_1_type, type, u1_extpro_1: $i > $i > $i).
thf(u1_memstr_0_type, type, u1_memstr_0: $i > $i > $i).
thf(u1_struct_0_type, type, u1_struct_0: $i > $i).
thf(u2_memstr_0_type, type, u2_memstr_0: $i > $i > $i).
thf(u2_struct_0_type, type, u2_struct_0: $i > $i).
thf(l1_compos_1_type, type, l1_compos_1: $i > $o).
thf(l1_extpro_1_type, type, l1_extpro_1: $i > $i > $o).
thf(l1_memstr_0_type, type, l1_memstr_0: $i > $i > $o).
thf(l1_struct_0_type, type, l1_struct_0: $i > $o).
thf(l2_struct_0_type, type, l2_struct_0: $i > $o).
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(m2_subset_1_type, type, m2_subset_1: $i > $i > $i > $o).
thf(p1_s2_scmpds_8_type, type, p1_s2_scmpds_8: $i > $o).
thf(r1_extpro_1_type, type, r1_extpro_1: $i > $i > $i > $i > $o).
thf(r1_scmpds_6_type, type, r1_scmpds_6: $i > $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_scmpds_6_type, type, r2_scmpds_6: $i > $i > $i > $o).
thf(v1_afinsq_1_type, type, v1_afinsq_1: $i > $o).
thf(v1_ami_2_type, type, v1_ami_2: $i > $o).
thf(v1_card_1_type, type, v1_card_1: $i > $o).
thf(v1_card_3_type, type, v1_card_3: $i > $o).
thf(v1_compos_0_type, type, v1_compos_0: $i > $o).
thf(v1_extpro_1_type, type, v1_extpro_1: $i > $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_scmpds_4_type, type, v1_scmpds_4: $i > $o).
thf(v1_scmpds_5_type, type, v1_scmpds_5: $i > $o).
thf(v1_setfam_1_type, type, v1_setfam_1: $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_zfmisc_1_type, type, v1_zfmisc_1: $i > $o).
thf(v2_card_3_type, type, v2_card_3: $i > $o).
thf(v2_compos_0_type, type, v2_compos_0: $i > $o).
thf(v2_compos_1_type, type, v2_compos_1: $i > $i > $o).
thf(v2_extpro_1_type, type, v2_extpro_1: $i > $i > $i > $o).
thf(v2_funct_1_type, type, v2_funct_1: $i > $o).
thf(v2_membered_type, type, v2_membered: $i > $o).
thf(v2_memstr_0_type, type, v2_memstr_0: $i > $i > $o).
thf(v2_ordinal1_type, type, v2_ordinal1: $i > $o).
thf(v2_relat_1_type, type, v2_relat_1: $i > $o).
thf(v2_scmpds_4_type, type, v2_scmpds_4: $i > $o).
thf(v2_setfam_1_type, type, v2_setfam_1: $i > $o).
thf(v2_struct_0_type, type, v2_struct_0: $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(v3_card_1_type, type, v3_card_1: $i > $i > $o).
thf(v3_card_3_type, type, v3_card_3: $i > $o).
thf(v3_compos_0_type, type, v3_compos_0: $i > $o).
thf(v3_compos_1_type, type, v3_compos_1: $i > $i > $o).
thf(v3_extpro_1_type, type, v3_extpro_1: $i > $i > $o).
thf(v3_funct_1_type, type, v3_funct_1: $i > $o).
thf(v3_membered_type, type, v3_membered: $i > $o).
thf(v3_memstr_0_type, type, v3_memstr_0: $i > $i > $o).
thf(v3_ordinal1_type, type, v3_ordinal1: $i > $o).
thf(v3_relat_1_type, type, v3_relat_1: $i > $o).
thf(v3_scmpds_4_type, type, v3_scmpds_4: $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(v4_card_3_type, type, v4_card_3: $i > $o).
thf(v4_compos_0_type, type, v4_compos_0: $i > $i > $o).
thf(v4_compos_1_type, type, v4_compos_1: $i > $i > $o).
thf(v4_funct_1_type, type, v4_funct_1: $i > $o).
thf(v4_membered_type, type, v4_membered: $i > $o).
thf(v4_memstr_0_type, type, v4_memstr_0: $i > $i > $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(v5_card_3_type, type, v5_card_3: $i > $o).
thf(v5_compos_0_type, type, v5_compos_0: $i > $o).
thf(v5_funct_1_type, type, v5_funct_1: $i > $i > $o).
thf(v5_membered_type, type, v5_membered: $i > $o).
thf(v5_memstr_0_type, type, v5_memstr_0: $i > $i > $i > $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(v6_compos_0_type, type, v6_compos_0: $i > $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(v7_ordinal1_type, type, v7_ordinal1: $i > $o).
thf(v7_valued_0_type, type, v7_valued_0: $i > $o).
thf(v8_valued_0_type, type, v8_valued_0: $i > $o).
thf(abstractness_v1_extpro_1, axiom,  (! [A: $i, B: $i] :  ( ( (l1_extpro_1 @ B)  @ A)  =>  ( ( (v1_extpro_1 @ B)  @ A)  =>  ( (= @ B)  @  ( ( ( ( ( ( (g1_extpro_1 @ A)  @  (u1_struct_0 @ B) )  @  (u2_struct_0 @ B) )  @  (u1_compos_1 @ B) )  @  ( (u1_memstr_0 @ A)  @ B) )  @  ( (u2_memstr_0 @ A)  @ B) )  @  ( (u1_extpro_1 @ A)  @ B) ) ) ) ) ) , file(extpro_1, v1_extpro_1)).
thf(antisymmetry_r2_hidden, axiom,  (! [A: $i, B: $i] :  ( ( (r2_hidden @ A)  @ B)  =>  ~ ( ( (r2_hidden @ B)  @ A) ) ) ) , file(hidden, r2_hidden)).
thf(cc10_card_3, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) ) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k4_card_3 @ B) )  =>  ( (v4_relat_1 @ C)  @ A) ) ) ) ) , file(card_3, cc10_card_3)).
thf(cc10_funct_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( (v1_funct_1 @ C)  &  ( (v5_funct_1 @ C)  @ B) ) )  =>  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  (v1_funct_1 @ C) ) ) ) ) ) ) , file(funct_1, cc10_funct_1)).
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(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(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(cc13_card_3, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k4_card_3 @ B) )  =>  ( (v1_partfun1 @ C)  @ A) ) ) ) ) , file(card_3, cc13_card_3)).
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(cc14_card_3, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k4_card_3 @ B) )  =>  ( (v1_partfun1 @ C)  @ A) ) ) ) ) , file(card_3, cc14_card_3)).
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(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(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(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(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_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_afinsq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_xboole_0 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_ordinal1 @ A)  &  (v1_funct_1 @ A) ) ) ) ) , file(afinsq_1, cc1_afinsq_1)).
thf(cc1_ami_3, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v7_ordinal1 @ A) )  =>  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v7_ordinal1 @ A)  &  ~ ( (v1_setfam_1 @ A) ) ) ) ) ) , file(ami_3, cc1_ami_3)).
thf(cc1_card_3, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_card_3 @ A) ) ) ) ) , file(card_3, cc1_card_3)).
thf(cc1_compos_0, axiom,  (! [A: $i] :  ( (v1_compos_0 @ A)  =>  (v1_relat_1 @ A) ) ) , file(compos_0, cc1_compos_0)).
thf(cc1_compos_1, axiom,  (! [A: $i] :  ( (l1_compos_1 @ A)  =>  (! [B: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_zfmisc_1 @ B)  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @ B)  &  (v1_finset_1 @ B) ) ) ) ) ) )  =>  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v4_compos_1 @ B)  @ A) ) ) ) ) ) ) ) ) ) ) , file(compos_1, cc1_compos_1)).
thf(cc1_funct_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_funct_1 @ A) ) ) , file(funct_1, cc1_funct_1)).
thf(cc1_funct_2, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v1_partfun1 @ C)  @ A)  =>  ( ( (v1_funct_2 @ C)  @ A)  @ B) ) ) ) ) , file(funct_2, cc1_funct_2)).
thf(cc1_grfunc_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) ) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( (v1_funct_1 @ C)  &  ( (v5_funct_1 @ C)  @ B) ) )  =>  ( (v1_relat_1 @ C)  &  ( (v1_funct_1 @ C)  &  ( (v5_funct_1 @ C)  @ A) ) ) ) ) ) ) , file(grfunc_1, cc1_grfunc_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_memstr_0, axiom,  (! [A: $i] :  ( ~ ( (v1_setfam_1 @ A) )  =>  ~ ( (v1_xboole_0 @ A) ) ) ) , file(memstr_0, cc1_memstr_0)).
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_pboole, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) )  =>  ( (v1_relat_1 @ B)  &  ( ~ ( (v3_relat_1 @ B) )  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) ) ) ) , file(pboole, cc1_pboole)).
thf(cc1_relat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_relat_1 @ A) ) ) , file(relat_1, cc1_relat_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_scmpds_4, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( ( (v5_relat_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  ( (v1_afinsq_1 @ A)  &  (v2_scmpds_4 @ A) ) ) ) ) ) ) )  =>  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( ( (v5_relat_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  ( (v1_afinsq_1 @ A)  &  (v1_scmpds_4 @ A) ) ) ) ) ) ) ) ) ) , file(scmpds_4, cc1_scmpds_4)).
thf(cc1_setfam_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_setfam_1 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) , file(setfam_1, cc1_setfam_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_xreal_0, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (v1_xreal_0 @ A) ) ) , file(xreal_0, cc1_xreal_0)).
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_zfmisc_1 @ A)  &  ( (v1_relat_1 @ A)  &  ( (v1_funct_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(cc2_afinsq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v5_ordinal1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v3_card_1 @ B)  @ A) ) ) ) )  =>  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v5_ordinal1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finset_1 @ B) ) ) ) ) ) ) ) ) , file(afinsq_1, cc2_afinsq_1)).
thf(cc2_card_3, axiom,  (! [A: $i, B: $i] :  ( (v1_setfam_1 @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v1_funct_1 @ C)  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) )  =>  ( (v2_relat_1 @ C)  &  ( (v1_funct_1 @ C)  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) ) ) ) ) ) ) ) , file(card_3, cc2_card_3)).
thf(cc2_compos_0, axiom,  (! [A: $i] :  ( (v5_compos_0 @ A)  =>  ~ ( (v1_xboole_0 @ A) ) ) ) , file(compos_0, cc2_compos_0)).
thf(cc2_compos_1, axiom,  (! [A: $i] :  ( (l1_compos_1 @ A)  =>  (! [B: $i] :  ( ( (v1_xboole_0 @ B)  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @ B)  &  (v1_finset_1 @ B) ) ) ) ) )  =>  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v2_compos_1 @ B)  @ A) ) ) ) ) ) ) ) ) ) , file(compos_1, cc2_compos_1)).
thf(cc2_funct_1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_funct_1 @ A) ) ) ) ) , file(funct_1, cc2_funct_1)).
thf(cc2_funct_2, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  =>  ( (v1_partfun1 @ C)  @ A) ) ) ) ) ) , file(funct_2, cc2_funct_2)).
thf(cc2_grfunc_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v5_funct_1 @ B)  @ A) ) ) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @ B) )  =>  ( (v5_funct_1 @ C)  @ A) ) ) ) ) , file(grfunc_1, cc2_grfunc_1)).
thf(cc2_int_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_int_1 @ A) ) ) , file(int_1, cc2_int_1)).
thf(cc2_memstr_0, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( (l1_memstr_0 @ B)  @ A) )  =>  (! [C: $i] :  ( ( (v1_xboole_0 @ C)  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( (v5_funct_1 @ C)  @  ( (k2_memstr_0 @ A)  @ B) ) ) ) ) )  =>  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( (v5_funct_1 @ C)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( ( (v4_memstr_0 @ C)  @ A)  @ B) ) ) ) ) ) ) ) ) , file(memstr_0, cc2_memstr_0)).
thf(cc2_nat_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  =>  ~ ( (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_pboole, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v3_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) )  =>  ( (v1_relat_1 @ B)  &  ( ~ ( (v2_relat_1 @ B) )  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) ) ) ) , file(pboole, cc2_pboole)).
thf(cc2_relat_1, axiom,  (! [A: $i] :  ( (v1_relat_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_relat_1 @ B) ) ) ) ) , file(relat_1, cc2_relat_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_setfam_1, axiom,  (! [A: $i] :  ( ~ ( (v2_setfam_1 @ A) )  =>  ~ ( (v1_xboole_0 @ A) ) ) ) , file(setfam_1, cc2_setfam_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(cc30_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k1_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc30_valued_0)).
thf(cc31_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k5_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, cc31_valued_0)).
thf(cc3_afinsq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v5_ordinal1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v3_card_1 @ B)  @ A) ) ) ) ) )  =>  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v5_ordinal1 @ B)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  ( (v1_finset_1 @ B)  &  ( (v3_card_1 @ B)  @ A) ) ) ) ) ) ) ) ) ) ) , file(afinsq_1, cc3_afinsq_1)).
thf(cc3_card_3, axiom,  (! [A: $i] :  ( (v3_card_3 @ A)  =>  ( (v4_funct_1 @ A)  &  (v2_card_3 @ A) ) ) ) , file(card_3, cc3_card_3)).
thf(cc3_compos_1, axiom,  (! [A: $i] :  ( (l1_compos_1 @ A)  =>  (! [B: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v2_compos_1 @ B)  @ A) ) ) ) ) ) )  =>  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v4_compos_1 @ B)  @ A) ) ) ) ) ) ) ) ) ) ) , file(compos_1, cc3_compos_1)).
thf(cc3_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_funct_1 @ B) ) ) ) ) , file(funct_1, cc3_funct_1)).
thf(cc3_funct_2, axiom,  (! [A: $i, B: $i] :  ( ~ ( (v1_xboole_0 @ B) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  =>  ( (v1_partfun1 @ C)  @ A) ) ) ) ) ) , file(funct_2, cc3_funct_2)).
thf(cc3_int_1, axiom,  (! [A: $i] :  ( (v1_int_1 @ A)  =>  (v1_xreal_0 @ A) ) ) , file(int_1, cc3_int_1)).
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_relat_1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v3_relat_1 @ A) ) ) ) , file(relat_1, cc3_relat_1)).
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_setfam_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_setfam_1 @ A) )  =>  ~ ( (v2_setfam_1 @ A) ) ) ) , file(setfam_1, cc3_setfam_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) )  =>  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc3_xxreal_0)).
thf(cc4_afinsq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k1_numbers)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k1_numbers)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  (v3_valued_0 @ A) ) ) ) ) ) ) ) , file(afinsq_1, cc4_afinsq_1)).
thf(cc4_card_3, axiom,  (! [A: $i] :  ( (v5_card_3 @ A)  =>  ( ~ ( (v1_finset_1 @ A) )  &  (v4_card_3 @ A) ) ) ) , file(card_3, cc4_card_3)).
thf(cc4_funct_1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_funct_1 @ A) ) ) ) ) , file(funct_1, cc4_funct_1)).
thf(cc4_funct_2, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) )  =>  ( ( ( (v1_funct_2 @ B)  @ A)  @ A)  =>  ( (v1_partfun1 @ B)  @ A) ) ) ) ) , file(funct_2, cc4_funct_2)).
thf(cc4_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v5_ordinal1 @ A) ) ) , file(ordinal1, cc4_ordinal1)).
thf(cc4_pboole, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) )  =>  ( (v1_relat_1 @ B)  &  ( ~ ( (v3_relat_1 @ B) )  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) ) ) ) , file(pboole, cc4_pboole)).
thf(cc4_relat_1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v2_relat_1 @ A) ) ) ) , file(relat_1, cc4_relat_1)).
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_setfam_1, axiom,  (! [A: $i] :  ( ~ ( (v1_zfmisc_1 @ A) )  =>  ~ ( (v2_setfam_1 @ A) ) ) ) , file(setfam_1, cc4_setfam_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] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) ) )  =>  ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) ) ) ) , file(xxreal_0, cc4_xxreal_0)).
thf(cc5_afinsq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k5_numbers)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k5_numbers)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  (v4_valued_0 @ A) ) ) ) ) ) ) ) , file(afinsq_1, cc5_afinsq_1)).
thf(cc5_card_3, axiom,  (! [A: $i] :  ( ( ~ ( (v1_finset_1 @ A) )  &  (v4_card_3 @ A) )  =>  (v5_card_3 @ A) ) ) , file(card_3, cc5_card_3)).
thf(cc5_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ~ ( (v3_funct_1 @ A) ) ) )  =>  ( ~ ( (v1_zfmisc_1 @ A) )  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) ) ) ) , file(funct_1, cc5_funct_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_pboole, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) )  =>  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) ) ) ) , file(pboole, cc5_pboole)).
thf(cc5_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @ B) )  =>  ( (v4_relat_1 @ C)  @ A) ) ) ) ) , file(relat_1, cc5_relat_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) )  =>  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v2_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc5_xxreal_0)).
thf(cc6_afinsq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_xboole_0 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_afinsq_1 @ A) ) ) ) ) , file(afinsq_1, cc6_afinsq_1)).
thf(cc6_card_3, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  (v4_card_3 @ A) ) ) , file(card_3, cc6_card_3)).
thf(cc6_funct_1, axiom,  (! [A: $i] :  ( ( (v1_zfmisc_1 @ A)  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_funct_1 @ A) ) ) ) ) , file(funct_1, cc6_funct_1)).
thf(cc6_ordinal1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc6_ordinal1)).
thf(cc6_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @ B) )  =>  ( (v5_relat_1 @ C)  @ A) ) ) ) ) , file(relat_1, cc6_relat_1)).
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] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v2_xxreal_0 @ A) ) ) )  =>  ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) ) ) ) , file(xxreal_0, cc6_xxreal_0)).
thf(cc7_afinsq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  (v1_afinsq_1 @ A) ) ) ) ) ) ) , file(afinsq_1, cc7_afinsq_1)).
thf(cc7_card_3, axiom,  (! [A: $i] :  ( (v4_card_3 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v4_card_3 @ B) ) ) ) ) , file(card_3, cc7_card_3)).
thf(cc7_funct_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v4_funct_1 @ A) ) ) , file(funct_1, cc7_funct_1)).
thf(cc7_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc7_ordinal1)).
thf(cc7_relat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  ( (v1_xboole_0 @ B)  &  ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) ) ) ) ) ) ) , file(relat_1, cc7_relat_1)).
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] :  ( ( (v1_xboole_0 @ A)  &  (v1_xxreal_0 @ A) )  =>  ( (v1_xxreal_0 @ A)  &  ( ~ ( (v2_xxreal_0 @ A) )  &  ~ ( (v3_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc7_xxreal_0)).
thf(cc8_afinsq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) ) ) ) ) , file(afinsq_1, cc8_afinsq_1)).
thf(cc8_card_3, axiom,  (! [A: $i] :  ( (v2_card_3 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v2_card_3 @ B) ) ) ) ) , file(card_3, cc8_card_3)).
thf(cc8_funct_1, axiom,  (! [A: $i] :  ( (v4_funct_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) ) ) ) ) ) , file(funct_1, cc8_funct_1)).
thf(cc8_funct_2, 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_funct_1 @ C)  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) )  =>  ( (v1_funct_1 @ C)  &  ( ~ ( (v1_xboole_0 @ C) )  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) ) ) ) ) ) ) ) , file(funct_2, cc8_funct_2)).
thf(cc8_ordinal1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc8_ordinal1)).
thf(cc8_relat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) )  =>  ( (v1_xboole_0 @ B)  &  ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) ) ) ) ) ) ) , file(relat_1, cc8_relat_1)).
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) ) ) )  =>  ( (v1_xboole_0 @ A)  &  (v1_xxreal_0 @ A) ) ) ) , file(xxreal_0, cc8_xxreal_0)).
thf(cc9_afinsq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  (v1_afinsq_1 @ A) ) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_ordinal1 @ A)  &  (v1_funct_1 @ A) ) ) ) ) , file(afinsq_1, cc9_afinsq_1)).
thf(cc9_card_3, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k4_card_3 @ A) )  =>  ( (v5_funct_1 @ B)  @ A) ) ) ) ) , file(card_3, cc9_card_3)).
thf(cc9_funct_1, axiom,  (! [A: $i] :  ( (v4_funct_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v4_funct_1 @ B) ) ) ) ) , file(funct_1, cc9_funct_1)).
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_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, cc9_valued_0)).
thf(commutativity_k1_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( (m1_subset_1 @ B)  @ k5_numbers) )  =>  ( (= @  ( (k1_nat_1 @ A)  @ B) )  @  ( (k1_nat_1 @ B)  @ A) ) ) ) , file(nat_1, k1_nat_1)).
thf(commutativity_k2_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k5_numbers)  &  (v7_ordinal1 @ B) )  =>  ( (= @  ( (k2_nat_1 @ A)  @ B) )  @  ( (k2_nat_1 @ B)  @ A) ) ) ) , file(nat_1, k2_nat_1)).
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_xcmplx_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( (= @  ( (k3_xcmplx_0 @ A)  @ B) )  @  ( (k3_xcmplx_0 @ B)  @ A) ) ) ) , file(xcmplx_0, k3_xcmplx_0)).
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(d10_compos_1, axiom,  (! [A: $i] :  ( (l1_compos_1 @ A)  =>  ( (= @  (k2_compos_1 @ A) )  @  (k6_compos_0 @  (u1_compos_1 @ A) ) ) ) ) , file(compos_1, d10_compos_1)).
thf(d10_memstr_0, axiom,  (! [A: $i] :  ( ~ ( (v1_setfam_1 @ A) )  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_memstr_0 @ B)  @ A) ) ) )  =>  (! [C: $i] :  ( (v7_ordinal1 @ C)  =>  ( (= @  ( ( (k7_memstr_0 @ A)  @ B)  @ C) )  @  ( (k16_funcop_1 @  (k4_struct_0 @ B) )  @ C) ) ) ) ) ) ) ) , file(memstr_0, d10_memstr_0)).
thf(d11_memstr_0, axiom,  (! [A: $i] :  ( ~ ( (v1_setfam_1 @ A) )  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_memstr_0 @ B)  @ A) ) ) )  =>  (! [C: $i] :  ( (v7_ordinal1 @ C)  =>  (! [D: $i] :  ( ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ D)  &  ( (v5_funct_1 @ D)  @  ( (k2_memstr_0 @ A)  @ B) ) ) ) )  =>  ( ( ( ( (v5_memstr_0 @ D)  @ A)  @ B)  @ C)  <=>  ( ( (r2_hidden @  (k4_struct_0 @ B) )  @  (k9_xtuple_0 @ D) )  &  ( (= @  ( ( (k5_memstr_0 @ A)  @ B)  @ D) )  @ C) ) ) ) ) ) ) ) ) ) ) , file(memstr_0, d11_memstr_0)).
thf(d12_ordinal1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  <=>  ( (r2_hidden @ A)  @ k4_ordinal1) ) ) , file(ordinal1, d12_ordinal1)).
thf(d13_memstr_0, axiom,  (! [A: $i] :  ( ~ ( (v1_setfam_1 @ A) )  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_memstr_0 @ B)  @ A) ) ) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( (v5_funct_1 @ C)  @  ( (k2_memstr_0 @ A)  @ B) ) ) ) )  =>  ( (= @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) )  @  ( (k1_funct_4 @ C)  @  ( ( (k7_memstr_0 @ A)  @ B)  @ k6_numbers) ) ) ) ) ) ) ) ) , file(memstr_0, d13_memstr_0)).
thf(d15_extpro_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_setfam_1 @ A) ) )  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( ( (v3_extpro_1 @ B)  @ A)  &  ( (l1_extpro_1 @ B)  @ A) ) ) ) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ k5_numbers)  &  ( ( (v5_relat_1 @ C)  @  (u1_compos_1 @ B) )  &  (v1_funct_1 @ C) ) ) )  =>  (! [D: $i] :  ( ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ D)  &  ( ( (v5_funct_1 @ D)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @ D)  @  (u1_struct_0 @ B) ) ) ) ) )  =>  ( ( ( ( (r1_extpro_1 @ A)  @ B)  @ C)  @ D)  =>  (! [E: $i] :  ( ( ( (m2_subset_1 @ E)  @ k1_numbers)  @ k5_numbers)  =>  ( ( (= @ E)  @  ( ( ( (k8_extpro_1 @ A)  @ B)  @ C)  @ D) )  <=>  ( ( (= @  ( ( ( (k3_extpro_1 @ A)  @ B)  @ C)  @  ( ( ( ( (k5_extpro_1 @ A)  @ B)  @ C)  @ D)  @ E) ) )  @  (k2_compos_1 @ B) )  &  (! [F: $i] :  ( ( ( (m2_subset_1 @ F)  @ k1_numbers)  @ k5_numbers)  =>  ( ( (= @  ( ( ( (k3_extpro_1 @ A)  @ B)  @ C)  @  ( ( ( ( (k5_extpro_1 @ A)  @ B)  @ C)  @ D)  @ F) ) )  @  (k2_compos_1 @ B) )  =>  ( (r1_xxreal_0 @ E)  @ F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(extpro_1, d15_extpro_1)).
thf(d16_compos_1, axiom,  (! [A: $i] :  ( (l1_compos_1 @ A)  =>  ( (= @  (k4_compos_1 @ A) )  @  (k3_afinsq_1 @  (k2_compos_1 @ A) ) ) ) ) , file(compos_1, d16_compos_1)).
