% Mizar problem: t5_cfdiff_2,cfdiff_2,1052,5 
include('Axioms/SET010^0.ax').
thf(n0_type, type, np__0: $i).
thf(n1_type, type, np__1: $i).
thf(n2_type, type, np__2: $i).
thf(n3_type, type, np__3: $i).
thf(g1_normsp_1_type, type, g1_normsp_1: $i > $i > $i > $i > $i > $i).
thf(g1_rltopsp1_type, type, g1_rltopsp1: $i > $i > $i > $i > $i > $i).
thf(g1_rlvect_1_type, type, g1_rlvect_1: $i > $i > $i > $i > $i).
thf(k10_finseq_1_type, type, k10_finseq_1: $i > $i > $i).
thf(k10_lopban_1_type, type, k10_lopban_1: $i > $i > $i).
thf(k10_pdiff_1_type, type, k10_pdiff_1: $i > $i > $i > $i > $i).
thf(k10_rsspace_type, type, k10_rsspace: $i > $i > $i).
thf(k10_rvsum_1_type, type, k10_rvsum_1: $i > $i > $i).
thf(k10_xtuple_0_type, type, k10_xtuple_0: $i > $i).
thf(k11_binop_2_type, type, k11_binop_2: $i > $i > $i).
thf(k11_pdiff_1_type, type, k11_pdiff_1: $i > $i > $i > $i > $i).
thf(k12_euclid_type, type, k12_euclid: $i > $i).
thf(k12_finseq_1_type, type, k12_finseq_1: $i > $i > $i).
thf(k12_rvsum_1_type, type, k12_rvsum_1: $i > $i).
thf(k15_euclid_type, type, k15_euclid: $i > $i).
thf(k15_lopban_1_type, type, k15_lopban_1: $i > $i > $i).
thf(k16_complex1_type, type, k16_complex1: $i > $i).
thf(k16_lopban_1_type, type, k16_lopban_1: $i > $i > $i).
thf(k16_rvsum_1_type, type, k16_rvsum_1: $i > $i).
thf(k17_complex1_type, type, k17_complex1: $i > $i).
thf(k17_euclid_type, type, k17_euclid: $i > $i).
thf(k17_lopban_1_type, type, k17_lopban_1: $i > $i > $i > $i > $i).
thf(k18_complex1_type, type, k18_complex1: $i > $i).
thf(k18_euclid_type, type, k18_euclid: $i > $i).
thf(k18_rvsum_1_type, type, k18_rvsum_1: $i > $i).
thf(k18_valued_1_type, type, k18_valued_1: $i > $i > $i).
thf(k19_euclid_type, type, k19_euclid: $i > $i > $i).
thf(k1_algstr_0_type, type, k1_algstr_0: $i > $i > $i > $i).
thf(k1_card_1_type, type, k1_card_1: $i > $i).
thf(k1_complex1_type, type, k1_complex1: $i > $i).
thf(k1_euclid_type, type, k1_euclid: $i > $i).
thf(k1_fdiff_1_type, type, k1_fdiff_1: $i > $i > $i).
thf(k1_finseq_1_type, type, k1_finseq_1: $i > $i).
thf(k1_finseq_7_type, type, k1_finseq_7: $i > $i > $i > $i > $i).
thf(k1_finsop_1_type, type, k1_finsop_1: $i > $i > $i > $i).
thf(k1_funct_1_type, type, k1_funct_1: $i > $i > $i).
thf(k1_funct_2_type, type, k1_funct_2: $i > $i > $i).
thf(k1_ndiff_1_type, type, k1_ndiff_1: $i > $i > $i > $i).
thf(k1_normsp_0_type, type, k1_normsp_0: $i > $i > $i).
thf(k1_normsp_1_type, type, k1_normsp_1: $i > $i > $i > $i).
thf(k1_numbers_type, type, k1_numbers: $i).
thf(k1_partfun1_type, type, k1_partfun1: $i > $i > $i > $i > $i > $i > $i).
thf(k1_pdiff_1_type, type, k1_pdiff_1: $i > $i > $i).
thf(k1_real_1_type, type, k1_real_1: $i > $i).
thf(k1_real_ns1_type, type, k1_real_ns1: $i > $i).
thf(k1_relset_1_type, type, k1_relset_1: $i > $i > $i).
thf(k1_rlvect_1_type, type, k1_rlvect_1: $i > $i > $i > $i).
thf(k1_rvsum_1_type, type, k1_rvsum_1: $i > $i).
thf(k1_seq_1_type, type, k1_seq_1: $i > $i > $i).
thf(k1_seq_2_type, type, k1_seq_2: $i > $i).
thf(k1_valued_1_type, type, k1_valued_1: $i > $i > $i).
thf(k1_xboole_0_type, type, k1_xboole_0: $i).
thf(k1_zfmisc_1_type, type, k1_zfmisc_1: $i > $i).
thf(k20_valued_1_type, type, k20_valued_1: $i > $i > $i > $i > $i > $i).
thf(k24_valued_1_type, type, k24_valued_1: $i > $i > $i).
thf(k2_complex1_type, type, k2_complex1: $i > $i).
thf(k2_finseq_1_type, type, k2_finseq_1: $i > $i).
thf(k2_finseq_2_type, type, k2_finseq_2: $i > $i > $i).
thf(k2_finseq_4_type, type, k2_finseq_4: $i > $i > $i > $i).
thf(k2_funcop_1_type, type, k2_funcop_1: $i > $i > $i).
thf(k2_funct_1_type, type, k2_funct_1: $i > $i).
thf(k2_funct_7_type, type, k2_funct_7: $i > $i > $i > $i).
thf(k2_lopban_1_type, type, k2_lopban_1: $i > $i > $i).
thf(k2_normsp_0_type, type, k2_normsp_0: $i > $i > $i).
thf(k2_rcomp_1_type, type, k2_rcomp_1: $i > $i > $i).
thf(k2_real_1_type, type, k2_real_1: $i > $i).
thf(k2_real_ns1_type, type, k2_real_ns1: $i > $i).
thf(k2_relset_1_type, type, k2_relset_1: $i > $i > $i).
thf(k2_rvsum_1_type, type, k2_rvsum_1: $i).
thf(k2_seq_2_type, type, k2_seq_2: $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(k30_valued_1_type, type, k30_valued_1: $i > $i).
thf(k31_binop_2_type, type, k31_binop_2: $i).
thf(k33_binop_2_type, type, k33_binop_2: $i).
thf(k34_binop_2_type, type, k34_binop_2: $i).
thf(k35_binop_2_type, type, k35_binop_2: $i).
thf(k35_valued_1_type, type, k35_valued_1: $i > $i).
thf(k37_valued_1_type, type, k37_valued_1: $i > $i > $i > $i).
thf(k39_valued_1_type, type, k39_valued_1: $i > $i).
thf(k3_complex1_type, type, k3_complex1: $i > $i).
thf(k3_finseq_1_type, type, k3_finseq_1: $i > $i).
thf(k3_funcop_1_type, type, k3_funcop_1: $i > $i > $i > $i).
thf(k3_funct_2_type, type, k3_funct_2: $i > $i > $i > $i > $i).
thf(k3_lopban_1_type, type, k3_lopban_1: $i > $i > $i).
thf(k3_ndiff_1_type, type, k3_ndiff_1: $i > $i > $i > $i > $i).
thf(k3_numbers_type, type, k3_numbers: $i).
thf(k3_pdiff_1_type, type, k3_pdiff_1: $i > $i > $i).
thf(k3_real_ns1_type, type, k3_real_ns1: $i > $i).
thf(k3_relat_1_type, type, k3_relat_1: $i > $i > $i).
thf(k3_rlvect_1_type, type, k3_rlvect_1: $i > $i > $i > $i).
thf(k3_rvsum_1_type, type, k3_rvsum_1: $i > $i).
thf(k3_square_1_type, type, k3_square_1: $i > $i).
thf(k3_xcmplx_0_type, type, k3_xcmplx_0: $i > $i > $i).
thf(k45_valued_1_type, type, k45_valued_1: $i > $i > $i).
thf(k4_complex1_type, type, k4_complex1: $i > $i).
thf(k4_euclid_type, type, k4_euclid: $i > $i).
thf(k4_finseq_2_type, type, k4_finseq_2: $i > $i > $i).
thf(k4_lopban_1_type, type, k4_lopban_1: $i > $i > $i).
thf(k4_normsp_0_type, type, k4_normsp_0: $i > $i > $i).
thf(k4_numbers_type, type, k4_numbers: $i).
thf(k4_ordinal1_type, type, k4_ordinal1: $i).
thf(k4_real_ns1_type, type, k4_real_ns1: $i > $i).
thf(k4_relat_1_type, type, k4_relat_1: $i > $i).
thf(k4_rvsum_1_type, type, k4_rvsum_1: $i > $i > $i).
thf(k4_struct_0_type, type, k4_struct_0: $i > $i).
thf(k4_xcmplx_0_type, type, k4_xcmplx_0: $i > $i).
thf(k4_xxreal_1_type, type, k4_xxreal_1: $i > $i > $i).
thf(k54_valued_1_type, type, k54_valued_1: $i > $i).
thf(k56_valued_1_type, type, k56_valued_1: $i > $i > $i > $i).
thf(k5_algstr_0_type, type, k5_algstr_0: $i > $i > $i > $i).
thf(k5_euclid_type, type, k5_euclid: $i > $i).
thf(k5_finseq_1_type, type, k5_finseq_1: $i > $i).
thf(k5_finseq_2_type, type, k5_finseq_2: $i > $i > $i > $i).
thf(k5_funcop_1_type, type, k5_funcop_1: $i > $i > $i > $i).
thf(k5_lopban_1_type, type, k5_lopban_1: $i > $i > $i).
thf(k5_numbers_type, type, k5_numbers: $i).
thf(k5_pdiff_1_type, type, k5_pdiff_1: $i > $i > $i).
thf(k5_square_1_type, type, k5_square_1: $i > $i).
thf(k5_xcmplx_0_type, type, k5_xcmplx_0: $i > $i).
thf(k6_finseqop_type, type, k6_finseqop: $i > $i > $i > $i).
thf(k6_normsp_1_type, type, k6_normsp_1: $i > $i > $i).
thf(k6_numbers_type, type, k6_numbers: $i).
thf(k6_partfun1_type, type, k6_partfun1: $i > $i).
thf(k6_pdiff_1_type, type, k6_pdiff_1: $i > $i > $i > $i).
thf(k6_rvsum_1_type, type, k6_rvsum_1: $i > $i).
thf(k6_square_1_type, type, k6_square_1: $i > $i).
thf(k6_xcmplx_0_type, type, k6_xcmplx_0: $i > $i > $i).
thf(k7_binop_2_type, type, k7_binop_2: $i > $i).
thf(k7_euclid_type, type, k7_euclid: $i > $i > $i > $i).
thf(k7_finseqop_type, type, k7_finseqop: $i > $i > $i > $i > $i).
thf(k7_lopban_1_type, type, k7_lopban_1: $i > $i > $i).
thf(k7_partfun1_type, type, k7_partfun1: $i > $i > $i > $i).
thf(k7_real_1_type, type, k7_real_1: $i > $i > $i).
thf(k7_relat_1_type, type, k7_relat_1: $i > $i > $i).
thf(k7_relset_1_type, type, k7_relset_1: $i > $i > $i > $i > $i).
thf(k7_square_1_type, type, k7_square_1: $i > $i).
thf(k8_euclid_type, type, k8_euclid: $i > $i > $i > $i).
thf(k8_funcop_1_type, type, k8_funcop_1: $i > $i > $i > $i).
thf(k8_funct_2_type, type, k8_funct_2: $i > $i > $i > $i > $i > $i).
thf(k8_lopban_1_type, type, k8_lopban_1: $i > $i > $i).
thf(k8_pdiff_1_type, type, k8_pdiff_1: $i > $i > $i > $i > $i).
thf(k8_real_1_type, type, k8_real_1: $i > $i > $i).
