% Mizar problem: s3_scpisort,scpisort,658,12 
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(n6_type, type, np__6: $i).
thf(n7_type, type, np__7: $i).
thf(n8_type, type, np__8: $i).
thf(f1_s3_scpisort_type, type, f1_s3_scpisort: $i).
thf(f2_s3_scpisort_type, type, f2_s3_scpisort: $i).
thf(f3_s3_scpisort_type, type, f3_s3_scpisort: $i).
thf(f4_s3_scpisort_type, type, f4_s3_scpisort: $i).
thf(f5_s3_scpisort_type, type, f5_s3_scpisort: $i).
thf(f6_s3_scpisort_type, type, f6_s3_scpisort: $i).
thf(g1_extpro_1_type, type, g1_extpro_1: $i > $i > $i > $i > $i > $i > $i > $i).
thf(k11_finseq_1_type, type, k11_finseq_1: $i > $i > $i > $i).
thf(k11_scmpds_2_type, type, k11_scmpds_2: $i > $i > $i > $i).
thf(k16_complex1_type, type, k16_complex1: $i > $i).
thf(k16_funcop_1_type, type, k16_funcop_1: $i > $i > $i).
thf(k1_ami_2_type, type, k1_ami_2: $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_funct_7_type, type, k1_funct_7: $i > $i > $i).
thf(k1_int_2_type, type, k1_int_2: $i > $i).
thf(k1_numbers_type, type, k1_numbers: $i).
thf(k1_scmpds_2_type, type, k1_scmpds_2: $i).
thf(k1_scmpds_i_type, type, k1_scmpds_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_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_7_type, type, k2_scmpds_7: $i > $i > $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_ami_2_type, type, k3_ami_2: $i).
thf(k3_numbers_type, type, k3_numbers: $i).
thf(k3_real_1_type, type, k3_real_1: $i > $i > $i).
thf(k3_relat_1_type, type, k3_relat_1: $i > $i > $i).
thf(k3_scmpds_4_type, type, k3_scmpds_4: $i > $i > $i).
thf(k3_xtuple_0_type, type, k3_xtuple_0: $i > $i > $i > $i).
thf(k4_ami_2_type, type, k4_ami_2: $i).
thf(k4_card_3_type, type, k4_card_3: $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_tarski_type, type, k4_tarski: $i > $i > $i).
thf(k4_xcmplx_0_type, type, k4_xcmplx_0: $i > $i).
thf(k5_numbers_type, type, k5_numbers: $i).
thf(k6_numbers_type, type, k6_numbers: $i).
thf(k6_scmpds_1_type, type, k6_scmpds_1: $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_memstr_0_type, type, k7_memstr_0: $i > $i > $i > $i).
thf(k8_memstr_0_type, type, k8_memstr_0: $i > $i > $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_s3_scpisort_type, type, p1_s3_scpisort: $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_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_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_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_1_type, type, v2_card_1: $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_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_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_compos_0_type, type, v3_compos_0: $i > $o).
thf(v3_extpro_1_type, type, v3_extpro_1: $i > $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_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_compos_1_type, type, v4_compos_1: $i > $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_scmpds_4_type, type, v4_scmpds_4: $i > $o).
thf(v4_valued_0_type, type, v4_valued_0: $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_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_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_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_zfmisc_1 @ A) )  =>  ( (v3_card_1 @ A)  @ np__1) ) ) , file(card_1, cc10_card_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_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_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(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_1, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(card_1, cc1_card_1)).
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_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_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_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(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_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_card_1 @ A) ) ) , file(card_1, cc2_card_1)).
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_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_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_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_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_card_1 @ A) ) ) , file(card_1, cc3_card_1)).
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_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_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_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_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (v1_finset_1 @ A) ) ) , file(card_1, cc4_card_1)).
thf(cc4_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v5_ordinal1 @ A) ) ) , file(ordinal1, cc4_ordinal1)).
thf(cc4_relset_1, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ A) ) )  =>  (v1_xboole_0 @ C) ) ) ) ) , file(relset_1, cc4_relset_1)).
thf(cc4_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_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_finset_1 @ A) ) ) , file(card_1, cc5_card_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_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_1, axiom,  (! [A: $i] :  ( ( (v3_ordinal1 @ A)  &  (v1_finset_1 @ A) )  =>  (v7_ordinal1 @ A) ) ) , file(card_1, cc6_card_1)).
thf(cc6_ordinal1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc6_ordinal1)).
thf(cc6_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) ) ) ) , file(valued_0, cc6_valued_0)).
thf(cc6_xxreal_0, axiom,  (! [A: $i] :  ( ( ~ ( (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_1, axiom,  (! [A: $i] :  ( ( (v3_card_1 @ A)  @ k1_xboole_0)  =>  (v1_xboole_0 @ A) ) ) , file(card_1, cc7_card_1)).
thf(cc7_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc7_ordinal1)).
thf(cc7_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) ) ) ) , file(valued_0, cc7_valued_0)).
thf(cc7_xxreal_0, axiom,  (! [A: $i] :  ( ( (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_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  ( (v3_card_1 @ A)  @ k1_xboole_0) ) ) , file(card_1, cc8_card_1)).
thf(cc8_ordinal1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc8_ordinal1)).
thf(cc8_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc8_valued_0)).
thf(cc8_xxreal_0, axiom,  (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  ( ~ ( (v2_xxreal_0 @ A) )  &  ~ ( (v3_xxreal_0 @ A) ) ) )  =>  ( (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_1, axiom,  (! [A: $i] :  ( ( (v3_card_1 @ A)  @ np__1)  =>  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_zfmisc_1 @ A) ) ) ) , file(card_1, cc9_card_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_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_real_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  ( (m1_subset_1 @ B)  @ k1_numbers) )  =>  ( (= @  ( (k3_real_1 @ A)  @ B) )  @  ( (k3_real_1 @ B)  @ A) ) ) ) , file(real_1, k3_real_1)).
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_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(d12_scmpds_2, 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)  =>  ( (= @  ( ( (k11_scmpds_2 @ A)  @ B)  @ C) )  @  ( ( (k3_xtuple_0 @ np__8)  @ k1_xboole_0)  @  ( ( (k11_finseq_1 @ A)  @ B)  @ C) ) ) ) ) ) ) ) ) , file(scmpds_2, d12_scmpds_2)).
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(d1_scmpds_2, axiom,  ( (= @ k1_scmpds_2)  @  ( ( ( ( ( ( (g1_extpro_1 @ np__2)  @ k1_ami_2)  @  ( (k1_funct_7 @ k5_numbers)  @ k1_ami_2) )  @ k1_scmpds_i)  @ k3_ami_2)  @ k4_ami_2)  @ k6_scmpds_1) ) , file(scmpds_2, d1_scmpds_2)).
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(d3_scmpds_2, axiom,  (! [A: $i] :  ( (v1_int_1 @ A)  =>  (! [B: $i] :  ( (v1_int_1 @ B)  =>  ( (= @  ( (k2_scmpds_2 @ A)  @ B) )  @  ( (k4_tarski @ np__1)  @  (k1_int_2 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) ) ) ) ) , file(scmpds_2, d3_scmpds_2)).
thf(dt_f1_s3_scpisort, axiom,  ( (v1_relat_1 @ f1_s3_scpisort)  &  ( ( (v4_relat_1 @ f1_s3_scpisort)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ f1_s3_scpisort)  &  ( ( (v5_funct_1 @ f1_s3_scpisort)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( ( (v1_partfun1 @ f1_s3_scpisort)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( ( ( (v5_memstr_0 @ f1_s3_scpisort)  @ np__2)  @ k1_scmpds_2)  @ k6_numbers) ) ) ) ) ) , file(scpisort, f1_s3_scpisort)).
thf(dt_f2_s3_scpisort, axiom,  ( ~ ( (v1_xboole_0 @ f2_s3_scpisort) )  &  ( (v1_relat_1 @ f2_s3_scpisort)  &  ( ( (v4_relat_1 @ f2_s3_scpisort)  @ k5_numbers)  &  ( ( (v5_relat_1 @ f2_s3_scpisort)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ f2_s3_scpisort)  &  ( (v1_finset_1 @ f2_s3_scpisort)  &  ( (v1_afinsq_1 @ f2_s3_scpisort)  &  ( ( (v2_compos_1 @ f2_s3_scpisort)  @ k1_scmpds_2)  &  (v3_scmpds_4 @ f2_s3_scpisort) ) ) ) ) ) ) ) ) , file(scpisort, f2_s3_scpisort)).