thf(d24_compos_1, axiom,  (! [A: $i] :  ( (l1_compos_1 @ A)  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  (v1_afinsq_1 @ B) ) ) ) ) )  =>  ( (= @  ( (k10_compos_1 @ A)  @ B) )  @  ( (k1_ordinal4 @ B)  @  (k4_compos_1 @ A) ) ) ) ) ) ) , file(compos_1, d24_compos_1)).
thf(d2_extpro_1, axiom,  (! [A: $i] :  ( ~ ( (v1_setfam_1 @ A) )  =>  (! [B: $i] :  ( ( ( (v2_memstr_0 @ B)  @ A)  &  ( (l1_extpro_1 @ B)  @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_compos_1 @ B) )  =>  (! [D: $i] :  ( ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ D)  &  ( ( (v5_funct_1 @ D)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @ D)  @  (u1_struct_0 @ B) ) ) ) ) )  =>  ( (= @  ( ( ( (k2_extpro_1 @ A)  @ B)  @ C)  @ D) )  @  ( (k1_funct_1 @  ( ( ( (k3_funct_2 @  (u1_compos_1 @ B) )  @  ( (k1_funct_2 @  (k4_card_3 @  ( (k3_relat_1 @  ( (u1_memstr_0 @ A)  @ B) )  @  ( (u2_memstr_0 @ A)  @ B) ) ) )  @  (k4_card_3 @  ( (k3_relat_1 @  ( (u1_memstr_0 @ A)  @ B) )  @  ( (u2_memstr_0 @ A)  @ B) ) ) ) )  @  ( (u1_extpro_1 @ A)  @ B) )  @ C) )  @ D) ) ) ) ) ) ) ) ) ) , file(extpro_1, d2_extpro_1)).
thf(d2_funcop_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( (= @  ( (k2_funcop_1 @ A)  @ B) )  @  ( (k2_zfmisc_1 @ A)  @  (k1_tarski @ B) ) ) ) ) , file(funcop_1, d2_funcop_1)).
thf(d2_memstr_0, axiom,  (! [A: $i] :  ( ~ ( (v1_setfam_1 @ A) )  =>  (! [B: $i] :  ( ( (l1_memstr_0 @ B)  @ A)  =>  ( (= @  ( (k2_memstr_0 @ A)  @ B) )  @  ( (k3_relat_1 @  ( (u1_memstr_0 @ A)  @ B) )  @  ( (u2_memstr_0 @ A)  @ B) ) ) ) ) ) ) , file(memstr_0, d2_memstr_0)).
thf(d2_scmpds_8, axiom,  (! [A: $i] :  ( ( (v1_ami_2 @ A)  &  ( (m1_subset_1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) ) )  =>  (! [B: $i] :  ( (v1_int_1 @ B)  =>  (! [C: $i] :  ( ( ~ ( (v1_xboole_0 @ C) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ k5_numbers)  &  ( ( (v5_relat_1 @ C)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ C)  &  ( (v1_finset_1 @ C)  &  (v1_afinsq_1 @ C) ) ) ) ) ) )  =>  ( (= @  ( ( (k1_scmpds_8 @ A)  @ B)  @ C) )  @  ( (k3_scmpds_4 @  ( (k2_scmpds_4 @  ( ( (k9_scmpds_2 @ A)  @ B)  @  ( (k2_nat_1 @  (k5_card_1 @ C) )  @ np__2) ) )  @ C) )  @  (k3_scmpds_2 @  (k4_xcmplx_0 @  ( (k2_nat_1 @  (k5_card_1 @ C) )  @ np__1) ) ) ) ) ) ) ) ) ) ) , file(scmpds_8, d2_scmpds_8)).
thf(d3_scmpds_6, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( ( (v5_relat_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  (v1_afinsq_1 @ A) ) ) ) ) ) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ B)  &  ( ( (v5_funct_1 @ B)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( (v1_partfun1 @ B)  @  (u1_struct_0 @ k1_scmpds_2) ) ) ) ) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ k5_numbers)  &  ( ( (v5_relat_1 @ C)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ C)  &  ( (v1_partfun1 @ C)  @ k5_numbers) ) ) ) )  =>  ( ( ( (r2_scmpds_6 @ A)  @ B)  @ C)  <=>  ( ( ( (r1_extpro_1 @ np__2)  @ k1_scmpds_2)  @  ( (k1_funct_4 @ C)  @  ( (k10_compos_1 @ k1_scmpds_2)  @ A) ) )  @  ( ( (k8_memstr_0 @ np__2)  @ k1_scmpds_2)  @ B) ) ) ) ) ) ) ) ) , file(scmpds_6, d3_scmpds_6)).
thf(d5_extpro_1, axiom,  (! [A: $i] :  ( ~ ( (v1_setfam_1 @ A) )  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_extpro_1 @ B)  @ A) ) ) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( ( (v5_relat_1 @ C)  @  (u1_compos_1 @ B) )  &  (v1_funct_1 @ C) ) )  =>  (! [D: $i] :  ( ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ D)  &  ( ( (v5_funct_1 @ D)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @ D)  @  (u1_struct_0 @ B) ) ) ) ) )  =>  ( (= @  ( ( ( (k3_extpro_1 @ A)  @ B)  @ C)  @ D) )  @  ( ( (k7_partfun1 @  (u1_compos_1 @ B) )  @ C)  @  ( ( (k5_memstr_0 @ A)  @ B)  @ D) ) ) ) ) ) ) ) ) ) ) , file(extpro_1, d5_extpro_1)).
thf(d5_scmpds_4, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( ( (v5_relat_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  (v1_afinsq_1 @ A) ) ) ) ) ) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ B)  &  ( ( (v5_funct_1 @ B)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( (v1_partfun1 @ B)  @  (u1_struct_0 @ k1_scmpds_2) ) ) ) ) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ k5_numbers)  &  ( ( (v5_relat_1 @ C)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ C)  &  ( (v1_partfun1 @ C)  @ k5_numbers) ) ) ) )  =>  ( (= @  ( ( (k6_scmpds_4 @ A)  @ B)  @ C) )  @  ( ( ( (k6_extpro_1 @ np__2)  @ k1_scmpds_2)  @  ( (k1_funct_4 @ C)  @  ( (k10_compos_1 @ k1_scmpds_2)  @ A) ) )  @ B) ) ) ) ) ) ) ) , file(scmpds_4, d5_scmpds_4)).
thf(d6_extpro_1, axiom,  (! [A: $i] :  ( ~ ( (v1_setfam_1 @ A) )  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_extpro_1 @ B)  @ A) ) ) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( (v5_funct_1 @ C)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @ C)  @  (u1_struct_0 @ B) ) ) ) ) )  =>  (! [D: $i] :  ( ( (v1_relat_1 @ D)  &  ( ( (v5_relat_1 @ D)  @  (u1_compos_1 @ B) )  &  (v1_funct_1 @ D) ) )  =>  ( (= @  ( ( ( (k4_extpro_1 @ A)  @ B)  @ C)  @ D) )  @  ( ( ( (k2_extpro_1 @ A)  @ B)  @  ( ( ( (k3_extpro_1 @ A)  @ B)  @ D)  @ C) )  @ C) ) ) ) ) ) ) ) ) ) , file(extpro_1, d6_extpro_1)).
thf(d7_memstr_0, axiom,  (! [A: $i] :  ( ~ ( (v1_setfam_1 @ A) )  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_memstr_0 @ B)  @ A) ) ) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( (v5_funct_1 @ C)  @  ( (k2_memstr_0 @ A)  @ B) ) ) ) )  =>  ( (= @  ( ( (k5_memstr_0 @ A)  @ B)  @ C) )  @  ( (k1_funct_1 @ C)  @  (k4_struct_0 @ B) ) ) ) ) ) ) ) ) , file(memstr_0, d7_memstr_0)).
thf(d8_memstr_0, axiom,  (! [A: $i] :  ( ~ ( (v1_setfam_1 @ A) )  =>  (! [B: $i] :  ( ( (l1_memstr_0 @ B)  @ A)  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( (v5_funct_1 @ C)  @  ( (k2_memstr_0 @ A)  @ B) ) ) ) )  =>  ( (= @  ( ( (k6_memstr_0 @ A)  @ B)  @ C) )  @  ( (k5_relat_1 @ C)  @  (k8_struct_0 @ B) ) ) ) ) ) ) ) ) , file(memstr_0, d8_memstr_0)).
thf(d9_funcop_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( (= @  ( (k16_funcop_1 @ A)  @ B) )  @  ( (k7_funcop_1 @  (k1_tarski @ A) )  @ B) ) ) ) , file(funcop_1, d9_funcop_1)).
thf(dt_f1_s2_scmpds_8, axiom,  (! [A: $i] :  ( ( (m2_subset_1 @  (f1_s2_scmpds_8 @ A) )  @ k1_numbers)  @ k5_numbers) ) , file(scmpds_8, f1_s2_scmpds_8)).
thf(dt_f2_s2_scmpds_8, axiom,  ( (v1_relat_1 @ f2_s2_scmpds_8)  &  ( ( (v4_relat_1 @ f2_s2_scmpds_8)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ f2_s2_scmpds_8)  &  ( ( (v5_funct_1 @ f2_s2_scmpds_8)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( ( (v1_partfun1 @ f2_s2_scmpds_8)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( ( ( (v5_memstr_0 @ f2_s2_scmpds_8)  @ np__2)  @ k1_scmpds_2)  @ k6_numbers) ) ) ) ) ) , file(scmpds_8, f2_s2_scmpds_8)).
thf(dt_f3_s2_scmpds_8, axiom,  ( (v1_relat_1 @ f3_s2_scmpds_8)  &  ( ( (v4_relat_1 @ f3_s2_scmpds_8)  @ k5_numbers)  &  ( ( (v5_relat_1 @ f3_s2_scmpds_8)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ f3_s2_scmpds_8)  &  ( (v1_partfun1 @ f3_s2_scmpds_8)  @ k5_numbers) ) ) ) ) , file(scmpds_8, f3_s2_scmpds_8)).
thf(dt_f4_s2_scmpds_8, axiom,  ( ~ ( (v1_xboole_0 @ f4_s2_scmpds_8) )  &  ( (v1_relat_1 @ f4_s2_scmpds_8)  &  ( ( (v4_relat_1 @ f4_s2_scmpds_8)  @ k5_numbers)  &  ( ( (v5_relat_1 @ f4_s2_scmpds_8)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ f4_s2_scmpds_8)  &  ( (v1_finset_1 @ f4_s2_scmpds_8)  &  ( (v1_afinsq_1 @ f4_s2_scmpds_8)  &  ( ( (v2_compos_1 @ f4_s2_scmpds_8)  @ k1_scmpds_2)  &  (v3_scmpds_4 @ f4_s2_scmpds_8) ) ) ) ) ) ) ) ) , file(scmpds_8, f4_s2_scmpds_8)).
thf(dt_f5_s2_scmpds_8, axiom,  ( (v1_ami_2 @ f5_s2_scmpds_8)  &  ( (m1_subset_1 @ f5_s2_scmpds_8)  @  (u1_struct_0 @ k1_scmpds_2) ) ) , file(scmpds_8, f5_s2_scmpds_8)).
thf(dt_f6_s2_scmpds_8, axiom,  (v1_int_1 @ f6_s2_scmpds_8) , file(scmpds_8, f6_s2_scmpds_8)).
thf(dt_g1_extpro_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i, G: $i] :  ( ( ( (m1_subset_1 @ C)  @ B)  &  ( ( (v1_compos_0 @ D)  &  ( (v2_compos_0 @ D)  &  ( (v3_compos_0 @ D)  &  (v5_compos_0 @ D) ) ) )  &  ( ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ B)  @ A)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ A) ) ) ) )  &  ( ( (v1_relat_1 @ F)  &  ( ( (v4_relat_1 @ F)  @ A)  &  ( (v1_funct_1 @ F)  &  ( (v1_partfun1 @ F)  @ A) ) ) )  &  ( (v1_funct_1 @ G)  &  ( ( ( (v1_funct_2 @ G)  @ D)  @  ( (k1_funct_2 @  (k4_card_3 @  ( (k3_relat_1 @ E)  @ F) ) )  @  (k4_card_3 @  ( (k3_relat_1 @ E)  @ F) ) ) )  &  ( (m1_subset_1 @ G)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ D)  @  ( (k1_funct_2 @  (k4_card_3 @  ( (k3_relat_1 @ E)  @ F) ) )  @  (k4_card_3 @  ( (k3_relat_1 @ E)  @ F) ) ) ) ) ) ) ) ) ) ) )  =>  ( ( (v1_extpro_1 @  ( ( ( ( ( ( (g1_extpro_1 @ A)  @ B)  @ C)  @ D)  @ E)  @ F)  @ G) )  @ A)  &  ( (l1_extpro_1 @  ( ( ( ( ( ( (g1_extpro_1 @ A)  @ B)  @ C)  @ D)  @ E)  @ F)  @ G) )  @ A) ) ) ) , file(extpro_1, g1_extpro_1)).
thf(dt_k10_compos_1, axiom,  (! [A: $i, B: $i] :  ( ( (l1_compos_1 @ A)  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  (v1_afinsq_1 @ B) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( (k10_compos_1 @ A)  @ B) )  &  ( ( (v4_relat_1 @  ( (k10_compos_1 @ A)  @ B) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  ( (k10_compos_1 @ A)  @ B) )  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @  ( (k10_compos_1 @ A)  @ B) )  &  (v1_finset_1 @  ( (k10_compos_1 @ A)  @ B) ) ) ) ) ) ) ) , file(compos_1, k10_compos_1)).
thf(dt_k10_xtuple_0, axiom, $true, file(xtuple_0, k10_xtuple_0)).
thf(dt_k16_funcop_1, axiom, $true, file(funcop_1, k16_funcop_1)).
thf(dt_k17_scmpds_2, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( ( (v5_funct_1 @ A)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( (v1_partfun1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) ) ) ) ) )  &  (v1_int_1 @ B) )  =>  ( (m1_subset_1 @  ( (k17_scmpds_2 @ A)  @ B) )  @ k5_numbers) ) ) , file(scmpds_2, k17_scmpds_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_funct_1, axiom, $true, file(funct_1, k1_funct_1)).
thf(dt_k1_funct_2, axiom, $true, file(funct_2, k1_funct_2)).
thf(dt_k1_funct_4, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  &  ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_4 @ A)  @ B) )  &  (v1_funct_1 @  ( (k1_funct_4 @ A)  @ B) ) ) ) ) , file(funct_4, k1_funct_4)).
thf(dt_k1_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( (m1_subset_1 @ B)  @ k5_numbers) )  =>  ( ( (m2_subset_1 @  ( (k1_nat_1 @ A)  @ B) )  @ k1_numbers)  @ k5_numbers) ) ) , file(nat_1, k1_nat_1)).
thf(dt_k1_numbers, axiom, $true, file(numbers, k1_numbers)).
thf(dt_k1_ordinal1, axiom, $true, file(ordinal1, k1_ordinal1)).
thf(dt_k1_ordinal4, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v5_ordinal1 @ A)  &  (v1_funct_1 @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( (v5_ordinal1 @ B)  &  (v1_funct_1 @ B) ) ) )  =>  ( (v1_relat_1 @  ( (k1_ordinal4 @ A)  @ B) )  &  ( (v5_ordinal1 @  ( (k1_ordinal4 @ A)  @ B) )  &  (v1_funct_1 @  ( (k1_ordinal4 @ A)  @ B) ) ) ) ) ) , file(ordinal4, k1_ordinal4)).
thf(dt_k1_scmpds_2, axiom,  ( ( (v1_extpro_1 @ k1_scmpds_2)  @ np__2)  &  ( (l1_extpro_1 @ k1_scmpds_2)  @ np__2) ) , file(scmpds_2, k1_scmpds_2)).
thf(dt_k1_scmpds_8, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_ami_2 @ A)  &  ( (m1_subset_1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) ) )  &  ( (v1_int_1 @ B)  &  ( ~ ( (v1_xboole_0 @ C) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ k5_numbers)  &  ( ( (v5_relat_1 @ C)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ C)  &  ( (v1_finset_1 @ C)  &  (v1_afinsq_1 @ C) ) ) ) ) ) ) ) )  =>  ( ~ ( (v1_xboole_0 @  ( ( (k1_scmpds_8 @ A)  @ B)  @ C) ) )  &  ( (v1_relat_1 @  ( ( (k1_scmpds_8 @ A)  @ B)  @ C) )  &  ( ( (v4_relat_1 @  ( ( (k1_scmpds_8 @ A)  @ B)  @ C) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  ( ( (k1_scmpds_8 @ A)  @ B)  @ C) )  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @  ( ( (k1_scmpds_8 @ A)  @ B)  @ C) )  &  ( (v1_finset_1 @  ( ( (k1_scmpds_8 @ A)  @ B)  @ C) )  &  (v1_afinsq_1 @  ( ( (k1_scmpds_8 @ A)  @ B)  @ C) ) ) ) ) ) ) ) ) ) , file(scmpds_8, k1_scmpds_8)).
thf(dt_k1_tarski, axiom, $true, file(tarski, k1_tarski)).
thf(dt_k1_xboole_0, axiom, $true, file(xboole_0, k1_xboole_0)).
thf(dt_k1_zfmisc_1, axiom, $true, file(zfmisc_1, k1_zfmisc_1)).
thf(dt_k2_compos_1, axiom,  (! [A: $i] :  ( (l1_compos_1 @ A)  =>  ( (m1_subset_1 @  (k2_compos_1 @ A) )  @  (u1_compos_1 @ A) ) ) ) , file(compos_1, k2_compos_1)).
thf(dt_k2_extpro_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( ( (v2_memstr_0 @ B)  @ A)  &  ( (l1_extpro_1 @ B)  @ A) )  &  ( ( (m1_subset_1 @ C)  @  (u1_compos_1 @ B) )  &  ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ D)  &  ( ( (v5_funct_1 @ D)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @ D)  @  (u1_struct_0 @ B) ) ) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( ( ( (k2_extpro_1 @ A)  @ B)  @ C)  @ D) )  &  ( ( (v4_relat_1 @  ( ( ( (k2_extpro_1 @ A)  @ B)  @ C)  @ D) )  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @  ( ( ( (k2_extpro_1 @ A)  @ B)  @ C)  @ D) )  &  ( ( (v5_funct_1 @  ( ( ( (k2_extpro_1 @ A)  @ B)  @ C)  @ D) )  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @  ( ( ( (k2_extpro_1 @ A)  @ B)  @ C)  @ D) )  @  (u1_struct_0 @ B) ) ) ) ) ) ) ) , file(extpro_1, k2_extpro_1)).
thf(dt_k2_funcop_1, axiom, $true, file(funcop_1, k2_funcop_1)).
thf(dt_k2_memstr_0, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( (l1_memstr_0 @ B)  @ A) )  =>  ( (v1_relat_1 @  ( (k2_memstr_0 @ A)  @ B) )  &  ( ( (v4_relat_1 @  ( (k2_memstr_0 @ A)  @ B) )  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @  ( (k2_memstr_0 @ A)  @ B) )  @  (u1_struct_0 @ B) ) ) ) ) ) ) , file(memstr_0, k2_memstr_0)).
thf(dt_k2_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k5_numbers)  &  (v7_ordinal1 @ B) )  =>  ( ( (m2_subset_1 @  ( (k2_nat_1 @ A)  @ B) )  @ k1_numbers)  @ k5_numbers) ) ) , file(nat_1, k2_nat_1)).
thf(dt_k2_scmpds_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_int_1 @ A)  &  (v1_int_1 @ B) )  =>  ( (v1_ami_2 @  ( (k2_scmpds_2 @ A)  @ B) )  &  ( (m1_subset_1 @  ( (k2_scmpds_2 @ A)  @ B) )  @  (u1_struct_0 @ k1_scmpds_2) ) ) ) ) , file(scmpds_2, k2_scmpds_2)).
thf(dt_k2_scmpds_4, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  (v1_afinsq_1 @ B) ) ) ) ) ) ) )  =>  ( ~ ( (v1_xboole_0 @  ( (k2_scmpds_4 @ A)  @ B) ) )  &  ( (v1_relat_1 @  ( (k2_scmpds_4 @ A)  @ B) )  &  ( ( (v4_relat_1 @  ( (k2_scmpds_4 @ A)  @ B) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  ( (k2_scmpds_4 @ A)  @ B) )  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @  ( (k2_scmpds_4 @ A)  @ B) )  &  ( (v1_finset_1 @  ( (k2_scmpds_4 @ A)  @ B) )  &  (v1_afinsq_1 @  ( (k2_scmpds_4 @ A)  @ B) ) ) ) ) ) ) ) ) ) , file(scmpds_4, k2_scmpds_4)).
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_afinsq_1, axiom, $true, file(afinsq_1, k3_afinsq_1)).
thf(dt_k3_compos_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (l1_compos_1 @ A)  &  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ k5_numbers) ) ) ) )  &  (v7_ordinal1 @ C) ) )  =>  ( (m1_subset_1 @  ( ( (k3_compos_1 @ A)  @ B)  @ C) )  @  (u1_compos_1 @ A) ) ) ) , file(compos_1, k3_compos_1)).
thf(dt_k3_extpro_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_extpro_1 @ B)  @ A) ) ) )  &  ( ( (v1_relat_1 @ C)  &  ( ( (v5_relat_1 @ C)  @  (u1_compos_1 @ B) )  &  (v1_funct_1 @ C) ) )  &  ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ D)  &  ( ( (v5_funct_1 @ D)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @ D)  @  (u1_struct_0 @ B) ) ) ) ) ) ) ) )  =>  ( (m1_subset_1 @  ( ( ( (k3_extpro_1 @ A)  @ B)  @ C)  @ D) )  @  (u1_compos_1 @ B) ) ) ) , file(extpro_1, k3_extpro_1)).
thf(dt_k3_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (m1_subset_1 @ D)  @ A) ) )  =>  ( (m1_subset_1 @  ( ( ( (k3_funct_2 @ A)  @ B)  @ C)  @ D) )  @ B) ) ) , file(funct_2, k3_funct_2)).
thf(dt_k3_numbers, axiom, $true, file(numbers, k3_numbers)).
thf(dt_k3_relat_1, axiom,  (! [A: $i, B: $i] :  (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) ) ) , file(relat_1, k3_relat_1)).
thf(dt_k3_scmpds_2, axiom,  (! [A: $i] :  ( (v1_int_1 @ A)  =>  ( (m1_subset_1 @  (k3_scmpds_2 @ A) )  @  (u1_compos_1 @ k1_scmpds_2) ) ) ) , file(scmpds_2, k3_scmpds_2)).
thf(dt_k3_scmpds_4, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( ( (v5_relat_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  (v1_afinsq_1 @ A) ) ) ) ) ) )  &  ( (m1_subset_1 @ B)  @  (u1_compos_1 @ k1_scmpds_2) ) )  =>  ( ~ ( (v1_xboole_0 @  ( (k3_scmpds_4 @ A)  @ B) ) )  &  ( (v1_relat_1 @  ( (k3_scmpds_4 @ A)  @ B) )  &  ( ( (v4_relat_1 @  ( (k3_scmpds_4 @ A)  @ B) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  ( (k3_scmpds_4 @ A)  @ B) )  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @  ( (k3_scmpds_4 @ A)  @ B) )  &  ( (v1_finset_1 @  ( (k3_scmpds_4 @ A)  @ B) )  &  (v1_afinsq_1 @  ( (k3_scmpds_4 @ A)  @ B) ) ) ) ) ) ) ) ) ) , file(scmpds_4, k3_scmpds_4)).
thf(dt_k3_xcmplx_0, axiom, $true, file(xcmplx_0, k3_xcmplx_0)).
thf(dt_k4_card_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (m1_subset_1 @  (k4_card_1 @ A) )  @ k4_ordinal1) ) ) , file(card_1, k4_card_1)).
thf(dt_k4_card_3, axiom, $true, file(card_3, k4_card_3)).
thf(dt_k4_compos_1, axiom,  (! [A: $i] :  ( (l1_compos_1 @ A)  =>  ( (v1_relat_1 @  (k4_compos_1 @ A) )  &  ( ( (v4_relat_1 @  (k4_compos_1 @ A) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  (k4_compos_1 @ A) )  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @  (k4_compos_1 @ A) )  &  (v1_finset_1 @  (k4_compos_1 @ A) ) ) ) ) ) ) ) , file(compos_1, k4_compos_1)).
thf(dt_k4_extpro_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_extpro_1 @ B)  @ A) ) ) )  &  ( ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( (v5_funct_1 @ C)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @ C)  @  (u1_struct_0 @ B) ) ) ) ) )  &  ( (v1_relat_1 @ D)  &  ( ( (v5_relat_1 @ D)  @  (u1_compos_1 @ B) )  &  (v1_funct_1 @ D) ) ) ) ) )  =>  ( (v1_relat_1 @  ( ( ( (k4_extpro_1 @ A)  @ B)  @ C)  @ D) )  &  ( ( (v4_relat_1 @  ( ( ( (k4_extpro_1 @ A)  @ B)  @ C)  @ D) )  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @  ( ( ( (k4_extpro_1 @ A)  @ B)  @ C)  @ D) )  &  ( ( (v5_funct_1 @  ( ( ( (k4_extpro_1 @ A)  @ B)  @ C)  @ D) )  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @  ( ( ( (k4_extpro_1 @ A)  @ B)  @ C)  @ D) )  @  (u1_struct_0 @ B) ) ) ) ) ) ) ) , file(extpro_1, k4_extpro_1)).
thf(dt_k4_numbers, axiom, $true, file(numbers, k4_numbers)).
thf(dt_k4_ordinal1, axiom, $true, file(ordinal1, k4_ordinal1)).