thf(k8_rsspace_type, type, k8_rsspace: $i > $i > $i).
thf(k8_rvsum_1_type, type, k8_rvsum_1: $i > $i > $i).
thf(k9_binop_2_type, type, k9_binop_2: $i > $i > $i).
thf(k9_euclid_type, type, k9_euclid: $i > $i > $i > $i).
thf(k9_finseq_1_type, type, k9_finseq_1: $i > $i).
thf(k9_funct_2_type, type, k9_funct_2: $i > $i > $i).
thf(k9_real_1_type, type, k9_real_1: $i > $i > $i).
thf(k9_rsspace_type, type, k9_rsspace: $i > $i > $i).
thf(k9_xtuple_0_type, type, k9_xtuple_0: $i > $i).
thf(u1_algstr_0_type, type, u1_algstr_0: $i > $i).
thf(u1_normsp_0_type, type, u1_normsp_0: $i > $i).
thf(u1_pre_topc_type, type, u1_pre_topc: $i > $i).
thf(u1_rlvect_1_type, type, u1_rlvect_1: $i > $i).
thf(u1_struct_0_type, type, u1_struct_0: $i > $i).
thf(u2_struct_0_type, type, u2_struct_0: $i > $i).
thf(l1_algstr_0_type, type, l1_algstr_0: $i > $o).
thf(l1_normsp_0_type, type, l1_normsp_0: $i > $o).
thf(l1_normsp_1_type, type, l1_normsp_1: $i > $o).
thf(l1_pre_topc_type, type, l1_pre_topc: $i > $o).
thf(l1_rltopsp1_type, type, l1_rltopsp1: $i > $o).
thf(l1_rlvect_1_type, type, l1_rlvect_1: $i > $o).
thf(l1_struct_0_type, type, l1_struct_0: $i > $o).
thf(l2_algstr_0_type, type, l2_algstr_0: $i > $o).
thf(l2_normsp_0_type, type, l2_normsp_0: $i > $o).
thf(l2_struct_0_type, type, l2_struct_0: $i > $o).
thf(m1_finseq_1_type, type, m1_finseq_1: $i > $i > $o).
thf(m1_finseq_2_type, type, m1_finseq_2: $i > $i > $o).
thf(m1_funct_2_type, type, m1_funct_2: $i > $i > $i > $o).
thf(m1_nfcont_1_type, type, m1_nfcont_1: $i > $i > $i > $o).
thf(m1_rcomp_1_type, type, m1_rcomp_1: $i > $i > $o).
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(m2_finseq_1_type, type, m2_finseq_1: $i > $i > $o).
thf(m2_finseq_2_type, type, m2_finseq_2: $i > $i > $i > $o).
thf(m2_funct_2_type, type, m2_funct_2: $i > $i > $i > $i > $o).
thf(m2_subset_1_type, type, m2_subset_1: $i > $i > $i > $o).
thf(r1_fdiff_1_type, type, r1_fdiff_1: $i > $i > $o).
thf(r1_funct_2_type, type, r1_funct_2: $i > $i > $i > $i > $i > $i > $o).
thf(r1_ndiff_1_type, type, r1_ndiff_1: $i > $i > $i > $i > $o).
thf(r1_pdiff_1_type, type, r1_pdiff_1: $i > $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_relset_1_type, type, r2_relset_1: $i > $i > $i > $i > $o).
thf(r3_pdiff_1_type, type, r3_pdiff_1: $i > $i > $i > $i > $o).
thf(v12_struct_0_type, type, v12_struct_0: $i > $i > $i > $o).
thf(v13_algstr_0_type, type, v13_algstr_0: $i > $o).
thf(v13_struct_0_type, type, v13_struct_0: $i > $i > $o).
thf(v13_vectsp_1_type, type, v13_vectsp_1: $i > $i > $i > $o).
thf(v1_binop_1_type, type, v1_binop_1: $i > $i > $o).
thf(v1_card_1_type, type, v1_card_1: $i > $o).
thf(v1_fdiff_1_type, type, v1_fdiff_1: $i > $i > $o).
thf(v1_finseq_1_type, type, v1_finseq_1: $i > $o).
thf(v1_finset_1_type, type, v1_finset_1: $i > $o).
thf(v1_funct_1_type, type, v1_funct_1: $i > $o).
thf(v1_funct_2_type, type, v1_funct_2: $i > $i > $i > $o).
thf(v1_int_1_type, type, v1_int_1: $i > $o).
thf(v1_lopban_1_type, type, v1_lopban_1: $i > $i > $i > $o).
thf(v1_membered_type, type, v1_membered: $i > $o).
thf(v1_ndiff_1_type, type, v1_ndiff_1: $i > $i > $i > $o).
thf(v1_normsp_1_type, type, v1_normsp_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_rlvect_1_type, type, v1_rlvect_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_binop_1_type, type, v2_binop_1: $i > $i > $o).
thf(v2_comseq_2_type, type, v2_comseq_2: $i > $o).
thf(v2_fdiff_1_type, type, v2_fdiff_1: $i > $o).
thf(v2_funct_1_type, type, v2_funct_1: $i > $o).
thf(v2_funct_2_type, type, v2_funct_2: $i > $i > $o).
thf(v2_lopban_1_type, type, v2_lopban_1: $i > $i > $i > $o).
thf(v2_membered_type, type, v2_membered: $i > $o).
thf(v2_monoid_0_type, type, v2_monoid_0: $i > $o).
thf(v2_ndiff_1_type, type, v2_ndiff_1: $i > $i > $i > $o).
thf(v2_normsp_1_type, type, v2_normsp_1: $i > $o).
thf(v2_ordinal1_type, type, v2_ordinal1: $i > $o).
thf(v2_pre_topc_type, type, v2_pre_topc: $i > $o).
thf(v2_relat_1_type, type, v2_relat_1: $i > $o).
thf(v2_rlvect_1_type, type, v2_rlvect_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_fdiff_1_type, type, v3_fdiff_1: $i > $o).
thf(v3_finseq_1_type, type, v3_finseq_1: $i > $o).
thf(v3_funct_2_type, type, v3_funct_2: $i > $i > $i > $o).
thf(v3_lopban_1_type, type, v3_lopban_1: $i > $o).
thf(v3_membered_type, type, v3_membered: $i > $o).
thf(v3_normsp_0_type, type, v3_normsp_0: $i > $o).
thf(v3_normsp_1_type, type, v3_normsp_1: $i > $i > $o).
thf(v3_ordinal1_type, type, v3_ordinal1: $i > $o).
thf(v3_rlvect_1_type, type, v3_rlvect_1: $i > $o).
thf(v3_valued_0_type, type, v3_valued_0: $i > $o).
thf(v3_valued_2_type, type, v3_valued_2: $i > $o).
thf(v3_xxreal_0_type, type, v3_xxreal_0: $i > $o).
thf(v4_funct_1_type, type, v4_funct_1: $i > $o).
thf(v4_membered_type, type, v4_membered: $i > $o).
thf(v4_normsp_0_type, type, v4_normsp_0: $i > $o).
thf(v4_relat_1_type, type, v4_relat_1: $i > $i > $o).
thf(v4_rlvect_1_type, type, v4_rlvect_1: $i > $o).
thf(v4_valued_0_type, type, v4_valued_0: $i > $o).
thf(v5_membered_type, type, v5_membered: $i > $o).
thf(v5_ordinal1_type, type, v5_ordinal1: $i > $o).
thf(v5_relat_1_type, type, v5_relat_1: $i > $i > $o).
thf(v5_rltopsp1_type, type, v5_rltopsp1: $i > $o).
thf(v5_rlvect_1_type, type, v5_rlvect_1: $i > $o).
thf(v5_valued_0_type, type, v5_valued_0: $i > $o).
thf(v6_membered_type, type, v6_membered: $i > $o).
thf(v6_ordinal1_type, type, v6_ordinal1: $i > $o).
thf(v6_rlvect_1_type, type, v6_rlvect_1: $i > $o).
thf(v6_valued_0_type, type, v6_valued_0: $i > $o).
thf(v7_membered_type, type, v7_membered: $i > $o).
thf(v7_ordinal1_type, type, v7_ordinal1: $i > $o).
thf(v7_rlvect_1_type, type, v7_rlvect_1: $i > $o).
thf(v7_struct_0_type, type, v7_struct_0: $i > $o).
thf(v7_valued_0_type, type, v7_valued_0: $i > $o).
thf(v8_rlvect_1_type, type, v8_rlvect_1: $i > $o).
thf(v8_struct_0_type, type, v8_struct_0: $i > $o).
thf(v8_valued_0_type, type, v8_valued_0: $i > $o).
thf(v9_struct_0_type, type, v9_struct_0: $i > $i > $o).
thf(abstractness_v1_normsp_1, axiom,  (! [A: $i] :  ( (l1_normsp_1 @ A)  =>  ( (v1_normsp_1 @ A)  =>  (A =  ( ( ( ( (g1_normsp_1 @  (u1_struct_0 @ A) )  @  (u2_struct_0 @ A) )  @  (u1_algstr_0 @ A) )  @  (u1_rlvect_1 @ A) )  @  (u1_normsp_0 @ A) ) ) ) ) ) , file(normsp_1, v1_normsp_1)).
thf(abstractness_v1_rlvect_1, axiom,  (! [A: $i] :  ( (l1_rlvect_1 @ A)  =>  ( (v1_rlvect_1 @ A)  =>  (A =  ( ( ( (g1_rlvect_1 @  (u1_struct_0 @ A) )  @  (u2_struct_0 @ A) )  @  (u1_algstr_0 @ A) )  @  (u1_rlvect_1 @ A) ) ) ) ) ) , file(rlvect_1, v1_rlvect_1)).
thf(abstractness_v5_rltopsp1, axiom,  (! [A: $i] :  ( (l1_rltopsp1 @ A)  =>  ( (v5_rltopsp1 @ A)  =>  (A =  ( ( ( ( (g1_rltopsp1 @  (u1_struct_0 @ A) )  @  (u2_struct_0 @ A) )  @  (u1_algstr_0 @ A) )  @  (u1_rlvect_1 @ A) )  @  (u1_pre_topc @ A) ) ) ) ) ) , file(rltopsp1, v5_rltopsp1)).
thf(antisymmetry_r2_hidden, axiom,  (! [A: $i, B: $i] :  ( ( (r2_hidden @ A)  @ B)  =>  ~ ( ( (r2_hidden @ B)  @ A) ) ) ) , file(hidden, r2_hidden)).
thf(cc10_membered, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k4_numbers) )  =>  (v5_membered @ A) ) ) , file(membered, cc10_membered)).
thf(cc10_ordinal1, axiom,  (! [A: $i] :  ( (v6_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v6_ordinal1 @ B) ) ) ) ) , file(ordinal1, cc10_ordinal1)).
thf(cc10_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ( ~ ( (v2_struct_0 @ A) )  &  (v7_struct_0 @ A) )  =>  ( (v13_struct_0 @ A)  @ np__1) ) ) ) , file(struct_0, cc10_struct_0)).
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_membered, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k5_numbers) )  =>  (v6_membered @ A) ) ) , file(membered, cc11_membered)).
thf(cc11_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ( (v13_struct_0 @ A)  @ np__1)  =>  ( ~ ( (v2_struct_0 @ A) )  &  (v7_struct_0 @ A) ) ) ) ) , file(struct_0, cc11_struct_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_membered, axiom,  (! [A: $i] :  ( (v1_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xcmplx_0 @ B) ) ) ) ) , file(membered, cc12_membered)).
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_membered, axiom,  (! [A: $i] :  ( (v2_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xxreal_0 @ B) ) ) ) ) , file(membered, cc13_membered)).
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_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xreal_0 @ B) ) ) ) ) , file(membered, cc14_membered)).