thf(dt_f3_s3_scpisort, axiom,  ( (v1_relat_1 @ f3_s3_scpisort)  &  ( ( (v4_relat_1 @ f3_s3_scpisort)  @ k5_numbers)  &  ( ( (v5_relat_1 @ f3_s3_scpisort)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ f3_s3_scpisort)  &  ( (v1_partfun1 @ f3_s3_scpisort)  @ k5_numbers) ) ) ) ) , file(scpisort, f3_s3_scpisort)).
thf(dt_f4_s3_scpisort, axiom,  ( (v1_ami_2 @ f4_s3_scpisort)  &  ( (m1_subset_1 @ f4_s3_scpisort)  @  (u1_struct_0 @ k1_scmpds_2) ) ) , file(scpisort, f4_s3_scpisort)).
thf(dt_f5_s3_scpisort, axiom,  (v1_int_1 @ f5_s3_scpisort) , file(scpisort, f5_s3_scpisort)).
thf(dt_f6_s3_scpisort, axiom,  ( (m1_subset_1 @ f6_s3_scpisort)  @ k5_numbers) , file(scpisort, f6_s3_scpisort)).
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_k11_finseq_1, axiom, $true, file(finseq_1, k11_finseq_1)).
thf(dt_k11_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 @  ( ( (k11_scmpds_2 @ A)  @ B)  @ C) )  @  (u1_compos_1 @ k1_scmpds_2) ) ) ) , file(scmpds_2, k11_scmpds_2)).
thf(dt_k16_complex1, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  (v1_xreal_0 @  (k16_complex1 @ A) ) ) ) , file(complex1, k16_complex1)).
thf(dt_k16_funcop_1, axiom, $true, file(funcop_1, k16_funcop_1)).
thf(dt_k1_ami_2, axiom, $true, file(ami_2, k1_ami_2)).
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_funct_7, axiom,  (! [A: $i, B: $i] :  ( (m1_subset_1 @  ( (k1_funct_7 @ A)  @ B) )  @ B) ) , file(funct_7, k1_funct_7)).
thf(dt_k1_int_2, axiom,  (! [A: $i] :  ( (v1_int_1 @ A)  =>  ( (m1_subset_1 @  (k1_int_2 @ A) )  @ k5_numbers) ) ) , file(int_2, k1_int_2)).
thf(dt_k1_numbers, axiom, $true, file(numbers, k1_numbers)).
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_i, axiom, $true, file(scmpds_i, k1_scmpds_i)).
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_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_7, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (v1_ami_2 @ A)  &  ( (m1_subset_1 @ A)  @  (u1_struct_0 @ k1_scmpds_2) ) )  &  ( (v1_int_1 @ B)  &  ( ( (m1_subset_1 @ C)  @ 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) ) ) ) ) ) ) ) ) )  =>  ( ~ ( (v1_xboole_0 @  ( ( ( (k2_scmpds_7 @ A)  @ B)  @ C)  @ D) ) )  &  ( (v1_relat_1 @  ( ( ( (k2_scmpds_7 @ A)  @ B)  @ C)  @ D) )  &  ( ( (v4_relat_1 @  ( ( ( (k2_scmpds_7 @ A)  @ B)  @ C)  @ D) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  ( ( ( (k2_scmpds_7 @ A)  @ B)  @ C)  @ D) )  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @  ( ( ( (k2_scmpds_7 @ A)  @ B)  @ C)  @ D) )  &  ( (v1_finset_1 @  ( ( ( (k2_scmpds_7 @ A)  @ B)  @ C)  @ D) )  &  (v1_afinsq_1 @  ( ( ( (k2_scmpds_7 @ A)  @ B)  @ C)  @ D) ) ) ) ) ) ) ) ) ) , file(scmpds_7, k2_scmpds_7)).
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_ami_2, axiom,  ( (v1_funct_1 @ k3_ami_2)  &  ( ( ( (v1_funct_2 @ k3_ami_2)  @ k1_ami_2)  @ np__2)  &  ( (m1_subset_1 @ k3_ami_2)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_ami_2)  @ np__2) ) ) ) ) , file(ami_2, k3_ami_2)).
thf(dt_k3_numbers, axiom, $true, file(numbers, k3_numbers)).
thf(dt_k3_real_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  ( (m1_subset_1 @ B)  @ k1_numbers) )  =>  ( (m1_subset_1 @  ( (k3_real_1 @ A)  @ B) )  @ k1_numbers) ) ) , file(real_1, k3_real_1)).
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_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_xtuple_0, axiom, $true, file(xtuple_0, k3_xtuple_0)).
thf(dt_k4_ami_2, axiom,  ( (v1_relat_1 @ k4_ami_2)  &  ( ( (v4_relat_1 @ k4_ami_2)  @ np__2)  &  ( (v1_funct_1 @ k4_ami_2)  &  ( (v1_partfun1 @ k4_ami_2)  @ np__2) ) ) ) , file(ami_2, k4_ami_2)).
thf(dt_k4_card_3, axiom, $true, file(card_3, k4_card_3)).
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_tarski, axiom, $true, file(tarski, k4_tarski)).
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_numbers, axiom,  ( (m1_subset_1 @ k5_numbers)  @  (k1_zfmisc_1 @ k1_numbers) ) , file(numbers, k5_numbers)).
thf(dt_k6_numbers, axiom,  ( ( (m2_subset_1 @ k6_numbers)  @ k1_numbers)  @ k5_numbers) , file(numbers, k6_numbers)).
thf(dt_k6_scmpds_1, axiom,  ( (v1_funct_1 @ k6_scmpds_1)  &  ( ( ( (v1_funct_2 @ k6_scmpds_1)  @ k1_scmpds_i)  @  ( (k1_funct_2 @  (k4_card_3 @  ( (k3_relat_1 @ k3_ami_2)  @ k4_ami_2) ) )  @  (k4_card_3 @  ( (k3_relat_1 @ k3_ami_2)  @ k4_ami_2) ) ) )  &  ( (m1_subset_1 @ k6_scmpds_1)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_scmpds_i)  @  ( (k1_funct_2 @  (k4_card_3 @  ( (k3_relat_1 @ k3_ami_2)  @ k4_ami_2) ) )  @  (k4_card_3 @  ( (k3_relat_1 @ k3_ami_2)  @ k4_ami_2) ) ) ) ) ) ) ) , file(scmpds_1, k6_scmpds_1)).
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_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_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_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(fc10_card_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_finset_1 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  ~ ( (v1_finset_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) , file(card_1, fc10_card_1)).
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_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_card_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_finset_1 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  ~ ( (v1_finset_1 @  ( (k2_zfmisc_1 @ B)  @ A) ) ) ) ) , file(card_1, fc11_card_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_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_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_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) ) ) ) ) ) ) )  &  ( (v4_scmpds_4 @ B)  &  ( (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) )  &  (v3_scmpds_4 @  ( (k3_scmpds_4 @ A)  @ B) ) ) ) ) ) ) ) ) ) ) , file(scmpds_4, fc12_scmpds_4)).
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_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_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_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_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_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_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_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_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_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_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) ) )  =>  (v1_scmpds_5 @  ( ( (k11_scmpds_2 @ A)  @ B)  @ C) ) ) ) , file(scmpds_5, fc18_scmpds_5)).