thf(dt_k4_struct_0, axiom,  (! [A: $i] :  ( (l2_struct_0 @ A)  =>  ( (m1_subset_1 @  (k4_struct_0 @ A) )  @  (u1_struct_0 @ A) ) ) ) , file(struct_0, k4_struct_0)).
thf(dt_k4_xcmplx_0, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) ) ) ) , file(xcmplx_0, k4_xcmplx_0)).
thf(dt_k5_card_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  ( (m1_subset_1 @  (k5_card_1 @ A) )  @ k4_ordinal1) ) ) , file(card_1, k5_card_1)).
thf(dt_k5_extpro_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_extpro_1 @ B)  @ A) ) ) )  &  ( ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ k5_numbers)  &  ( ( (v5_relat_1 @ C)  @  (u1_compos_1 @ B) )  &  (v1_funct_1 @ C) ) ) )  &  ( ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ D)  &  ( ( (v5_funct_1 @ D)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @ D)  @  (u1_struct_0 @ B) ) ) ) ) )  &  (v7_ordinal1 @ E) ) ) ) )  =>  ( (v1_relat_1 @  ( ( ( ( (k5_extpro_1 @ A)  @ B)  @ C)  @ D)  @ E) )  &  ( ( (v4_relat_1 @  ( ( ( ( (k5_extpro_1 @ A)  @ B)  @ C)  @ D)  @ E) )  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @  ( ( ( ( (k5_extpro_1 @ A)  @ B)  @ C)  @ D)  @ E) )  &  ( ( (v5_funct_1 @  ( ( ( ( (k5_extpro_1 @ A)  @ B)  @ C)  @ D)  @ E) )  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @  ( ( ( ( (k5_extpro_1 @ A)  @ B)  @ C)  @ D)  @ E) )  @  (u1_struct_0 @ B) ) ) ) ) ) ) ) , file(extpro_1, k5_extpro_1)).
thf(dt_k5_memstr_0, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_memstr_0 @ B)  @ A) ) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( (v5_funct_1 @ C)  @  ( (k2_memstr_0 @ A)  @ B) ) ) ) ) ) )  =>  ( ( (m2_subset_1 @  ( ( (k5_memstr_0 @ A)  @ B)  @ C) )  @ k1_numbers)  @ k5_numbers) ) ) , file(memstr_0, k5_memstr_0)).
thf(dt_k5_numbers, axiom,  ( (m1_subset_1 @ k5_numbers)  @  (k1_zfmisc_1 @ k1_numbers) ) , file(numbers, k5_numbers)).
thf(dt_k5_relat_1, axiom,  (! [A: $i, B: $i] :  ( (v1_relat_1 @ A)  =>  (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) , file(relat_1, k5_relat_1)).
thf(dt_k61_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  &  (v7_ordinal1 @ B) )  =>  ( (v1_relat_1 @  ( (k61_valued_1 @ A)  @ B) )  &  (v1_funct_1 @  ( (k61_valued_1 @ A)  @ B) ) ) ) ) , file(valued_1, k61_valued_1)).
thf(dt_k6_compos_0, axiom,  (! [A: $i] :  ( (v5_compos_0 @ A)  =>  ( (m1_subset_1 @  (k6_compos_0 @ A) )  @ A) ) ) , file(compos_0, k6_compos_0)).
thf(dt_k6_extpro_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_setfam_1 @ A) ) )  &  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( ( (v3_extpro_1 @ B)  @ A)  &  ( (l1_extpro_1 @ B)  @ A) ) ) ) )  &  ( ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ k5_numbers)  &  ( ( (v5_relat_1 @ C)  @  (u1_compos_1 @ B) )  &  (v1_funct_1 @ C) ) ) )  &  ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ D)  &  ( ( (v5_funct_1 @ D)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @ D)  @  (u1_struct_0 @ B) ) ) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( ( ( (k6_extpro_1 @ A)  @ B)  @ C)  @ D) )  &  ( ( (v4_relat_1 @  ( ( ( (k6_extpro_1 @ A)  @ B)  @ C)  @ D) )  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @  ( ( ( (k6_extpro_1 @ A)  @ B)  @ C)  @ D) )  &  ( ( (v5_funct_1 @  ( ( ( (k6_extpro_1 @ A)  @ B)  @ C)  @ D) )  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @  ( ( ( (k6_extpro_1 @ A)  @ B)  @ C)  @ D) )  @  (u1_struct_0 @ B) ) ) ) ) ) ) ) , file(extpro_1, k6_extpro_1)).
thf(dt_k6_memstr_0, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( (l1_memstr_0 @ B)  @ A)  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( (v5_funct_1 @ C)  @  ( (k2_memstr_0 @ A)  @ B) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( ( (k6_memstr_0 @ A)  @ B)  @ C) )  &  ( ( (v4_relat_1 @  ( ( (k6_memstr_0 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @  ( ( (k6_memstr_0 @ A)  @ B)  @ C) )  &  ( (v5_funct_1 @  ( ( (k6_memstr_0 @ A)  @ B)  @ C) )  @  ( (k2_memstr_0 @ A)  @ B) ) ) ) ) ) ) , file(memstr_0, k6_memstr_0)).
thf(dt_k6_numbers, axiom,  ( ( (m2_subset_1 @ k6_numbers)  @ k1_numbers)  @ k5_numbers) , file(numbers, k6_numbers)).
thf(dt_k6_scmpds_4, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( ( (v5_relat_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  (v1_afinsq_1 @ A) ) ) ) ) ) )  &  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ B)  &  ( ( (v5_funct_1 @ B)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( (v1_partfun1 @ B)  @  (u1_struct_0 @ k1_scmpds_2) ) ) ) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ k5_numbers)  &  ( ( (v5_relat_1 @ C)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ C)  &  ( (v1_partfun1 @ C)  @ k5_numbers) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( ( (k6_scmpds_4 @ A)  @ B)  @ C) )  &  ( ( (v4_relat_1 @  ( ( (k6_scmpds_4 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @  ( ( (k6_scmpds_4 @ A)  @ B)  @ C) )  &  ( ( (v5_funct_1 @  ( ( (k6_scmpds_4 @ A)  @ B)  @ C) )  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( (v1_partfun1 @  ( ( (k6_scmpds_4 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ k1_scmpds_2) ) ) ) ) ) ) ) , file(scmpds_4, k6_scmpds_4)).
thf(dt_k6_xcmplx_0, axiom, $true, file(xcmplx_0, k6_xcmplx_0)).
thf(dt_k7_funcop_1, axiom,  (! [A: $i, B: $i] :  ( (v1_funct_1 @  ( (k7_funcop_1 @ A)  @ B) )  &  ( ( ( (v1_funct_2 @  ( (k7_funcop_1 @ A)  @ B) )  @ A)  @  (k1_tarski @ B) )  &  ( (m1_subset_1 @  ( (k7_funcop_1 @ A)  @ B) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @  (k1_tarski @ B) ) ) ) ) ) ) , file(funcop_1, k7_funcop_1)).
thf(dt_k7_memstr_0, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_memstr_0 @ B)  @ A) ) ) )  &  (v7_ordinal1 @ C) ) )  =>  ( (v1_relat_1 @  ( ( (k7_memstr_0 @ A)  @ B)  @ C) )  &  ( ( (v4_relat_1 @  ( ( (k7_memstr_0 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @  ( ( (k7_memstr_0 @ A)  @ B)  @ C) )  &  ( (v5_funct_1 @  ( ( (k7_memstr_0 @ A)  @ B)  @ C) )  @  ( (k2_memstr_0 @ A)  @ B) ) ) ) ) ) ) , file(memstr_0, k7_memstr_0)).
thf(dt_k7_partfun1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) )  =>  ( (m1_subset_1 @  ( ( (k7_partfun1 @ A)  @ B)  @ C) )  @ A) ) ) , file(partfun1, k7_partfun1)).
thf(dt_k8_extpro_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_setfam_1 @ A) ) )  &  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( ( (v3_extpro_1 @ B)  @ A)  &  ( (l1_extpro_1 @ B)  @ A) ) ) ) )  &  ( ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ k5_numbers)  &  ( ( (v5_relat_1 @ C)  @  (u1_compos_1 @ B) )  &  (v1_funct_1 @ C) ) ) )  &  ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ D)  &  ( ( (v5_funct_1 @ D)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @ D)  @  (u1_struct_0 @ B) ) ) ) ) ) ) ) )  =>  ( ( (m2_subset_1 @  ( ( ( (k8_extpro_1 @ A)  @ B)  @ C)  @ D) )  @ k1_numbers)  @ k5_numbers) ) ) , file(extpro_1, k8_extpro_1)).
thf(dt_k8_memstr_0, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_memstr_0 @ B)  @ A) ) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( (v5_funct_1 @ C)  @  ( (k2_memstr_0 @ A)  @ B) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) )  &  ( ( (v4_relat_1 @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) )  &  ( (v5_funct_1 @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) )  @  ( (k2_memstr_0 @ A)  @ B) ) ) ) ) ) ) , file(memstr_0, k8_memstr_0)).
thf(dt_k8_struct_0, axiom,  (! [A: $i] :  ( (l2_struct_0 @ A)  =>  ( (m1_subset_1 @  (k8_struct_0 @ A) )  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) ) ) , file(struct_0, k8_struct_0)).
thf(dt_k9_scmpds_2, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_ami_2 @ A)  &  ( (m1_subset_1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) ) )  &  ( (v1_int_1 @ B)  &  (v1_int_1 @ C) ) )  =>  ( (m1_subset_1 @  ( ( (k9_scmpds_2 @ A)  @ B)  @ C) )  @  (u1_compos_1 @ k1_scmpds_2) ) ) ) , file(scmpds_2, k9_scmpds_2)).
thf(dt_k9_xtuple_0, axiom, $true, file(xtuple_0, k9_xtuple_0)).
thf(dt_l1_compos_1, axiom, $true, file(compos_1, l1_compos_1)).
thf(dt_l1_extpro_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (l1_extpro_1 @ B)  @ A)  =>  ( ( (l1_memstr_0 @ B)  @ A)  &  (l1_compos_1 @ B) ) ) ) ) , file(extpro_1, l1_extpro_1)).
thf(dt_l1_memstr_0, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (l1_memstr_0 @ B)  @ A)  =>  (l2_struct_0 @ B) ) ) ) , file(memstr_0, l1_memstr_0)).
thf(dt_l1_struct_0, axiom, $true, file(struct_0, l1_struct_0)).
thf(dt_l2_struct_0, axiom,  (! [A: $i] :  ( (l2_struct_0 @ A)  =>  (l1_struct_0 @ A) ) ) , file(struct_0, l2_struct_0)).
thf(dt_m1_subset_1, axiom, $true, file(subset_1, m1_subset_1)).
thf(dt_m2_subset_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) ) ) )  =>  (! [C: $i] :  ( ( ( (m2_subset_1 @ C)  @ A)  @ B)  =>  ( (m1_subset_1 @ C)  @ A) ) ) ) ) , file(subset_1, m2_subset_1)).
thf(dt_u1_compos_1, axiom,  (! [A: $i] :  ( (l1_compos_1 @ A)  =>  ( (v1_compos_0 @  (u1_compos_1 @ A) )  &  ( (v2_compos_0 @  (u1_compos_1 @ A) )  &  ( (v3_compos_0 @  (u1_compos_1 @ A) )  &  (v5_compos_0 @  (u1_compos_1 @ A) ) ) ) ) ) ) , file(compos_1, u1_compos_1)).
thf(dt_u1_extpro_1, axiom,  (! [A: $i, B: $i] :  ( ( (l1_extpro_1 @ B)  @ A)  =>  ( (v1_funct_1 @  ( (u1_extpro_1 @ A)  @ B) )  &  ( ( ( (v1_funct_2 @  ( (u1_extpro_1 @ A)  @ B) )  @  (u1_compos_1 @ B) )  @  ( (k1_funct_2 @  (k4_card_3 @  ( (k3_relat_1 @  ( (u1_memstr_0 @ A)  @ B) )  @  ( (u2_memstr_0 @ A)  @ B) ) ) )  @  (k4_card_3 @  ( (k3_relat_1 @  ( (u1_memstr_0 @ A)  @ B) )  @  ( (u2_memstr_0 @ A)  @ B) ) ) ) )  &  ( (m1_subset_1 @  ( (u1_extpro_1 @ A)  @ B) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_compos_1 @ B) )  @  ( (k1_funct_2 @  (k4_card_3 @  ( (k3_relat_1 @  ( (u1_memstr_0 @ A)  @ B) )  @  ( (u2_memstr_0 @ A)  @ B) ) ) )  @  (k4_card_3 @  ( (k3_relat_1 @  ( (u1_memstr_0 @ A)  @ B) )  @  ( (u2_memstr_0 @ A)  @ B) ) ) ) ) ) ) ) ) ) ) , file(extpro_1, u1_extpro_1)).
thf(dt_u1_memstr_0, axiom,  (! [A: $i, B: $i] :  ( ( (l1_memstr_0 @ B)  @ A)  =>  ( (v1_funct_1 @  ( (u1_memstr_0 @ A)  @ B) )  &  ( ( ( (v1_funct_2 @  ( (u1_memstr_0 @ A)  @ B) )  @  (u1_struct_0 @ B) )  @ A)  &  ( (m1_subset_1 @  ( (u1_memstr_0 @ A)  @ B) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_struct_0 @ B) )  @ A) ) ) ) ) ) ) , file(memstr_0, u1_memstr_0)).
thf(dt_u1_struct_0, axiom, $true, file(struct_0, u1_struct_0)).
thf(dt_u2_memstr_0, axiom,  (! [A: $i, B: $i] :  ( ( (l1_memstr_0 @ B)  @ A)  =>  ( (v1_relat_1 @  ( (u2_memstr_0 @ A)  @ B) )  &  ( ( (v4_relat_1 @  ( (u2_memstr_0 @ A)  @ B) )  @ A)  &  ( (v1_funct_1 @  ( (u2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @  ( (u2_memstr_0 @ A)  @ B) )  @ A) ) ) ) ) ) , file(memstr_0, u2_memstr_0)).
thf(dt_u2_struct_0, axiom,  (! [A: $i] :  ( (l2_struct_0 @ A)  =>  ( (m1_subset_1 @  (u2_struct_0 @ A) )  @  (u1_struct_0 @ A) ) ) ) , file(struct_0, u2_struct_0)).
thf(existence_l1_compos_1, axiom,  (? [A: $i] :  (l1_compos_1 @ A) ) , file(compos_1, l1_compos_1)).
thf(existence_l1_extpro_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (l1_extpro_1 @ B)  @ A) ) ) , file(extpro_1, l1_extpro_1)).
thf(existence_l1_memstr_0, axiom,  (! [A: $i] :  (? [B: $i] :  ( (l1_memstr_0 @ B)  @ A) ) ) , file(memstr_0, l1_memstr_0)).
thf(existence_l1_struct_0, axiom,  (? [A: $i] :  (l1_struct_0 @ A) ) , file(struct_0, l1_struct_0)).
thf(existence_l2_struct_0, axiom,  (? [A: $i] :  (l2_struct_0 @ A) ) , file(struct_0, l2_struct_0)).
thf(existence_m1_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m1_subset_1 @ B)  @ A) ) ) , file(subset_1, m1_subset_1)).
thf(existence_m2_subset_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) ) ) )  =>  (? [C: $i] :  ( ( (m2_subset_1 @ C)  @ A)  @ B) ) ) ) , file(subset_1, m2_subset_1)).
thf(fc103_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  &  (v7_ordinal1 @ B) )  =>  ( (v1_relat_1 @  ( (k61_valued_1 @ A)  @ B) )  &  ( ( (v4_relat_1 @  ( (k61_valued_1 @ A)  @ B) )  @ k5_numbers)  &  (v1_funct_1 @  ( (k61_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc103_valued_1)).
thf(fc104_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) )  &  (v7_ordinal1 @ B) )  =>  ( (v1_relat_1 @  ( (k61_valued_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k61_valued_1 @ A)  @ B) )  &  (v1_finset_1 @  ( (k61_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc104_valued_1)).
thf(fc105_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) )  &  (v7_ordinal1 @ C) ) )  =>  ( (v1_relat_1 @  ( (k61_valued_1 @ B)  @ C) )  &  ( ( (v5_relat_1 @  ( (k61_valued_1 @ B)  @ C) )  @ A)  &  (v1_funct_1 @  ( (k61_valued_1 @ B)  @ C) ) ) ) ) ) , file(valued_1, fc105_valued_1)).
thf(fc106_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_xboole_0 @ A) ) )  &  (v7_ordinal1 @ B) )  =>  ( (v1_relat_1 @  ( (k61_valued_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k61_valued_1 @ A)  @ B) )  &  (v1_xboole_0 @  ( (k61_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc106_valued_1)).
thf(fc107_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ~ ( (v1_xboole_0 @ A) ) ) ) )  &  (v7_ordinal1 @ B) )  =>  ( (v1_relat_1 @  ( (k61_valued_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k61_valued_1 @ A)  @ B) )  &  ~ ( (v1_xboole_0 @  ( (k61_valued_1 @ A)  @ B) ) ) ) ) ) ) , file(valued_1, fc107_valued_1)).
thf(fc108_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v4_relat_1 @ A)  @ k5_numbers) )  =>  (v6_membered @  (k9_xtuple_0 @ A) ) ) ) , file(valued_1, fc108_valued_1)).
thf(fc10_card_3, axiom,  (v5_card_3 @ k4_ordinal1) , file(card_3, fc10_card_3)).
thf(fc10_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  (v1_setfam_1 @  (k10_xtuple_0 @ A) ) ) ) , file(funct_1, fc10_funct_1)).
thf(fc10_funct_2, axiom,  (! [A: $i, B: $i] :  (v4_funct_1 @  ( (k1_funct_2 @ A)  @ B) ) ) , file(funct_2, fc10_funct_2)).
thf(fc10_funct_4, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v5_relat_1 @ C)  @ A)  &  (v1_funct_1 @ C) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_4 @ B)  @ C) )  &  ( ( (v5_relat_1 @  ( (k1_funct_4 @ B)  @ C) )  @ A)  &  (v1_funct_1 @  ( (k1_funct_4 @ B)  @ C) ) ) ) ) ) , file(funct_4, fc10_funct_4)).
thf(fc10_memstr_0, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_memstr_0 @ B)  @ A) ) ) )  &  (v7_ordinal1 @ C) ) )  =>  ( ~ ( (v1_xboole_0 @  ( ( (k7_memstr_0 @ A)  @ B)  @ C) ) )  &  ( (v1_relat_1 @  ( ( (k7_memstr_0 @ A)  @ B)  @ C) )  &  ( ( (v4_relat_1 @  ( ( (k7_memstr_0 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @  ( ( (k7_memstr_0 @ A)  @ B)  @ C) )  &  ( ( (v5_funct_1 @  ( ( (k7_memstr_0 @ A)  @ B)  @ C) )  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( ( ( (v5_memstr_0 @  ( ( (k7_memstr_0 @ A)  @ B)  @ C) )  @ A)  @ B)  @ C) ) ) ) ) ) ) ) , file(memstr_0, fc10_memstr_0)).
thf(fc10_nat_1, axiom,  (! [A: $i, B: $i] :  ( (v3_ordinal1 @ A)  =>  (v5_ordinal1 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(nat_1, fc10_nat_1)).
thf(fc10_relat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_xboole_0 @  (k9_xtuple_0 @ A) ) ) ) , file(relat_1, fc10_relat_1)).
thf(fc10_relset_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_relat_1 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k9_xtuple_0 @ A) ) ) ) )  =>  ( ~ ( (v1_xboole_0 @  ( (k5_relat_1 @ A)  @ B) ) )  &  (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(relset_1, fc10_relset_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(fc11_funct_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  (v1_funct_1 @ A) ) ) )  &  ( (m1_subset_1 @ B)  @  (k9_xtuple_0 @ A) ) )  =>  ~ ( (v1_xboole_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) ) , file(funct_1, fc11_funct_1)).
thf(fc11_funct_4, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  &  ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v5_funct_1 @ B)  @ A) ) )  &  ( (v1_relat_1 @ C)  &  ( (v1_funct_1 @ C)  &  ( (v5_funct_1 @ C)  @ A) ) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_4 @ B)  @ C) )  &  ( (v1_funct_1 @  ( (k1_funct_4 @ B)  @ C) )  &  ( (v5_funct_1 @  ( (k1_funct_4 @ B)  @ C) )  @ A) ) ) ) ) , file(funct_4, fc11_funct_4)).
thf(fc11_memstr_0, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_memstr_0 @ B)  @ A) ) ) )  &  ( (v7_ordinal1 @ C)  &  ( ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ D)  &  ( (v5_funct_1 @ D)  @  ( (k2_memstr_0 @ A)  @ B) ) ) ) )  &  ( (v1_relat_1 @ E)  &  ( ( (v4_relat_1 @ E)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ E)  &  ( ( (v5_funct_1 @ E)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( ( ( (v5_memstr_0 @ E)  @ A)  @ B)  @ C) ) ) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_4 @ D)  @ E) )  &  ( (v1_funct_1 @  ( (k1_funct_4 @ D)  @ E) )  &  ( ( ( (v5_memstr_0 @  ( (k1_funct_4 @ D)  @ E) )  @ A)  @ B)  @ C) ) ) ) ) , file(memstr_0, fc11_memstr_0)).
thf(fc11_relat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_xboole_0 @  (k10_xtuple_0 @ A) ) ) ) , file(relat_1, fc11_relat_1)).
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(fc12_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_funct_1 @ A) ) )  =>  (v1_zfmisc_1 @  (k10_xtuple_0 @ A) ) ) ) , file(funct_1, fc12_funct_1)).
thf(fc12_memstr_0, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_memstr_0 @ B)  @ A) ) ) )  &  ( (v7_ordinal1 @ C)  &  ( ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ D)  &  ( ( (v5_funct_1 @ D)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( ( ( (v5_memstr_0 @ D)  @ A)  @ B)  @ C) ) ) ) )  &  ( (v1_relat_1 @ E)  &  ( ( (v4_relat_1 @ E)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ E)  &  ( ( (v5_funct_1 @ E)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( ( (v4_memstr_0 @ E)  @ A)  @ B) ) ) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_4 @ D)  @ E) )  &  ( (v1_funct_1 @  ( (k1_funct_4 @ D)  @ E) )  &  ( ( ( (v5_memstr_0 @  ( (k1_funct_4 @ D)  @ E) )  @ A)  @ B)  @ C) ) ) ) ) , file(memstr_0, fc12_memstr_0)).
thf(fc12_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ B) )  =>  ( (v1_xboole_0 @  ( (k3_relat_1 @ A)  @ B) )  &  (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(relat_1, fc12_relat_1)).
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(fc13_afinsq_1, axiom,  (! [A: $i] :  ( (v3_card_1 @  (k3_afinsq_1 @ A) )  @ np__1) ) , file(afinsq_1, fc13_afinsq_1)).
thf(fc13_card_3, axiom,  (! [A: $i, B: $i] :  ( ~ ( (v1_finset_1 @ A) )  =>  ~ ( (v1_finset_1 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) ) , file(card_3, fc13_card_3)).
thf(fc13_compos_1, axiom,  (! [A: $i, B: $i] :  ( ( (l1_compos_1 @ A)  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  (v1_afinsq_1 @ B) ) ) ) ) ) )  =>  ( ~ ( (v1_xboole_0 @  ( (k10_compos_1 @ A)  @ B) ) )  &  ( (v1_relat_1 @  ( (k10_compos_1 @ A)  @ B) )  &  ( ( (v4_relat_1 @  ( (k10_compos_1 @ A)  @ B) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  ( (k10_compos_1 @ A)  @ B) )  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @  ( (k10_compos_1 @ A)  @ B) )  &  ( (v1_finset_1 @  ( (k10_compos_1 @ A)  @ B) )  &  (v1_afinsq_1 @  ( (k10_compos_1 @ A)  @ B) ) ) ) ) ) ) ) ) ) , file(compos_1, fc13_compos_1)).
thf(fc13_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ~ ( (v3_funct_1 @ A) ) ) )  =>  ~ ( (v1_zfmisc_1 @  (k10_xtuple_0 @ A) ) ) ) ) , file(funct_1, fc13_funct_1)).
thf(fc13_funct_4, axiom,  (! [A: $i, B: $i] :  (v1_zfmisc_1 @  ( (k16_funcop_1 @ A)  @ B) ) ) , file(funct_4, fc13_funct_4)).
thf(fc13_memstr_0, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_memstr_0 @ B)  @ A) ) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( (v5_funct_1 @ C)  @  ( (k2_memstr_0 @ A)  @ B) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) )  &  ( ( (v4_relat_1 @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) )  &  ( ( (v5_funct_1 @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) )  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( ( ( (v5_memstr_0 @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) )  @ A)  @ B)  @ k6_numbers) ) ) ) ) ) ) , file(memstr_0, fc13_memstr_0)).
thf(fc13_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ B) )  =>  ( (v1_xboole_0 @  ( (k3_relat_1 @ B)  @ A) )  &  (v1_relat_1 @  ( (k3_relat_1 @ B)  @ A) ) ) ) ) , file(relat_1, fc13_relat_1)).