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_membered, axiom,  (! [A: $i] :  ( (v4_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_rat_1 @ B) ) ) ) ) , file(membered, cc15_membered)).
thf(cc15_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v4_valued_0 @ B) ) ) ) ) , file(valued_0, cc15_valued_0)).
thf(cc16_membered, axiom,  (! [A: $i] :  ( (v5_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_int_1 @ B) ) ) ) ) , file(membered, cc16_membered)).
thf(cc16_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v1_valued_0 @ C) ) ) ) ) , file(valued_0, cc16_valued_0)).
thf(cc17_membered, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v7_ordinal1 @ B) ) ) ) ) , file(membered, cc17_membered)).
thf(cc17_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ~ ( (v7_struct_0 @ A) )  =>  ~ ( (v2_struct_0 @ A) ) ) ) ) , file(struct_0, cc17_struct_0)).
thf(cc17_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v2_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v2_valued_0 @ C) ) ) ) ) , file(valued_0, cc17_valued_0)).
thf(cc18_membered, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v6_membered @ A) ) ) , file(membered, cc18_membered)).
thf(cc18_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v3_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v3_valued_0 @ C) ) ) ) ) , file(valued_0, cc18_valued_0)).
thf(cc19_membered, axiom,  (! [A: $i] :  ( (v1_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_membered @ B) ) ) ) ) , file(membered, cc19_membered)).
thf(cc19_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v4_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v5_relat_1 @ C)  @ k3_numbers) ) ) ) ) , file(valued_0, cc19_valued_0)).
thf(cc1_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_euclid @ A) )  =>  ( (v3_card_1 @ B)  @ A) ) ) ) ) , file(euclid, cc1_euclid)).
thf(cc1_fdiff_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k1_numbers) ) )  =>  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k5_numbers)  @ k1_numbers)  &  ( (v1_fdiff_1 @ A)  @ k6_numbers) ) )  =>  ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k5_numbers)  @ k1_numbers)  &  (v2_comseq_2 @ A) ) ) ) ) ) , file(fdiff_1, cc1_fdiff_1)).
thf(cc1_funct_2, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v1_partfun1 @ C)  @ A)  =>  ( ( (v1_funct_2 @ C)  @ A)  @ B) ) ) ) ) , file(funct_2, cc1_funct_2)).
thf(cc1_membered, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  (v5_membered @ A) ) ) , file(membered, cc1_membered)).
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_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( (v2_struct_0 @ A)  =>  (v7_struct_0 @ A) ) ) ) , file(struct_0, cc1_struct_0)).
thf(cc1_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) ) ) ) , file(valued_0, cc1_valued_0)).
thf(cc1_xcmplx_0, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, cc1_xcmplx_0)).
thf(cc1_xreal_0, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (v1_xreal_0 @ A) ) ) , file(xreal_0, cc1_xreal_0)).
thf(cc20_membered, axiom,  (! [A: $i] :  ( (v2_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v2_membered @ B) ) ) ) ) , file(membered, cc20_membered)).
thf(cc20_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v5_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v5_relat_1 @ C)  @ k4_numbers) ) ) ) ) , file(valued_0, cc20_valued_0)).
thf(cc21_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v3_membered @ B) ) ) ) ) , file(membered, cc21_membered)).
thf(cc21_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v6_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v4_valued_0 @ C) ) ) ) ) , file(valued_0, cc21_valued_0)).
thf(cc22_membered, axiom,  (! [A: $i] :  ( (v4_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v4_membered @ B) ) ) ) ) , file(membered, cc22_membered)).
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_membered, axiom,  (! [A: $i] :  ( (v5_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v5_membered @ B) ) ) ) ) , file(membered, cc23_membered)).
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_membered, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v6_membered @ B) ) ) ) ) , file(membered, cc24_membered)).
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(cc25_membered, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  =>  (v6_membered @ A) ) ) , file(membered, cc25_membered)).
thf(cc26_membered, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v7_membered @ A) ) ) , file(membered, cc26_membered)).
thf(cc2_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @  (k15_euclid @ A) ) )  =>  (v1_finseq_1 @ B) ) ) ) ) , file(euclid, cc2_euclid)).
thf(cc2_funct_2, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  =>  ( (v1_partfun1 @ C)  @ A) ) ) ) ) ) , file(funct_2, cc2_funct_2)).
thf(cc2_membered, axiom,  (! [A: $i] :  ( (v5_membered @ A)  =>  (v4_membered @ A) ) ) , file(membered, cc2_membered)).
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_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ~ ( (v7_struct_0 @ A) )  =>  ~ ( (v2_struct_0 @ A) ) ) ) ) , file(struct_0, cc2_struct_0)).
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_xcmplx_0, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, cc2_xcmplx_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_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @  (k15_euclid @ A) ) )  =>  (v3_valued_0 @ B) ) ) ) ) , file(euclid, cc3_euclid)).
thf(cc3_funct_2, axiom,  (! [A: $i, B: $i] :  ( ~ ( (v1_xboole_0 @ B) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  =>  ( (v1_partfun1 @ C)  @ A) ) ) ) ) ) , file(funct_2, cc3_funct_2)).
thf(cc3_membered, axiom,  (! [A: $i] :  ( (v4_membered @ A)  =>  (v3_membered @ A) ) ) , file(membered, cc3_membered)).
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_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @  (k15_euclid @ A) ) )  =>  ( (v3_card_1 @ B)  @ A) ) ) ) ) , file(euclid, cc4_euclid)).
thf(cc4_funct_2, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) )  =>  ( ( ( (v1_funct_2 @ B)  @ A)  @ A)  =>  ( (v1_partfun1 @ B)  @ A) ) ) ) ) , file(funct_2, cc4_funct_2)).
thf(cc4_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (v2_membered @ A) ) ) , file(membered, cc4_membered)).
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_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( (v2_struct_0 @ A)  =>  ( (v2_struct_0 @ A)  &  (v8_struct_0 @ A) ) ) ) ) , file(struct_0, cc4_struct_0)).
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_funct_2, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v1_funct_1 @ C)  &  ( ( (v3_funct_2 @ C)  @ A)  @ B) )  =>  ( (v1_funct_1 @ C)  &  ( (v2_funct_1 @ C)  &  ( (v2_funct_2 @ C)  @ B) ) ) ) ) ) ) , file(funct_2, cc5_funct_2)).
thf(cc5_membered, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  (v1_membered @ A) ) ) , file(membered, cc5_membered)).
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_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ~ ( (v8_struct_0 @ A) )  =>  ( ~ ( (v2_struct_0 @ A) )  &  ~ ( (v8_struct_0 @ A) ) ) ) ) ) , file(struct_0, cc5_struct_0)).
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_funct_2, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v1_funct_1 @ C)  &  ( (v2_funct_1 @ C)  &  ( (v2_funct_2 @ C)  @ B) ) )  =>  ( (v1_funct_1 @ C)  &  ( ( (v3_funct_2 @ C)  @ A)  @ B) ) ) ) ) ) , file(funct_2, cc6_funct_2)).
thf(cc6_ordinal1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc6_ordinal1)).
thf(cc6_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( (v7_struct_0 @ A)  =>  (v8_struct_0 @ A) ) ) ) , file(struct_0, cc6_struct_0)).
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_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc7_ordinal1)).
thf(cc7_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ~ ( (v8_struct_0 @ A) )  =>  ~ ( (v7_struct_0 @ A) ) ) ) ) , file(struct_0, cc7_struct_0)).
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_funct_2, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v1_funct_1 @ C)  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) )  =>  ( (v1_funct_1 @ C)  &  ( ~ ( (v1_xboole_0 @ C) )  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) ) ) ) ) ) ) ) , file(funct_2, cc8_funct_2)).
thf(cc8_membered, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k1_numbers) )  =>  (v3_membered @ A) ) ) , file(membered, cc8_membered)).
thf(cc8_ordinal1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc8_ordinal1)).
thf(cc8_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( (v2_struct_0 @ A)  =>  ( (v13_struct_0 @ A)  @ k1_xboole_0) ) ) ) , file(struct_0, cc8_struct_0)).
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_funct_2, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( ( (m1_funct_2 @ C)  @ A)  @ B)  =>  (v4_funct_1 @ C) ) ) ) , file(funct_2, cc9_funct_2)).
thf(cc9_membered, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k3_numbers) )  =>  (v4_membered @ A) ) ) , file(membered, cc9_membered)).
thf(cc9_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v6_ordinal1 @ A) ) ) , file(ordinal1, cc9_ordinal1)).
thf(cc9_struct_0, axiom,  (! [A: $i] :  ( (l1_struct_0 @ A)  =>  ( ( (v13_struct_0 @ A)  @ k1_xboole_0)  =>  (v2_struct_0 @ A) ) ) ) , file(struct_0, cc9_struct_0)).
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_k11_binop_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  ( ( (k11_binop_2 @ A)  @ B)  =  ( (k11_binop_2 @ B)  @ A) ) ) ) , file(binop_2, k11_binop_2)).
thf(commutativity_k18_valued_1, 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) ) ) )  =>  ( ( (k18_valued_1 @ A)  @ B)  =  ( (k18_valued_1 @ B)  @ A) ) ) ) , file(valued_1, k18_valued_1)).
thf(commutativity_k1_valued_1, 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) ) ) )  =>  ( ( (k1_valued_1 @ A)  @ B)  =  ( (k1_valued_1 @ B)  @ A) ) ) ) , file(valued_1, k1_valued_1)).
thf(commutativity_k20_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( (v3_membered @ B)  &  ( (v3_membered @ C)  &  ( ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  &  ( (v1_funct_1 @ E)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) )  =>  ( ( ( ( ( (k20_valued_1 @ A)  @ B)  @ C)  @ D)  @ E)  =  ( ( ( ( (k20_valued_1 @ A)  @ B)  @ C)  @ E)  @ D) ) ) ) , file(valued_1, k20_valued_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_rlvect_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v2_rlvect_1 @ A)  &  (l1_algstr_0 @ A) )  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) ) ) )  =>  ( ( ( (k3_rlvect_1 @ A)  @ B)  @ C)  =  ( ( (k3_rlvect_1 @ A)  @ C)  @ B) ) ) ) , file(rlvect_1, k3_rlvect_1)).
thf(commutativity_k3_xcmplx_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( ( (k3_xcmplx_0 @ A)  @ B)  =  ( (k3_xcmplx_0 @ B)  @ A) ) ) ) , file(xcmplx_0, k3_xcmplx_0)).
thf(commutativity_k4_rvsum_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v3_valued_0 @ B)  &  (v1_finseq_1 @ B) ) ) ) )  =>  ( ( (k4_rvsum_1 @ A)  @ B)  =  ( (k4_rvsum_1 @ B)  @ A) ) ) ) , file(rvsum_1, k4_rvsum_1)).
thf(commutativity_k7_euclid, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v7_ordinal1 @ A)  &  ( ( (m1_subset_1 @ B)  @  (k1_euclid @ A) )  &  ( (m1_subset_1 @ C)  @  (k1_euclid @ A) ) ) )  =>  ( ( ( (k7_euclid @ A)  @ B)  @ C)  =  ( ( (k7_euclid @ A)  @ C)  @ B) ) ) ) , file(euclid, k7_euclid)).
thf(commutativity_k7_real_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k1_numbers)  &  (v1_xreal_0 @ B) )  =>  ( ( (k7_real_1 @ A)  @ B)  =  ( (k7_real_1 @ B)  @ A) ) ) ) , file(real_1, k7_real_1)).
thf(commutativity_k8_real_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k1_numbers)  &  (v1_xreal_0 @ B) )  =>  ( ( (k8_real_1 @ A)  @ B)  =  ( (k8_real_1 @ B)  @ A) ) ) ) , file(real_1, k8_real_1)).
thf(commutativity_k9_binop_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  ( ( (k9_binop_2 @ A)  @ B)  =  ( (k9_binop_2 @ B)  @ A) ) ) ) , file(binop_2, k9_binop_2)).
thf(connectedness_r1_xxreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v1_xxreal_0 @ B) )  =>  ( ( (r1_xxreal_0 @ A)  @ B)  |  ( (r1_xxreal_0 @ B)  @ A) ) ) ) , file(xxreal_0, r1_xxreal_0)).