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_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_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_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_xboole_0, axiom,  (v1_xboole_0 @ k1_xboole_0) , file(xboole_0, fc1_xboole_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(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(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(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_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_scmpds_4, 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) ) )  =>  (v4_scmpds_4 @  ( ( (k11_scmpds_2 @ A)  @ B)  @ C) ) ) ) , file(scmpds_4, fc3_scmpds_4)).
thf(fc3_scmpds_7, axiom,  (! [A: $i, B: $i, C: $i, D: $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)  &  ( (m1_subset_1 @ D)  @ k5_numbers) ) ) )  =>  ( ~ ( (v1_xboole_0 @  ( ( ( (k2_scmpds_7 @ B)  @ C)  @ D)  @ A) ) )  &  ( (v1_relat_1 @  ( ( ( (k2_scmpds_7 @ B)  @ C)  @ D)  @ A) )  &  ( ( (v4_relat_1 @  ( ( ( (k2_scmpds_7 @ B)  @ C)  @ D)  @ A) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  ( ( ( (k2_scmpds_7 @ B)  @ C)  @ D)  @ A) )  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @  ( ( ( (k2_scmpds_7 @ B)  @ C)  @ D)  @ A) )  &  ( (v1_finset_1 @  ( ( ( (k2_scmpds_7 @ B)  @ C)  @ D)  @ A) )  &  ( (v1_afinsq_1 @  ( ( ( (k2_scmpds_7 @ B)  @ C)  @ D)  @ A) )  &  (v3_scmpds_4 @  ( ( ( (k2_scmpds_7 @ B)  @ C)  @ D)  @ A) ) ) ) ) ) ) ) ) ) ) , file(scmpds_7, fc3_scmpds_7)).
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(fc4_card_1, axiom,  (v1_card_1 @ k4_ordinal1) , file(card_1, fc4_card_1)).
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_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_scmpds_7, axiom,  (! [A: $i, B: $i, C: $i, D: $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)  &  ( (m1_subset_1 @ D)  @ k5_numbers) ) ) )  =>  ( ~ ( (v1_xboole_0 @  ( ( ( (k2_scmpds_7 @ B)  @ C)  @ D)  @ A) ) )  &  ( (v1_relat_1 @  ( ( ( (k2_scmpds_7 @ B)  @ C)  @ D)  @ A) )  &  ( ( (v4_relat_1 @  ( ( ( (k2_scmpds_7 @ B)  @ C)  @ D)  @ A) )  @ k5_numbers)  &  ( ( (v5_relat_1 @  ( ( ( (k2_scmpds_7 @ B)  @ C)  @ D)  @ A) )  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @  ( ( ( (k2_scmpds_7 @ B)  @ C)  @ D)  @ A) )  &  ( (v1_finset_1 @  ( ( ( (k2_scmpds_7 @ B)  @ C)  @ D)  @ A) )  &  ( (v1_afinsq_1 @  ( ( ( (k2_scmpds_7 @ B)  @ C)  @ D)  @ A) )  &  ( (v2_compos_1 @  ( ( ( (k2_scmpds_7 @ B)  @ C)  @ D)  @ A) )  @ k1_scmpds_2) ) ) ) ) ) ) ) ) ) , file(scmpds_7, fc4_scmpds_7)).
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_card_1, axiom,  (v2_card_1 @ k4_ordinal1) , file(card_1, fc5_card_1)).
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_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(fc6_ordinal1, axiom,  ( ~ ( (v1_xboole_0 @ k4_ordinal1) )  &  (v3_ordinal1 @ k4_ordinal1) ) , file(ordinal1, fc6_ordinal1)).
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_card_1, axiom,  ~ ( (v1_finset_1 @ k4_ordinal1) ) , file(card_1, fc7_card_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_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(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_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_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 @  ( ( (k11_scmpds_2 @ A)  @ B)  @ C) )  @  (u1_compos_1 @ k1_scmpds_2) ) ) ) , file(scmpds_5, fc8_scmpds_5)).
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_1, axiom,  (! [A: $i] :  ( ~ ( (v1_finset_1 @ A) )  =>  ~ ( (v1_finset_1 @  (k1_zfmisc_1 @ A) ) ) ) ) , file(card_1, fc9_card_1)).
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_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(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(projectivity_k16_complex1, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  (k16_complex1 @  (k16_complex1 @ A) ) )  @  (k16_complex1 @ A) ) ) ) , file(complex1, k16_complex1)).
thf(projectivity_k1_int_2, axiom,  (! [A: $i] :  ( (v1_int_1 @ A)  =>  ( (= @  (k1_int_2 @  (k1_int_2 @ A) ) )  @  (k1_int_2 @ A) ) ) ) , file(int_2, k1_int_2)).
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(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_1, axiom,  (? [A: $i] :  (v1_card_1 @ A) ) , file(card_1, rc1_card_1)).
thf(rc1_compos_0, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_compos_0 @ A) ) ) , file(compos_0, rc1_compos_0)).
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_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_scmpds_5, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( ( (v6_compos_0 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v4_scmpds_4 @ A)  &  (v1_scmpds_5 @ A) ) ) ) ) , file(scmpds_5, rc1_scmpds_5)).
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_card_1, axiom,  (? [A: $i] :  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  ( (v3_ordinal1 @ A)  &  ( (v1_finset_1 @ A)  &  (v1_card_1 @ A) ) ) ) ) ) , file(card_1, rc2_card_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_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_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_1, axiom,  (? [A: $i] :  ~ ( (v1_finset_1 @ A) ) ) , file(card_1, rc3_card_1)).
thf(rc3_compos_0, axiom,  (? [A: $i] :  ( (v1_compos_0 @ A)  &  (v5_compos_0 @ A) ) ) , file(compos_0, rc3_compos_0)).
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_scmpds_4, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (u1_compos_1 @ k1_scmpds_2) )  &  (v4_scmpds_4 @ A) ) ) , file(scmpds_4, rc3_scmpds_4)).
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_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_1, axiom,  (! [A: $i] :  ( ~ ( (v1_finset_1 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( (v1_finset_1 @ B) ) ) ) ) ) , file(card_1, rc4_card_1)).
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_ordinal1, axiom,  (? [A: $i] :  (v7_ordinal1 @ A) ) , file(ordinal1, rc4_ordinal1)).
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_1, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (? [B: $i] :  ( (v3_card_1 @ B)  @ A) ) ) ) , file(card_1, rc5_card_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(rc6_card_1, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v3_card_1 @ B)  @ A) ) ) ) ) ) , file(card_1, rc6_card_1)).
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_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_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_card_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( (v3_card_1 @ B)  @ np__1) ) ) ) ) , file(card_1, rc7_card_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(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(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(redefinition_k1_int_2, axiom,  (! [A: $i] :  ( (v1_int_1 @ A)  =>  ( (= @  (k1_int_2 @ A) )  @  (k16_complex1 @ A) ) ) ) , file(int_2, k1_int_2)).
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_real_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  ( (m1_subset_1 @ B)  @ k1_numbers) )  =>  ( (= @  ( (k3_real_1 @ A)  @ B) )  @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(real_1, k3_real_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_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_r6, axiom,  ( (r1_xxreal_0 @ np__0)  @ np__6) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_r6)).
thf(rqLessOrEqual__r1_xxreal_0__r0_r7, axiom,  ( (r1_xxreal_0 @ np__0)  @ np__7) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_r7)).
thf(rqLessOrEqual__r1_xxreal_0__r0_r8, axiom,  ( (r1_xxreal_0 @ np__0)  @ np__8) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_r8)).
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_rm6, axiom,  ~ ( ( (r1_xxreal_0 @ np__0)  @  (k4_xcmplx_0 @ np__6) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_rm6)).
thf(rqLessOrEqual__r1_xxreal_0__r0_rm7, axiom,  ~ ( ( (r1_xxreal_0 @ np__0)  @  (k4_xcmplx_0 @ np__7) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_rm7)).
thf(rqLessOrEqual__r1_xxreal_0__r0_rm8, axiom,  ~ ( ( (r1_xxreal_0 @ np__0)  @  (k4_xcmplx_0 @ np__8) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_rm8)).
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_r6, axiom,  ( (r1_xxreal_0 @ np__1)  @ np__6) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r6)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r7, axiom,  ( (r1_xxreal_0 @ np__1)  @ np__7) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r7)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r8, axiom,  ( (r1_xxreal_0 @ np__1)  @ np__8) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r8)).
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_rm6, axiom,  ~ ( ( (r1_xxreal_0 @ np__1)  @  (k4_xcmplx_0 @ np__6) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_rm6)).
thf(rqLessOrEqual__r1_xxreal_0__r1_rm7, axiom,  ~ ( ( (r1_xxreal_0 @ np__1)  @  (k4_xcmplx_0 @ np__7) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_rm7)).
thf(rqLessOrEqual__r1_xxreal_0__r1_rm8, axiom,  ~ ( ( (r1_xxreal_0 @ np__1)  @  (k4_xcmplx_0 @ np__8) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_rm8)).