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(fc14_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  (v4_funct_1 @  (k1_tarski @ A) ) ) ) , file(funct_1, fc14_funct_1)).
thf(fc14_memstr_0, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_memstr_0 @ B)  @ A) ) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( (v5_funct_1 @ C)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @ C)  @  (u1_struct_0 @ B) ) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) )  &  ( ( (v4_relat_1 @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) )  &  ( ( (v5_funct_1 @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) )  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ B) ) ) ) ) ) ) ) , file(memstr_0, fc14_memstr_0)).
thf(fc14_scmpds_4, axiom,  ( (v1_relat_1 @  (k4_compos_1 @ k1_scmpds_2) )  &  ( ( (v4_relat_1 @  (k4_compos_1 @ k1_scmpds_2) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  (k4_compos_1 @ k1_scmpds_2) )  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @  (k4_compos_1 @ k1_scmpds_2) )  &  ( (v1_finset_1 @  (k4_compos_1 @ k1_scmpds_2) )  &  ( (v2_scmpds_4 @  (k4_compos_1 @ k1_scmpds_2) )  &  (v3_scmpds_4 @  (k4_compos_1 @ k1_scmpds_2) ) ) ) ) ) ) ) , file(scmpds_4, fc14_scmpds_4)).
thf(fc14_scmpds_5, axiom,  (v1_scmpds_5 @  (k2_compos_1 @ k1_scmpds_2) ) , file(scmpds_5, fc14_scmpds_5)).
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(fc15_compos_1, axiom,  (! [A: $i] :  ( (l1_compos_1 @ A)  =>  ( (v1_relat_1 @  (k4_compos_1 @ A) )  &  ( ( (v4_relat_1 @  (k4_compos_1 @ A) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  (k4_compos_1 @ A) )  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @  (k4_compos_1 @ A) )  &  ( (v1_finset_1 @  (k4_compos_1 @ A) )  &  ~ ( ( (v2_compos_1 @  (k4_compos_1 @ A) )  @ A) ) ) ) ) ) ) ) ) , file(compos_1, fc15_compos_1)).
thf(fc15_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_relat_1 @ B)  &  (v2_relat_1 @ B) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v2_relat_1 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(relat_1, fc15_relat_1)).
thf(fc15_scmpds_4, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( ( (v5_relat_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  ( (v1_afinsq_1 @ A)  &  (v3_scmpds_4 @ A) ) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( (k10_compos_1 @ k1_scmpds_2)  @ A) )  &  ( ( (v4_relat_1 @  ( (k10_compos_1 @ k1_scmpds_2)  @ A) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  ( (k10_compos_1 @ k1_scmpds_2)  @ A) )  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @  ( (k10_compos_1 @ k1_scmpds_2)  @ A) )  &  ( (v1_finset_1 @  ( (k10_compos_1 @ k1_scmpds_2)  @ A) )  &  (v3_scmpds_4 @  ( (k10_compos_1 @ k1_scmpds_2)  @ A) ) ) ) ) ) ) ) ) , file(scmpds_4, fc15_scmpds_4)).
thf(fc15_scmpds_5, axiom,  (! [A: $i] :  ( ( (v1_scmpds_5 @ A)  &  ( (m1_subset_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) ) )  =>  ( ~ ( (v1_xboole_0 @  (k3_afinsq_1 @ A) ) )  &  ( (v1_relat_1 @  (k3_afinsq_1 @ A) )  &  ( ( (v4_relat_1 @  (k3_afinsq_1 @ A) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  (k3_afinsq_1 @ A) )  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @  (k3_afinsq_1 @ A) )  &  ( (v1_finset_1 @  (k3_afinsq_1 @ A) )  &  ( (v1_afinsq_1 @  (k3_afinsq_1 @ A) )  &  (v2_scmpds_4 @  (k3_afinsq_1 @ A) ) ) ) ) ) ) ) ) ) ) , file(scmpds_5, fc15_scmpds_5)).
thf(fc15_xreal_0, axiom,  (! [A: $i] :  ( ( ~ ( (v2_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  =>  ( (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) )  &  ~ ( (v3_xxreal_0 @  (k4_xcmplx_0 @ A) ) ) ) ) ) , file(xreal_0, fc15_xreal_0)).
thf(fc16_afinsq_1, axiom,  (! [A: $i, B: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v5_ordinal1 @  ( (k2_funcop_1 @ A)  @ B) )  &  (v1_finset_1 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) ) , file(afinsq_1, fc16_afinsq_1)).
thf(fc16_compos_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (l1_compos_1 @ A)  &  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ A) )  &  (v1_funct_1 @ B) ) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ k5_numbers)  &  ( ( (v5_relat_1 @ C)  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @ C)  &  ~ ( ( (v2_compos_1 @ C)  @ A) ) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_4 @ B)  @ C) )  &  ( (v1_funct_1 @  ( (k1_funct_4 @ B)  @ C) )  &  ~ ( ( (v2_compos_1 @  ( (k1_funct_4 @ B)  @ C) )  @ A) ) ) ) ) ) , file(compos_1, fc16_compos_1)).
thf(fc16_funct_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) )  &  ( (v1_relat_1 @ C)  &  ( (v1_funct_1 @ C)  &  ( (v5_funct_1 @ C)  @ B) ) ) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ C)  @ A) )  &  ( (v5_funct_1 @  ( (k5_relat_1 @ C)  @ A) )  @ B) ) ) ) , file(funct_1, fc16_funct_1)).
thf(fc16_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_xboole_0 @ B) )  =>  ( (v1_xboole_0 @  ( (k5_relat_1 @ A)  @ B) )  &  (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(relat_1, fc16_relat_1)).
thf(fc16_scmpds_4, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  =>  ( ~ ( (v1_xboole_0 @  (k3_afinsq_1 @  (k3_scmpds_2 @ A) ) ) )  &  ( (v1_relat_1 @  (k3_afinsq_1 @  (k3_scmpds_2 @ A) ) )  &  ( ( (v4_relat_1 @  (k3_afinsq_1 @  (k3_scmpds_2 @ A) ) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  (k3_afinsq_1 @  (k3_scmpds_2 @ A) ) )  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @  (k3_afinsq_1 @  (k3_scmpds_2 @ A) ) )  &  ( (v1_finset_1 @  (k3_afinsq_1 @  (k3_scmpds_2 @ A) ) )  &  ( (v1_afinsq_1 @  (k3_afinsq_1 @  (k3_scmpds_2 @ A) ) )  &  (v3_scmpds_4 @  (k3_afinsq_1 @  (k3_scmpds_2 @ A) ) ) ) ) ) ) ) ) ) ) ) , file(scmpds_4, fc16_scmpds_4)).
thf(fc16_xreal_0, axiom,  (! [A: $i] :  ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  =>  ( (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) )  &  ~ ( (v2_xxreal_0 @  (k4_xcmplx_0 @ A) ) ) ) ) ) , file(xreal_0, fc16_xreal_0)).
thf(fc17_afinsq_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (m1_subset_1 @ B)  @ A) )  =>  ( (v5_relat_1 @  (k3_afinsq_1 @ B) )  @ A) ) ) , file(afinsq_1, fc17_afinsq_1)).
thf(fc17_funct_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (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) ) ) ) ) , file(funct_1, fc17_funct_1)).
thf(fc17_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_xboole_0 @  ( (k5_relat_1 @ A)  @ B) )  &  (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(relat_1, fc17_relat_1)).
thf(fc17_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 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc17_xreal_0)).
thf(fc18_compos_1, axiom,  (! [A: $i, B: $i] :  ( ( (l1_compos_1 @ A)  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v1_afinsq_1 @ B)  &  ( (v2_compos_1 @ B)  @ A) ) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( (k10_compos_1 @ A)  @ B) )  &  ( ( (v4_relat_1 @  ( (k10_compos_1 @ A)  @ B) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  ( (k10_compos_1 @ A)  @ B) )  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @  ( (k10_compos_1 @ A)  @ B) )  &  ( (v1_finset_1 @  ( (k10_compos_1 @ A)  @ B) )  &  ( (v4_compos_1 @  ( (k10_compos_1 @ A)  @ B) )  @ A) ) ) ) ) ) ) ) , file(compos_1, fc18_compos_1)).
thf(fc18_funct_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_zfmisc_1 @ A) )  &  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  ~ ( (v1_zfmisc_1 @  (k9_xtuple_0 @ A) ) ) ) ) , file(funct_1, fc18_funct_1)).
thf(fc18_memstr_0, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_memstr_0 @ B)  @ A) ) ) )  &  (v7_ordinal1 @ C) ) )  =>  ( (v1_relat_1 @  ( ( (k7_memstr_0 @ A)  @ B)  @ C) )  &  ( ( (v4_relat_1 @  ( ( (k7_memstr_0 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @  ( ( (k7_memstr_0 @ A)  @ B)  @ C) )  &  ( ( (v5_funct_1 @  ( ( (k7_memstr_0 @ A)  @ B)  @ C) )  @  ( (k2_memstr_0 @ A)  @ B) )  &  (v1_finset_1 @  ( ( (k7_memstr_0 @ A)  @ B)  @ C) ) ) ) ) ) ) ) , file(memstr_0, fc18_memstr_0)).
thf(fc18_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v2_xxreal_0 @  ( (k6_xcmplx_0 @ B)  @ A) ) ) ) ) , file(xreal_0, fc18_xreal_0)).
thf(fc19_funct_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v3_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  (v1_xboole_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(funct_1, fc19_funct_1)).
thf(fc19_memstr_0, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( (l1_memstr_0 @ B)  @ A)  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( (v5_funct_1 @ C)  @  ( (k2_memstr_0 @ A)  @ B) )  &  (v1_finset_1 @ C) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( ( (k6_memstr_0 @ A)  @ B)  @ C) )  &  ( ( (v4_relat_1 @  ( ( (k6_memstr_0 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @  ( ( (k6_memstr_0 @ A)  @ B)  @ C) )  &  ( ( (v5_funct_1 @  ( ( (k6_memstr_0 @ A)  @ B)  @ C) )  @  ( (k2_memstr_0 @ A)  @ B) )  &  (v1_finset_1 @  ( ( (k6_memstr_0 @ A)  @ B)  @ C) ) ) ) ) ) ) ) , file(memstr_0, fc19_memstr_0)).
thf(fc19_scmpds_4, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_int_1 @ A)  &  ( ( (v1_ami_2 @ B)  &  ( (m1_subset_1 @ B)  @  (u1_struct_0 @ k1_scmpds_2) ) )  &  ( (m1_subset_1 @ C)  @ k5_numbers) ) )  =>  ( ~ ( (v1_xboole_0 @  (k3_afinsq_1 @  ( ( (k9_scmpds_2 @ B)  @ A)  @ C) ) ) )  &  ( (v1_relat_1 @  (k3_afinsq_1 @  ( ( (k9_scmpds_2 @ B)  @ A)  @ C) ) )  &  ( ( (v4_relat_1 @  (k3_afinsq_1 @  ( ( (k9_scmpds_2 @ B)  @ A)  @ C) ) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  (k3_afinsq_1 @  ( ( (k9_scmpds_2 @ B)  @ A)  @ C) ) )  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @  (k3_afinsq_1 @  ( ( (k9_scmpds_2 @ B)  @ A)  @ C) ) )  &  ( (v1_finset_1 @  (k3_afinsq_1 @  ( ( (k9_scmpds_2 @ B)  @ A)  @ C) ) )  &  ( (v1_afinsq_1 @  (k3_afinsq_1 @  ( ( (k9_scmpds_2 @ B)  @ A)  @ C) ) )  &  (v3_scmpds_4 @  (k3_afinsq_1 @  ( ( (k9_scmpds_2 @ B)  @ A)  @ C) ) ) ) ) ) ) ) ) ) ) ) , file(scmpds_4, fc19_scmpds_4)).
thf(fc19_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 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc19_xreal_0)).
thf(fc1_afinsq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) )  =>  (v7_ordinal1 @  (k9_xtuple_0 @ A) ) ) ) , file(afinsq_1, fc1_afinsq_1)).
thf(fc1_card_3, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_card_3 @ A) ) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  (v1_card_3 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(card_3, fc1_card_3)).
thf(fc1_compos_1, axiom,  (! [A: $i] :  ( (l1_compos_1 @ A)  =>  ( ~ ( (v1_xboole_0 @  (k4_compos_1 @ A) ) )  &  ( (v1_relat_1 @  (k4_compos_1 @ A) )  &  ( ( (v4_relat_1 @  (k4_compos_1 @ A) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  (k4_compos_1 @ A) )  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @  (k4_compos_1 @ A) )  &  ( (v1_finset_1 @  (k4_compos_1 @ A) )  &  (v1_afinsq_1 @  (k4_compos_1 @ A) ) ) ) ) ) ) ) ) ) , file(compos_1, fc1_compos_1)).
thf(fc1_funct_2, axiom,  (! [A: $i, B: $i] :  ( ~ ( (v1_xboole_0 @ B) )  =>  ~ ( (v1_xboole_0 @  ( (k1_funct_2 @ A)  @ B) ) ) ) ) , file(funct_2, fc1_funct_2)).
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_numbers, axiom,  ~ ( (v1_xboole_0 @ k1_numbers) ) , file(numbers, fc1_numbers)).
thf(fc1_ordinal1, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  (k1_ordinal1 @ A) ) ) ) , file(ordinal1, fc1_ordinal1)).
thf(fc1_pboole, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @ B)  &  ( (v1_funct_1 @ D)  &  ( (v1_partfun1 @ D)  @ B) ) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ C)  @ D) )  &  ( ( (v4_relat_1 @  ( (k3_relat_1 @ C)  @ D) )  @ A)  &  ( (v1_funct_1 @  ( (k3_relat_1 @ C)  @ D) )  &  ( (v1_partfun1 @  ( (k3_relat_1 @ C)  @ D) )  @ A) ) ) ) ) ) , file(pboole, fc1_pboole)).
thf(fc1_scmpds_2, axiom,  ( ~ ( (v2_struct_0 @ k1_scmpds_2) )  &  ( (v1_extpro_1 @ k1_scmpds_2)  @ np__2) ) , file(scmpds_2, fc1_scmpds_2)).
thf(fc1_scmpds_6, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  =>  ( (v6_compos_0 @  (k3_scmpds_2 @  ( (k2_nat_1 @ A)  @ np__1) ) )  @  (u1_compos_1 @ k1_scmpds_2) ) ) ) , file(scmpds_6, fc1_scmpds_6)).
thf(fc1_scmpds_8, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( ( (v5_relat_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  ( (v1_afinsq_1 @ A)  &  (v3_scmpds_4 @ A) ) ) ) ) ) ) )  &  ( ( (v1_ami_2 @ B)  &  ( (m1_subset_1 @ B)  @  (u1_struct_0 @ k1_scmpds_2) ) )  &  (v1_int_1 @ C) ) )  =>  ( ~ ( (v1_xboole_0 @  ( ( (k1_scmpds_8 @ B)  @ C)  @ A) ) )  &  ( (v1_relat_1 @  ( ( (k1_scmpds_8 @ B)  @ C)  @ A) )  &  ( ( (v4_relat_1 @  ( ( (k1_scmpds_8 @ B)  @ C)  @ A) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  ( ( (k1_scmpds_8 @ B)  @ C)  @ A) )  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @  ( ( (k1_scmpds_8 @ B)  @ C)  @ A) )  &  ( (v1_finset_1 @  ( ( (k1_scmpds_8 @ B)  @ C)  @ A) )  &  ( (v1_afinsq_1 @  ( ( (k1_scmpds_8 @ B)  @ C)  @ A) )  &  (v3_scmpds_4 @  ( ( (k1_scmpds_8 @ B)  @ C)  @ A) ) ) ) ) ) ) ) ) ) ) , file(scmpds_8, fc1_scmpds_8)).
thf(fc1_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) )  =>  (v1_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc1_valued_0)).
thf(fc1_xboole_0, axiom,  (v1_xboole_0 @ k1_xboole_0) , file(xboole_0, fc1_xboole_0)).
thf(fc20_compos_0, axiom,  (! [A: $i] :  ( ( (v1_compos_0 @ A)  &  (v5_compos_0 @ A) )  =>  ( (v4_compos_0 @  (k6_compos_0 @ A) )  @ A) ) ) , file(compos_0, fc20_compos_0)).
thf(fc20_memstr_0, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_memstr_0 @ B)  @ A) ) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( (v5_funct_1 @ C)  @  ( (k2_memstr_0 @ A)  @ B) )  &  (v1_finset_1 @ C) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) )  &  ( ( (v4_relat_1 @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) )  &  ( ( (v5_funct_1 @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) )  @  ( (k2_memstr_0 @ A)  @ B) )  &  (v1_finset_1 @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) ) ) ) ) ) ) ) , file(memstr_0, fc20_memstr_0)).
thf(fc20_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v3_xxreal_0 @  ( (k6_xcmplx_0 @ B)  @ A) ) ) ) , file(xreal_0, fc20_xreal_0)).
thf(fc21_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 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc21_xreal_0)).
thf(fc22_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v2_xxreal_0 @  ( (k6_xcmplx_0 @ B)  @ A) ) ) ) , file(xreal_0, fc22_xreal_0)).
thf(fc23_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_relat_1 @ A) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  (v3_relat_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(relat_1, fc23_relat_1)).
thf(fc23_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 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc23_xreal_0)).
thf(fc24_relat_1, axiom,  (! [A: $i] :  ( ( (v1_zfmisc_1 @ A)  &  (v1_relat_1 @ A) )  =>  (v1_zfmisc_1 @  (k9_xtuple_0 @ A) ) ) ) , file(relat_1, fc24_relat_1)).
thf(fc24_scmpds_5, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( ( (v5_relat_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  ( (v1_afinsq_1 @ A)  &  ( (v2_compos_1 @ A)  @ k1_scmpds_2) ) ) ) ) ) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v1_afinsq_1 @ B)  &  ( (v2_compos_1 @ B)  @ k1_scmpds_2) ) ) ) ) ) ) ) )  =>  ( (v5_ordinal1 @  ( (k1_ordinal4 @ A)  @ B) )  &  ( (v1_relat_1 @  ( (k1_ordinal4 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k1_ordinal4 @ A)  @ B) )  &  ( (v2_compos_1 @  ( (k1_ordinal4 @ A)  @ B) )  @ k1_scmpds_2) ) ) ) ) ) , file(scmpds_5, fc24_scmpds_5)).
thf(fc24_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 @  ( (k3_xcmplx_0 @ B)  @ A) ) ) ) ) , file(xreal_0, fc24_xreal_0)).
thf(fc25_relat_1, axiom,  (! [A: $i] :  ( ( (v1_zfmisc_1 @ A)  &  (v1_relat_1 @ A) )  =>  (v1_zfmisc_1 @  (k10_xtuple_0 @ A) ) ) ) , file(relat_1, fc25_relat_1)).
thf(fc25_scmpds_5, axiom,  (! [A: $i] :  ( ( ( (v6_compos_0 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (m1_subset_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) ) )  =>  ( (v2_compos_1 @  (k3_afinsq_1 @ A) )  @ k1_scmpds_2) ) ) , file(scmpds_5, fc25_scmpds_5)).
thf(fc25_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v3_xxreal_0 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc25_xreal_0)).
thf(fc26_relat_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_relat_1 @ C)  &  ( (v5_relat_1 @ C)  @ B) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ C)  @ A) )  &  ( (v5_relat_1 @  ( (k5_relat_1 @ C)  @ A) )  @ B) ) ) ) , file(relat_1, fc26_relat_1)).
thf(fc26_scmpds_5, axiom,  (! [A: $i, B: $i] :  ( ( ( ( (v6_compos_0 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (m1_subset_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v1_afinsq_1 @ B)  &  ( (v2_compos_1 @ B)  @ k1_scmpds_2) ) ) ) ) ) ) ) )  =>  ( ~ ( (v1_xboole_0 @  ( (k2_scmpds_4 @ A)  @ B) ) )  &  ( (v1_relat_1 @  ( (k2_scmpds_4 @ A)  @ B) )  &  ( ( (v4_relat_1 @  ( (k2_scmpds_4 @ A)  @ B) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  ( (k2_scmpds_4 @ A)  @ B) )  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @  ( (k2_scmpds_4 @ A)  @ B) )  &  ( (v1_finset_1 @  ( (k2_scmpds_4 @ A)  @ B) )  &  ( (v1_afinsq_1 @  ( (k2_scmpds_4 @ A)  @ B) )  &  ( (v2_compos_1 @  ( (k2_scmpds_4 @ A)  @ B) )  @ k1_scmpds_2) ) ) ) ) ) ) ) ) ) , file(scmpds_5, fc26_scmpds_5)).
thf(fc26_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 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc26_xreal_0)).
thf(fc27_relat_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_relat_1 @ C)  &  ( (v4_relat_1 @ C)  @ B) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ C)  @ A) )  &  ( ( (v4_relat_1 @  ( (k5_relat_1 @ C)  @ A) )  @ A)  &  ( (v4_relat_1 @  ( (k5_relat_1 @ C)  @ A) )  @ B) ) ) ) ) , file(relat_1, fc27_relat_1)).
thf(fc27_scmpds_5, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( ( (v5_relat_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  ( (v1_afinsq_1 @ A)  &  ( (v2_compos_1 @ A)  @ k1_scmpds_2) ) ) ) ) ) ) )  &  ( ( (v6_compos_0 @ B)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (m1_subset_1 @ B)  @  (u1_compos_1 @ k1_scmpds_2) ) ) )  =>  ( ~ ( (v1_xboole_0 @  ( (k3_scmpds_4 @ A)  @ B) ) )  &  ( (v1_relat_1 @  ( (k3_scmpds_4 @ A)  @ B) )  &  ( ( (v4_relat_1 @  ( (k3_scmpds_4 @ A)  @ B) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  ( (k3_scmpds_4 @ A)  @ B) )  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @  ( (k3_scmpds_4 @ A)  @ B) )  &  ( (v1_finset_1 @  ( (k3_scmpds_4 @ A)  @ B) )  &  ( (v1_afinsq_1 @  ( (k3_scmpds_4 @ A)  @ B) )  &  ( (v2_compos_1 @  ( (k3_scmpds_4 @ A)  @ B) )  @ k1_scmpds_2) ) ) ) ) ) ) ) ) ) , file(scmpds_5, fc27_scmpds_5)).
thf(fc29_relat_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) )  &  (v1_relat_1 @ C) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ C)  @ B) )  &  ( (v5_relat_1 @  ( (k3_relat_1 @ C)  @ B) )  @ A) ) ) ) , file(relat_1, fc29_relat_1)).
thf(fc29_scmpds_5, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( ( (v5_relat_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  ( (v1_afinsq_1 @ A)  &  (v2_scmpds_4 @ A) ) ) ) ) ) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v1_afinsq_1 @ B)  &  ( (v2_scmpds_4 @ B)  &  (v3_scmpds_4 @ B) ) ) ) ) ) ) ) ) )  =>  ( ~ ( (v1_xboole_0 @  ( (k1_ordinal4 @ A)  @ B) ) )  &  ( (v1_relat_1 @  ( (k1_ordinal4 @ A)  @ B) )  &  ( ( (v4_relat_1 @  ( (k1_ordinal4 @ A)  @ B) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  ( (k1_ordinal4 @ A)  @ B) )  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @  ( (k1_ordinal4 @ A)  @ B) )  &  ( (v1_finset_1 @  ( (k1_ordinal4 @ A)  @ B) )  &  ( (v1_afinsq_1 @  ( (k1_ordinal4 @ A)  @ B) )  &  (v2_scmpds_4 @  ( (k1_ordinal4 @ A)  @ B) ) ) ) ) ) ) ) ) ) ) , file(scmpds_5, fc29_scmpds_5)).
thf(fc2_afinsq_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) )  &  (v7_ordinal1 @ B) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  (v1_finset_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(afinsq_1, fc2_afinsq_1)).
thf(fc2_card_3, axiom,  (! [A: $i, B: $i] :  ( (v1_card_1 @ B)  =>  (v1_card_3 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(card_3, fc2_card_3)).
thf(fc2_compos_1, axiom,  (! [A: $i] :  ( (l1_compos_1 @ A)  =>  ( ~ ( (v1_xboole_0 @  (k4_compos_1 @ A) ) )  &  ( (v1_zfmisc_1 @  (k4_compos_1 @ A) )  &  ( (v1_relat_1 @  (k4_compos_1 @ A) )  &  ( ( (v4_relat_1 @  (k4_compos_1 @ A) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  (k4_compos_1 @ A) )  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @  (k4_compos_1 @ A) )  &  ( (v1_finset_1 @  (k4_compos_1 @ A) )  &  (v1_afinsq_1 @  (k4_compos_1 @ A) ) ) ) ) ) ) ) ) ) ) , file(compos_1, fc2_compos_1)).
thf(fc2_funct_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  &  ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v1_funct_1 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(funct_1, fc2_funct_1)).
thf(fc2_funct_2, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  ( (k1_funct_2 @ A)  @ A) ) ) ) , file(funct_2, fc2_funct_2)).
thf(fc2_int_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_int_1 @ A)  &  (v1_int_1 @ B) )  =>  (v1_int_1 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) , file(int_1, fc2_int_1)).
thf(fc2_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  (v7_ordinal1 @ B) )  =>  (v7_ordinal1 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) , file(nat_1, fc2_nat_1)).
thf(fc2_ordinal1, axiom,  (! [A: $i] :  ( (v3_ordinal1 @ A)  =>  ( ~ ( (v1_xboole_0 @  (k1_ordinal1 @ A) ) )  &  (v3_ordinal1 @  (k1_ordinal1 @ A) ) ) ) ) , file(ordinal1, fc2_ordinal1)).
thf(fc2_pboole, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) )  &  ( (m1_subset_1 @ C)  @ A) ) )  =>  ~ ( (v1_xboole_0 @  ( (k1_funct_1 @ B)  @ C) ) ) ) ) , file(pboole, fc2_pboole)).
thf(fc2_scmpds_2, axiom,  ( ( (v2_memstr_0 @ k1_scmpds_2)  @ np__2)  &  ( ( (v3_memstr_0 @ k1_scmpds_2)  @ np__2)  &  ( (v1_extpro_1 @ k1_scmpds_2)  @ np__2) ) ) , file(scmpds_2, fc2_scmpds_2)).