thf(d10_euclid, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (u1_struct_0 @  (k15_euclid @ np__2) ) )  =>  ( (k18_euclid @ A)  =  ( (k1_seq_1 @ A)  @ np__2) ) ) ) , file(euclid, d10_euclid)).
thf(d11_pdiff_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (m2_subset_1 @ A)  @ k1_numbers)  @ k5_numbers) )  =>  (! [B: $i] :  ( ( ( (m2_subset_1 @ B)  @ k1_numbers)  @ k5_numbers)  =>  (! [C: $i] :  ( ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @ k1_numbers) ) ) )  =>  (! [D: $i] :  ( ( ( (m2_finseq_2 @ D)  @ k1_numbers)  @  (k1_euclid @ A) )  =>  ( ( ( ( (r3_pdiff_1 @ A)  @ B)  @ C)  @ D)  <=>  ( (r1_fdiff_1 @  ( ( ( ( ( (k1_partfun1 @ k1_numbers)  @  (k1_euclid @ A) )  @  (k1_euclid @ A) )  @ k1_numbers)  @  ( ( (k6_pdiff_1 @ A)  @ B)  @ D) )  @ C) )  @  ( (k1_seq_1 @  ( (k1_pdiff_1 @ B)  @ A) )  @ D) ) ) ) ) ) ) ) ) ) ) , file(pdiff_1, d11_pdiff_1)).
thf(d12_complex1, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (k16_complex1 @ A)  =  (k7_square_1 @  ( (k7_real_1 @  (k5_square_1 @  (k3_complex1 @ A) ) )  @  (k5_square_1 @  (k4_complex1 @ A) ) ) ) ) ) ) , file(complex1, d12_complex1)).
thf(d12_pdiff_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (m2_subset_1 @ A)  @ k1_numbers)  @ k5_numbers) )  =>  (! [B: $i] :  ( ( ( (m2_subset_1 @ B)  @ k1_numbers)  @ k5_numbers)  =>  (! [C: $i] :  ( ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @ k1_numbers) ) ) )  =>  (! [D: $i] :  ( ( ( (m2_finseq_2 @ D)  @ k1_numbers)  @  (k1_euclid @ A) )  =>  ( ( ( ( (k10_pdiff_1 @ A)  @ B)  @ C)  @ D)  =  ( (k1_fdiff_1 @  ( ( ( ( ( (k1_partfun1 @ k1_numbers)  @  (k1_euclid @ A) )  @  (k1_euclid @ A) )  @ k1_numbers)  @  ( ( (k6_pdiff_1 @ A)  @ B)  @ D) )  @ C) )  @  ( (k1_seq_1 @  ( (k1_pdiff_1 @ B)  @ A) )  @ D) ) ) ) ) ) ) ) ) ) ) , file(pdiff_1, d12_pdiff_1)).
thf(d12_rvsum_1, axiom,  (! [A: $i] :  ( ( (m2_finseq_1 @ A)  @ k1_numbers)  =>  ( (k18_rvsum_1 @ A)  =  ( ( (k1_finsop_1 @ k1_numbers)  @ A)  @ k33_binop_2) ) ) ) , file(rvsum_1, d12_rvsum_1)).
thf(d14_lopban_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  ( (v3_normsp_0 @ A)  &  ( (v4_normsp_0 @ A)  &  ( (v2_normsp_1 @ A)  &  (l1_normsp_1 @ A) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  ( (v13_algstr_0 @ B)  &  ( (v2_rlvect_1 @ B)  &  ( (v3_rlvect_1 @ B)  &  ( (v4_rlvect_1 @ B)  &  ( (v5_rlvect_1 @ B)  &  ( (v6_rlvect_1 @ B)  &  ( (v7_rlvect_1 @ B)  &  ( (v8_rlvect_1 @ B)  &  ( (v3_normsp_0 @ B)  &  ( (v4_normsp_0 @ B)  &  ( (v2_normsp_1 @ B)  &  (l1_normsp_1 @ B) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ( (k16_lopban_1 @ A)  @ B)  =  ( ( ( ( (g1_normsp_1 @  ( (k10_lopban_1 @ A)  @ B) )  @  ( (k10_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k8_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k9_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k15_lopban_1 @ A)  @ B) ) ) ) ) ) ) , file(lopban_1, d14_lopban_1)).
thf(d1_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (k1_euclid @ A)  =  ( (k4_finseq_2 @ A)  @ k1_numbers) ) ) ) , file(euclid, d1_euclid)).
thf(d1_funct_2, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( ~ ( (B = k1_xboole_0) )  =>  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  <=>  (A =  ( (k1_relset_1 @ A)  @ C) ) ) )  &  ( (B = k1_xboole_0)  =>  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  <=>  (C = k1_xboole_0) ) ) ) ) ) ) ) , file(funct_2, d1_funct_2)).
thf(d1_nfcont_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  ( (v3_normsp_0 @ A)  &  ( (v4_normsp_0 @ A)  &  ( (v2_normsp_1 @ A)  &  (l1_normsp_1 @ A) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  =>  ( ( ( (m1_nfcont_1 @ C)  @ A)  @ B)  <=>  (? [D: $i] :  ( ( (m1_subset_1 @ D)  @ k1_numbers)  &  ( ~ ( ( (r1_xxreal_0 @ D)  @ k6_numbers) )  &  ( (r1_tarski @  ( ( (replSep1 @  (^ [E: $i] :  ( (m1_subset_1 @ E)  @  (u1_struct_0 @ A) ) ) )  @  (^ [E: $i] : E) )  @  (^ [E: $i] :  ~ ( ( (r1_xxreal_0 @ D)  @  ( (k1_normsp_0 @ A)  @  ( ( (k5_algstr_0 @ A)  @ E)  @ B) ) ) ) ) ) )  @ C) ) ) ) ) ) ) ) ) ) ) , file(nfcont_1, d1_nfcont_1)).
thf(d1_normsp_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_normsp_1 @ A) )  =>  ( (v2_normsp_1 @ A)  <=>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) )  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @ k1_numbers)  =>  ( ( ( (k1_normsp_0 @ A)  @  ( ( (k1_rlvect_1 @ A)  @ B)  @ D) )  =  ( (k8_real_1 @  (k18_complex1 @ D) )  @  ( (k1_normsp_0 @ A)  @ B) ) )  &  ( (r1_xxreal_0 @  ( (k1_normsp_0 @ A)  @  ( ( (k1_algstr_0 @ A)  @ B)  @ C) ) )  @  ( (k7_real_1 @  ( (k1_normsp_0 @ A)  @ B) )  @  ( (k1_normsp_0 @ A)  @ C) ) ) ) ) ) ) ) ) ) ) ) ) , file(normsp_1, d1_normsp_1)).
thf(d1_pdiff_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  (! [C: $i] :  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @  (k1_euclid @ B) )  @ k1_numbers)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ B) )  @ k1_numbers) ) ) ) )  =>  ( (C =  ( (k1_pdiff_1 @ A)  @ B) )  <=>  (! [D: $i] :  ( ( ( (m2_finseq_2 @ D)  @ k1_numbers)  @  (k1_euclid @ B) )  =>  ( ( (k1_seq_1 @ C)  @ D)  =  ( (k1_seq_1 @ D)  @ A) ) ) ) ) ) ) ) ) ) ) , file(pdiff_1, d1_pdiff_1)).
thf(d1_rvsum_1, axiom,  (k34_binop_2 =  ( ( ( (k7_finseqop @ k1_numbers)  @ k33_binop_2)  @  (k6_partfun1 @ k1_numbers) )  @ k31_binop_2) ) , file(rvsum_1, d1_rvsum_1)).
thf(d2_fdiff_1, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) )  =>  ( (v2_fdiff_1 @ A)  <=>  ( ( (v1_partfun1 @ A)  @ k1_numbers)  &  (! [B: $i] :  ( ( (v2_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ k5_numbers)  @ k1_numbers)  &  ( ( (v1_fdiff_1 @ B)  @ k6_numbers)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k1_numbers) ) ) ) ) ) )  =>  ( (v2_comseq_2 @  ( ( ( ( (k20_valued_1 @ k5_numbers)  @ k1_numbers)  @ k1_numbers)  @  ( ( (k37_valued_1 @ k5_numbers)  @ k1_numbers)  @ B) )  @  ( ( ( ( (k8_funct_2 @ k5_numbers)  @ k1_numbers)  @ k1_numbers)  @ B)  @ A) ) )  &  ( (k2_seq_2 @  ( ( ( ( (k20_valued_1 @ k5_numbers)  @ k1_numbers)  @ k1_numbers)  @  ( ( (k37_valued_1 @ k5_numbers)  @ k1_numbers)  @ B) )  @  ( ( ( ( (k8_funct_2 @ k5_numbers)  @ k1_numbers)  @ k1_numbers)  @ B)  @ A) ) )  = k6_numbers) ) ) ) ) ) ) ) , file(fdiff_1, d2_fdiff_1)).
thf(d2_ndiff_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  (l1_rlvect_1 @ A) ) ) ) ) ) ) ) ) )  =>  (! [B: $i] :  ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ k5_numbers)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @  (u1_struct_0 @ A) ) ) ) ) )  =>  (! [C: $i] :  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ k5_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k1_numbers) ) ) ) )  =>  (! [D: $i] :  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ k5_numbers)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @  (u1_struct_0 @ A) ) ) ) ) )  =>  ( (D =  ( ( (k1_ndiff_1 @ A)  @ B)  @ C) )  <=>  (! [E: $i] :  ( ( ( (m2_subset_1 @ E)  @ k1_numbers)  @ k5_numbers)  =>  ( ( ( (k1_normsp_1 @ A)  @ D)  @ E)  =  ( ( (k1_rlvect_1 @ A)  @  ( ( (k1_normsp_1 @ A)  @ B)  @ E) )  @  ( (k1_seq_1 @ C)  @ E) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(ndiff_1, d2_ndiff_1)).
thf(d2_partfun1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  ( ( (v1_partfun1 @ B)  @ A)  <=>  ( ( (k1_relset_1 @ A)  @ B)  = A) ) ) ) ) , file(partfun1, d2_partfun1)).
thf(d3_fdiff_1, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) )  =>  ( (v3_fdiff_1 @ A)  <=>  ( ( (v1_partfun1 @ A)  @ k1_numbers)  &  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @ k1_numbers)  &  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @ k1_numbers)  =>  ( ( (k1_seq_1 @ A)  @ C)  =  ( (k8_real_1 @ B)  @ C) ) ) ) ) ) ) ) ) ) , file(fdiff_1, d3_fdiff_1)).
thf(d3_lopban_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  (l2_struct_0 @ B) )  =>  ( ( (k4_lopban_1 @ A)  @ B)  =  ( ( (k8_funcop_1 @  (u1_struct_0 @ B) )  @ A)  @  (k4_struct_0 @ B) ) ) ) ) ) , file(lopban_1, d3_lopban_1)).
thf(d3_pdiff_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (v1_funct_1 @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @ k1_numbers) ) ) )  =>  ( ( (k3_pdiff_1 @ A)  @ B)  =  ( (k3_relat_1 @ B)  @  (k2_funct_1 @  ( (k1_pdiff_1 @ np__1)  @ np__1) ) ) ) ) ) ) ) , file(pdiff_1, d3_pdiff_1)).
thf(d3_rvsum_1, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  ( (k3_rvsum_1 @ A)  =  ( ( (k5_funcop_1 @ k35_binop_2)  @ A)  @  (k6_partfun1 @ k1_numbers) ) ) ) ) , file(rvsum_1, d3_rvsum_1)).
thf(d3_tarski, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (r1_tarski @ A)  @ B)  <=>  (! [C: $i] :  ( ( (r2_hidden @ C)  @ A)  =>  ( (r2_hidden @ C)  @ B) ) ) ) ) ) , file(tarski, d3_tarski)).