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_r6, axiom,  ( (r1_xxreal_0 @ np__2)  @ np__6) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_r6)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r7, axiom,  ( (r1_xxreal_0 @ np__2)  @ np__7) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_r7)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r8, axiom,  ( (r1_xxreal_0 @ np__2)  @ np__8) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_r8)).
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_rm6, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @  (k4_xcmplx_0 @ np__6) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_rm6)).
thf(rqLessOrEqual__r1_xxreal_0__r2_rm7, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @  (k4_xcmplx_0 @ np__7) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_rm7)).
thf(rqLessOrEqual__r1_xxreal_0__r2_rm8, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @  (k4_xcmplx_0 @ np__8) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_rm8)).
thf(rqLessOrEqual__r1_xxreal_0__r6_r0, axiom,  ~ ( ( (r1_xxreal_0 @ np__6)  @ np__0) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r6_r0)).
thf(rqLessOrEqual__r1_xxreal_0__r6_r1, axiom,  ~ ( ( (r1_xxreal_0 @ np__6)  @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r6_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r6_r2, axiom,  ~ ( ( (r1_xxreal_0 @ np__6)  @ np__2) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r6_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r6_r6, axiom,  ( (r1_xxreal_0 @ np__6)  @ np__6) , file(arithm, rqLessOrEqual__r1_xxreal_0__r6_r6)).
thf(rqLessOrEqual__r1_xxreal_0__r6_r7, axiom,  ( (r1_xxreal_0 @ np__6)  @ np__7) , file(arithm, rqLessOrEqual__r1_xxreal_0__r6_r7)).
thf(rqLessOrEqual__r1_xxreal_0__r6_r8, axiom,  ( (r1_xxreal_0 @ np__6)  @ np__8) , file(arithm, rqLessOrEqual__r1_xxreal_0__r6_r8)).
thf(rqLessOrEqual__r1_xxreal_0__r6_rm1, axiom,  ~ ( ( (r1_xxreal_0 @ np__6)  @  (k4_xcmplx_0 @ np__1) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r6_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__r6_rm2, axiom,  ~ ( ( (r1_xxreal_0 @ np__6)  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r6_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__r6_rm6, axiom,  ~ ( ( (r1_xxreal_0 @ np__6)  @  (k4_xcmplx_0 @ np__6) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r6_rm6)).
thf(rqLessOrEqual__r1_xxreal_0__r6_rm7, axiom,  ~ ( ( (r1_xxreal_0 @ np__6)  @  (k4_xcmplx_0 @ np__7) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r6_rm7)).
thf(rqLessOrEqual__r1_xxreal_0__r6_rm8, axiom,  ~ ( ( (r1_xxreal_0 @ np__6)  @  (k4_xcmplx_0 @ np__8) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r6_rm8)).
thf(rqLessOrEqual__r1_xxreal_0__r7_r0, axiom,  ~ ( ( (r1_xxreal_0 @ np__7)  @ np__0) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r7_r0)).
thf(rqLessOrEqual__r1_xxreal_0__r7_r1, axiom,  ~ ( ( (r1_xxreal_0 @ np__7)  @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r7_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r7_r2, axiom,  ~ ( ( (r1_xxreal_0 @ np__7)  @ np__2) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r7_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r7_r6, axiom,  ~ ( ( (r1_xxreal_0 @ np__7)  @ np__6) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r7_r6)).
thf(rqLessOrEqual__r1_xxreal_0__r7_r7, axiom,  ( (r1_xxreal_0 @ np__7)  @ np__7) , file(arithm, rqLessOrEqual__r1_xxreal_0__r7_r7)).
thf(rqLessOrEqual__r1_xxreal_0__r7_r8, axiom,  ( (r1_xxreal_0 @ np__7)  @ np__8) , file(arithm, rqLessOrEqual__r1_xxreal_0__r7_r8)).
thf(rqLessOrEqual__r1_xxreal_0__r7_rm1, axiom,  ~ ( ( (r1_xxreal_0 @ np__7)  @  (k4_xcmplx_0 @ np__1) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r7_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__r7_rm2, axiom,  ~ ( ( (r1_xxreal_0 @ np__7)  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r7_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__r7_rm7, axiom,  ~ ( ( (r1_xxreal_0 @ np__7)  @  (k4_xcmplx_0 @ np__7) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r7_rm7)).
thf(rqLessOrEqual__r1_xxreal_0__r8_r0, axiom,  ~ ( ( (r1_xxreal_0 @ np__8)  @ np__0) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r8_r0)).
thf(rqLessOrEqual__r1_xxreal_0__r8_r1, axiom,  ~ ( ( (r1_xxreal_0 @ np__8)  @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r8_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r8_r2, axiom,  ~ ( ( (r1_xxreal_0 @ np__8)  @ np__2) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r8_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r8_r6, axiom,  ~ ( ( (r1_xxreal_0 @ np__8)  @ np__6) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r8_r6)).
thf(rqLessOrEqual__r1_xxreal_0__r8_r7, axiom,  ~ ( ( (r1_xxreal_0 @ np__8)  @ np__7) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r8_r7)).
thf(rqLessOrEqual__r1_xxreal_0__r8_r8, axiom,  ( (r1_xxreal_0 @ np__8)  @ np__8) , file(arithm, rqLessOrEqual__r1_xxreal_0__r8_r8)).
thf(rqLessOrEqual__r1_xxreal_0__r8_rm1, axiom,  ~ ( ( (r1_xxreal_0 @ np__8)  @  (k4_xcmplx_0 @ np__1) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r8_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__r8_rm2, axiom,  ~ ( ( (r1_xxreal_0 @ np__8)  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r8_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__r8_rm6, axiom,  ~ ( ( (r1_xxreal_0 @ np__8)  @  (k4_xcmplx_0 @ np__6) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r8_rm6)).
thf(rqLessOrEqual__r1_xxreal_0__r8_rm8, axiom,  ~ ( ( (r1_xxreal_0 @ np__8)  @  (k4_xcmplx_0 @ np__8) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r8_rm8)).
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_r6, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @ np__6) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_r6)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_r7, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @ np__7) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_r7)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_r8, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @ np__8) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_r8)).
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__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_r6, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @ np__6) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_r6)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_r7, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @ np__7) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_r7)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_r8, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @ np__8) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_r8)).
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__rm6_r0, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__6) )  @ np__0) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm6_r0)).
thf(rqLessOrEqual__r1_xxreal_0__rm6_r1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__6) )  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm6_r1)).
thf(rqLessOrEqual__r1_xxreal_0__rm6_r2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__6) )  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm6_r2)).
thf(rqLessOrEqual__r1_xxreal_0__rm6_r6, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__6) )  @ np__6) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm6_r6)).
thf(rqLessOrEqual__r1_xxreal_0__rm6_rm6, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__6) )  @  (k4_xcmplx_0 @ np__6) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm6_rm6)).
thf(rqLessOrEqual__r1_xxreal_0__rm6_rm8, axiom,  ~ ( ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__6) )  @  (k4_xcmplx_0 @ np__8) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm6_rm8)).
thf(rqLessOrEqual__r1_xxreal_0__rm8_r0, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__8) )  @ np__0) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm8_r0)).
thf(rqLessOrEqual__r1_xxreal_0__rm8_r1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__8) )  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm8_r1)).
thf(rqLessOrEqual__r1_xxreal_0__rm8_r2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__8) )  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm8_r2)).
thf(rqLessOrEqual__r1_xxreal_0__rm8_r8, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__8) )  @ np__8) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm8_r8)).
thf(rqLessOrEqual__r1_xxreal_0__rm8_rm2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__8) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm8_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__rm8_rm8, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__8) )  @  (k4_xcmplx_0 @ np__8) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm8_rm8)).
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_r6_r6, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @ np__6) )  @ np__6) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r6_r6)).
thf(rqRealAdd__k2_xcmplx_0__r0_r7_r7, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @ np__7) )  @ np__7) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r7_r7)).
thf(rqRealAdd__k2_xcmplx_0__r0_r8_r8, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @ np__8) )  @ np__8) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r8_r8)).