thf(fc2_scmpds_6, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  =>  ( (v6_compos_0 @  (k3_scmpds_2 @  (k4_xcmplx_0 @  ( (k2_nat_1 @ A)  @ np__1) ) ) )  @  (u1_compos_1 @ k1_scmpds_2) ) ) ) , file(scmpds_6, fc2_scmpds_6)).
thf(fc2_scmpds_8, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( ( (v5_relat_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  ( (v1_afinsq_1 @ A)  &  ( (v2_compos_1 @ A)  @ k1_scmpds_2) ) ) ) ) ) ) )  &  ( ( (v1_ami_2 @ B)  &  ( (m1_subset_1 @ B)  @  (u1_struct_0 @ k1_scmpds_2) ) )  &  (v1_int_1 @ C) ) )  =>  ( ~ ( (v1_xboole_0 @  ( ( (k1_scmpds_8 @ B)  @ C)  @ A) ) )  &  ( (v1_relat_1 @  ( ( (k1_scmpds_8 @ B)  @ C)  @ A) )  &  ( ( (v4_relat_1 @  ( ( (k1_scmpds_8 @ B)  @ C)  @ A) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  ( ( (k1_scmpds_8 @ B)  @ C)  @ A) )  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @  ( ( (k1_scmpds_8 @ B)  @ C)  @ A) )  &  ( (v1_finset_1 @  ( ( (k1_scmpds_8 @ B)  @ C)  @ A) )  &  ( (v1_afinsq_1 @  ( ( (k1_scmpds_8 @ B)  @ C)  @ A) )  &  ( (v2_compos_1 @  ( ( (k1_scmpds_8 @ B)  @ C)  @ A) )  @ k1_scmpds_2) ) ) ) ) ) ) ) ) ) , file(scmpds_8, fc2_scmpds_8)).
thf(fc2_setfam_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (v1_setfam_1 @  (k1_tarski @ A) ) ) ) , file(setfam_1, fc2_setfam_1)).
thf(fc2_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) )  =>  (v2_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc2_valued_0)).
thf(fc2_xboole_0, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  (k1_tarski @ A) ) ) ) , file(xboole_0, fc2_xboole_0)).
thf(fc30_relat_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  &  (v1_relat_1 @ C) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ B)  @ C) )  &  ( (v4_relat_1 @  ( (k3_relat_1 @ B)  @ C) )  @ A) ) ) ) , file(relat_1, fc30_relat_1)).
thf(fc30_scmpds_5, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_scmpds_5 @ A)  &  ( (m1_subset_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v1_afinsq_1 @ B)  &  ( (v2_scmpds_4 @ B)  &  (v3_scmpds_4 @ B) ) ) ) ) ) ) ) ) )  =>  ( ~ ( (v1_xboole_0 @  ( (k2_scmpds_4 @ A)  @ B) ) )  &  ( (v1_relat_1 @  ( (k2_scmpds_4 @ A)  @ B) )  &  ( ( (v4_relat_1 @  ( (k2_scmpds_4 @ A)  @ B) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  ( (k2_scmpds_4 @ A)  @ B) )  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @  ( (k2_scmpds_4 @ A)  @ B) )  &  ( (v1_finset_1 @  ( (k2_scmpds_4 @ A)  @ B) )  &  ( (v1_afinsq_1 @  ( (k2_scmpds_4 @ A)  @ B) )  &  (v2_scmpds_4 @  ( (k2_scmpds_4 @ A)  @ B) ) ) ) ) ) ) ) ) ) ) , file(scmpds_5, fc30_scmpds_5)).
thf(fc3_afinsq_1, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  (k3_afinsq_1 @ A) ) ) ) , file(afinsq_1, fc3_afinsq_1)).
thf(fc3_card_3, axiom,  (! [A: $i, B: $i] :  ( (v1_card_1 @ B)  =>  (v1_card_3 @  ( (k16_funcop_1 @ A)  @ B) ) ) ) , file(card_3, fc3_card_3)).
thf(fc3_compos_1, axiom,  (! [A: $i] :  ( (l1_compos_1 @ A)  =>  ( (v1_relat_1 @  (k4_compos_1 @ A) )  &  ( ( (v4_relat_1 @  (k4_compos_1 @ A) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  (k4_compos_1 @ A) )  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @  (k4_compos_1 @ A) )  &  ( (v1_finset_1 @  (k4_compos_1 @ A) )  &  ( ( (v3_compos_1 @  (k4_compos_1 @ A) )  @ A)  &  ( (v4_compos_1 @  (k4_compos_1 @ A) )  @ A) ) ) ) ) ) ) ) ) , file(compos_1, fc3_compos_1)).
thf(fc3_funct_2, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_xboole_0 @ B) )  =>  (v1_xboole_0 @  ( (k1_funct_2 @ A)  @ B) ) ) ) , file(funct_2, fc3_funct_2)).
thf(fc3_funct_4, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ~ ( (v1_xboole_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_4 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k1_funct_4 @ A)  @ B) )  &  ~ ( (v1_xboole_0 @  ( (k1_funct_4 @ A)  @ B) ) ) ) ) ) ) , file(funct_4, fc3_funct_4)).
thf(fc3_int_1, axiom,  (! [A: $i] :  ( (v1_int_1 @ A)  =>  ( (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) )  &  (v1_int_1 @  (k4_xcmplx_0 @ A) ) ) ) ) , file(int_1, fc3_int_1)).
thf(fc3_memstr_0, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( (l1_memstr_0 @ B)  @ A) ) )  =>  ( (v1_relat_1 @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v2_relat_1 @  ( (k2_memstr_0 @ A)  @ B) )  &  ( ( (v4_relat_1 @  ( (k2_memstr_0 @ A)  @ B) )  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @  ( (k2_memstr_0 @ A)  @ B) )  @  (u1_struct_0 @ B) ) ) ) ) ) ) ) , file(memstr_0, fc3_memstr_0)).
thf(fc3_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v7_ordinal1 @ B) ) )  =>  ~ ( (v1_xboole_0 @  ( (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(fc3_scmpds_2, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( ( (v5_funct_1 @ A)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( (v1_partfun1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) ) ) ) ) )  &  ( (v1_ami_2 @ B)  &  ( (m1_subset_1 @ B)  @  (u1_struct_0 @ k1_scmpds_2) ) ) )  =>  (v1_int_1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(scmpds_2, fc3_scmpds_2)).
thf(fc3_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  (v3_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc3_valued_0)).
thf(fc3_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  ( (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) )  &  (v1_xreal_0 @  (k4_xcmplx_0 @ A) ) ) ) ) , file(xreal_0, fc3_xreal_0)).
thf(fc43_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  (v1_valued_0 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc43_valued_0)).
thf(fc44_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  (v2_valued_0 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc44_valued_0)).
thf(fc45_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  (v3_valued_0 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc45_valued_0)).
thf(fc46_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  ( (v5_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  @ k3_numbers) ) ) ) , file(valued_0, fc46_valued_0)).
thf(fc47_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  ( (v5_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  @ k4_numbers) ) ) ) , file(valued_0, fc47_valued_0)).
thf(fc48_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  (v4_valued_0 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc48_valued_0)).
thf(fc4_card_3, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  (v4_funct_1 @  (k4_card_3 @ A) ) ) ) , file(card_3, fc4_card_3)).
thf(fc4_extpro_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_extpro_1 @ B)  @ A)  &  ( (l1_extpro_1 @ B)  @ A) ) ) )  =>  ( ( (v2_extpro_1 @  (k2_compos_1 @ B) )  @ A)  @ B) ) ) , file(extpro_1, fc4_extpro_1)).
thf(fc4_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ A)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k3_relat_1 @ D)  @ C) )  &  ( ( (v1_funct_2 @  ( (k3_relat_1 @ D)  @ C) )  @ A)  @ B) ) ) ) , file(funct_2, fc4_funct_2)).
thf(fc4_funct_4, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ~ ( (v1_xboole_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_4 @ B)  @ A) )  &  ( (v1_funct_1 @  ( (k1_funct_4 @ B)  @ A) )  &  ~ ( (v1_xboole_0 @  ( (k1_funct_4 @ B)  @ A) ) ) ) ) ) ) , file(funct_4, fc4_funct_4)).
thf(fc4_int_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_int_1 @ A)  &  (v1_int_1 @ B) )  =>  (v1_int_1 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(int_1, fc4_int_1)).
thf(fc4_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v7_ordinal1 @ B) ) )  =>  ~ ( (v1_xboole_0 @  ( (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_scmpds_2, axiom,  ( ( (v1_extpro_1 @ k1_scmpds_2)  @ np__2)  &  ( (v3_extpro_1 @ k1_scmpds_2)  @ np__2) ) , file(scmpds_2, fc4_scmpds_2)).
thf(fc4_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  =>  (v4_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc4_valued_0)).
thf(fc55_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_relat_1 @ B)  &  (v1_valued_0 @ B) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v1_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc55_valued_0)).
thf(fc56_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_relat_1 @ B)  &  (v2_valued_0 @ B) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v2_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc56_valued_0)).
thf(fc57_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_relat_1 @ B)  &  (v3_valued_0 @ B) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v3_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc57_valued_0)).
thf(fc58_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ k3_numbers) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  ( (v5_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  @ k3_numbers) ) ) ) , file(valued_0, fc58_valued_0)).
thf(fc59_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ k4_numbers) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  ( (v5_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  @ k4_numbers) ) ) ) , file(valued_0, fc59_valued_0)).
thf(fc5_afinsq_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v5_ordinal1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finset_1 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k1_ordinal4 @ A)  @ B) )  &  ( (v5_ordinal1 @  ( (k1_ordinal4 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k1_ordinal4 @ A)  @ B) )  &  (v1_finset_1 @  ( (k1_ordinal4 @ A)  @ B) ) ) ) ) ) ) , file(afinsq_1, fc5_afinsq_1)).
thf(fc5_card_3, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  =>  ~ ( (v1_xboole_0 @  (k4_card_3 @ A) ) ) ) ) , file(card_3, fc5_card_3)).
thf(fc5_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ B)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ B) ) ) ) )  &  ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k3_relat_1 @ D)  @ C) )  &  ( ( (v1_funct_2 @  ( (k3_relat_1 @ D)  @ C) )  @ A)  @ B) ) ) ) , file(funct_2, fc5_funct_2)).
thf(fc5_funct_4, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  (v1_funct_1 @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  (v1_funct_1 @ B) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_4 @ A)  @ B) )  &  ( (v2_relat_1 @  ( (k1_funct_4 @ A)  @ B) )  &  (v1_funct_1 @  ( (k1_funct_4 @ A)  @ B) ) ) ) ) ) , file(funct_4, fc5_funct_4)).
thf(fc5_ordinal1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v5_ordinal1 @ A) ) )  &  (v3_ordinal1 @ B) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  ( ( (v5_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  @  (k10_xtuple_0 @ A) )  &  (v5_ordinal1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) ) , file(ordinal1, fc5_ordinal1)).
thf(fc5_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  (v5_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc5_valued_0)).
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(fc60_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_relat_1 @ B)  &  (v4_valued_0 @ B) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v4_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc60_valued_0)).
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(fc67_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_xcmplx_0 @ B)  =>  (v1_valued_0 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(valued_0, fc67_valued_0)).
thf(fc68_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_xxreal_0 @ B)  =>  (v2_valued_0 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(valued_0, fc68_valued_0)).
thf(fc69_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_xreal_0 @ B)  =>  (v3_valued_0 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(valued_0, fc69_valued_0)).
thf(fc6_afinsq_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v5_ordinal1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finset_1 @ B) ) ) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v5_relat_1 @ C)  @ A)  &  ( (v5_ordinal1 @ C)  &  ( (v1_funct_1 @ C)  &  (v1_finset_1 @ C) ) ) ) ) )  =>  ( (v1_relat_1 @  ( (k1_ordinal4 @ B)  @ C) )  &  ( ( (v5_relat_1 @  ( (k1_ordinal4 @ B)  @ C) )  @ A)  &  ( (v5_ordinal1 @  ( (k1_ordinal4 @ B)  @ C) )  &  (v1_funct_1 @  ( (k1_ordinal4 @ B)  @ C) ) ) ) ) ) ) , file(afinsq_1, fc6_afinsq_1)).
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_relat_1, axiom,  (! [A: $i, B: $i] :  (v1_relat_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) , file(relat_1, fc6_relat_1)).
thf(fc6_scmpds_5, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_ami_2 @ A)  &  ( (m1_subset_1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) ) )  &  ( (v1_int_1 @ B)  &  (v1_int_1 @ C) ) )  =>  ( (v6_compos_0 @  ( ( (k9_scmpds_2 @ A)  @ B)  @ C) )  @  (u1_compos_1 @ k1_scmpds_2) ) ) ) , file(scmpds_5, fc6_scmpds_5)).
thf(fc6_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  (v6_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc6_valued_0)).
thf(fc6_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  (v1_xreal_0 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc6_xreal_0)).
thf(fc70_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_rat_1 @ B)  =>  ( (v5_relat_1 @  ( (k2_funcop_1 @ A)  @ B) )  @ k3_numbers) ) ) , file(valued_0, fc70_valued_0)).
thf(fc71_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_int_1 @ B)  =>  ( (v5_relat_1 @  ( (k2_funcop_1 @ A)  @ B) )  @ k4_numbers) ) ) , file(valued_0, fc71_valued_0)).
thf(fc72_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v7_ordinal1 @ B)  =>  (v4_valued_0 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(valued_0, fc72_valued_0)).
thf(fc73_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_valued_0 @ B) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_4 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k1_funct_4 @ A)  @ B) )  &  (v1_valued_0 @  ( (k1_funct_4 @ A)  @ B) ) ) ) ) ) , file(valued_0, fc73_valued_0)).
thf(fc74_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_valued_0 @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v2_valued_0 @ B) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_4 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k1_funct_4 @ A)  @ B) )  &  (v2_valued_0 @  ( (k1_funct_4 @ A)  @ B) ) ) ) ) ) , file(valued_0, fc74_valued_0)).
thf(fc75_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_valued_0 @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v3_valued_0 @ B) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_4 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k1_funct_4 @ A)  @ B) )  &  (v3_valued_0 @  ( (k1_funct_4 @ A)  @ B) ) ) ) ) ) , file(valued_0, fc75_valued_0)).
thf(fc76_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k3_numbers)  &  (v1_funct_1 @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ k3_numbers)  &  (v1_funct_1 @ B) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_4 @ A)  @ B) )  &  ( ( (v5_relat_1 @  ( (k1_funct_4 @ A)  @ B) )  @ k3_numbers)  &  (v1_funct_1 @  ( (k1_funct_4 @ A)  @ B) ) ) ) ) ) , file(valued_0, fc76_valued_0)).
thf(fc77_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k4_numbers)  &  (v1_funct_1 @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ k4_numbers)  &  (v1_funct_1 @ B) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_4 @ A)  @ B) )  &  ( ( (v5_relat_1 @  ( (k1_funct_4 @ A)  @ B) )  @ k4_numbers)  &  (v1_funct_1 @  ( (k1_funct_4 @ A)  @ B) ) ) ) ) ) , file(valued_0, fc77_valued_0)).
thf(fc78_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v4_valued_0 @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v4_valued_0 @ B) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_4 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k1_funct_4 @ A)  @ B) )  &  (v4_valued_0 @  ( (k1_funct_4 @ A)  @ B) ) ) ) ) ) , file(valued_0, fc78_valued_0)).
thf(fc79_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_xcmplx_0 @ B)  =>  (v1_valued_0 @  ( (k16_funcop_1 @ A)  @ B) ) ) ) , file(valued_0, fc79_valued_0)).
thf(fc7_afinsq_1, axiom,  (! [A: $i] :  ( (v1_relat_1 @  (k3_afinsq_1 @ A) )  &  (v1_funct_1 @  (k3_afinsq_1 @ A) ) ) ) , file(afinsq_1, fc7_afinsq_1)).
thf(fc7_card_3, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  (v2_card_3 @  (k1_tarski @ A) ) ) ) , file(card_3, fc7_card_3)).
thf(fc7_funct_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_funct_1 @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v2_funct_1 @ B) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v2_funct_1 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(funct_1, fc7_funct_1)).
thf(fc7_funct_4, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  (v1_funct_1 @ C) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_4 @ B)  @ C) )  &  ( ( (v4_relat_1 @  ( (k1_funct_4 @ B)  @ C) )  @ A)  &  (v1_funct_1 @  ( (k1_funct_4 @ B)  @ C) ) ) ) ) ) , file(funct_4, fc7_funct_4)).
thf(fc7_numbers, axiom,  ~ ( (v1_finset_1 @ k3_numbers) ) , file(numbers, fc7_numbers)).
thf(fc7_ordinal1, axiom,  (! [A: $i] :  ( ( (v3_ordinal1 @ A)  &  (v7_ordinal1 @ A) )  =>  (v7_ordinal1 @  (k1_ordinal1 @ A) ) ) ) , file(ordinal1, fc7_ordinal1)).
thf(fc7_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  (v1_xreal_0 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc7_xreal_0)).
thf(fc80_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_xxreal_0 @ B)  =>  (v2_valued_0 @  ( (k16_funcop_1 @ A)  @ B) ) ) ) , file(valued_0, fc80_valued_0)).
thf(fc81_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_xreal_0 @ B)  =>  (v3_valued_0 @  ( (k16_funcop_1 @ A)  @ B) ) ) ) , file(valued_0, fc81_valued_0)).
thf(fc82_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_rat_1 @ B)  =>  ( (v5_relat_1 @  ( (k16_funcop_1 @ A)  @ B) )  @ k3_numbers) ) ) , file(valued_0, fc82_valued_0)).
thf(fc83_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_int_1 @ B)  =>  ( (v5_relat_1 @  ( (k16_funcop_1 @ A)  @ B) )  @ k4_numbers) ) ) , file(valued_0, fc83_valued_0)).
thf(fc84_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v7_ordinal1 @ B)  =>  (v4_valued_0 @  ( (k16_funcop_1 @ A)  @ B) ) ) ) , file(valued_0, fc84_valued_0)).
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_afinsq_1, axiom,  (! [A: $i] :  ( (v5_ordinal1 @  (k3_afinsq_1 @ A) )  &  (v1_finset_1 @  (k3_afinsq_1 @ A) ) ) ) , file(afinsq_1, fc8_afinsq_1)).
thf(fc8_funct_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  ( (v1_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  &  (v1_funct_1 @  ( (k5_relat_1 @ A)  @ B) ) ) ) ) , file(funct_1, fc8_funct_1)).
thf(fc8_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ B)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ C) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k3_relat_1 @ D)  @ E) )  &  ( ( (v1_funct_2 @  ( (k3_relat_1 @ D)  @ E) )  @ A)  @ C) ) ) ) , file(funct_2, fc8_funct_2)).
thf(fc8_funct_4, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  (v1_funct_1 @ C) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_4 @ B)  @ C) )  &  ( ( (v4_relat_1 @  ( (k1_funct_4 @ B)  @ C) )  @ A)  &  ( (v1_funct_1 @  ( (k1_funct_4 @ B)  @ C) )  &  ( (v1_partfun1 @  ( (k1_funct_4 @ B)  @ C) )  @ A) ) ) ) ) ) , file(funct_4, fc8_funct_4)).
thf(fc8_memstr_0, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( (l1_memstr_0 @ B)  @ A)  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( (v5_funct_1 @ C)  @  ( (k2_memstr_0 @ A)  @ B) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( ( (k6_memstr_0 @ A)  @ B)  @ C) )  &  ( ( (v4_relat_1 @  ( ( (k6_memstr_0 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @  ( ( (k6_memstr_0 @ A)  @ B)  @ C) )  &  ( ( (v5_funct_1 @  ( ( (k6_memstr_0 @ A)  @ B)  @ C) )  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( ( (v4_memstr_0 @  ( ( (k6_memstr_0 @ A)  @ B)  @ C) )  @ A)  @ B) ) ) ) ) ) ) , file(memstr_0, fc8_memstr_0)).
thf(fc8_nat_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k5_numbers)  @ k5_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k5_numbers) ) ) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ k5_numbers)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ B) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ C) )  &  ( ( (v4_relat_1 @  ( (k3_relat_1 @ A)  @ C) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  ( (k3_relat_1 @ A)  @ C) )  @ B)  &  (v1_funct_1 @  ( (k3_relat_1 @ A)  @ C) ) ) ) ) ) ) , file(nat_1, fc8_nat_1)).
thf(fc8_numbers, axiom,  ~ ( (v1_finset_1 @ k1_numbers) ) , file(numbers, fc8_numbers)).
thf(fc8_relat_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_relat_1 @ A) )  =>  ~ ( (v1_xboole_0 @  (k9_xtuple_0 @ A) ) ) ) ) , file(relat_1, fc8_relat_1)).
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(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(fc91_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v5_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v5_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v5_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc91_valued_0)).
thf(fc92_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v7_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v7_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v7_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc92_valued_0)).
thf(fc93_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v6_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v6_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v5_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc93_valued_0)).
thf(fc94_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v8_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v8_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v7_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc94_valued_0)).
thf(fc95_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v6_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v5_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v6_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc95_valued_0)).
thf(fc96_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v6_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v5_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ B)  @ A) )  &  (v6_valued_0 @  ( (k3_relat_1 @ B)  @ A) ) ) ) ) , file(valued_0, fc96_valued_0)).
thf(fc97_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v8_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v7_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v8_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc97_valued_0)).
thf(fc98_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v8_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v7_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ B)  @ A) )  &  (v8_valued_0 @  ( (k3_relat_1 @ B)  @ A) ) ) ) ) , file(valued_0, fc98_valued_0)).
thf(fc9_card_3, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  (v3_card_3 @  (k4_card_3 @ A) ) ) ) , file(card_3, fc9_card_3)).
thf(fc9_funct_4, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  (v1_funct_1 @ C) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_4 @ C)  @ B) )  &  ( ( (v4_relat_1 @  ( (k1_funct_4 @ C)  @ B) )  @ A)  &  ( (v1_funct_1 @  ( (k1_funct_4 @ C)  @ B) )  &  ( (v1_partfun1 @  ( (k1_funct_4 @ C)  @ B) )  @ A) ) ) ) ) ) , file(funct_4, fc9_funct_4)).
thf(fc9_nat_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k5_numbers)  @ k5_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k5_numbers) ) ) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ k5_numbers)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ B) ) ) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ C) )  &  ( (v1_partfun1 @  ( (k3_relat_1 @ A)  @ C) )  @ k5_numbers) ) ) ) , file(nat_1, fc9_nat_1)).
thf(fc9_relat_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_relat_1 @ A) )  =>  ~ ( (v1_xboole_0 @  (k10_xtuple_0 @ A) ) ) ) ) , file(relat_1, fc9_relat_1)).
thf(fc9_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @  ( (k2_zfmisc_1 @ B)  @ C) ) ) )  =>  (v1_relat_1 @  (k10_xtuple_0 @ D) ) ) ) , file(relset_1, fc9_relset_1)).
thf(fc9_scmpds_4, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( ( (v5_relat_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  ( (v1_afinsq_1 @ A)  &  (v3_scmpds_4 @ A) ) ) ) ) ) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v1_afinsq_1 @ B)  &  (v3_scmpds_4 @ B) ) ) ) ) ) ) ) )  =>  ( ~ ( (v1_xboole_0 @  ( (k1_ordinal4 @ A)  @ B) ) )  &  ( (v1_relat_1 @  ( (k1_ordinal4 @ A)  @ B) )  &  ( ( (v4_relat_1 @  ( (k1_ordinal4 @ A)  @ B) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  ( (k1_ordinal4 @ A)  @ B) )  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @  ( (k1_ordinal4 @ A)  @ B) )  &  ( (v1_finset_1 @  ( (k1_ordinal4 @ A)  @ B) )  &  ( (v1_afinsq_1 @  ( (k1_ordinal4 @ A)  @ B) )  &  (v3_scmpds_4 @  ( (k1_ordinal4 @ A)  @ B) ) ) ) ) ) ) ) ) ) ) , file(scmpds_4, fc9_scmpds_4)).