thf(d4_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (k4_euclid @ A)  =  ( ( (k5_finseq_2 @ k1_numbers)  @ A)  @ k6_numbers) ) ) ) , file(euclid, d4_euclid)).
thf(d4_fdiff_1, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) )  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (r1_fdiff_1 @ A)  @ B)  <=>  (? [C: $i] :  ( ( (m1_rcomp_1 @ C)  @ B)  &  ( ( (r1_tarski @ C)  @  ( (k1_relset_1 @ k1_numbers)  @ A) )  &  (? [D: $i] :  ( ( (v1_funct_1 @ D)  &  ( (v3_fdiff_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) )  &  (? [E: $i] :  ( ( (v1_funct_1 @ E)  &  ( (v2_fdiff_1 @ E)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) )  &  (! [F: $i] :  ( ( (m1_subset_1 @ F)  @ k1_numbers)  =>  ( ( (r2_hidden @ F)  @ C)  =>  ( ( (k9_real_1 @  ( (k1_seq_1 @ A)  @ F) )  @  ( (k1_seq_1 @ A)  @ B) )  =  ( (k7_real_1 @  ( (k1_seq_1 @ D)  @  ( (k9_real_1 @ F)  @ B) ) )  @  ( (k1_seq_1 @ E)  @  ( (k9_real_1 @ F)  @ B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(fdiff_1, d4_fdiff_1)).
thf(d4_lopban_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  ( (v13_algstr_0 @ B)  &  ( (v2_rlvect_1 @ B)  &  ( (v3_rlvect_1 @ B)  &  ( (v4_rlvect_1 @ B)  &  ( (v5_rlvect_1 @ B)  &  ( (v6_rlvect_1 @ B)  &  ( (v7_rlvect_1 @ B)  &  ( (v8_rlvect_1 @ B)  &  (l1_rlvect_1 @ B) ) ) ) ) ) ) ) ) )  =>  ( ( (k5_lopban_1 @ A)  @ B)  =  ( ( ( (g1_rlvect_1 @  ( (k9_funct_2 @ A)  @  (u1_struct_0 @ B) ) )  @  ( (k4_lopban_1 @ A)  @ B) )  @  ( (k2_lopban_1 @ A)  @ B) )  @  ( (k3_lopban_1 @ A)  @ B) ) ) ) ) ) ) , file(lopban_1, d4_lopban_1)).
thf(d4_ndiff_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  ( (v3_normsp_0 @ A)  &  ( (v4_normsp_0 @ A)  &  ( (v2_normsp_1 @ A)  &  (l1_normsp_1 @ A) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  =>  (! [C: $i] :  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ k5_numbers)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @  (u1_struct_0 @ A) ) ) ) ) )  =>  ( ( ( (v1_ndiff_1 @ C)  @ A)  @ B)  <=>  ( ( (v3_normsp_1 @ C)  @ A)  &  ( ( (k6_normsp_1 @ A)  @ C)  = B) ) ) ) ) ) ) ) ) , file(ndiff_1, d4_ndiff_1)).
thf(d4_normsp_0, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_normsp_0 @ A) )  =>  (! [B: $i] :  ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ k5_numbers)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @  (u1_struct_0 @ A) ) ) ) ) )  =>  (! [C: $i] :  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ k5_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k1_numbers) ) ) ) )  =>  ( (C =  ( (k4_normsp_0 @ A)  @ B) )  <=>  (! [D: $i] :  ( ( ( (m2_subset_1 @ D)  @ k1_numbers)  @ k5_numbers)  =>  ( ( ( ( (k3_funct_2 @ k5_numbers)  @ k1_numbers)  @ C)  @ D)  =  ( (k1_normsp_0 @ A)  @  ( ( ( (k3_funct_2 @ k5_numbers)  @  (u1_struct_0 @ A) )  @ B)  @ D) ) ) ) ) ) ) ) ) ) ) ) , file(normsp_0, d4_normsp_0)).
thf(d4_real_ns1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  ( (v1_normsp_1 @ B)  &  (l1_normsp_1 @ B) ) )  =>  ( (B =  (k4_real_ns1 @ A) )  <=>  ( ( (u1_struct_0 @ B)  =  (k1_euclid @ A) )  &  ( ( (k4_struct_0 @ B)  =  (k5_euclid @ A) )  &  ( ( ( ( ( ( (r1_funct_2 @  ( (k2_zfmisc_1 @  (u1_struct_0 @ B) )  @  (u1_struct_0 @ B) ) )  @  (u1_struct_0 @ B) )  @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @  (k1_euclid @ A) ) )  @  (k1_euclid @ A) )  @  (u1_algstr_0 @ B) )  @  (k1_real_ns1 @ A) )  &  ( ( ( ( ( ( (r1_funct_2 @  ( (k2_zfmisc_1 @ k1_numbers)  @  (u1_struct_0 @ B) ) )  @  (u1_struct_0 @ B) )  @  ( (k2_zfmisc_1 @ k1_numbers)  @  (k1_euclid @ A) ) )  @  (k1_euclid @ A) )  @  (u1_rlvect_1 @ B) )  @  (k2_real_ns1 @ A) )  &  ( ( ( ( ( (r1_funct_2 @  (u1_struct_0 @ B) )  @ k1_numbers)  @  (k1_euclid @ A) )  @ k1_numbers)  @  (u1_normsp_0 @ B) )  @  (k3_real_ns1 @ A) ) ) ) ) ) ) ) ) ) ) , file(real_ns1, d4_real_ns1)).
thf(d4_rvsum_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v3_valued_0 @ B)  &  (v1_finseq_1 @ B) ) ) )  =>  ( ( (k4_rvsum_1 @ A)  @ B)  =  ( ( (k3_funcop_1 @ k33_binop_2)  @ A)  @ B) ) ) ) ) ) , file(rvsum_1, d4_rvsum_1)).
thf(d5_euclid, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_finseq_1 @ A)  &  (v3_valued_0 @ A) ) ) )  =>  ( (k12_euclid @ A)  =  (k7_square_1 @  (k18_rvsum_1 @  (k12_rvsum_1 @ A) ) ) ) ) ) , file(euclid, d5_euclid)).
thf(d5_fdiff_1, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) )  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (r1_fdiff_1 @ A)  @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @ k1_numbers)  =>  ( (C =  ( (k1_fdiff_1 @ A)  @ B) )  <=>  (? [D: $i] :  ( ( (m1_rcomp_1 @ D)  @ B)  &  ( ( (r1_tarski @ D)  @  ( (k1_relset_1 @ k1_numbers)  @ A) )  &  (? [E: $i] :  ( ( (v1_funct_1 @ E)  &  ( (v3_fdiff_1 @ E)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) )  &  (? [F: $i] :  ( ( (v1_funct_1 @ F)  &  ( (v2_fdiff_1 @ F)  &  ( (m1_subset_1 @ F)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) )  &  ( (C =  ( (k1_seq_1 @ E)  @ np__1) )  &  (! [G: $i] :  ( ( (m1_subset_1 @ G)  @ k1_numbers)  =>  ( ( (r2_hidden @ G)  @ D)  =>  ( ( (k9_real_1 @  ( (k1_seq_1 @ A)  @ G) )  @  ( (k1_seq_1 @ A)  @ B) )  =  ( (k7_real_1 @  ( (k1_seq_1 @ E)  @  ( (k9_real_1 @ G)  @ B) ) )  @  ( (k1_seq_1 @ F)  @  ( (k9_real_1 @ G)  @ B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(fdiff_1, d5_fdiff_1)).
thf(d5_lopban_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_rlvect_1 @ A) )  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  (l1_rlvect_1 @ B) )  =>  (! [C: $i] :  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ B) )  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ B) ) ) ) ) )  =>  ( ( ( (v1_lopban_1 @ C)  @ A)  @ B)  <=>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @  (u1_struct_0 @ A) )  =>  (! [E: $i] :  ( ( (m1_subset_1 @ E)  @ k1_numbers)  =>  ( ( ( ( (k3_funct_2 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ B) )  @ C)  @  ( ( (k1_rlvect_1 @ A)  @ D)  @ E) )  =  ( ( (k1_rlvect_1 @ B)  @  ( ( ( (k3_funct_2 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ B) )  @ C)  @ D) )  @ E) ) ) ) ) ) ) ) ) ) ) ) ) , file(lopban_1, d5_lopban_1)).
thf(d5_ndiff_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v7_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  ( (v3_normsp_0 @ A)  &  ( (v4_normsp_0 @ A)  &  ( (v2_normsp_1 @ A)  &  (l1_normsp_1 @ A) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ~ ( (v7_struct_0 @ B) )  &  ( (v13_algstr_0 @ B)  &  ( (v2_rlvect_1 @ B)  &  ( (v3_rlvect_1 @ B)  &  ( (v4_rlvect_1 @ B)  &  ( (v5_rlvect_1 @ B)  &  ( (v6_rlvect_1 @ B)  &  ( (v7_rlvect_1 @ B)  &  ( (v8_rlvect_1 @ B)  &  ( (v3_normsp_0 @ B)  &  ( (v4_normsp_0 @ B)  &  ( (v2_normsp_1 @ B)  &  (l1_normsp_1 @ B) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C: $i] :  ( ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ B) ) ) ) )  =>  ( ( ( (v2_ndiff_1 @ C)  @ A)  @ B)  <=>  ( ( (v1_partfun1 @ C)  @  (u1_struct_0 @ A) )  &  (! [D: $i] :  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ k5_numbers)  @  (u1_struct_0 @ A) )  &  ( ( ( (v12_struct_0 @ D)  @ k5_numbers)  @ A)  &  ( ( ( (v1_ndiff_1 @ D)  @ A)  @  (k4_struct_0 @ A) )  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @  (u1_struct_0 @ A) ) ) ) ) ) ) )  =>  ( ( (v3_normsp_1 @  ( ( (k1_ndiff_1 @ B)  @  ( ( ( ( (k8_funct_2 @ k5_numbers)  @  (u1_struct_0 @ B) )  @  (u1_struct_0 @ A) )  @ D)  @ C) )  @  ( ( (k37_valued_1 @ k5_numbers)  @ k1_numbers)  @  ( (k4_normsp_0 @ A)  @ D) ) ) )  @ B)  &  ( ( (k6_normsp_1 @ B)  @  ( ( (k1_ndiff_1 @ B)  @  ( ( ( ( (k8_funct_2 @ k5_numbers)  @  (u1_struct_0 @ B) )  @  (u1_struct_0 @ A) )  @ D)  @ C) )  @  ( ( (k37_valued_1 @ k5_numbers)  @ k1_numbers)  @  ( (k4_normsp_0 @ A)  @ D) ) ) )  =  (k4_struct_0 @ B) ) ) ) ) ) ) ) ) ) ) ) ) , file(ndiff_1, d5_ndiff_1)).
thf(d5_pdiff_1, axiom,  (! [A: $i] :  ( ( ( (m2_subset_1 @ A)  @ k1_numbers)  @ k5_numbers)  =>  (! [B: $i] :  ( ( (m2_finseq_1 @ B)  @ k1_numbers)  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  (v1_funct_1 @ C) )  =>  ( (C =  ( (k5_pdiff_1 @ A)  @ B) )  <=>  ( ( (k9_xtuple_0 @ C)  = k1_numbers)  &  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @ k1_numbers)  =>  ( ( (k1_funct_1 @ C)  @ D)  =  ( ( ( (k1_finseq_7 @ k1_numbers)  @ B)  @ A)  @ D) ) ) ) ) ) ) ) ) ) ) ) , file(pdiff_1, d5_pdiff_1)).
thf(d5_rvsum_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  =>  ( (k6_rvsum_1 @ A)  =  ( (k3_relat_1 @ A)  @ k31_binop_2) ) ) ) , file(rvsum_1, d5_rvsum_1)).
thf(d6_partfun1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) )  =>  (! [C: $i] :  ( ( (r2_hidden @ C)  @  (k9_xtuple_0 @ B) )  =>  ( ( ( (k7_partfun1 @ A)  @ B)  @ C)  =  ( (k1_funct_1 @ B)  @ C) ) ) ) ) ) ) , file(partfun1, d6_partfun1)).