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__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_r6_r7, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @ np__6) )  @ np__7) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r6_r7)).
thf(rqRealAdd__k2_xcmplx_0__r1_r7_r8, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @ np__7) )  @ np__8) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r7_r8)).
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_rm7_rm6, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__7) ) )  @  (k4_xcmplx_0 @ np__6) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm7_rm6)).
thf(rqRealAdd__k2_xcmplx_0__r1_rm8_rm7, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__8) ) )  @  (k4_xcmplx_0 @ np__7) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm8_rm7)).
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_r6_r8, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__2)  @ np__6) )  @ np__8) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_r6_r8)).
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_rm8_rm6, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__2)  @  (k4_xcmplx_0 @ np__8) ) )  @  (k4_xcmplx_0 @ np__6) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm8_rm6)).
thf(rqRealAdd__k2_xcmplx_0__r6_r0_r6, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__6)  @ np__0) )  @ np__6) , file(arithm, rqRealAdd__k2_xcmplx_0__r6_r0_r6)).
thf(rqRealAdd__k2_xcmplx_0__r6_r1_r7, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__6)  @ np__1) )  @ np__7) , file(arithm, rqRealAdd__k2_xcmplx_0__r6_r1_r7)).
thf(rqRealAdd__k2_xcmplx_0__r6_r2_r8, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__6)  @ np__2) )  @ np__8) , file(arithm, rqRealAdd__k2_xcmplx_0__r6_r2_r8)).
thf(rqRealAdd__k2_xcmplx_0__r6_rm6_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__6)  @  (k4_xcmplx_0 @ np__6) ) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r6_rm6_r0)).
thf(rqRealAdd__k2_xcmplx_0__r6_rm7_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__6)  @  (k4_xcmplx_0 @ np__7) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r6_rm7_rm1)).
thf(rqRealAdd__k2_xcmplx_0__r6_rm8_rm2, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__6)  @  (k4_xcmplx_0 @ np__8) ) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r6_rm8_rm2)).
thf(rqRealAdd__k2_xcmplx_0__r7_r0_r7, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__7)  @ np__0) )  @ np__7) , file(arithm, rqRealAdd__k2_xcmplx_0__r7_r0_r7)).
thf(rqRealAdd__k2_xcmplx_0__r7_r1_r8, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__7)  @ np__1) )  @ np__8) , file(arithm, rqRealAdd__k2_xcmplx_0__r7_r1_r8)).
thf(rqRealAdd__k2_xcmplx_0__r7_rm1_r6, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__7)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__6) , file(arithm, rqRealAdd__k2_xcmplx_0__r7_rm1_r6)).
thf(rqRealAdd__k2_xcmplx_0__r7_rm6_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__7)  @  (k4_xcmplx_0 @ np__6) ) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r7_rm6_r1)).
thf(rqRealAdd__k2_xcmplx_0__r7_rm7_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__7)  @  (k4_xcmplx_0 @ np__7) ) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r7_rm7_r0)).
thf(rqRealAdd__k2_xcmplx_0__r7_rm8_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__7)  @  (k4_xcmplx_0 @ np__8) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r7_rm8_rm1)).
thf(rqRealAdd__k2_xcmplx_0__r8_r0_r8, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__8)  @ np__0) )  @ np__8) , file(arithm, rqRealAdd__k2_xcmplx_0__r8_r0_r8)).
thf(rqRealAdd__k2_xcmplx_0__r8_rm1_r7, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__8)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__7) , file(arithm, rqRealAdd__k2_xcmplx_0__r8_rm1_r7)).
thf(rqRealAdd__k2_xcmplx_0__r8_rm2_r6, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__8)  @  (k4_xcmplx_0 @ np__2) ) )  @ np__6) , file(arithm, rqRealAdd__k2_xcmplx_0__r8_rm2_r6)).
thf(rqRealAdd__k2_xcmplx_0__r8_rm6_r2, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__8)  @  (k4_xcmplx_0 @ np__6) ) )  @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r8_rm6_r2)).
thf(rqRealAdd__k2_xcmplx_0__r8_rm7_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__8)  @  (k4_xcmplx_0 @ np__7) ) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r8_rm7_r1)).
thf(rqRealAdd__k2_xcmplx_0__r8_rm8_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__8)  @  (k4_xcmplx_0 @ np__8) ) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r8_rm8_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_r7_r6, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__7) )  @ np__6) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r7_r6)).
thf(rqRealAdd__k2_xcmplx_0__rm1_r8_r7, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__8) )  @ np__7) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r8_r7)).
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_rm6_rm7, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__6) ) )  @  (k4_xcmplx_0 @ np__7) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_rm6_rm7)).
thf(rqRealAdd__k2_xcmplx_0__rm1_rm7_rm8, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__7) ) )  @  (k4_xcmplx_0 @ np__8) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_rm7_rm8)).
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_r8_r6, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__8) )  @ np__6) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r8_r6)).
thf(rqRealAdd__k2_xcmplx_0__rm2_rm6_rm8, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__6) ) )  @  (k4_xcmplx_0 @ np__8) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_rm6_rm8)).
thf(rqRealAdd__k2_xcmplx_0__rm6_r6_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__6) )  @ np__6) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm6_r6_r0)).
thf(rqRealAdd__k2_xcmplx_0__rm6_r7_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__6) )  @ np__7) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__rm6_r7_r1)).
thf(rqRealAdd__k2_xcmplx_0__rm6_r8_r2, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__6) )  @ np__8) )  @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__rm6_r8_r2)).
thf(rqRealAdd__k2_xcmplx_0__rm6_rm1_rm7, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__6) )  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ np__7) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm6_rm1_rm7)).
thf(rqRealAdd__k2_xcmplx_0__rm6_rm2_rm8, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__6) )  @  (k4_xcmplx_0 @ np__2) ) )  @  (k4_xcmplx_0 @ np__8) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm6_rm2_rm8)).
thf(rqRealAdd__k2_xcmplx_0__rm7_r1_rm6, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__7) )  @ np__1) )  @  (k4_xcmplx_0 @ np__6) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm7_r1_rm6)).
thf(rqRealAdd__k2_xcmplx_0__rm7_r7_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__7) )  @ np__7) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm7_r7_r0)).
thf(rqRealAdd__k2_xcmplx_0__rm7_r8_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__7) )  @ np__8) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__rm7_r8_r1)).
thf(rqRealAdd__k2_xcmplx_0__rm7_rm1_rm8, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__7) )  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ np__8) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm7_rm1_rm8)).
thf(rqRealAdd__k2_xcmplx_0__rm8_r1_rm7, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__8) )  @ np__1) )  @  (k4_xcmplx_0 @ np__7) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm8_r1_rm7)).
thf(rqRealAdd__k2_xcmplx_0__rm8_r2_rm6, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__8) )  @ np__2) )  @  (k4_xcmplx_0 @ np__6) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm8_r2_rm6)).
thf(rqRealAdd__k2_xcmplx_0__rm8_r6_rm2, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__8) )  @ np__6) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm8_r6_rm2)).
thf(rqRealAdd__k2_xcmplx_0__rm8_r7_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__8) )  @ np__7) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm8_r7_rm1)).
thf(rqRealAdd__k2_xcmplx_0__rm8_r8_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__8) )  @ np__8) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm8_r8_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_r6_rm6, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @ np__6) )  @  (k4_xcmplx_0 @ np__6) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r6_rm6)).
thf(rqRealDiff__k6_xcmplx_0__r0_r7_rm7, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @ np__7) )  @  (k4_xcmplx_0 @ np__7) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r7_rm7)).
thf(rqRealDiff__k6_xcmplx_0__r0_r8_rm8, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @ np__8) )  @  (k4_xcmplx_0 @ np__8) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r8_rm8)).
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_rm6_r6, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__6) ) )  @ np__6) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm6_r6)).
thf(rqRealDiff__k6_xcmplx_0__r0_rm7_r7, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__7) ) )  @ np__7) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm7_r7)).
thf(rqRealDiff__k6_xcmplx_0__r0_rm8_r8, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__8) ) )  @ np__8) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm8_r8)).
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_r7_rm6, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @ np__7) )  @  (k4_xcmplx_0 @ np__6) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r7_rm6)).
thf(rqRealDiff__k6_xcmplx_0__r1_r8_rm7, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @ np__8) )  @  (k4_xcmplx_0 @ np__7) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r8_rm7)).