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(free_g1_extpro_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i, G: $i] :  ( ( ( (m1_subset_1 @ C)  @ B)  &  ( ( (v1_compos_0 @ D)  &  ( (v2_compos_0 @ D)  &  ( (v3_compos_0 @ D)  &  (v5_compos_0 @ D) ) ) )  &  ( ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ B)  @ A)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ A) ) ) ) )  &  ( ( (v1_relat_1 @ F)  &  ( ( (v4_relat_1 @ F)  @ A)  &  ( (v1_funct_1 @ F)  &  ( (v1_partfun1 @ F)  @ A) ) ) )  &  ( (v1_funct_1 @ G)  &  ( ( ( (v1_funct_2 @ G)  @ D)  @  ( (k1_funct_2 @  (k4_card_3 @  ( (k3_relat_1 @ E)  @ F) ) )  @  (k4_card_3 @  ( (k3_relat_1 @ E)  @ F) ) ) )  &  ( (m1_subset_1 @ G)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ D)  @  ( (k1_funct_2 @  (k4_card_3 @  ( (k3_relat_1 @ E)  @ F) ) )  @  (k4_card_3 @  ( (k3_relat_1 @ E)  @ F) ) ) ) ) ) ) ) ) ) ) )  =>  (! [H: $i, I: $i, J: $i, K: $i, L: $i, M: $i, N: $i] :  ( ( (= @  ( ( ( ( ( ( (g1_extpro_1 @ A)  @ B)  @ C)  @ D)  @ E)  @ F)  @ G) )  @  ( ( ( ( ( ( (g1_extpro_1 @ H)  @ I)  @ J)  @ K)  @ L)  @ M)  @ N) )  =>  ( ( (= @ A)  @ H)  &  ( ( (= @ B)  @ I)  &  ( ( (= @ C)  @ J)  &  ( ( (= @ D)  @ K)  &  ( ( (= @ E)  @ L)  &  ( ( (= @ F)  @ M)  &  ( (= @ G)  @ N) ) ) ) ) ) ) ) ) ) ) , file(extpro_1, g1_extpro_1)).
thf(idempotence_k1_funct_4, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  &  ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) ) )  =>  ( (= @  ( (k1_funct_4 @ A)  @ A) )  @ A) ) ) , file(funct_4, k1_funct_4)).
thf(ie1_afinsq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) )  =>  ( (= @  (k1_card_1 @ A) )  @  (k9_xtuple_0 @ A) ) ) ) , file(afinsq_1, ie1_afinsq_1)).
thf(ie1_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (m1_subset_1 @ D)  @ A) ) ) )  =>  ( (= @  ( ( (k7_partfun1 @ B)  @ C)  @ D) )  @  ( ( ( (k3_funct_2 @ A)  @ B)  @ C)  @ D) ) ) ) , file(funct_2, ie1_funct_2)).
thf(involutiveness_k4_xcmplx_0, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  (k4_xcmplx_0 @  (k4_xcmplx_0 @ A) ) )  @ A) ) ) , file(xcmplx_0, k4_xcmplx_0)).
thf(l16_scmpds_8, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( ( (v5_relat_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  (v1_afinsq_1 @ A) ) ) ) ) ) )  =>  (! [B: $i] :  ( ( (v1_ami_2 @ B)  &  ( (m1_subset_1 @ B)  @  (u1_struct_0 @ k1_scmpds_2) ) )  =>  (! [C: $i] :  ( (v1_int_1 @ C)  =>  ( (r1_tarski @  ( (k61_valued_1 @ A)  @ np__1) )  @  ( ( (k1_scmpds_8 @ B)  @ C)  @ A) ) ) ) ) ) ) ) , file(scmpds_8, l16_scmpds_8)).
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_k5_card_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  ( (= @  (k5_card_1 @  (k5_card_1 @ A) ) )  @  (k5_card_1 @ A) ) ) ) , file(card_1, k5_card_1)).
thf(projectivity_k6_memstr_0, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( (l1_memstr_0 @ B)  @ A)  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( (v5_funct_1 @ C)  @  ( (k2_memstr_0 @ A)  @ B) ) ) ) ) ) )  =>  ( (= @  ( ( (k6_memstr_0 @ A)  @ B)  @  ( ( (k6_memstr_0 @ A)  @ B)  @ C) ) )  @  ( ( (k6_memstr_0 @ A)  @ B)  @ C) ) ) ) , file(memstr_0, k6_memstr_0)).
thf(projectivity_k8_memstr_0, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_memstr_0 @ B)  @ A) ) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( (v5_funct_1 @ C)  @  ( (k2_memstr_0 @ A)  @ B) ) ) ) ) ) )  =>  ( (= @  ( ( (k8_memstr_0 @ A)  @ B)  @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) ) )  @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) ) ) ) , file(memstr_0, k8_memstr_0)).
thf(rc10_extpro_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_setfam_1 @ A) ) )  =>  (? [B: $i] :  ( ( (l1_extpro_1 @ B)  @ A)  &  ( ~ ( (v2_struct_0 @ B) )  &  ( (v3_memstr_0 @ B)  @ A) ) ) ) ) ) , file(extpro_1, rc10_extpro_1)).
thf(rc1_afinsq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v5_ordinal1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finset_1 @ B) ) ) ) ) ) ) , file(afinsq_1, rc1_afinsq_1)).
thf(rc1_card_3, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_card_3 @ A) ) ) ) , file(card_3, rc1_card_3)).
thf(rc1_compos_0, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_compos_0 @ A) ) ) , file(compos_0, rc1_compos_0)).
thf(rc1_extpro_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (l1_extpro_1 @ B)  @ A)  &  ( (v1_extpro_1 @ B)  @ A) ) ) ) , file(extpro_1, rc1_extpro_1)).
thf(rc1_funct_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) ) ) , file(funct_1, rc1_funct_1)).
thf(rc1_funct_2, 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)  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) ) ) ) ) ) ) ) , file(funct_2, rc1_funct_2)).
thf(rc1_int_1, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  &  ( (v1_xxreal_0 @ A)  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xreal_0 @ A)  &  (v1_int_1 @ A) ) ) ) ) ) , file(int_1, rc1_int_1)).
thf(rc1_nat_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  ( (v3_ordinal1 @ A)  &  ( (v7_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, rc1_nat_1)).
thf(rc1_ordinal1, axiom,  (? [A: $i] :  (v3_ordinal1 @ A) ) , file(ordinal1, rc1_ordinal1)).
thf(rc1_pboole, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) , file(pboole, rc1_pboole)).
thf(rc1_relat_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_relat_1 @ A) ) ) , file(relat_1, rc1_relat_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_scmpds_2, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) )  &  (v1_ami_2 @ A) ) ) , file(scmpds_2, rc1_scmpds_2)).
thf(rc1_setfam_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_setfam_1 @ A) ) ) , file(setfam_1, rc1_setfam_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_xboole_0, axiom,  (? [A: $i] :  (v1_xboole_0 @ A) ) , file(xboole_0, rc1_xboole_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(rc2_afinsq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v5_ordinal1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v1_xboole_0 @ B)  &  (v1_finset_1 @ B) ) ) ) ) ) ) ) , file(afinsq_1, rc2_afinsq_1)).
thf(rc2_compos_0, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( (v1_compos_0 @ A)  &  ( (v2_compos_0 @ A)  &  (v3_compos_0 @ A) ) ) ) ) ) , file(compos_0, rc2_compos_0)).
thf(rc2_compos_1, axiom,  (! [A: $i] :  ( (l1_compos_1 @ A)  =>  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @ B)  &  ( ( (v3_card_1 @ B)  @ np__1)  &  (v1_afinsq_1 @ B) ) ) ) ) ) ) ) ) , file(compos_1, rc2_compos_1)).
thf(rc2_extpro_1, axiom,  (! [A: $i] :  ( ~ ( (v1_setfam_1 @ A) )  =>  (? [B: $i] :  ( ( (l1_extpro_1 @ B)  @ A)  &  ~ ( (v2_struct_0 @ B) ) ) ) ) ) , file(extpro_1, rc2_extpro_1)).
thf(rc2_funct_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_funct_1 @ A) ) ) ) , file(funct_1, rc2_funct_1)).
thf(rc2_int_1, axiom,  (? [A: $i] :  (v1_int_1 @ A) ) , file(int_1, rc2_int_1)).
thf(rc2_nat_1, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k1_numbers) )  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v3_ordinal1 @ A) ) ) ) , file(nat_1, rc2_nat_1)).
thf(rc2_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  (v3_ordinal1 @ A) ) ) ) ) , file(ordinal1, rc2_ordinal1)).
thf(rc2_pboole, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( (v3_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) ) , file(pboole, rc2_pboole)).
thf(rc2_relat_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  (v2_relat_1 @ A) ) ) , file(relat_1, rc2_relat_1)).
thf(rc2_scmpds_5, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v5_ordinal1 @ A)  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( ( (v5_relat_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  ( (v1_afinsq_1 @ A)  &  ( ( (v2_compos_1 @ A)  @ k1_scmpds_2)  &  ( (v2_scmpds_4 @ A)  &  (v3_scmpds_4 @ A) ) ) ) ) ) ) ) ) ) ) ) , file(scmpds_5, rc2_scmpds_5)).
thf(rc2_setfam_1, axiom,  (? [A: $i] :  ~ ( (v2_setfam_1 @ A) ) ) , file(setfam_1, rc2_setfam_1)).
thf(rc2_valued_0, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k3_numbers)  &  ( ( (v5_relat_1 @ A)  @ k4_numbers)  &  ( (v1_funct_1 @ A)  &  ( (v3_funct_1 @ A)  &  (v4_valued_0 @ A) ) ) ) ) ) ) ) , file(valued_0, rc2_valued_0)).
thf(rc2_valued_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ~ ( (v1_xboole_0 @ A) ) ) ) ) ) , file(valued_1, rc2_valued_1)).
thf(rc2_xboole_0, axiom,  (? [A: $i] :  ~ ( (v1_xboole_0 @ A) ) ) , file(xboole_0, rc2_xboole_0)).
thf(rc2_xreal_0, axiom,  (? [A: $i] :  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc2_xreal_0)).
thf(rc2_xxreal_0, axiom,  (? [A: $i] :  ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) ) ) , file(xxreal_0, rc2_xxreal_0)).
thf(rc3_afinsq_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v5_ordinal1 @ B)  &  ( (v1_funct_1 @ B)  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_finset_1 @ B) ) ) ) ) ) ) ) ) , file(afinsq_1, rc3_afinsq_1)).
thf(rc3_card_3, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v4_funct_1 @ A)  &  (v2_card_3 @ A) ) ) ) , file(card_3, rc3_card_3)).
thf(rc3_compos_0, axiom,  (? [A: $i] :  ( (v1_compos_0 @ A)  &  (v5_compos_0 @ A) ) ) , file(compos_0, rc3_compos_0)).
thf(rc3_funct_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  (v1_funct_1 @ A) ) ) ) , file(funct_1, rc3_funct_1)).
thf(rc3_memstr_0, axiom,  (! [A: $i] :  ( ~ ( (v1_setfam_1 @ A) )  =>  (? [B: $i] :  ( ( (l1_memstr_0 @ B)  @ A)  &  ( (v2_memstr_0 @ B)  @ A) ) ) ) ) , file(memstr_0, rc3_memstr_0)).
thf(rc3_nat_1, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  ( (v3_ordinal1 @ A)  &  ( (v7_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, rc3_nat_1)).
thf(rc3_ordinal1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  (v5_ordinal1 @ B) ) ) ) ) ) , file(ordinal1, rc3_ordinal1)).
thf(rc3_pboole, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) ) ) ) , file(pboole, rc3_pboole)).
thf(rc3_relat_1, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v5_relat_1 @ C)  @ B) ) ) ) ) , file(relat_1, rc3_relat_1)).
thf(rc3_setfam_1, axiom,  (! [A: $i] :  ( ~ ( (v2_setfam_1 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  &  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) , file(setfam_1, rc3_setfam_1)).
thf(rc3_valued_0, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k5_numbers) ) )  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( ( (v5_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ( ( (v1_partfun1 @ A)  @ k5_numbers)  &  ( ( ( (v1_funct_2 @ A)  @ k5_numbers)  @ k5_numbers)  &  ( (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_valued_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_finset_1 @ A) ) ) ) ) ) , file(valued_1, rc3_valued_1)).
thf(rc3_xreal_0, axiom,  (? [A: $i] :  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc3_xreal_0)).
thf(rc3_xxreal_0, axiom,  (? [A: $i] :  ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) ) ) , file(xxreal_0, rc3_xxreal_0)).
thf(rc4_afinsq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( (v5_ordinal1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v3_card_1 @ B)  @ A) ) ) ) ) ) ) ) , file(afinsq_1, rc4_afinsq_1)).
thf(rc4_card_3, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v3_card_3 @ A) ) ) , file(card_3, rc4_card_3)).
thf(rc4_compos_0, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( (v1_compos_0 @ A)  &  ( (v2_compos_0 @ A)  &  ( (v3_compos_0 @ A)  &  (v5_compos_0 @ A) ) ) ) ) ) ) , file(compos_0, rc4_compos_0)).
thf(rc4_extpro_1, axiom,  (! [A: $i] :  ( ~ ( (v1_setfam_1 @ A) )  =>  (? [B: $i] :  ( ( (l1_extpro_1 @ B)  @ A)  &  ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( (v3_extpro_1 @ B)  @ A) ) ) ) ) ) ) , file(extpro_1, rc4_extpro_1)).
thf(rc4_funct_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  (v1_funct_1 @ A) ) ) ) ) , file(funct_1, rc4_funct_1)).
thf(rc4_ordinal1, axiom,  (? [A: $i] :  (v7_ordinal1 @ A) ) , file(ordinal1, rc4_ordinal1)).
thf(rc4_valued_0, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v3_funct_1 @ B)  &  ( ( (v1_funct_2 @ B)  @ k5_numbers)  @ A) ) ) ) ) ) ) ) ) , file(valued_0, rc4_valued_0)).
thf(rc4_valued_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  ( (v3_card_1 @ A)  @ np__1) ) ) ) ) ) , file(valued_1, rc4_valued_1)).
thf(rc4_xreal_0, axiom,  (? [A: $i] :  ( (v1_xboole_0 @ A)  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc4_xreal_0)).
thf(rc4_xxreal_0, axiom,  (? [A: $i] :  ( (v1_xboole_0 @ A)  &  (v1_xxreal_0 @ A) ) ) , file(xxreal_0, rc4_xxreal_0)).
thf(rc5_card_3, axiom,  (? [A: $i] :  (v5_card_3 @ A) ) , file(card_3, rc5_card_3)).
thf(rc5_compos_0, axiom,  (! [A: $i] :  ( ( (v1_compos_0 @ A)  &  (v5_compos_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  &  ( (v4_compos_0 @ B)  @ A) ) ) ) ) , file(compos_0, rc5_compos_0)).
thf(rc5_extpro_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_extpro_1 @ B)  @ A)  &  ( (l1_extpro_1 @ B)  @ A) ) ) )  =>  (? [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_compos_1 @ B) )  &  ( ( (v2_extpro_1 @ C)  @ A)  @ B) ) ) ) ) , file(extpro_1, rc5_extpro_1)).
thf(rc5_funct_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ~ ( (v3_funct_1 @ A) ) ) ) ) , file(funct_1, rc5_funct_1)).
thf(rc5_memstr_0, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( (l1_memstr_0 @ B)  @ A) )  =>  (? [C: $i] :  ( (v1_xboole_0 @ C)  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( (v5_funct_1 @ C)  @  ( (k2_memstr_0 @ A)  @ B) ) ) ) ) ) ) ) ) , file(memstr_0, rc5_memstr_0)).
thf(rc5_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v7_ordinal1 @ A) ) ) , file(ordinal1, rc5_ordinal1)).
thf(rc5_valued_0, axiom,  (! [A: $i] :  ( ~ ( (v2_setfam_1 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ A) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ k5_numbers)  &  ( ( (v1_funct_2 @ B)  @ k5_numbers)  @ A) ) ) ) ) ) ) ) ) ) ) ) , file(valued_0, rc5_valued_0)).
thf(rc5_valued_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( ( (v5_relat_1 @ B)  @ k3_numbers)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  ( (v1_valued_0 @ B)  &  ( (v2_valued_0 @ B)  &  ( (v3_valued_0 @ B)  &  (v4_valued_0 @ B) ) ) ) ) ) ) ) ) ) ) , file(valued_1, rc5_valued_1)).
thf(rc6_card_3, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ~ ( (v1_finset_1 @ A) ) ) ) ) , file(card_3, rc6_card_3)).
thf(rc6_compos_0, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_zfmisc_1 @ A) )  &  ( (v1_relat_1 @ A)  &  ( (v1_compos_0 @ A)  &  ( (v2_compos_0 @ A)  &  ( (v3_compos_0 @ A)  &  (v5_compos_0 @ A) ) ) ) ) ) ) ) , file(compos_0, rc6_compos_0)).
thf(rc6_funct_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) ) ) ) ) ) , file(funct_1, rc6_funct_1)).
thf(rc6_memstr_0, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_memstr_0 @ B)  @ A) ) ) )  &  (v7_ordinal1 @ C) ) )  =>  (? [D: $i] :  ( ~ ( (v1_xboole_0 @ D) )  &  ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ D)  &  ( ( (v5_funct_1 @ D)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( ( (v1_partfun1 @ D)  @  (u1_struct_0 @ B) )  &  ( ( ( (v5_memstr_0 @ D)  @ A)  @ B)  @ C) ) ) ) ) ) ) ) ) ) , file(memstr_0, rc6_memstr_0)).
thf(rc6_pboole, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ A) ) ) ) )  =>  (? [C: $i] :  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v1_funct_1 @ C)  &  ( ( (v5_funct_1 @ C)  @ B)  &  ( (v1_partfun1 @ C)  @ A) ) ) ) ) ) ) ) , file(pboole, rc6_pboole)).
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(rc7_funct_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v4_funct_1 @ A) ) ) , file(funct_1, rc7_funct_1)).
thf(rc7_memstr_0, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_setfam_1 @ A) )  &  ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_memstr_0 @ B)  @ A) ) ) ) )  =>  (? [C: $i] :  ( ~ ( (v1_xboole_0 @ C) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( (v5_funct_1 @ C)  @  ( (k2_memstr_0 @ A)  @ B) ) ) ) ) ) ) ) ) , file(memstr_0, rc7_memstr_0)).
thf(rc7_pboole, axiom,  (! [A: $i, B: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [C: $i] :  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ B)  &  ( ( (v5_relat_1 @ C)  @ A)  &  ( (v1_funct_1 @ C)  &  ( (v1_partfun1 @ C)  @ B) ) ) ) ) ) ) ) , file(pboole, rc7_pboole)).
thf(rc8_extpro_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_setfam_1 @ A) ) )  =>  (? [B: $i] :  ( ( (l1_extpro_1 @ B)  @ A)  &  ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( ( (v1_extpro_1 @ B)  @ A)  &  ( (v3_extpro_1 @ B)  @ A) ) ) ) ) ) ) ) ) , file(extpro_1, rc8_extpro_1)).
thf(rc8_funct_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) )  =>  (? [C: $i] :  ( (v1_xboole_0 @ C)  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v1_funct_1 @ C)  &  ( (v5_funct_1 @ C)  @ B) ) ) ) ) ) ) ) , file(funct_1, rc8_funct_1)).
thf(rc9_funct_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( (v2_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) ) ) ) ) , file(funct_1, rc9_funct_1)).
thf(rd1_afinsq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) )  =>  ( (= @  ( (k1_ordinal4 @ A)  @ k1_xboole_0) )  @ A) ) ) , file(afinsq_1, rd1_afinsq_1)).
thf(rd1_extpro_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_setfam_1 @ A) ) )  &  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_extpro_1 @ B)  @ A) ) ) )  &  ( ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ k5_numbers)  &  ( ( (v5_relat_1 @ C)  @  (u1_compos_1 @ B) )  &  (v1_funct_1 @ C) ) ) )  &  ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ D)  &  ( ( (v5_funct_1 @ D)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @ D)  @  (u1_struct_0 @ B) ) ) ) ) ) ) ) )  =>  ( (= @  ( ( ( ( (k5_extpro_1 @ A)  @ B)  @ C)  @ D)  @ k6_numbers) )  @ D) ) ) , file(extpro_1, rd1_extpro_1)).
thf(rd1_funct_4, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_xboole_0 @ B) ) ) )  =>  ( (= @  ( (k1_funct_4 @ B)  @ A) )  @ A) ) ) , file(funct_4, rd1_funct_4)).
thf(rd1_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  (v1_funct_1 @ A) ) )  =>  ( (= @  ( (k61_valued_1 @ A)  @ k6_numbers) )  @ A) ) ) , file(valued_1, rd1_valued_1)).
thf(rd2_afinsq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) )  =>  ( (= @  ( (k1_ordinal4 @ k1_xboole_0)  @ A) )  @ A) ) ) , file(afinsq_1, rd2_afinsq_1)).
thf(rd2_funct_4, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_xboole_0 @ B) ) ) )  =>  ( (= @  ( (k1_funct_4 @ A)  @ B) )  @ A) ) ) , file(funct_4, rd2_funct_4)).
thf(rd3_funct_4, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  &  ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) ) )  =>  ( (= @  ( (k1_funct_4 @  ( (k1_funct_4 @ A)  @ B) )  @ B) )  @  ( (k1_funct_4 @ A)  @ B) ) ) ) , file(funct_4, rd3_funct_4)).
thf(rd4_relat_1, axiom,  (! [A: $i] :  ( (v1_relat_1 @ A)  =>  ( (= @  ( (k5_relat_1 @ A)  @  (k9_xtuple_0 @ A) ) )  @ A) ) ) , file(relat_1, rd4_relat_1)).
thf(rd5_relat_1, axiom,  (! [A: $i, B: $i] :  ( (v1_relat_1 @ A)  =>  ( (= @  ( (k5_relat_1 @  ( (k5_relat_1 @ A)  @ B) )  @ B) )  @  ( (k5_relat_1 @ A)  @ B) ) ) ) , file(relat_1, rd5_relat_1)).
thf(rd8_relat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  ( (= @  ( (k5_relat_1 @ B)  @ A) )  @ B) ) ) , file(relat_1, rd8_relat_1)).
thf(redefinition_k1_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( (m1_subset_1 @ B)  @ k5_numbers) )  =>  ( (= @  ( (k1_nat_1 @ A)  @ B) )  @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(nat_1, k1_nat_1)).
thf(redefinition_k2_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k5_numbers)  &  (v7_ordinal1 @ B) )  =>  ( (= @  ( (k2_nat_1 @ A)  @ B) )  @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(nat_1, k2_nat_1)).
thf(redefinition_k3_compos_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (l1_compos_1 @ A)  &  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ A) )  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ k5_numbers) ) ) ) )  &  (v7_ordinal1 @ C) ) )  =>  ( (= @  ( ( (k3_compos_1 @ A)  @ B)  @ C) )  @  ( (k1_funct_1 @ B)  @ C) ) ) ) , file(compos_1, k3_compos_1)).
thf(redefinition_k3_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (m1_subset_1 @ D)  @ A) ) )  =>  ( (= @  ( ( ( (k3_funct_2 @ A)  @ B)  @ C)  @ D) )  @  ( (k1_funct_1 @ C)  @ D) ) ) ) , file(funct_2, k3_funct_2)).
thf(redefinition_k4_card_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (= @  (k4_card_1 @ A) )  @  (k1_ordinal1 @ A) ) ) ) , file(card_1, k4_card_1)).
thf(redefinition_k5_card_1, axiom,  (! [A: $i] :  ( (v1_finset_1 @ A)  =>  ( (= @  (k5_card_1 @ A) )  @  (k1_card_1 @ A) ) ) ) , file(card_1, k5_card_1)).
thf(redefinition_k5_numbers, axiom,  ( (= @ k5_numbers)  @ k4_ordinal1) , file(numbers, k5_numbers)).
thf(redefinition_k6_numbers, axiom,  ( (= @ k6_numbers)  @ k1_xboole_0) , file(numbers, k6_numbers)).
thf(redefinition_k7_funcop_1, axiom,  (! [A: $i, B: $i] :  ( (= @  ( (k7_funcop_1 @ A)  @ B) )  @  ( (k2_funcop_1 @ A)  @ B) ) ) , file(funcop_1, k7_funcop_1)).
thf(redefinition_m2_subset_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) ) ) )  =>  (! [C: $i] :  ( ( ( (m2_subset_1 @ C)  @ A)  @ B)  <=>  ( (m1_subset_1 @ C)  @ B) ) ) ) ) , file(subset_1, m2_subset_1)).
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__r0_r2, axiom,  ( (r1_xxreal_0 @ np__0)  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r0_r3, axiom,  ( (r1_xxreal_0 @ np__0)  @ np__3) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_r3)).
thf(rqLessOrEqual__r1_xxreal_0__r0_rm1, axiom,  ~ ( ( (r1_xxreal_0 @ np__0)  @  (k4_xcmplx_0 @ np__1) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__r0_rm2, axiom,  ~ ( ( (r1_xxreal_0 @ np__0)  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__r0_rm3, axiom,  ~ ( ( (r1_xxreal_0 @ np__0)  @  (k4_xcmplx_0 @ np__3) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_rm3)).
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(rqLessOrEqual__r1_xxreal_0__r1_r2, axiom,  ( (r1_xxreal_0 @ np__1)  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r3, axiom,  ( (r1_xxreal_0 @ np__1)  @ np__3) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r3)).
thf(rqLessOrEqual__r1_xxreal_0__r1_rm1, axiom,  ~ ( ( (r1_xxreal_0 @ np__1)  @  (k4_xcmplx_0 @ np__1) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__r1_rm2, axiom,  ~ ( ( (r1_xxreal_0 @ np__1)  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__r1_rm3, axiom,  ~ ( ( (r1_xxreal_0 @ np__1)  @  (k4_xcmplx_0 @ np__3) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_rm3)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r0, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @ np__0) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_r0)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r1, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r2, axiom,  ( (r1_xxreal_0 @ np__2)  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r3, axiom,  ( (r1_xxreal_0 @ np__2)  @ np__3) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_r3)).
thf(rqLessOrEqual__r1_xxreal_0__r2_rm1, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @  (k4_xcmplx_0 @ np__1) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__r2_rm2, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__r2_rm3, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @  (k4_xcmplx_0 @ np__3) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_rm3)).
thf(rqLessOrEqual__r1_xxreal_0__r3_r0, axiom,  ~ ( ( (r1_xxreal_0 @ np__3)  @ np__0) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_r0)).
thf(rqLessOrEqual__r1_xxreal_0__r3_r1, axiom,  ~ ( ( (r1_xxreal_0 @ np__3)  @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r3_r2, axiom,  ~ ( ( (r1_xxreal_0 @ np__3)  @ np__2) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r3_r3, axiom,  ( (r1_xxreal_0 @ np__3)  @ np__3) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_r3)).
thf(rqLessOrEqual__r1_xxreal_0__r3_rm1, axiom,  ~ ( ( (r1_xxreal_0 @ np__3)  @  (k4_xcmplx_0 @ np__1) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__r3_rm2, axiom,  ~ ( ( (r1_xxreal_0 @ np__3)  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__r3_rm3, axiom,  ~ ( ( (r1_xxreal_0 @ np__3)  @  (k4_xcmplx_0 @ np__3) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_rm3)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_r0, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @ np__0) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_r0)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_r1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_r1)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_r2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_r2)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_r3, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @ np__3) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_r3)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_rm1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_rm2, axiom,  ~ ( ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_rm3, axiom,  ~ ( ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__3) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_rm3)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_r0, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @ np__0) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_r0)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_r1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_r1)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_r2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_r2)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_r3, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @ np__3) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_r3)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_rm1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_rm2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_rm3, axiom,  ~ ( ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__3) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_rm3)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_r0, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @ np__0) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_r0)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_r1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_r1)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_r2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_r2)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_r3, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @ np__3) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_r3)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_rm1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_rm2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_rm3, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_rm3)).