thf(d6_rcomp_1, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ k1_numbers) )  =>  ( ( (m1_rcomp_1 @ B)  @ A)  <=>  (? [C: $i] :  ( (v1_xreal_0 @ C)  &  ( ~ ( ( (r1_xxreal_0 @ C)  @ k6_numbers) )  &  (B =  ( (k2_rcomp_1 @  ( (k6_xcmplx_0 @ A)  @ C) )  @  ( (k2_xcmplx_0 @ A)  @ C) ) ) ) ) ) ) ) ) ) ) , file(rcomp_1, d6_rcomp_1)).
thf(d6_rvsum_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v3_valued_0 @ B)  &  (v1_finseq_1 @ B) ) ) )  =>  ( ( (k8_rvsum_1 @ A)  @ B)  =  ( ( (k3_funcop_1 @ k34_binop_2)  @ A)  @ B) ) ) ) ) ) , file(rvsum_1, d6_rvsum_1)).
thf(d6_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  ( (k30_valued_1 @ A)  =  ( (k24_valued_1 @ A)  @  (k4_xcmplx_0 @ np__1) ) ) ) ) , file(valued_1, d6_valued_1)).
thf(d7_lopban_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  (l1_rlvect_1 @ A) ) ) ) ) ) ) ) ) )  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  ( (v13_algstr_0 @ B)  &  ( (v2_rlvect_1 @ B)  &  ( (v3_rlvect_1 @ B)  &  ( (v4_rlvect_1 @ B)  &  ( (v5_rlvect_1 @ B)  &  ( (v6_rlvect_1 @ B)  &  ( (v7_rlvect_1 @ B)  &  ( (v8_rlvect_1 @ B)  &  (l1_rlvect_1 @ B) ) ) ) ) ) ) ) ) )  =>  ( ( (k8_lopban_1 @ A)  @ B)  =  ( ( ( (g1_rlvect_1 @  ( (k7_lopban_1 @ A)  @ B) )  @  ( (k10_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k8_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k9_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) ) ) ) ) ) ) , file(lopban_1, d7_lopban_1)).
thf(d7_ndiff_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v7_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  ( (v3_normsp_0 @ A)  &  ( (v4_normsp_0 @ A)  &  ( (v2_normsp_1 @ A)  &  (l1_normsp_1 @ A) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ~ ( (v7_struct_0 @ B) )  &  ( (v13_algstr_0 @ B)  &  ( (v2_rlvect_1 @ B)  &  ( (v3_rlvect_1 @ B)  &  ( (v4_rlvect_1 @ B)  &  ( (v5_rlvect_1 @ B)  &  ( (v6_rlvect_1 @ B)  &  ( (v7_rlvect_1 @ B)  &  ( (v8_rlvect_1 @ B)  &  ( (v3_normsp_0 @ B)  &  ( (v4_normsp_0 @ B)  &  ( (v2_normsp_1 @ B)  &  (l1_normsp_1 @ B) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C: $i] :  ( ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ B) ) ) ) )  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @  (u1_struct_0 @ A) )  =>  ( ( ( ( (r1_ndiff_1 @ A)  @ B)  @ C)  @ D)  =>  (! [E: $i] :  ( ( (m1_subset_1 @ E)  @  (u1_struct_0 @  ( (k16_lopban_1 @ A)  @ B) ) )  =>  ( (E =  ( ( ( (k3_ndiff_1 @ A)  @ B)  @ C)  @ D) )  <=>  (? [F: $i] :  ( ( ( (m1_nfcont_1 @ F)  @ A)  @ D)  &  ( ( (r1_tarski @ F)  @  ( (k1_relset_1 @  (u1_struct_0 @ A) )  @ C) )  &  (? [G: $i] :  ( ( (v1_funct_1 @ G)  &  ( ( ( (v2_ndiff_1 @ G)  @ A)  @ B)  &  ( (m1_subset_1 @ G)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ B) ) ) ) ) )  &  (! [H: $i] :  ( ( (m1_subset_1 @ H)  @  (u1_struct_0 @ A) )  =>  ( ( (r2_hidden @ H)  @ F)  =>  ( ( ( (k5_algstr_0 @ B)  @  ( ( (k7_partfun1 @  (u1_struct_0 @ B) )  @ C)  @ H) )  @  ( ( (k7_partfun1 @  (u1_struct_0 @ B) )  @ C)  @ D) )  =  ( ( (k3_rlvect_1 @ B)  @  ( ( ( (k17_lopban_1 @ A)  @ B)  @ E)  @  ( ( (k5_algstr_0 @ A)  @ H)  @ D) ) )  @  ( ( (k7_partfun1 @  (u1_struct_0 @ B) )  @ G)  @  ( ( (k5_algstr_0 @ A)  @ H)  @ D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(ndiff_1, d7_ndiff_1)).
thf(d7_pdiff_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (m2_subset_1 @ A)  @ k1_numbers)  @ k5_numbers) )  =>  (! [B: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( ( (m2_subset_1 @ B)  @ k1_numbers)  @ k5_numbers) )  =>  (! [C: $i] :  ( ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @  (k1_euclid @ B) ) ) ) )  =>  (! [D: $i] :  ( ( ( (m2_finseq_2 @ D)  @ k1_numbers)  @  (k1_euclid @ A) )  =>  ( ( ( ( (r1_pdiff_1 @ A)  @ B)  @ C)  @ D)  <=>  (? [E: $i] :  ( ( (v1_funct_1 @ E)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_struct_0 @  (k4_real_ns1 @ A) ) )  @  (u1_struct_0 @  (k4_real_ns1 @ B) ) ) ) ) )  &  (? [F: $i] :  ( ( (m1_subset_1 @ F)  @  (u1_struct_0 @  (k4_real_ns1 @ A) ) )  &  ( (C = E)  &  ( (D = F)  &  ( ( ( (r1_ndiff_1 @  (k4_real_ns1 @ A) )  @  (k4_real_ns1 @ B) )  @ E)  @ F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(pdiff_1, d7_pdiff_1)).
thf(d7_rvsum_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (k10_rvsum_1 @ A)  @ B)  =  ( (k3_relat_1 @ A)  @  (k3_rvsum_1 @ B) ) ) ) ) ) ) , file(rvsum_1, d7_rvsum_1)).
thf(d8_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) )  =>  ( (B =  (k9_finseq_1 @ A) )  <=>  ( ( (k9_xtuple_0 @ B)  =  (k2_finseq_1 @ np__1) )  &  ( ( (k1_funct_1 @ B)  @ np__1)  = A) ) ) ) ) ) , file(finseq_1, d8_finseq_1)).
thf(d8_pdiff_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (m2_subset_1 @ A)  @ k1_numbers)  @ k5_numbers) )  =>  (! [B: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( ( (m2_subset_1 @ B)  @ k1_numbers)  @ k5_numbers) )  =>  (! [C: $i] :  ( ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @  (k1_euclid @ B) ) ) ) )  =>  (! [D: $i] :  ( ( ( (m2_finseq_2 @ D)  @ k1_numbers)  @  (k1_euclid @ A) )  =>  ( ( ( ( (r1_pdiff_1 @ A)  @ B)  @ C)  @ D)  =>  (! [E: $i] :  ( ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @  (k1_euclid @ A) )  @  (k1_euclid @ B) )  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @  (k1_euclid @ B) ) ) ) ) )  =>  ( (E =  ( ( ( (k8_pdiff_1 @ A)  @ B)  @ C)  @ D) )  <=>  (? [F: $i] :  ( ( (v1_funct_1 @ F)  &  ( (m1_subset_1 @ F)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_struct_0 @  (k4_real_ns1 @ A) ) )  @  (u1_struct_0 @  (k4_real_ns1 @ B) ) ) ) ) )  &  (? [G: $i] :  ( ( (m1_subset_1 @ G)  @  (u1_struct_0 @  (k4_real_ns1 @ A) ) )  &  ( (C = F)  &  ( (D = G)  &  (E =  ( ( ( (k3_ndiff_1 @  (k4_real_ns1 @ A) )  @  (k4_real_ns1 @ B) )  @ F)  @ G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(pdiff_1, d8_pdiff_1)).
thf(d8_rvsum_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  =>  ( (k12_rvsum_1 @ A)  =  ( (k3_relat_1 @ A)  @ k2_rvsum_1) ) ) ) , file(rvsum_1, d8_rvsum_1)).
thf(d8_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  ( (k39_valued_1 @ A)  =  ( (k18_valued_1 @ A)  @ A) ) ) ) , file(valued_1, d8_valued_1)).
thf(d8_xcmplx_0, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  (! [B: $i] :  ( (v1_xcmplx_0 @ B)  =>  ( ( (k6_xcmplx_0 @ A)  @ B)  =  ( (k2_xcmplx_0 @ A)  @  (k4_xcmplx_0 @ B) ) ) ) ) ) ) , file(xcmplx_0, d8_xcmplx_0)).
thf(d9_euclid, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (u1_struct_0 @  (k15_euclid @ np__2) ) )  =>  ( (k17_euclid @ A)  =  ( (k1_seq_1 @ A)  @ np__1) ) ) ) , file(euclid, d9_euclid)).
thf(d9_lopban_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  ( (v3_normsp_0 @ A)  &  ( (v4_normsp_0 @ A)  &  ( (v2_normsp_1 @ A)  &  (l1_normsp_1 @ A) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  ( (v13_algstr_0 @ B)  &  ( (v2_rlvect_1 @ B)  &  ( (v3_rlvect_1 @ B)  &  ( (v4_rlvect_1 @ B)  &  ( (v5_rlvect_1 @ B)  &  ( (v6_rlvect_1 @ B)  &  ( (v7_rlvect_1 @ B)  &  ( (v8_rlvect_1 @ B)  &  ( (v3_normsp_0 @ B)  &  ( (v4_normsp_0 @ B)  &  ( (v2_normsp_1 @ B)  &  (l1_normsp_1 @ B) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  (u1_struct_0 @  ( (k8_lopban_1 @ A)  @ B) ) ) )  =>  ( (C =  ( (k10_lopban_1 @ A)  @ B) )  <=>  (! [D: $i] :  ( ( (r2_hidden @ D)  @ C)  <=>  ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ B) )  &  ( ( ( (v13_vectsp_1 @ D)  @ A)  @ B)  &  ( ( ( (v1_lopban_1 @ D)  @ A)  @ B)  &  ( ( ( (v2_lopban_1 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(lopban_1, d9_lopban_1)).
thf(d9_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_valued_0 @ B) ) )  =>  ( ( (k45_valued_1 @ A)  @ B)  =  ( (k1_valued_1 @ A)  @  (k30_valued_1 @ B) ) ) ) ) ) ) , file(valued_1, d9_valued_1)).
thf(dt_g1_normsp_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( (m1_subset_1 @ B)  @ A)  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A) ) ) ) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @  ( (k2_zfmisc_1 @ k1_numbers)  @ A) )  @ A)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ A) )  @ A) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ k1_numbers)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ k1_numbers) ) ) ) ) ) ) )  =>  ( (v1_normsp_1 @  ( ( ( ( (g1_normsp_1 @ A)  @ B)  @ C)  @ D)  @ E) )  &  (l1_normsp_1 @  ( ( ( ( (g1_normsp_1 @ A)  @ B)  @ C)  @ D)  @ E) ) ) ) ) , file(normsp_1, g1_normsp_1)).
thf(dt_g1_rltopsp1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( (m1_subset_1 @ B)  @ A)  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A) ) ) ) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @  ( (k2_zfmisc_1 @ k1_numbers)  @ A) )  @ A)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ A) )  @ A) ) ) ) )  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @ A) ) ) ) ) )  =>  ( (v5_rltopsp1 @  ( ( ( ( (g1_rltopsp1 @ A)  @ B)  @ C)  @ D)  @ E) )  &  (l1_rltopsp1 @  ( ( ( ( (g1_rltopsp1 @ A)  @ B)  @ C)  @ D)  @ E) ) ) ) ) , file(rltopsp1, g1_rltopsp1)).