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_rm6_r7, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__6) ) )  @ np__7) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_rm6_r7)).
thf(rqRealDiff__k6_xcmplx_0__r1_rm7_r8, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__7) ) )  @ np__8) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_rm7_r8)).
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_r8_rm6, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__2)  @ np__8) )  @  (k4_xcmplx_0 @ np__6) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r8_rm6)).
thf(rqRealDiff__k6_xcmplx_0__r2_rm6_r8, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__2)  @  (k4_xcmplx_0 @ np__6) ) )  @ np__8) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_rm6_r8)).
thf(rqRealDiff__k6_xcmplx_0__r6_r0_r6, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__6)  @ np__0) )  @ np__6) , file(arithm, rqRealDiff__k6_xcmplx_0__r6_r0_r6)).
thf(rqRealDiff__k6_xcmplx_0__r6_r6_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__6)  @ np__6) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r6_r6_r0)).
thf(rqRealDiff__k6_xcmplx_0__r6_r7_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__6)  @ np__7) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r6_r7_rm1)).
thf(rqRealDiff__k6_xcmplx_0__r6_r8_rm2, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__6)  @ np__8) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r6_r8_rm2)).
thf(rqRealDiff__k6_xcmplx_0__r6_rm1_r7, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__6)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__7) , file(arithm, rqRealDiff__k6_xcmplx_0__r6_rm1_r7)).
thf(rqRealDiff__k6_xcmplx_0__r6_rm2_r8, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__6)  @  (k4_xcmplx_0 @ np__2) ) )  @ np__8) , file(arithm, rqRealDiff__k6_xcmplx_0__r6_rm2_r8)).
thf(rqRealDiff__k6_xcmplx_0__r7_r0_r7, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__7)  @ np__0) )  @ np__7) , file(arithm, rqRealDiff__k6_xcmplx_0__r7_r0_r7)).
thf(rqRealDiff__k6_xcmplx_0__r7_r1_r6, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__7)  @ np__1) )  @ np__6) , file(arithm, rqRealDiff__k6_xcmplx_0__r7_r1_r6)).
thf(rqRealDiff__k6_xcmplx_0__r7_r6_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__7)  @ np__6) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r7_r6_r1)).
thf(rqRealDiff__k6_xcmplx_0__r7_r7_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__7)  @ np__7) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r7_r7_r0)).
thf(rqRealDiff__k6_xcmplx_0__r7_r8_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__7)  @ np__8) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r7_r8_rm1)).
thf(rqRealDiff__k6_xcmplx_0__r7_rm1_r8, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__7)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__8) , file(arithm, rqRealDiff__k6_xcmplx_0__r7_rm1_r8)).
thf(rqRealDiff__k6_xcmplx_0__r8_r0_r8, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__8)  @ np__0) )  @ np__8) , file(arithm, rqRealDiff__k6_xcmplx_0__r8_r0_r8)).
thf(rqRealDiff__k6_xcmplx_0__r8_r1_r7, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__8)  @ np__1) )  @ np__7) , file(arithm, rqRealDiff__k6_xcmplx_0__r8_r1_r7)).
thf(rqRealDiff__k6_xcmplx_0__r8_r2_r6, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__8)  @ np__2) )  @ np__6) , file(arithm, rqRealDiff__k6_xcmplx_0__r8_r2_r6)).
thf(rqRealDiff__k6_xcmplx_0__r8_r6_r2, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__8)  @ np__6) )  @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r8_r6_r2)).
thf(rqRealDiff__k6_xcmplx_0__r8_r7_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__8)  @ np__7) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r8_r7_r1)).
thf(rqRealDiff__k6_xcmplx_0__r8_r8_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__8)  @ np__8) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r8_r8_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_r6_rm7, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__6) )  @  (k4_xcmplx_0 @ np__7) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r6_rm7)).
thf(rqRealDiff__k6_xcmplx_0__rm1_r7_rm8, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__7) )  @  (k4_xcmplx_0 @ np__8) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r7_rm8)).
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_rm7_r6, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__7) ) )  @ np__6) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm7_r6)).
thf(rqRealDiff__k6_xcmplx_0__rm1_rm8_r7, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__8) ) )  @ np__7) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm8_r7)).
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_r6_rm8, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__6) )  @  (k4_xcmplx_0 @ np__8) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_r6_rm8)).
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_rm8_r6, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__8) ) )  @ np__6) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm8_r6)).
thf(rqRealDiff__k6_xcmplx_0__rm6_r1_rm7, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__6) )  @ np__1) )  @  (k4_xcmplx_0 @ np__7) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm6_r1_rm7)).
thf(rqRealDiff__k6_xcmplx_0__rm6_r2_rm8, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__6) )  @ np__2) )  @  (k4_xcmplx_0 @ np__8) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm6_r2_rm8)).
thf(rqRealDiff__k6_xcmplx_0__rm6_rm6_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__6) )  @  (k4_xcmplx_0 @ np__6) ) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm6_rm6_r0)).
thf(rqRealDiff__k6_xcmplx_0__rm6_rm7_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__6) )  @  (k4_xcmplx_0 @ np__7) ) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__rm6_rm7_r1)).
thf(rqRealDiff__k6_xcmplx_0__rm6_rm8_r2, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__6) )  @  (k4_xcmplx_0 @ np__8) ) )  @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__rm6_rm8_r2)).
thf(rqRealDiff__k6_xcmplx_0__rm7_r0_rm7, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__7) )  @ np__0) )  @  (k4_xcmplx_0 @ np__7) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm7_r0_rm7)).
thf(rqRealDiff__k6_xcmplx_0__rm7_r1_rm8, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__7) )  @ np__1) )  @  (k4_xcmplx_0 @ np__8) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm7_r1_rm8)).
thf(rqRealDiff__k6_xcmplx_0__rm7_rm1_rm6, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__7) )  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ np__6) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm7_rm1_rm6)).
thf(rqRealDiff__k6_xcmplx_0__rm7_rm6_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__7) )  @  (k4_xcmplx_0 @ np__6) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm7_rm6_rm1)).
thf(rqRealDiff__k6_xcmplx_0__rm7_rm7_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__7) )  @  (k4_xcmplx_0 @ np__7) ) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm7_rm7_r0)).
thf(rqRealDiff__k6_xcmplx_0__rm7_rm8_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__7) )  @  (k4_xcmplx_0 @ np__8) ) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__rm7_rm8_r1)).
thf(rqRealDiff__k6_xcmplx_0__rm8_rm1_rm7, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__8) )  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ np__7) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm8_rm1_rm7)).
thf(rqRealDiff__k6_xcmplx_0__rm8_rm2_rm6, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__8) )  @  (k4_xcmplx_0 @ np__2) ) )  @  (k4_xcmplx_0 @ np__6) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm8_rm2_rm6)).
thf(rqRealDiff__k6_xcmplx_0__rm8_rm6_rm2, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__8) )  @  (k4_xcmplx_0 @ np__6) ) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm8_rm6_rm2)).
thf(rqRealDiff__k6_xcmplx_0__rm8_rm7_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__8) )  @  (k4_xcmplx_0 @ np__7) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm8_rm7_rm1)).
thf(rqRealDiff__k6_xcmplx_0__rm8_rm8_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__8) )  @  (k4_xcmplx_0 @ np__8) ) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm8_rm8_r0)).
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__r6_rm6, axiom,  ( (= @  (k4_xcmplx_0 @ np__6) )  @  (k4_xcmplx_0 @ np__6) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r6_rm6)).
thf(rqRealNeg__k4_xcmplx_0__r7_rm7, axiom,  ( (= @  (k4_xcmplx_0 @ np__7) )  @  (k4_xcmplx_0 @ np__7) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r7_rm7)).
thf(rqRealNeg__k4_xcmplx_0__r8_rm8, axiom,  ( (= @  (k4_xcmplx_0 @ np__8) )  @  (k4_xcmplx_0 @ np__8) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r8_rm8)).