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__r0_r2_r2, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @ np__2) )  @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r2_r2)).
thf(rqRealAdd__k2_xcmplx_0__r0_r3_r3, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @ np__3) )  @ np__3) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r3_r3)).
thf(rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1)).
thf(rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__2) ) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2)).
thf(rqRealAdd__k2_xcmplx_0__r0_rm3_rm3, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__3) ) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm3_rm3)).
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(rqRealAdd__k2_xcmplx_0__r1_r1_r2, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @ np__1) )  @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r1_r2)).
thf(rqRealAdd__k2_xcmplx_0__r1_r2_r3, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @ np__2) )  @ np__3) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r2_r3)).
thf(rqRealAdd__k2_xcmplx_0__r1_rm1_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm1_r0)).
thf(rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__2) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1)).
thf(rqRealAdd__k2_xcmplx_0__r1_rm3_rm2, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__3) ) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm3_rm2)).
thf(rqRealAdd__k2_xcmplx_0__r2_r0_r2, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__2)  @ np__0) )  @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_r0_r2)).
thf(rqRealAdd__k2_xcmplx_0__r2_r1_r3, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__2)  @ np__1) )  @ np__3) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_r1_r3)).
thf(rqRealAdd__k2_xcmplx_0__r2_rm1_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__2)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm1_r1)).
thf(rqRealAdd__k2_xcmplx_0__r2_rm2_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__2)  @  (k4_xcmplx_0 @ np__2) ) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm2_r0)).
thf(rqRealAdd__k2_xcmplx_0__r2_rm3_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__2)  @  (k4_xcmplx_0 @ np__3) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm3_rm1)).
thf(rqRealAdd__k2_xcmplx_0__r3_r0_r3, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__3)  @ np__0) )  @ np__3) , file(arithm, rqRealAdd__k2_xcmplx_0__r3_r0_r3)).
thf(rqRealAdd__k2_xcmplx_0__r3_rm1_r2, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__3)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r3_rm1_r2)).
thf(rqRealAdd__k2_xcmplx_0__r3_rm2_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__3)  @  (k4_xcmplx_0 @ np__2) ) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r3_rm2_r1)).
thf(rqRealAdd__k2_xcmplx_0__r3_rm3_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__3)  @  (k4_xcmplx_0 @ np__3) ) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r3_rm3_r0)).
thf(rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__0) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1)).
thf(rqRealAdd__k2_xcmplx_0__rm1_r1_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__1) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r1_r0)).
thf(rqRealAdd__k2_xcmplx_0__rm1_r2_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r2_r1)).
thf(rqRealAdd__k2_xcmplx_0__rm1_r3_r2, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__3) )  @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r3_r2)).
thf(rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2)).
thf(rqRealAdd__k2_xcmplx_0__rm1_rm2_rm3, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__2) ) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_rm2_rm3)).
thf(rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1)).
thf(rqRealAdd__k2_xcmplx_0__rm2_r2_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__2) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r2_r0)).
thf(rqRealAdd__k2_xcmplx_0__rm2_r3_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__3) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r3_r1)).
thf(rqRealAdd__k2_xcmplx_0__rm2_rm1_rm3, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_rm1_rm3)).
thf(rqRealAdd__k2_xcmplx_0__rm3_r1_rm2, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @ np__1) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm3_r1_rm2)).
thf(rqRealAdd__k2_xcmplx_0__rm3_r2_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @ np__2) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm3_r2_rm1)).
thf(rqRealAdd__k2_xcmplx_0__rm3_r3_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @ np__3) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm3_r3_r0)).
thf(rqRealDiff__k6_xcmplx_0__r0_r0_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @ np__0) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r0_r0)).
thf(rqRealDiff__k6_xcmplx_0__r0_r1_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r1_rm1)).
thf(rqRealDiff__k6_xcmplx_0__r0_r2_rm2, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @ np__2) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r2_rm2)).
thf(rqRealDiff__k6_xcmplx_0__r0_r3_rm3, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @ np__3) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r3_rm3)).
thf(rqRealDiff__k6_xcmplx_0__r0_rm1_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm1_r1)).
thf(rqRealDiff__k6_xcmplx_0__r0_rm2_r2, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__2) ) )  @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm2_r2)).
thf(rqRealDiff__k6_xcmplx_0__r0_rm3_r3, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__3) ) )  @ np__3) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm3_r3)).
thf(rqRealDiff__k6_xcmplx_0__r1_r0_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @ np__0) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r0_r1)).
thf(rqRealDiff__k6_xcmplx_0__r1_r1_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @ np__1) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r1_r0)).
thf(rqRealDiff__k6_xcmplx_0__r1_r2_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @ np__2) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r2_rm1)).
thf(rqRealDiff__k6_xcmplx_0__r1_r3_rm2, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @ np__3) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r3_rm2)).
thf(rqRealDiff__k6_xcmplx_0__r1_rm1_r2, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_rm1_r2)).
thf(rqRealDiff__k6_xcmplx_0__r1_rm2_r3, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__2) ) )  @ np__3) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_rm2_r3)).
thf(rqRealDiff__k6_xcmplx_0__r2_r0_r2, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__2)  @ np__0) )  @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r0_r2)).
thf(rqRealDiff__k6_xcmplx_0__r2_r1_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__2)  @ np__1) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r1_r1)).
thf(rqRealDiff__k6_xcmplx_0__r2_r2_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__2)  @ np__2) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r2_r0)).
thf(rqRealDiff__k6_xcmplx_0__r2_r3_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__2)  @ np__3) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r3_rm1)).
thf(rqRealDiff__k6_xcmplx_0__r2_rm1_r3, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__2)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__3) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_rm1_r3)).
thf(rqRealDiff__k6_xcmplx_0__r3_r0_r3, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__3)  @ np__0) )  @ np__3) , file(arithm, rqRealDiff__k6_xcmplx_0__r3_r0_r3)).
thf(rqRealDiff__k6_xcmplx_0__r3_r1_r2, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__3)  @ np__1) )  @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r3_r1_r2)).
thf(rqRealDiff__k6_xcmplx_0__r3_r2_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__3)  @ np__2) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r3_r2_r1)).
thf(rqRealDiff__k6_xcmplx_0__r3_r3_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__3)  @ np__3) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r3_r3_r0)).
thf(rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__0) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1)).
thf(rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__1) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2)).
thf(rqRealDiff__k6_xcmplx_0__rm1_r2_rm3, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r2_rm3)).
thf(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0)).
thf(rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__2) ) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1)).
thf(rqRealDiff__k6_xcmplx_0__rm1_rm3_r2, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__3) ) )  @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm3_r2)).
thf(rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__0) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2)).
thf(rqRealDiff__k6_xcmplx_0__rm2_r1_rm3, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__1) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_r1_rm3)).
thf(rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1)).
thf(rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__2) ) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0)).
thf(rqRealDiff__k6_xcmplx_0__rm2_rm3_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__3) ) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm3_r1)).
thf(rqRealDiff__k6_xcmplx_0__rm3_r0_rm3, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @ np__0) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm3_r0_rm3)).
thf(rqRealDiff__k6_xcmplx_0__rm3_rm1_rm2, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm3_rm1_rm2)).
thf(rqRealDiff__k6_xcmplx_0__rm3_rm2_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__2) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm3_rm2_rm1)).
thf(rqRealDiff__k6_xcmplx_0__rm3_rm3_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__3) ) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm3_rm3_r0)).
thf(rqRealMult__k3_xcmplx_0__r0_r0_r0, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__0)  @ np__0) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_r0_r0)).
thf(rqRealMult__k3_xcmplx_0__r0_r1_r0, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__0)  @ np__1) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_r1_r0)).
thf(rqRealMult__k3_xcmplx_0__r0_r2_r0, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__0)  @ np__2) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_r2_r0)).
thf(rqRealMult__k3_xcmplx_0__r0_r3_r0, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__0)  @ np__3) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_r3_r0)).
thf(rqRealMult__k3_xcmplx_0__r0_rm2_r0, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__2) ) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_rm2_r0)).
thf(rqRealMult__k3_xcmplx_0__r0_rm3_r0, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__3) ) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_rm3_r0)).
thf(rqRealMult__k3_xcmplx_0__r1_r0_r0, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__1)  @ np__0) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r1_r0_r0)).
thf(rqRealMult__k3_xcmplx_0__r1_r1_r1, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__1)  @ np__1) )  @ np__1) , file(arithm, rqRealMult__k3_xcmplx_0__r1_r1_r1)).
thf(rqRealMult__k3_xcmplx_0__r1_r2_r2, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__1)  @ np__2) )  @ np__2) , file(arithm, rqRealMult__k3_xcmplx_0__r1_r2_r2)).
thf(rqRealMult__k3_xcmplx_0__r1_r3_r3, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__1)  @ np__3) )  @ np__3) , file(arithm, rqRealMult__k3_xcmplx_0__r1_r3_r3)).
thf(rqRealMult__k3_xcmplx_0__r1_rm2_rm2, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__2) ) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__r1_rm2_rm2)).
thf(rqRealMult__k3_xcmplx_0__r1_rm3_rm3, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__3) ) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__r1_rm3_rm3)).
thf(rqRealMult__k3_xcmplx_0__r2_r0_r0, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__2)  @ np__0) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r2_r0_r0)).
thf(rqRealMult__k3_xcmplx_0__r2_r1_r2, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__2)  @ np__1) )  @ np__2) , file(arithm, rqRealMult__k3_xcmplx_0__r2_r1_r2)).
thf(rqRealMult__k3_xcmplx_0__r3_r0_r0, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__3)  @ np__0) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r3_r0_r0)).
thf(rqRealMult__k3_xcmplx_0__r3_r1_r3, axiom,  ( (= @  ( (k3_xcmplx_0 @ np__3)  @ np__1) )  @ np__3) , file(arithm, rqRealMult__k3_xcmplx_0__r3_r1_r3)).
thf(rqRealMult__k3_xcmplx_0__rm2_r0_r0, axiom,  ( (= @  ( (k3_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__0) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__rm2_r0_r0)).
thf(rqRealMult__k3_xcmplx_0__rm2_r1_rm2, axiom,  ( (= @  ( (k3_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__1) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rm2_r1_rm2)).
thf(rqRealMult__k3_xcmplx_0__rm3_r0_r0, axiom,  ( (= @  ( (k3_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @ np__0) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__rm3_r0_r0)).
thf(rqRealMult__k3_xcmplx_0__rm3_r1_rm3, axiom,  ( (= @  ( (k3_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @ np__1) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rm3_r1_rm3)).
thf(rqRealNeg__k4_xcmplx_0__r0_r0, axiom,  ( (= @  (k4_xcmplx_0 @ np__0) )  @ np__0) , file(arithm, rqRealNeg__k4_xcmplx_0__r0_r0)).
thf(rqRealNeg__k4_xcmplx_0__r1_rm1, axiom,  ( (= @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r1_rm1)).
thf(rqRealNeg__k4_xcmplx_0__r2_rm2, axiom,  ( (= @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r2_rm2)).
thf(rqRealNeg__k4_xcmplx_0__r3_rm3, axiom,  ( (= @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r3_rm3)).
thf(rqRealNeg__k4_xcmplx_0__rm1_r1, axiom,  ( (= @  (k4_xcmplx_0 @  (k4_xcmplx_0 @ np__1) ) )  @ np__1) , file(arithm, rqRealNeg__k4_xcmplx_0__rm1_r1)).
thf(rqRealNeg__k4_xcmplx_0__rm2_r2, axiom,  ( (= @  (k4_xcmplx_0 @  (k4_xcmplx_0 @ np__2) ) )  @ np__2) , file(arithm, rqRealNeg__k4_xcmplx_0__rm2_r2)).
thf(rqRealNeg__k4_xcmplx_0__rm3_r3, axiom,  ( (= @  (k4_xcmplx_0 @  (k4_xcmplx_0 @ np__3) ) )  @ np__3) , file(arithm, rqRealNeg__k4_xcmplx_0__rm3_r3)).
thf(rqSucc__k1_ordinal1__r0_r1, axiom,  ( (= @  (k1_ordinal1 @ np__0) )  @ np__1) , file(arithm, rqSucc__k1_ordinal1__r0_r1)).
thf(rqSucc__k1_ordinal1__r1_r2, axiom,  ( (= @  (k1_ordinal1 @ np__1) )  @ np__2) , file(arithm, rqSucc__k1_ordinal1__r1_r2)).
thf(rqSucc__k1_ordinal1__r2_r3, axiom,  ( (= @  (k1_ordinal1 @ np__2) )  @ np__3) , file(arithm, rqSucc__k1_ordinal1__r2_r3)).
thf(spc0_boole, axiom,  (v1_xboole_0 @ np__0) , file(boole, spc0_boole)).
thf(spc0_numerals, axiom,  ( ( ( (m2_subset_1 @ np__0)  @ k1_numbers)  @ k5_numbers)  &  ( ( (m1_subset_1 @ np__0)  @ k5_numbers)  &  ( (m1_subset_1 @ np__0)  @ k1_numbers) ) ) , file(numerals, spc0_numerals)).
thf(spc1_arithm, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( (= @  ( (k2_xcmplx_0 @ A)  @  (k4_xcmplx_0 @ B) ) )  @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(arithm, spc1_arithm)).
thf(spc1_boole, axiom,  ~ ( (v1_xboole_0 @ np__1) ) , file(boole, spc1_boole)).
thf(spc1_numerals, axiom,  ( ( (v2_xxreal_0 @ np__1)  &  ( ( (m2_subset_1 @ np__1)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ np__1)  @ k5_numbers)  &  ( (m1_subset_1 @ np__1)  @ k1_numbers) ) ) , file(numerals, spc1_numerals)).
thf(spc2_arithm, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  ( (k3_xcmplx_0 @ A)  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ A) ) ) ) , file(arithm, spc2_arithm)).
thf(spc2_boole, axiom,  ~ ( (v1_xboole_0 @ np__2) ) , file(boole, spc2_boole)).
thf(spc2_numerals, axiom,  ( ( (v2_xxreal_0 @ np__2)  &  ( ( (m2_subset_1 @ np__2)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ np__2)  @ k5_numbers)  &  ( (m1_subset_1 @ np__2)  @ k1_numbers) ) ) , file(numerals, spc2_numerals)).
thf(spc3_boole, axiom,  ~ ( (v1_xboole_0 @ np__3) ) , file(boole, spc3_boole)).
thf(spc3_numerals, axiom,  ( ( (v2_xxreal_0 @ np__3)  &  ( ( (m2_subset_1 @ np__3)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ np__3)  @ k5_numbers)  &  ( (m1_subset_1 @ np__3)  @ k1_numbers) ) ) , file(numerals, spc3_numerals)).
thf(spc5_arithm, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_xcmplx_0 @ A)  &  ( (v1_xcmplx_0 @ B)  &  (v1_xcmplx_0 @ C) ) )  =>  ( (= @  ( (k3_xcmplx_0 @  ( (k2_xcmplx_0 @ A)  @ B) )  @ C) )  @  ( (k2_xcmplx_0 @  ( (k3_xcmplx_0 @ A)  @ C) )  @  ( (k3_xcmplx_0 @ B)  @ C) ) ) ) ) , file(arithm, spc5_arithm)).
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(spc7_arithm, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_xcmplx_0 @ A)  &  ( (v1_xcmplx_0 @ B)  &  (v1_xcmplx_0 @ C) ) )  =>  ( (= @  ( (k3_xcmplx_0 @  ( (k3_xcmplx_0 @ A)  @ B) )  @ C) )  @  ( (k3_xcmplx_0 @ A)  @  ( (k3_xcmplx_0 @ B)  @ C) ) ) ) ) , file(arithm, spc6_arithm)).
thf(spc8_arithm, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ A) )  @  (k4_xcmplx_0 @ B) ) )  @  (k4_xcmplx_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) ) , file(arithm, spc8_arithm)).
thf(spc9_arithm, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ A) )  @  (k4_xcmplx_0 @ B) ) )  @  ( (k6_xcmplx_0 @ B)  @ A) ) ) ) , file(arithm, spc9_arithm)).
thf(t10_nat_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  ~ ( ( ( (r1_xxreal_0 @ A)  @ B)  &  (! [C: $i] :  ( (v7_ordinal1 @ C)  =>  ~ ( ( (= @ B)  @  ( (k2_xcmplx_0 @ A)  @ C) ) ) ) ) ) ) ) ) ) ) , file(nat_1, t10_nat_1)).
thf(t11_funct_4, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  (v1_funct_1 @ C) )  =>  ( ~ ( ( (r2_hidden @ A)  @  (k9_xtuple_0 @ B) ) )  =>  ( (= @  ( (k1_funct_1 @  ( (k1_funct_4 @ C)  @ B) )  @ A) )  @  ( (k1_funct_1 @ C)  @ A) ) ) ) ) ) ) ) , file(funct_4, t11_funct_4)).
thf(t11_scmpds_6, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ B)  &  ( ( (v5_funct_1 @ B)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( (v1_partfun1 @ B)  @  (u1_struct_0 @ k1_scmpds_2) ) ) ) ) )  =>  (! [C: $i] :  ( ( ~ ( (v1_xboole_0 @ C) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ k5_numbers)  &  ( ( (v5_relat_1 @ C)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ C)  &  ( (v1_finset_1 @ C)  &  (v1_afinsq_1 @ C) ) ) ) ) ) )  =>  (! [D: $i] :  ( ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @ k5_numbers)  &  ( ( (v5_relat_1 @ D)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ D)  &  ( (v1_partfun1 @ D)  @ k5_numbers) ) ) ) )  =>  ( (= @  ( ( ( (k3_extpro_1 @ np__2)  @ k1_scmpds_2)  @  ( (k1_funct_4 @ D)  @  ( (k10_compos_1 @ k1_scmpds_2)  @  ( (k2_scmpds_4 @ A)  @ C) ) ) )  @  ( ( (k8_memstr_0 @ np__2)  @ k1_scmpds_2)  @ B) ) )  @ A) ) ) ) ) ) ) ) ) , file(scmpds_6, t11_scmpds_6)).
thf(t143_pboole, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ~ ( (v1_xboole_0 @ B) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( ( (v5_relat_1 @ C)  @ B)  &  ( (v1_funct_1 @ C)  &  ( (v1_partfun1 @ C)  @ A) ) ) ) )  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @ A)  =>  ( (= @  ( (k1_funct_1 @ C)  @ D) )  @  ( ( (k7_partfun1 @ B)  @ C)  @ D) ) ) ) ) ) ) ) ) ) , file(pboole, t143_pboole)).
thf(t15_scmpds_4, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_compos_1 @ k1_scmpds_2) )  =>  (! [C: $i] :  ( ( ~ ( (v1_xboole_0 @ C) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ k5_numbers)  &  ( ( (v5_relat_1 @ C)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ C)  &  ( (v1_finset_1 @ C)  &  (v1_afinsq_1 @ C) ) ) ) ) ) )  =>  ( (= @  ( (k3_scmpds_4 @  ( (k2_scmpds_4 @ A)  @ C) )  @ B) )  @  ( (k2_scmpds_4 @ A)  @  ( (k3_scmpds_4 @ C)  @ B) ) ) ) ) ) ) ) ) , file(scmpds_4, t15_scmpds_4)).
thf(t15_scmpds_5, axiom,  (! [A: $i] :  ( ( (v1_ami_2 @ A)  &  ( (m1_subset_1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) ) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ B)  &  ( ( (v5_funct_1 @ B)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( (v1_partfun1 @ B)  @  (u1_struct_0 @ k1_scmpds_2) ) ) ) ) )  =>  ( (= @  ( (k1_funct_1 @  ( ( (k8_memstr_0 @ np__2)  @ k1_scmpds_2)  @ B) )  @ A) )  @  ( (k1_funct_1 @ B)  @ A) ) ) ) ) ) , file(scmpds_5, t15_scmpds_5)).
thf(t18_scmpds_4, axiom,  (! [A: $i] :  ( ( (v1_ami_2 @ A)  &  ( (m1_subset_1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ k5_numbers)  =>  ~ ( ( (r2_hidden @ A)  @  (k9_xtuple_0 @  ( ( (k7_memstr_0 @ np__2)  @ k1_scmpds_2)  @ B) ) ) ) ) ) ) ) , file(scmpds_4, t18_scmpds_4)).
thf(t18_scmpds_6, axiom,  (! [A: $i] :  ( ( (v1_ami_2 @ A)  &  ( (m1_subset_1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) ) )  =>  (! [B: $i] :  ( (v1_int_1 @ B)  =>  (! [C: $i] :  ( (v1_int_1 @ C)  =>  ~ ( ( (= @  ( ( (k9_scmpds_2 @ A)  @ B)  @ C) )  @  (k2_compos_1 @ k1_scmpds_2) ) ) ) ) ) ) ) ) , file(scmpds_6, t18_scmpds_6)).
thf(t18_scmpds_7, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( ( (v5_funct_1 @ A)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( (v1_partfun1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) ) ) ) ) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ k5_numbers) ) ) ) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ k5_numbers)  &  ( ( (v5_relat_1 @ C)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ C)  &  ( (v1_partfun1 @ C)  @ k5_numbers) ) ) ) )  =>  (! [D: $i] :  ( ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ D)  &  ( ( (v5_funct_1 @ D)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( ( (v1_partfun1 @ D)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( ( ( (v5_memstr_0 @ D)  @ np__2)  @ k1_scmpds_2)  @ k6_numbers) ) ) ) ) )  =>  (! [E: $i] :  ( ( ~ ( (v1_xboole_0 @ E) )  &  ( (v1_relat_1 @ E)  &  ( ( (v4_relat_1 @ E)  @ k5_numbers)  &  ( ( (v5_relat_1 @ E)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ E)  &  ( (v1_finset_1 @ E)  &  ( (v1_afinsq_1 @ E)  &  ( ( (v2_compos_1 @ E)  @ k1_scmpds_2)  &  (v3_scmpds_4 @ E) ) ) ) ) ) ) ) )  =>  ( ( ( (r1_tarski @  ( (k10_compos_1 @ k1_scmpds_2)  @ E) )  @ B)  &  ( ( ( (r1_scmpds_6 @ E)  @ D)  @ B)  &  ( ( (r2_scmpds_6 @ E)  @ D)  @ B) ) )  =>  (! [F: $i] :  ( ( ( (m2_subset_1 @ F)  @ k1_numbers)  @ k5_numbers)  =>  ( ( ( (r1_tarski @  ( (k61_valued_1 @ E)  @ F) )  @ C)  &  ( ( (= @  ( ( (k5_memstr_0 @ np__2)  @ k1_scmpds_2)  @ A) )  @ F)  &  ( (= @  ( ( (k6_memstr_0 @ np__2)  @ k1_scmpds_2)  @ D) )  @  ( ( (k6_memstr_0 @ np__2)  @ k1_scmpds_2)  @ A) ) ) )  =>  ( ( (= @  ( ( (k5_memstr_0 @ np__2)  @ k1_scmpds_2)  @  ( ( ( ( (k5_extpro_1 @ np__2)  @ k1_scmpds_2)  @ C)  @ A)  @  ( ( ( (k8_extpro_1 @ np__2)  @ k1_scmpds_2)  @ B)  @ D) ) ) )  @  ( (k2_nat_1 @  (k5_card_1 @ E) )  @ F) )  &  ( (= @  ( ( (k6_memstr_0 @ np__2)  @ k1_scmpds_2)  @  ( ( ( ( (k5_extpro_1 @ np__2)  @ k1_scmpds_2)  @ B)  @ D)  @  ( ( ( (k8_extpro_1 @ np__2)  @ k1_scmpds_2)  @ B)  @ D) ) ) )  @  ( ( (k6_memstr_0 @ np__2)  @ k1_scmpds_2)  @  ( ( ( ( (k5_extpro_1 @ np__2)  @ k1_scmpds_2)  @ C)  @ A)  @  ( ( ( (k8_extpro_1 @ np__2)  @ k1_scmpds_2)  @ B)  @ D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(scmpds_7, t18_scmpds_7)).
thf(t1_arithm, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  ( (k2_xcmplx_0 @ A)  @ k6_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_scmpds_7, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( ( (v5_funct_1 @ A)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( (v1_partfun1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) ) ) ) ) )  =>  (! [B: $i] :  ( ( ( (m2_subset_1 @ B)  @ k1_numbers)  @ k5_numbers)  =>  (! [C: $i] :  ( ( ( (m2_subset_1 @ C)  @ k1_numbers)  @ k5_numbers)  =>  ( ( (= @  ( ( (k5_memstr_0 @ np__2)  @ k1_scmpds_2)  @ A) )  @ B)  =>  ( (= @  ( (k17_scmpds_2 @ A)  @  ( (k6_xcmplx_0 @ C)  @ B) ) )  @ C) ) ) ) ) ) ) ) , file(scmpds_7, t1_scmpds_7)).
thf(t1_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (r2_hidden @ A)  @ B)  =>  ( (m1_subset_1 @ A)  @ B) ) ) ) , file(subset, t1_subset)).
thf(t1_xboole_1, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( ( (r1_tarski @ A)  @ B)  &  ( (r1_tarski @ B)  @ C) )  =>  ( (r1_tarski @ A)  @ C) ) ) ) ) , file(xboole_1, t1_xboole_1)).
thf(t1_xxreal_0, axiom,  (! [A: $i] :  ( (v1_xxreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xxreal_0 @ B)  =>  ( ( ( (r1_xxreal_0 @ A)  @ B)  &  ( (r1_xxreal_0 @ B)  @ A) )  =>  ( (= @ A)  @ B) ) ) ) ) ) , file(xxreal_0, t1_xxreal_0)).
thf(t23_extpro_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_setfam_1 @ A) ) )  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( ( (v3_extpro_1 @ B)  @ A)  &  ( (l1_extpro_1 @ B)  @ A) ) ) ) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ k5_numbers)  &  ( ( (v5_relat_1 @ C)  @  (u1_compos_1 @ B) )  &  (v1_funct_1 @ C) ) ) )  =>  (! [D: $i] :  ( ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ D)  &  ( ( (v5_funct_1 @ D)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @ D)  @  (u1_struct_0 @ B) ) ) ) ) )  =>  ( ( ( ( (r1_extpro_1 @ A)  @ B)  @ C)  @ D)  =>  ( (= @  ( ( ( (k6_extpro_1 @ A)  @ B)  @ C)  @ D) )  @  ( ( ( ( (k5_extpro_1 @ A)  @ B)  @ C)  @ D)  @  ( ( ( (k8_extpro_1 @ A)  @ B)  @ C)  @ D) ) ) ) ) ) ) ) ) ) ) ) , file(extpro_1, t23_extpro_1)).
thf(t25_funct_4, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) )  =>  ( (r1_tarski @ A)  @  ( (k1_funct_4 @ B)  @ A) ) ) ) ) ) , file(funct_4, t25_funct_4)).
thf(t2_arithm, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  ( (k3_xcmplx_0 @ A)  @ k6_numbers) )  @ k6_numbers) ) ) , file(arithm, t2_arithm)).
thf(t2_grfunc_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) )  =>  ( ( (r1_tarski @ A)  @ B)  <=>  ( ( (r1_tarski @  (k9_xtuple_0 @ A) )  @  (k9_xtuple_0 @ B) )  &  (! [C: $i] :  ( ( (r2_hidden @ C)  @  (k9_xtuple_0 @ A) )  =>  ( (= @  ( (k1_funct_1 @ A)  @ C) )  @  ( (k1_funct_1 @ B)  @ C) ) ) ) ) ) ) ) ) ) , file(grfunc_1, t2_grfunc_1)).