thf(dt_g1_rlvect_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (m1_subset_1 @ B)  @ A)  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A) ) ) ) )  &  ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @  ( (k2_zfmisc_1 @ k1_numbers)  @ A) )  @ A)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ A) )  @ A) ) ) ) ) ) )  =>  ( (v1_rlvect_1 @  ( ( ( (g1_rlvect_1 @ A)  @ B)  @ C)  @ D) )  &  (l1_rlvect_1 @  ( ( ( (g1_rlvect_1 @ A)  @ B)  @ C)  @ D) ) ) ) ) , file(rlvect_1, g1_rlvect_1)).
thf(dt_k10_finseq_1, axiom, $true, file(finseq_1, k10_finseq_1)).
thf(dt_k10_lopban_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  ( (v3_normsp_0 @ A)  &  ( (v4_normsp_0 @ A)  &  ( (v2_normsp_1 @ A)  &  (l1_normsp_1 @ A) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ~ ( (v2_struct_0 @ B) )  &  ( (v13_algstr_0 @ B)  &  ( (v2_rlvect_1 @ B)  &  ( (v3_rlvect_1 @ B)  &  ( (v4_rlvect_1 @ B)  &  ( (v5_rlvect_1 @ B)  &  ( (v6_rlvect_1 @ B)  &  ( (v7_rlvect_1 @ B)  &  ( (v8_rlvect_1 @ B)  &  ( (v3_normsp_0 @ B)  &  ( (v4_normsp_0 @ B)  &  ( (v2_normsp_1 @ B)  &  (l1_normsp_1 @ B) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (m1_subset_1 @  ( (k10_lopban_1 @ A)  @ B) )  @  (k1_zfmisc_1 @  (u1_struct_0 @  ( (k8_lopban_1 @ A)  @ B) ) ) ) ) ) , file(lopban_1, k10_lopban_1)).
thf(dt_k10_pdiff_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (m1_subset_1 @ A)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ B)  @ k5_numbers)  &  ( ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @ k1_numbers) ) ) )  &  ( (m1_subset_1 @ D)  @  (k1_euclid @ A) ) ) ) )  =>  (v1_xreal_0 @  ( ( ( (k10_pdiff_1 @ A)  @ B)  @ C)  @ D) ) ) ) , file(pdiff_1, k10_pdiff_1)).
thf(dt_k10_rsspace, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  (l1_rlvect_1 @ A) ) ) ) ) ) ) ) ) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) )  =>  ( (m1_subset_1 @  ( (k10_rsspace @ A)  @ B) )  @ B) ) ) , file(rsspace, k10_rsspace)).
thf(dt_k10_rvsum_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  &  (v1_xreal_0 @ B) )  =>  ( (m2_finseq_1 @  ( (k10_rvsum_1 @ A)  @ B) )  @ k1_numbers) ) ) , file(rvsum_1, k10_rvsum_1)).
thf(dt_k10_xtuple_0, axiom, $true, file(xtuple_0, k10_xtuple_0)).
thf(dt_k11_binop_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  ( (m1_subset_1 @  ( (k11_binop_2 @ A)  @ B) )  @ k1_numbers) ) ) , file(binop_2, k11_binop_2)).
thf(dt_k11_pdiff_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (m1_subset_1 @ A)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ B)  @ k5_numbers)  &  ( ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @ k1_numbers) ) ) )  &  ( (m1_subset_1 @ D)  @  (k1_euclid @ A) ) ) ) )  =>  ( (m1_subset_1 @  ( ( ( (k11_pdiff_1 @ A)  @ B)  @ C)  @ D) )  @ k1_numbers) ) ) , file(pdiff_1, k11_pdiff_1)).
thf(dt_k12_euclid, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_finseq_1 @ A)  &  (v3_valued_0 @ A) ) ) )  =>  ( (m1_subset_1 @  (k12_euclid @ A) )  @ k1_numbers) ) ) , file(euclid, k12_euclid)).
thf(dt_k12_finseq_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (m1_subset_1 @ B)  @ A) )  =>  ( (m2_finseq_1 @  ( (k12_finseq_1 @ A)  @ B) )  @ A) ) ) , file(finseq_1, k12_finseq_1)).
thf(dt_k12_rvsum_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  =>  ( (m2_finseq_1 @  (k12_rvsum_1 @ A) )  @ k1_numbers) ) ) , file(rvsum_1, k12_rvsum_1)).
thf(dt_k15_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v5_rltopsp1 @  (k15_euclid @ A) )  &  (l1_rltopsp1 @  (k15_euclid @ A) ) ) ) ) , file(euclid, k15_euclid)).
thf(dt_k15_lopban_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  ( (v3_normsp_0 @ A)  &  ( (v4_normsp_0 @ A)  &  ( (v2_normsp_1 @ A)  &  (l1_normsp_1 @ A) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ~ ( (v2_struct_0 @ B) )  &  ( (v13_algstr_0 @ B)  &  ( (v2_rlvect_1 @ B)  &  ( (v3_rlvect_1 @ B)  &  ( (v4_rlvect_1 @ B)  &  ( (v5_rlvect_1 @ B)  &  ( (v6_rlvect_1 @ B)  &  ( (v7_rlvect_1 @ B)  &  ( (v8_rlvect_1 @ B)  &  ( (v3_normsp_0 @ B)  &  ( (v4_normsp_0 @ B)  &  ( (v2_normsp_1 @ B)  &  (l1_normsp_1 @ B) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k15_lopban_1 @ A)  @ B) )  &  ( ( ( (v1_funct_2 @  ( (k15_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) )  @ k1_numbers)  &  ( (m1_subset_1 @  ( (k15_lopban_1 @ A)  @ B) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k10_lopban_1 @ A)  @ B) )  @ k1_numbers) ) ) ) ) ) ) , file(lopban_1, k15_lopban_1)).
thf(dt_k16_complex1, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  (v1_xreal_0 @  (k16_complex1 @ A) ) ) ) , file(complex1, k16_complex1)).
thf(dt_k16_lopban_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  ( (v3_normsp_0 @ A)  &  ( (v4_normsp_0 @ A)  &  ( (v2_normsp_1 @ A)  &  (l1_normsp_1 @ A) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ~ ( (v2_struct_0 @ B) )  &  ( (v13_algstr_0 @ B)  &  ( (v2_rlvect_1 @ B)  &  ( (v3_rlvect_1 @ B)  &  ( (v4_rlvect_1 @ B)  &  ( (v5_rlvect_1 @ B)  &  ( (v6_rlvect_1 @ B)  &  ( (v7_rlvect_1 @ B)  &  ( (v8_rlvect_1 @ B)  &  ( (v3_normsp_0 @ B)  &  ( (v4_normsp_0 @ B)  &  ( (v2_normsp_1 @ B)  &  (l1_normsp_1 @ B) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ~ ( (v2_struct_0 @  ( (k16_lopban_1 @ A)  @ B) ) )  &  (l1_normsp_1 @  ( (k16_lopban_1 @ A)  @ B) ) ) ) ) , file(lopban_1, k16_lopban_1)).
thf(dt_k16_rvsum_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  =>  (v1_xcmplx_0 @  (k16_rvsum_1 @ A) ) ) ) , file(rvsum_1, k16_rvsum_1)).
thf(dt_k17_complex1, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (m1_subset_1 @  (k17_complex1 @ A) )  @ k1_numbers) ) ) , file(complex1, k17_complex1)).
thf(dt_k17_euclid, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (u1_struct_0 @  (k15_euclid @ np__2) ) )  =>  ( (m1_subset_1 @  (k17_euclid @ A) )  @ k1_numbers) ) ) , file(euclid, k17_euclid)).
thf(dt_k17_lopban_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  ( (v3_normsp_0 @ A)  &  ( (v4_normsp_0 @ A)  &  ( (v2_normsp_1 @ A)  &  (l1_normsp_1 @ A) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ( ~ ( (v2_struct_0 @ B) )  &  ( (v13_algstr_0 @ B)  &  ( (v2_rlvect_1 @ B)  &  ( (v3_rlvect_1 @ B)  &  ( (v4_rlvect_1 @ B)  &  ( (v5_rlvect_1 @ B)  &  ( (v6_rlvect_1 @ B)  &  ( (v7_rlvect_1 @ B)  &  ( (v8_rlvect_1 @ B)  &  ( (v3_normsp_0 @ B)  &  ( (v4_normsp_0 @ B)  &  ( (v2_normsp_1 @ B)  &  (l1_normsp_1 @ B) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @  ( (k16_lopban_1 @ A)  @ B) ) )  &  ( (m1_subset_1 @ D)  @  (u1_struct_0 @ A) ) ) ) )  =>  ( (m1_subset_1 @  ( ( ( (k17_lopban_1 @ A)  @ B)  @ C)  @ D) )  @  (u1_struct_0 @ B) ) ) ) , file(lopban_1, k17_lopban_1)).
thf(dt_k18_complex1, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (m1_subset_1 @  (k18_complex1 @ A) )  @ k1_numbers) ) ) , file(complex1, k18_complex1)).
thf(dt_k18_euclid, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (u1_struct_0 @  (k15_euclid @ np__2) ) )  =>  ( (m1_subset_1 @  (k18_euclid @ A) )  @ k1_numbers) ) ) , file(euclid, k18_euclid)).
thf(dt_k18_rvsum_1, axiom,  (! [A: $i] :  ( ( (m1_finseq_1 @ A)  @ k1_numbers)  =>  ( (m1_subset_1 @  (k18_rvsum_1 @ A) )  @ k1_numbers) ) ) , file(rvsum_1, k18_rvsum_1)).
thf(dt_k18_valued_1, 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 @  ( (k18_valued_1 @ A)  @ B) )  &  (v1_funct_1 @  ( (k18_valued_1 @ A)  @ B) ) ) ) ) , file(valued_1, k18_valued_1)).
thf(dt_k19_euclid, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  ( (m1_subset_1 @  ( (k19_euclid @ A)  @ B) )  @  (u1_struct_0 @  (k15_euclid @ np__2) ) ) ) ) , file(euclid, k19_euclid)).
thf(dt_k1_algstr_0, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (l1_algstr_0 @ A)  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) ) ) )  =>  ( (m1_subset_1 @  ( ( (k1_algstr_0 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ A) ) ) ) , file(algstr_0, k1_algstr_0)).
thf(dt_k1_card_1, axiom,  (! [A: $i] :  (v1_card_1 @  (k1_card_1 @ A) ) ) , file(card_1, k1_card_1)).
thf(dt_k1_complex1, axiom, $true, file(complex1, k1_complex1)).
thf(dt_k1_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (m1_finseq_2 @  (k1_euclid @ A) )  @ k1_numbers) ) ) , file(euclid, k1_euclid)).
thf(dt_k1_fdiff_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_funct_1 @ A)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) )  &  (v1_xreal_0 @ B) )  =>  ( (m1_subset_1 @  ( (k1_fdiff_1 @ A)  @ B) )  @ k1_numbers) ) ) , file(fdiff_1, k1_fdiff_1)).
thf(dt_k1_finseq_1, axiom, $true, file(finseq_1, k1_finseq_1)).
thf(dt_k1_finseq_7, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (m1_finseq_1 @ B)  @ A)  &  ( (v7_ordinal1 @ C)  &  ( (m1_subset_1 @ D)  @ A) ) ) )  =>  ( (m2_finseq_1 @  ( ( ( (k1_finseq_7 @ A)  @ B)  @ C)  @ D) )  @ A) ) ) , file(finseq_7, k1_finseq_7)).
thf(dt_k1_finsop_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (m1_finseq_1 @ B)  @ A)  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A) ) ) ) ) ) )  =>  ( (m1_subset_1 @  ( ( (k1_finsop_1 @ A)  @ B)  @ C) )  @ A) ) ) , file(finsop_1, k1_finsop_1)).