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__rm6_r6, axiom,  ( (= @  (k4_xcmplx_0 @  (k4_xcmplx_0 @ np__6) ) )  @ np__6) , file(arithm, rqRealNeg__k4_xcmplx_0__rm6_r6)).
thf(rqRealNeg__k4_xcmplx_0__rm7_r7, axiom,  ( (= @  (k4_xcmplx_0 @  (k4_xcmplx_0 @ np__7) ) )  @ np__7) , file(arithm, rqRealNeg__k4_xcmplx_0__rm7_r7)).
thf(rqRealNeg__k4_xcmplx_0__rm8_r8, axiom,  ( (= @  (k4_xcmplx_0 @  (k4_xcmplx_0 @ np__8) ) )  @ np__8) , file(arithm, rqRealNeg__k4_xcmplx_0__rm8_r8)).
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_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(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(spc6_boole, axiom,  ~ ( (v1_xboole_0 @ np__6) ) , file(boole, spc6_boole)).
thf(spc6_numerals, axiom,  ( ( (v2_xxreal_0 @ np__6)  &  ( ( (m2_subset_1 @ np__6)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ np__6)  @ k5_numbers)  &  ( (m1_subset_1 @ np__6)  @ k1_numbers) ) ) , file(numerals, spc6_numerals)).
thf(spc7_boole, axiom,  ~ ( (v1_xboole_0 @ np__7) ) , file(boole, spc7_boole)).
thf(spc7_numerals, axiom,  ( ( (v2_xxreal_0 @ np__7)  &  ( ( (m2_subset_1 @ np__7)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ np__7)  @ k5_numbers)  &  ( (m1_subset_1 @ np__7)  @ k1_numbers) ) ) , file(numerals, spc7_numerals)).
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(spc8_boole, axiom,  ~ ( (v1_xboole_0 @ np__8) ) , file(boole, spc8_boole)).
thf(spc8_numerals, axiom,  ( ( (v2_xxreal_0 @ np__8)  &  ( ( (m2_subset_1 @ np__8)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ np__8)  @ k5_numbers)  &  ( (m1_subset_1 @ np__8)  @ k1_numbers) ) ) , file(numerals, spc8_numerals)).
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(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(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_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (r2_hidden @ A)  @ B)  =>  ( (m1_subset_1 @ A)  @ B) ) ) ) , file(subset, t1_subset)).
thf(t2_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( ( (r1_xxreal_0 @ A)  @ B)  &  (v3_xxreal_0 @ B) )  =>  (v3_xxreal_0 @ A) ) ) ) ) ) , file(real, t2_real)).
thf(t2_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ A)  @ B)  =>  ( (v1_xboole_0 @ B)  |  ( (r2_hidden @ A)  @ B) ) ) ) ) , file(subset, t2_subset)).
thf(t2_xxreal_0, axiom,  (! [A: $i] :  ( (v1_xxreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xxreal_0 @ B)  =>  (! [C: $i] :  ( (v1_xxreal_0 @ C)  =>  ( ( ( (r1_xxreal_0 @ A)  @ B)  &  ( (r1_xxreal_0 @ B)  @ C) )  =>  ( (r1_xxreal_0 @ A)  @ C) ) ) ) ) ) ) ) , file(xxreal_0, t2_xxreal_0)).
thf(t3_int_1, axiom,  (! [A: $i] :  ( (v1_int_1 @ A)  =>  ( ( (r1_xxreal_0 @ k6_numbers)  @ A)  =>  ( (r2_hidden @ A)  @ k5_numbers) ) ) ) , file(int_1, t3_int_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(t44_xreal_1, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ~ ( ( (r1_xxreal_0 @ A)  @ k6_numbers) )  &  ( (r1_xxreal_0 @ B)  @  ( (k6_xcmplx_0 @ B)  @ A) ) ) ) ) ) ) ) , file(xreal_1, t44_xreal_1)).
thf(t47_scmpds_7, axiom,  (! [A: $i] :  ( ( (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_partfun1 @ A)  @ k5_numbers) ) ) ) )  =>  (! [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_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) ) )  =>  (! [F: $i] :  ( (v1_int_1 @ F)  =>  (! [G: $i] :  ( ( ( (m2_subset_1 @ G)  @ k1_numbers)  @ k5_numbers)  =>  ( ( (r1_xxreal_0 @  ( (k1_funct_1 @ B)  @  ( (k2_scmpds_2 @  ( (k1_funct_1 @ B)  @ D) )  @ F) ) )  @ k6_numbers)  =>  ( (= @  ( (k1_funct_1 @  ( ( (k6_scmpds_4 @  ( ( ( (k2_scmpds_7 @ D)  @ F)  @ G)  @ C) )  @  ( ( (k8_memstr_0 @ np__2)  @ k1_scmpds_2)  @ B) )  @ A) )  @ E) )  @  ( (k1_funct_1 @ B)  @ E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(scmpds_7, t47_scmpds_7)).
thf(t4_arithm, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  ( (k6_xcmplx_0 @ A)  @ k6_numbers) )  @ A) ) ) , file(arithm, t4_arithm)).
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_scpisort, 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) ) ) )  =>  ( (= @  ( ( (k8_memstr_0 @ np__2)  @ k1_scmpds_2)  @ A) )  @  ( ( (k8_memstr_0 @ np__2)  @ k1_scmpds_2)  @ B) ) ) ) ) ) ) , file(scpisort, t4_scpisort)).
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(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(t7_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( ( (r2_hidden @ A)  @ B)  &  (v1_xboole_0 @ B) ) ) ) ) , file(boole, t7_boole)).
thf(t7_int_1, axiom,  (! [A: $i] :  ( (v1_int_1 @ A)  =>  (! [B: $i] :  ( (v1_int_1 @ B)  =>  ( ~ ( ( (r1_xxreal_0 @ B)  @ A) )  =>  ( (r1_xxreal_0 @  ( (k3_real_1 @ A)  @ np__1) )  @ B) ) ) ) ) ) , file(int_1, t7_int_1)).
thf(t7_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ~ ( ( (r1_xxreal_0 @ A)  @ B) )  &  ( ~ ( (v2_xxreal_0 @ A) )  &  ~ ( (v3_xxreal_0 @ B) ) ) ) ) ) ) ) ) , file(real, t7_real)).
thf(t8_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( (v1_xboole_0 @ A)  &  ( ~ ( ( (= @ A)  @ B) )  &  (v1_xboole_0 @ B) ) ) ) ) ) , file(boole, t8_boole)).
thf(t8_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ~ ( ( (r1_xxreal_0 @ A)  @ B) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  ~ ( (v2_xxreal_0 @ A) ) ) ) ) ) ) ) ) , file(real, t8_real)).
thf(s1_nat_1, axiom,  (! [A: $i > $o] :  ( ( (A @ k6_numbers)  &  (! [B: $i] :  ( ( ( (m2_subset_1 @ B)  @ k1_numbers)  @ k5_numbers)  =>  ( (A @ B)  =>  (A @  ( (k2_nat_1 @ B)  @ np__1) ) ) ) ) )  =>  (! [B: $i] :  ( ( ( (m2_subset_1 @ B)  @ k1_numbers)  @ k5_numbers)  =>  (A @ B) ) ) ) ) , file(nat_1, s1_nat_1)).