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_hidden @ A)  @ B) ) ) ) ) , file(subset, t2_subset)).
thf(t36_extpro_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_setfam_1 @ A) ) )  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( ( (v3_extpro_1 @ B)  @ A)  &  ( (l1_extpro_1 @ B)  @ A) ) ) ) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ k5_numbers)  &  ( ( (v5_relat_1 @ C)  @  (u1_compos_1 @ B) )  &  ( (v1_funct_1 @ C)  &  ( (v1_partfun1 @ C)  @ k5_numbers) ) ) ) )  =>  (! [D: $i] :  ( ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ D)  &  ( ( (v5_funct_1 @ D)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @ D)  @  (u1_struct_0 @ B) ) ) ) ) )  =>  ( ( ( ( (r1_extpro_1 @ A)  @ B)  @ C)  @ D)  =>  (! [E: $i] :  ( ( ( (m2_subset_1 @ E)  @ k1_numbers)  @ k5_numbers)  =>  ( ( (r1_xxreal_0 @  ( ( ( (k8_extpro_1 @ A)  @ B)  @ C)  @ D) )  @ E)  =>  ( (= @  ( ( ( (k3_extpro_1 @ A)  @ B)  @ C)  @  ( ( ( ( (k5_extpro_1 @ A)  @ B)  @ C)  @ D)  @ E) ) )  @  (k2_compos_1 @ B) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(extpro_1, t36_extpro_1)).
thf(t3_arithm, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  ( (k3_xcmplx_0 @ np__1)  @ A) )  @ A) ) ) , file(arithm, t3_arithm)).
thf(t3_extpro_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_setfam_1 @ A) ) )  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_extpro_1 @ B)  @ A) ) ) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ k5_numbers)  &  ( ( (v5_relat_1 @ C)  @  (u1_compos_1 @ B) )  &  (v1_funct_1 @ C) ) ) )  =>  (! [D: $i] :  ( ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ D)  &  ( ( (v5_funct_1 @ D)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @ D)  @  (u1_struct_0 @ B) ) ) ) ) )  =>  (! [E: $i] :  ( (v7_ordinal1 @ E)  =>  ( (= @  ( ( ( ( (k5_extpro_1 @ A)  @ B)  @ C)  @ D)  @  ( (k1_nat_1 @ E)  @ np__1) ) )  @  ( ( ( (k4_extpro_1 @ A)  @ B)  @  ( ( ( ( (k5_extpro_1 @ A)  @ B)  @ C)  @ D)  @ E) )  @ C) ) ) ) ) ) ) ) ) ) ) ) , file(extpro_1, t3_extpro_1)).
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(t44_memstr_0, axiom,  (! [A: $i] :  ( ~ ( (v1_setfam_1 @ A) )  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_memstr_0 @ B)  @ A) ) ) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( (v5_funct_1 @ C)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( ( ( (v5_memstr_0 @ C)  @ A)  @ B)  @ k6_numbers) ) ) ) )  =>  ( (= @  ( ( (k8_memstr_0 @ A)  @ B)  @ C) )  @ C) ) ) ) ) ) ) , file(memstr_0, t44_memstr_0)).
thf(t4_arithm, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  ( (k6_xcmplx_0 @ A)  @ k6_numbers) )  @ A) ) ) , file(arithm, t4_arithm)).
thf(t4_extpro_1, axiom,  (! [A: $i] :  ( ( ( (m2_subset_1 @ A)  @ k1_numbers)  @ k5_numbers)  =>  (! [B: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ~ ( (v1_setfam_1 @ B) ) )  =>  (! [C: $i] :  ( ( ~ ( (v2_struct_0 @ C) )  &  ( ( (v2_memstr_0 @ C)  @ B)  &  ( ( (v3_memstr_0 @ C)  @ B)  &  ( (l1_extpro_1 @ C)  @ B) ) ) )  =>  (! [D: $i] :  ( ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @  (u1_struct_0 @ C) )  &  ( (v1_funct_1 @ D)  &  ( ( (v5_funct_1 @ D)  @  ( (k2_memstr_0 @ B)  @ C) )  &  ( (v1_partfun1 @ D)  @  (u1_struct_0 @ C) ) ) ) ) )  =>  (! [E: $i] :  ( ( (v1_relat_1 @ E)  &  ( ( (v4_relat_1 @ E)  @ k5_numbers)  &  ( ( (v5_relat_1 @ E)  @  (u1_compos_1 @ C) )  &  (v1_funct_1 @ E) ) ) )  =>  (! [F: $i] :  ( ( ( (m2_subset_1 @ F)  @ k1_numbers)  @ k5_numbers)  =>  ( (= @  ( ( ( ( (k5_extpro_1 @ B)  @ C)  @ E)  @ D)  @  ( (k2_nat_1 @ A)  @ F) ) )  @  ( ( ( ( (k5_extpro_1 @ B)  @ C)  @ E)  @  ( ( ( ( (k5_extpro_1 @ B)  @ C)  @ E)  @ D)  @ A) )  @ F) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(extpro_1, t4_extpro_1)).
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_hidden @ A)  @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ C) ) )  =>  ( (m1_subset_1 @ A)  @ C) ) ) ) ) , file(subset, t4_subset)).
thf(t54_scmpds_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( ( (v5_funct_1 @ A)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( (v1_partfun1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) ) ) ) ) )  =>  (! [B: $i] :  ( (v1_int_1 @ B)  =>  ( ( (= @  ( (k1_funct_1 @  ( ( ( (k2_extpro_1 @ np__2)  @ k1_scmpds_2)  @  (k3_scmpds_2 @ B) )  @ A) )  @  (k4_struct_0 @ k1_scmpds_2) ) )  @  ( (k17_scmpds_2 @ A)  @ B) )  &  (! [C: $i] :  ( ( (v1_ami_2 @ C)  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ k1_scmpds_2) ) )  =>  ( (= @  ( (k1_funct_1 @  ( ( ( (k2_extpro_1 @ np__2)  @ k1_scmpds_2)  @  (k3_scmpds_2 @ B) )  @ A) )  @ C) )  @  ( (k1_funct_1 @ A)  @ C) ) ) ) ) ) ) ) ) , file(scmpds_2, t54_scmpds_2)).
thf(t57_scmpds_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( ( (v5_funct_1 @ A)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( (v1_partfun1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) ) ) ) ) )  =>  (! [B: $i] :  ( (v1_int_1 @ B)  =>  (! [C: $i] :  ( (v1_int_1 @ C)  =>  (! [D: $i] :  ( ( (v1_ami_2 @ D)  &  ( (m1_subset_1 @ D)  @  (u1_struct_0 @ k1_scmpds_2) ) )  =>  (! [E: $i] :  ( ( (v1_ami_2 @ E)  &  ( (m1_subset_1 @ E)  @  (u1_struct_0 @ k1_scmpds_2) ) )  =>  ( ( ( (r1_xxreal_0 @ k6_numbers)  @  ( (k1_funct_1 @ A)  @  ( (k2_scmpds_2 @  ( (k1_funct_1 @ A)  @ D) )  @ B) ) )  =>  ( (= @  ( (k1_funct_1 @  ( ( ( (k2_extpro_1 @ np__2)  @ k1_scmpds_2)  @  ( ( (k9_scmpds_2 @ D)  @ B)  @ C) )  @ A) )  @  (k4_struct_0 @ k1_scmpds_2) ) )  @  ( (k17_scmpds_2 @ A)  @ C) ) )  &  ( ( ~ ( ( (r1_xxreal_0 @ k6_numbers)  @  ( (k1_funct_1 @ A)  @  ( (k2_scmpds_2 @  ( (k1_funct_1 @ A)  @ D) )  @ B) ) ) )  =>  ( (= @  ( (k1_funct_1 @  ( ( ( (k2_extpro_1 @ np__2)  @ k1_scmpds_2)  @  ( ( (k9_scmpds_2 @ D)  @ B)  @ C) )  @ A) )  @  (k4_struct_0 @ k1_scmpds_2) ) )  @  (k4_card_1 @  ( ( (k5_memstr_0 @ np__2)  @ k1_scmpds_2)  @ A) ) ) )  &  ( (= @  ( (k1_funct_1 @  ( ( ( (k2_extpro_1 @ np__2)  @ k1_scmpds_2)  @  ( ( (k9_scmpds_2 @ D)  @ B)  @ C) )  @ A) )  @ E) )  @  ( (k1_funct_1 @ A)  @ E) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(scmpds_2, t57_scmpds_2)).
thf(t5_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (r1_xxreal_0 @ A)  @ B)  =>  ( (v1_xboole_0 @ B)  |  ( (v3_xxreal_0 @ A)  |  (v2_xxreal_0 @ B) ) ) ) ) ) ) ) , file(real, t5_real)).
thf(t5_subset, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ~ ( ( ( (r2_hidden @ 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)  =>  ( (v1_xboole_0 @ A)  |  ( (v2_xxreal_0 @ B)  |  (v3_xxreal_0 @ A) ) ) ) ) ) ) ) , file(real, t6_real)).
thf(t6_xreal_1, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  (! [C: $i] :  ( (v1_xreal_0 @ C)  =>  ( ( (r1_xxreal_0 @ A)  @ B)  <=>  ( (r1_xxreal_0 @  ( (k2_xcmplx_0 @ A)  @ C) )  @  ( (k2_xcmplx_0 @ B)  @ C) ) ) ) ) ) ) ) ) , file(xreal_1, t6_xreal_1)).
thf(t74_afinsq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_ordinal1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v5_ordinal1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finset_1 @ B) ) ) )  =>  ( (r1_tarski @ A)  @  ( (k1_ordinal4 @ A)  @ B) ) ) ) ) ) , file(afinsq_1, t74_afinsq_1)).
thf(t78_memstr_0, axiom,  (! [A: $i] :  ( ~ ( (v1_setfam_1 @ A) )  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ( (v2_memstr_0 @ B)  @ A)  &  ( ( (v3_memstr_0 @ B)  @ A)  &  ( (l1_memstr_0 @ B)  @ A) ) ) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( (v5_funct_1 @ C)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @ C)  @  (u1_struct_0 @ B) ) ) ) ) )  =>  (! [D: $i] :  ( ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ D)  &  ( ( (v5_funct_1 @ D)  @  ( (k2_memstr_0 @ A)  @ B) )  &  ( (v1_partfun1 @ D)  @  (u1_struct_0 @ B) ) ) ) ) )  =>  ( ( ( (= @  ( ( (k5_memstr_0 @ A)  @ B)  @ C) )  @  ( ( (k5_memstr_0 @ A)  @ B)  @ D) )  &  ( (= @  ( ( (k6_memstr_0 @ A)  @ B)  @ C) )  @  ( ( (k6_memstr_0 @ A)  @ B)  @ D) ) )  =>  ( (= @ C)  @ D) ) ) ) ) ) ) ) ) ) , file(memstr_0, t78_memstr_0)).
thf(t7_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( ( (r2_hidden @ 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(t7_scmpds_8, axiom,  (! [A: $i] :  ( ( (v1_ami_2 @ A)  &  ( (m1_subset_1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) ) )  =>  (! [B: $i] :  ( (v1_int_1 @ B)  =>  (! [C: $i] :  ( ( ( (m2_subset_1 @ C)  @ k1_numbers)  @ k5_numbers)  =>  (! [D: $i] :  ( ( ~ ( (v1_xboole_0 @ D) )  &  ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @ k5_numbers)  &  ( ( (v5_relat_1 @ D)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ D)  &  ( (v1_finset_1 @ D)  &  (v1_afinsq_1 @ D) ) ) ) ) ) )  =>  ( ~ ( ( (r1_xxreal_0 @  ( (k2_nat_1 @  (k5_card_1 @ D) )  @ np__2) )  @ C) )  <=>  ( (r2_hidden @ C)  @  (k9_xtuple_0 @  ( ( (k1_scmpds_8 @ A)  @ B)  @ D) ) ) ) ) ) ) ) ) ) ) ) , file(scmpds_8, t7_scmpds_8)).
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(t8_scmpds_4, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( ( (v5_funct_1 @ A)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( (v1_partfun1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) ) ) ) ) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ B)  &  ( ( (v5_funct_1 @ B)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( (v1_partfun1 @ B)  @  (u1_struct_0 @ k1_scmpds_2) ) ) ) ) )  =>  ( (! [C: $i] :  ( ( (v1_ami_2 @ C)  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ k1_scmpds_2) ) )  =>  ( (= @  ( (k1_funct_1 @ A)  @ C) )  @  ( (k1_funct_1 @ B)  @ C) ) ) )  <=>  ( (= @  ( ( (k6_memstr_0 @ np__2)  @ k1_scmpds_2)  @ A) )  @  ( ( (k6_memstr_0 @ np__2)  @ k1_scmpds_2)  @ B) ) ) ) ) ) ) , file(scmpds_4, t8_scmpds_4)).
thf(t8_scmpds_8, axiom,  (! [A: $i] :  ( ( (v1_ami_2 @ A)  &  ( (m1_subset_1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) ) )  =>  (! [B: $i] :  ( (v1_int_1 @ B)  =>  (! [C: $i] :  ( ( ~ ( (v1_xboole_0 @ C) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ k5_numbers)  &  ( ( (v5_relat_1 @ C)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ C)  &  ( (v1_finset_1 @ C)  &  (v1_afinsq_1 @ C) ) ) ) ) ) )  =>  ( ( (= @  ( (k1_funct_1 @  ( ( (k1_scmpds_8 @ A)  @ B)  @ C) )  @ k6_numbers) )  @  ( ( (k9_scmpds_2 @ A)  @ B)  @  ( (k2_nat_1 @  (k5_card_1 @ C) )  @ np__2) ) )  &  ( (= @  ( (k1_funct_1 @  ( ( (k1_scmpds_8 @ A)  @ B)  @ C) )  @  ( (k2_nat_1 @  (k5_card_1 @ C) )  @ np__1) ) )  @  (k3_scmpds_2 @  (k4_xcmplx_0 @  ( (k2_nat_1 @  (k5_card_1 @ C) )  @ np__1) ) ) ) ) ) ) ) ) ) ) , file(scmpds_8, t8_scmpds_8)).
thf(s1_scmpds_8, axiom,  (! [A: $i > $o] :  (! [B: $i] :  (! [C: $i] :  (! [D: $i] :  (! [E: $i] :  (! [F: $i] :  (! [G: $i > $i] :  ( ( (! [H: $i] :  ( ( (m2_subset_1 @  (G @ H) )  @ k1_numbers)  @ k5_numbers) )  &  ( ( (v1_relat_1 @ F)  &  ( ( (v4_relat_1 @ F)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ F)  &  ( ( (v5_funct_1 @ F)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( ( (v1_partfun1 @ F)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( ( ( (v5_memstr_0 @ F)  @ np__2)  @ k1_scmpds_2)  @ k6_numbers) ) ) ) ) )  &  ( ( (v1_relat_1 @ E)  &  ( ( (v4_relat_1 @ E)  @ k5_numbers)  &  ( ( (v5_relat_1 @ E)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ E)  &  ( (v1_partfun1 @ E)  @ k5_numbers) ) ) ) )  &  ( ( ~ ( (v1_xboole_0 @ D) )  &  ( (v1_relat_1 @ D)  &  ( ( (v4_relat_1 @ D)  @ k5_numbers)  &  ( ( (v5_relat_1 @ D)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ D)  &  ( (v1_finset_1 @ D)  &  ( (v1_afinsq_1 @ D)  &  ( ( (v2_compos_1 @ D)  @ k1_scmpds_2)  &  (v3_scmpds_4 @ D) ) ) ) ) ) ) ) )  &  ( ( (v1_ami_2 @ C)  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ k1_scmpds_2) ) )  &  (v1_int_1 @ B) ) ) ) ) )  =>  ( ( (! [I: $i] :  ( ( (v1_relat_1 @ I)  &  ( ( (v4_relat_1 @ I)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ I)  &  ( ( (v5_funct_1 @ I)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( ( (v1_partfun1 @ I)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( ( ( (v5_memstr_0 @ I)  @ np__2)  @ k1_scmpds_2)  @ k6_numbers) ) ) ) ) )  =>  ( ( (A @ I)  &  ( (= @  (G @ I) )  @ k6_numbers) )  =>  ( (r1_xxreal_0 @ k6_numbers)  @  ( (k1_funct_1 @ I)  @  ( (k2_scmpds_2 @  ( (k1_funct_1 @ F)  @ C) )  @ B) ) ) ) ) )  &  ( (A @ F)  &  (! [I: $i] :  ( ( (v1_relat_1 @ I)  &  ( ( (v4_relat_1 @ I)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ I)  &  ( ( (v5_funct_1 @ I)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( ( (v1_partfun1 @ I)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( ( ( (v5_memstr_0 @ I)  @ np__2)  @ k1_scmpds_2)  @ k6_numbers) ) ) ) ) )  =>  (! [J: $i] :  ( ( (v1_relat_1 @ J)  &  ( ( (v4_relat_1 @ J)  @ k5_numbers)  &  ( ( (v5_relat_1 @ J)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ J)  &  ( (v1_partfun1 @ J)  @ k5_numbers) ) ) ) )  =>  ( ( (A @ I)  &  ( (= @  ( (k1_funct_1 @ I)  @ C) )  @  ( (k1_funct_1 @ F)  @ C) ) )  =>  ( ( (r1_xxreal_0 @ k6_numbers)  @  ( (k1_funct_1 @ I)  @  ( (k2_scmpds_2 @  ( (k1_funct_1 @ F)  @ C) )  @ B) ) )  |  ( ( (= @  ( (k1_funct_1 @  ( ( (k6_scmpds_4 @ D)  @ I)  @ J) )  @ C) )  @  ( (k1_funct_1 @ I)  @ C) )  &  ( ( ( (r1_scmpds_6 @ D)  @ I)  @ J)  &  ( ( ( (r2_scmpds_6 @ D)  @ I)  @ J)  &  ( ~ ( ( (r1_xxreal_0 @  (G @ I) )  @  (G @  ( ( (k8_memstr_0 @ np__2)  @ k1_scmpds_2)  @  ( ( (k6_scmpds_4 @ D)  @ I)  @ J) ) ) ) )  &  (A @  ( ( (k8_memstr_0 @ np__2)  @ k1_scmpds_2)  @  ( ( (k6_scmpds_4 @ D)  @ I)  @ J) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ( ( (r1_scmpds_6 @  ( ( (k1_scmpds_8 @ C)  @ B)  @ D) )  @ F)  @ E)  &  ( ( (r2_scmpds_6 @  ( ( (k1_scmpds_8 @ C)  @ B)  @ D) )  @ F)  @ E) ) ) ) ) ) ) ) ) ) ) , file(scmpds_8, s1_scmpds_8)).
thf(s2_scmpds_8, conjecture,  ( ( ~ ( ( (r1_xxreal_0 @ k6_numbers)  @  ( (k1_funct_1 @ f2_s2_scmpds_8)  @  ( (k2_scmpds_2 @  ( (k1_funct_1 @ f2_s2_scmpds_8)  @ f5_s2_scmpds_8) )  @ f6_s2_scmpds_8) ) ) )  &  ( (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( ( (v5_funct_1 @ A)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( ( (v1_partfun1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( ( ( (v5_memstr_0 @ A)  @ np__2)  @ k1_scmpds_2)  @ k6_numbers) ) ) ) ) )  =>  ( ( (p1_s2_scmpds_8 @ A)  &  ( (= @  (f1_s2_scmpds_8 @ A) )  @ k6_numbers) )  =>  ( (r1_xxreal_0 @ k6_numbers)  @  ( (k1_funct_1 @ A)  @  ( (k2_scmpds_2 @  ( (k1_funct_1 @ f2_s2_scmpds_8)  @ f5_s2_scmpds_8) )  @ f6_s2_scmpds_8) ) ) ) ) )  &  ( (p1_s2_scmpds_8 @ f2_s2_scmpds_8)  &  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ A)  &  ( ( (v5_funct_1 @ A)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( ( (v1_partfun1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( ( ( (v5_memstr_0 @ A)  @ np__2)  @ k1_scmpds_2)  @ k6_numbers) ) ) ) ) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k5_numbers)  &  ( ( (v5_relat_1 @ B)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ B)  &  ( (v1_partfun1 @ B)  @ k5_numbers) ) ) ) )  =>  ( ( (p1_s2_scmpds_8 @ A)  &  ( (= @  ( (k1_funct_1 @ A)  @ f5_s2_scmpds_8) )  @  ( (k1_funct_1 @ f2_s2_scmpds_8)  @ f5_s2_scmpds_8) ) )  =>  ( ( (r1_xxreal_0 @ k6_numbers)  @  ( (k1_funct_1 @ A)  @  ( (k2_scmpds_2 @  ( (k1_funct_1 @ f2_s2_scmpds_8)  @ f5_s2_scmpds_8) )  @ f6_s2_scmpds_8) ) )  |  ( ( (= @  ( (k1_funct_1 @  ( ( (k6_scmpds_4 @ f4_s2_scmpds_8)  @ A)  @ B) )  @ f5_s2_scmpds_8) )  @  ( (k1_funct_1 @ A)  @ f5_s2_scmpds_8) )  &  ( ( ( (r1_scmpds_6 @ f4_s2_scmpds_8)  @ A)  @ B)  &  ( ( ( (r2_scmpds_6 @ f4_s2_scmpds_8)  @ A)  @ B)  &  ( ~ ( ( (r1_xxreal_0 @  (f1_s2_scmpds_8 @ A) )  @  (f1_s2_scmpds_8 @  ( ( (k8_memstr_0 @ np__2)  @ k1_scmpds_2)  @  ( ( (k6_scmpds_4 @ f4_s2_scmpds_8)  @ A)  @ B) ) ) ) )  &  (p1_s2_scmpds_8 @  ( ( (k8_memstr_0 @ np__2)  @ k1_scmpds_2)  @  ( ( (k6_scmpds_4 @ f4_s2_scmpds_8)  @ A)  @ B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (= @  ( ( (k6_scmpds_4 @  ( ( (k1_scmpds_8 @ f5_s2_scmpds_8)  @ f6_s2_scmpds_8)  @ f4_s2_scmpds_8) )  @ f2_s2_scmpds_8)  @ f3_s2_scmpds_8) )  @  ( ( (k6_scmpds_4 @  ( ( (k1_scmpds_8 @ f5_s2_scmpds_8)  @ f6_s2_scmpds_8)  @ f4_s2_scmpds_8) )  @  ( ( (k8_memstr_0 @ np__2)  @ k1_scmpds_2)  @  ( ( (k6_scmpds_4 @ f4_s2_scmpds_8)  @ f2_s2_scmpds_8)  @ f3_s2_scmpds_8) ) )  @ f3_s2_scmpds_8) ) ) , file(scmpds_8, s2_scmpds_8)).