thf(s2_scpisort, axiom,  (! [A: $i > $o] :  (! [B: $i] :  (! [C: $i] :  (! [D: $i] :  (! [E: $i] :  (! [F: $i] :  (! [G: $i] :  ( ( ( (v1_relat_1 @ G)  &  ( ( (v4_relat_1 @ G)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ G)  &  ( ( (v5_funct_1 @ G)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( ( (v1_partfun1 @ G)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( ( ( (v5_memstr_0 @ G)  @ np__2)  @ k1_scmpds_2)  @ k6_numbers) ) ) ) ) )  &  ( ( (v1_relat_1 @ F)  &  ( ( (v4_relat_1 @ F)  @ k5_numbers)  &  ( ( (v5_relat_1 @ F)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ F)  &  ( (v1_partfun1 @ F)  @ k5_numbers) ) ) ) )  &  ( ( ~ ( (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) ) ) ) ) ) ) ) )  &  ( ( (v1_ami_2 @ D)  &  ( (m1_subset_1 @ D)  @  (u1_struct_0 @ k1_scmpds_2) ) )  &  ( (v1_int_1 @ C)  &  ( (m1_subset_1 @ B)  @ k5_numbers) ) ) ) ) )  =>  ( ( ~ ( ( (r1_xxreal_0 @ B)  @ k6_numbers) )  &  ( ~ ( ( (r1_xxreal_0 @  ( (k1_funct_1 @ G)  @  ( (k2_scmpds_2 @  ( (k1_funct_1 @ G)  @ D) )  @ C) ) )  @ k6_numbers) )  &  ( (A @ G)  &  (! [H: $i] :  ( ( (v1_relat_1 @ H)  &  ( ( (v4_relat_1 @ H)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ H)  &  ( ( (v5_funct_1 @ H)  @  ( (k2_memstr_0 @ np__2)  @ k1_scmpds_2) )  &  ( ( (v1_partfun1 @ H)  @  (u1_struct_0 @ k1_scmpds_2) )  &  ( ( ( (v5_memstr_0 @ H)  @ np__2)  @ k1_scmpds_2)  @ k6_numbers) ) ) ) ) )  =>  (! [I: $i] :  ( ( (v1_relat_1 @ I)  &  ( ( (v4_relat_1 @ I)  @ k5_numbers)  &  ( ( (v5_relat_1 @ I)  @  (u1_compos_1 @ k1_scmpds_2) )  &  ( (v1_funct_1 @ I)  &  ( (v1_partfun1 @ I)  @ k5_numbers) ) ) ) )  =>  ( ( (A @ H)  &  ( (= @  ( (k1_funct_1 @ H)  @ D) )  @  ( (k1_funct_1 @ G)  @ D) ) )  =>  ( ( (r1_xxreal_0 @  ( (k1_funct_1 @ H)  @  ( (k2_scmpds_2 @  ( (k1_funct_1 @ G)  @ D) )  @ C) ) )  @ k6_numbers)  |  ( ( (= @  ( (k1_funct_1 @  ( ( (k6_scmpds_4 @  ( (k3_scmpds_4 @ E)  @  ( ( (k11_scmpds_2 @ D)  @ C)  @  (k4_xcmplx_0 @ B) ) ) )  @ H)  @ I) )  @ D) )  @  ( (k1_funct_1 @ H)  @ D) )  &  ( ( (= @  ( (k1_funct_1 @  ( ( (k6_scmpds_4 @  ( (k3_scmpds_4 @ E)  @  ( ( (k11_scmpds_2 @ D)  @ C)  @  (k4_xcmplx_0 @ B) ) ) )  @ H)  @ I) )  @  ( (k2_scmpds_2 @  ( (k1_funct_1 @ G)  @ D) )  @ C) ) )  @  ( (k6_xcmplx_0 @  ( (k1_funct_1 @ H)  @  ( (k2_scmpds_2 @  ( (k1_funct_1 @ G)  @ D) )  @ C) ) )  @ B) )  &  ( ( ( (r1_scmpds_6 @ E)  @ H)  @ I)  &  ( ( ( (r2_scmpds_6 @ E)  @ H)  @ I)  &  (A @  ( ( (k8_memstr_0 @ np__2)  @ k1_scmpds_2)  @  ( ( (k6_scmpds_4 @  ( (k3_scmpds_4 @ E)  @  ( ( (k11_scmpds_2 @ D)  @ C)  @  (k4_xcmplx_0 @ B) ) ) )  @ H)  @ I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (= @  ( ( (k6_scmpds_4 @  ( ( ( (k2_scmpds_7 @ D)  @ C)  @ B)  @ E) )  @ G)  @ F) )  @  ( ( (k6_scmpds_4 @  ( ( ( (k2_scmpds_7 @ D)  @ C)  @ B)  @ E) )  @  ( ( (k8_memstr_0 @ np__2)  @ k1_scmpds_2)  @  ( ( (k6_scmpds_4 @  ( (k3_scmpds_4 @ E)  @  ( ( (k11_scmpds_2 @ D)  @ C)  @  (k4_xcmplx_0 @ B) ) ) )  @ G)  @ F) ) )  @ F) ) ) ) ) ) ) ) ) ) ) , file(scpisort, s2_scpisort)).
thf(s3_scpisort, conjecture,  ( ( ~ ( ( (r1_xxreal_0 @ f6_s3_scpisort)  @ k6_numbers) )  &  ( (p1_s3_scpisort @ f1_s3_scpisort)  &  (! [A: $i] :  ( ( (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_partfun1 @ A)  @ k5_numbers) ) ) ) )  =>  (! [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) )  &  ( ( ( (v5_memstr_0 @ B)  @ np__2)  @ k1_scmpds_2)  @ k6_numbers) ) ) ) ) )  =>  ( ( (p1_s3_scpisort @ B)  &  ( (= @  ( (k1_funct_1 @ B)  @ f4_s3_scpisort) )  @  ( (k1_funct_1 @ f1_s3_scpisort)  @ f4_s3_scpisort) ) )  =>  ( ( (r1_xxreal_0 @  ( (k1_funct_1 @ B)  @  ( (k2_scmpds_2 @  ( (k1_funct_1 @ f1_s3_scpisort)  @ f4_s3_scpisort) )  @ f5_s3_scpisort) ) )  @ k6_numbers)  |  ( ( (= @  ( (k1_funct_1 @  ( ( (k6_scmpds_4 @  ( (k3_scmpds_4 @ f2_s3_scpisort)  @  ( ( (k11_scmpds_2 @ f4_s3_scpisort)  @ f5_s3_scpisort)  @  (k4_xcmplx_0 @ f6_s3_scpisort) ) ) )  @ B)  @ A) )  @ f4_s3_scpisort) )  @  ( (k1_funct_1 @ B)  @ f4_s3_scpisort) )  &  ( ( (= @  ( (k1_funct_1 @  ( ( (k6_scmpds_4 @  ( (k3_scmpds_4 @ f2_s3_scpisort)  @  ( ( (k11_scmpds_2 @ f4_s3_scpisort)  @ f5_s3_scpisort)  @  (k4_xcmplx_0 @ f6_s3_scpisort) ) ) )  @ B)  @ A) )  @  ( (k2_scmpds_2 @  ( (k1_funct_1 @ f1_s3_scpisort)  @ f4_s3_scpisort) )  @ f5_s3_scpisort) ) )  @  ( (k6_xcmplx_0 @  ( (k1_funct_1 @ B)  @  ( (k2_scmpds_2 @  ( (k1_funct_1 @ f1_s3_scpisort)  @ f4_s3_scpisort) )  @ f5_s3_scpisort) ) )  @ f6_s3_scpisort) )  &  ( ( ( (r1_scmpds_6 @ f2_s3_scpisort)  @ B)  @ A)  &  ( ( ( (r2_scmpds_6 @ f2_s3_scpisort)  @ B)  @ A)  &  (p1_s3_scpisort @  ( ( (k8_memstr_0 @ np__2)  @ k1_scmpds_2)  @  ( ( (k6_scmpds_4 @  ( (k3_scmpds_4 @ f2_s3_scpisort)  @  ( ( (k11_scmpds_2 @ f4_s3_scpisort)  @ f5_s3_scpisort)  @  (k4_xcmplx_0 @ f6_s3_scpisort) ) ) )  @ B)  @ A) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ( (r1_xxreal_0 @  ( (k1_funct_1 @  ( ( (k6_scmpds_4 @  ( ( ( (k2_scmpds_7 @ f4_s3_scpisort)  @ f5_s3_scpisort)  @ f6_s3_scpisort)  @ f2_s3_scpisort) )  @ f1_s3_scpisort)  @ f3_s3_scpisort) )  @  ( (k2_scmpds_2 @  ( (k1_funct_1 @ f1_s3_scpisort)  @ f4_s3_scpisort) )  @ f5_s3_scpisort) ) )  @ k6_numbers)  &  (p1_s3_scpisort @  ( ( (k8_memstr_0 @ np__2)  @ k1_scmpds_2)  @  ( ( (k6_scmpds_4 @  ( ( ( (k2_scmpds_7 @ f4_s3_scpisort)  @ f5_s3_scpisort)  @ f6_s3_scpisort)  @ f2_s3_scpisort) )  @ f1_s3_scpisort)  @ f3_s3_scpisort) ) ) ) ) , file(scpisort, s3_scpisort)).