thf(dt_k1_funct_1, axiom, $true, file(funct_1, k1_funct_1)).
thf(dt_k1_funct_2, axiom, $true, file(funct_2, k1_funct_2)).
thf(dt_k1_ndiff_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  (l1_rlvect_1 @ A) ) ) ) ) ) ) ) ) )  &  ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ k5_numbers)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @  (u1_struct_0 @ A) ) ) ) ) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ k5_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k1_numbers) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( ( (k1_ndiff_1 @ A)  @ B)  @ C) )  &  ( ( ( (v1_funct_2 @  ( ( (k1_ndiff_1 @ A)  @ B)  @ C) )  @ k5_numbers)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @  ( ( (k1_ndiff_1 @ A)  @ B)  @ C) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @  (u1_struct_0 @ A) ) ) ) ) ) ) ) , file(ndiff_1, k1_ndiff_1)).
thf(dt_k1_normsp_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_normsp_0 @ A) )  &  ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) ) )  =>  ( (m1_subset_1 @  ( (k1_normsp_0 @ A)  @ B) )  @ k1_numbers) ) ) , file(normsp_0, k1_normsp_0)).
thf(dt_k1_normsp_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_struct_0 @ A) )  &  ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ k5_numbers)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @  (u1_struct_0 @ A) ) ) ) ) )  &  ( (m1_subset_1 @ C)  @ k5_numbers) ) )  =>  ( (m1_subset_1 @  ( ( (k1_normsp_1 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ A) ) ) ) , file(normsp_1, k1_normsp_1)).
thf(dt_k1_numbers, axiom, $true, file(numbers, k1_numbers)).
thf(dt_k1_partfun1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] :  ( ( ( (v1_funct_1 @ E)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  &  ( (v1_funct_1 @ F)  &  ( (m1_subset_1 @ F)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ C)  @ D) ) ) ) )  =>  ( (v1_funct_1 @  ( ( ( ( ( (k1_partfun1 @ A)  @ B)  @ C)  @ D)  @ E)  @ F) )  &  ( (m1_subset_1 @  ( ( ( ( ( (k1_partfun1 @ A)  @ B)  @ C)  @ D)  @ E)  @ F) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ D) ) ) ) ) ) , file(partfun1, k1_partfun1)).
thf(dt_k1_pdiff_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  (v7_ordinal1 @ B) )  =>  ( (v1_funct_1 @  ( (k1_pdiff_1 @ A)  @ B) )  &  ( ( ( (v1_funct_2 @  ( (k1_pdiff_1 @ A)  @ B) )  @  (k1_euclid @ B) )  @ k1_numbers)  &  ( (m1_subset_1 @  ( (k1_pdiff_1 @ A)  @ B) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ B) )  @ k1_numbers) ) ) ) ) ) ) , file(pdiff_1, k1_pdiff_1)).
thf(dt_k1_real_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  ( (m1_subset_1 @  (k1_real_1 @ A) )  @ k1_numbers) ) ) , file(real_1, k1_real_1)).
thf(dt_k1_real_ns1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v1_funct_1 @  (k1_real_ns1 @ A) )  &  ( ( ( (v1_funct_2 @  (k1_real_ns1 @ A) )  @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @  (k1_euclid @ A) ) )  @  (k1_euclid @ A) )  &  ( (m1_subset_1 @  (k1_real_ns1 @ A) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @  (k1_euclid @ A) ) )  @  (k1_euclid @ A) ) ) ) ) ) ) ) , file(real_ns1, k1_real_ns1)).
thf(dt_k1_relset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  ( (m1_subset_1 @  ( (k1_relset_1 @ A)  @ B) )  @  (k1_zfmisc_1 @ A) ) ) ) , file(relset_1, k1_relset_1)).
thf(dt_k1_rlvect_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_rlvect_1 @ A) )  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  (v1_xreal_0 @ C) ) )  =>  ( (m1_subset_1 @  ( ( (k1_rlvect_1 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ A) ) ) ) , file(rlvect_1, k1_rlvect_1)).
thf(dt_k1_rvsum_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  ( (m1_subset_1 @  (k1_rvsum_1 @ A) )  @  (k1_zfmisc_1 @ k1_numbers) ) ) ) , file(rvsum_1, k1_rvsum_1)).
thf(dt_k1_seq_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_valued_0 @ A) ) )  =>  ( (m1_subset_1 @  ( (k1_seq_1 @ A)  @ B) )  @ k1_numbers) ) ) , file(seq_1, k1_seq_1)).
thf(dt_k1_seq_2, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k5_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k1_numbers) ) ) ) )  =>  (v1_xreal_0 @  (k1_seq_2 @ A) ) ) ) , file(seq_2, k1_seq_2)).
thf(dt_k1_valued_1, 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_valued_1 @ A)  @ B) )  &  (v1_funct_1 @  ( (k1_valued_1 @ A)  @ B) ) ) ) ) , file(valued_1, k1_valued_1)).
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_k20_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( (v3_membered @ B)  &  ( (v3_membered @ C)  &  ( ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  &  ( (v1_funct_1 @ E)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( ( ( ( (k20_valued_1 @ A)  @ B)  @ C)  @ D)  @ E) )  &  ( (m1_subset_1 @  ( ( ( ( (k20_valued_1 @ A)  @ B)  @ C)  @ D)  @ E) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ k1_numbers) ) ) ) ) ) , file(valued_1, k20_valued_1)).
thf(dt_k24_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  &  (v1_xcmplx_0 @ B) )  =>  ( (v1_relat_1 @  ( (k24_valued_1 @ A)  @ B) )  &  (v1_funct_1 @  ( (k24_valued_1 @ A)  @ B) ) ) ) ) , file(valued_1, k24_valued_1)).
thf(dt_k2_complex1, axiom, $true, file(complex1, k2_complex1)).
thf(dt_k2_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (m1_subset_1 @  (k2_finseq_1 @ A) )  @  (k1_zfmisc_1 @ k5_numbers) ) ) ) , file(finseq_1, k2_finseq_1)).
thf(dt_k2_finseq_2, axiom,  (! [A: $i, B: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v1_relat_1 @  ( (k2_finseq_2 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k2_finseq_2 @ A)  @ B) )  &  (v1_finseq_1 @  ( (k2_finseq_2 @ A)  @ B) ) ) ) ) ) , file(finseq_2, k2_finseq_2)).
thf(dt_k2_finseq_4, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (m1_subset_1 @ B)  @ A)  &  ( (m1_subset_1 @ C)  @ A) ) )  =>  ( (m2_finseq_1 @  ( ( (k2_finseq_4 @ A)  @ B)  @ C) )  @ A) ) ) , file(finseq_4, k2_finseq_4)).
thf(dt_k2_funcop_1, axiom, $true, file(funcop_1, k2_funcop_1)).
thf(dt_k2_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  ( (v1_relat_1 @  (k2_funct_1 @ A) )  &  (v1_funct_1 @  (k2_funct_1 @ A) ) ) ) ) , file(funct_1, k2_funct_1)).
thf(dt_k2_funct_7, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  ( (v1_relat_1 @  ( ( (k2_funct_7 @ A)  @ B)  @ C) )  &  (v1_funct_1 @  ( ( (k2_funct_7 @ A)  @ B)  @ C) ) ) ) ) , file(funct_7, k2_funct_7)).
thf(dt_k2_lopban_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v2_struct_0 @ B) )  &  (l2_algstr_0 @ B) ) )  =>  ( (v1_funct_1 @  ( (k2_lopban_1 @ A)  @ B) )  &  ( ( ( (v1_funct_2 @  ( (k2_lopban_1 @ A)  @ B) )  @  ( (k2_zfmisc_1 @  ( (k9_funct_2 @ A)  @  (u1_struct_0 @ B) ) )  @  ( (k9_funct_2 @ A)  @  (u1_struct_0 @ B) ) ) )  @  ( (k9_funct_2 @ A)  @  (u1_struct_0 @ B) ) )  &  ( (m1_subset_1 @  ( (k2_lopban_1 @ A)  @ B) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k9_funct_2 @ A)  @  (u1_struct_0 @ B) ) )  @  ( (k9_funct_2 @ A)  @  (u1_struct_0 @ B) ) ) )  @  ( (k9_funct_2 @ A)  @  (u1_struct_0 @ B) ) ) ) ) ) ) ) ) , file(lopban_1, k2_lopban_1)).
thf(dt_k2_normsp_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_normsp_0 @ A) )  &  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @  (u1_struct_0 @ A) )  &  (v1_funct_1 @ B) ) ) )  =>  ( (v1_relat_1 @  ( (k2_normsp_0 @ A)  @ B) )  &  (v1_funct_1 @  ( (k2_normsp_0 @ A)  @ B) ) ) ) ) , file(normsp_0, k2_normsp_0)).
thf(dt_k2_rcomp_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v1_xxreal_0 @ B) )  =>  ( (m1_subset_1 @  ( (k2_rcomp_1 @ A)  @ B) )  @  (k1_zfmisc_1 @ k1_numbers) ) ) ) , file(rcomp_1, k2_rcomp_1)).
thf(dt_k2_real_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  ( (m1_subset_1 @  (k2_real_1 @ A) )  @ k1_numbers) ) ) , file(real_1, k2_real_1)).
thf(dt_k2_real_ns1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v1_funct_1 @  (k2_real_ns1 @ A) )  &  ( ( ( (v1_funct_2 @  (k2_real_ns1 @ A) )  @  ( (k2_zfmisc_1 @ k1_numbers)  @  (k1_euclid @ A) ) )  @  (k1_euclid @ A) )  &  ( (m1_subset_1 @  (k2_real_ns1 @ A) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @  (k1_euclid @ A) ) )  @  (k1_euclid @ A) ) ) ) ) ) ) ) , file(real_ns1, k2_real_ns1)).
thf(dt_k2_relset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) )  =>  ( (m1_subset_1 @  ( (k2_relset_1 @ A)  @ B) )  @  (k1_zfmisc_1 @ A) ) ) ) , file(relset_1, k2_relset_1)).
thf(dt_k2_rvsum_1, axiom,  ( (v1_funct_1 @ k2_rvsum_1)  &  ( ( ( (v1_funct_2 @ k2_rvsum_1)  @ k1_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ k2_rvsum_1)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) ) , file(rvsum_1, k2_rvsum_1)).
thf(dt_k2_seq_2, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k5_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k1_numbers) ) ) ) )  =>  ( (m1_subset_1 @  (k2_seq_2 @ A) )  @ k1_numbers) ) ) , file(seq_2, k2_seq_2)).
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_k30_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  ( (v1_relat_1 @  (k30_valued_1 @ A) )  &  ( (v1_funct_1 @  (k30_valued_1 @ A) )  &  (v1_valued_0 @  (k30_valued_1 @ A) ) ) ) ) ) , file(valued_1, k30_valued_1)).
thf(dt_k31_binop_2, axiom,  ( (v1_funct_1 @ k31_binop_2)  &  ( ( ( (v1_funct_2 @ k31_binop_2)  @ k1_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ k31_binop_2)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) ) , file(binop_2, k31_binop_2)).
thf(dt_k33_binop_2, axiom,  ( (v1_funct_1 @ k33_binop_2)  &  ( ( ( (v1_funct_2 @ k33_binop_2)  @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) )  @ k1_numbers)  &  ( (m1_subset_1 @ k33_binop_2)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) )  @ k1_numbers) ) ) ) ) , file(binop_2, k33_binop_2)).
thf(dt_k34_binop_2, axiom,  ( (v1_funct_1 @ k34_binop_2)  &  ( ( ( (v1_funct_2 @ k34_binop_2)  @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) )  @ k1_numbers)  &  ( (m1_subset_1 @ k34_binop_2)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) )  @ k1_numbers) ) ) ) ) , file(binop_2, k34_binop_2)).
thf(dt_k35_binop_2, axiom,  ( (v1_funct_1 @ k35_binop_2)  &  ( ( ( (v1_funct_2 @ k35_binop_2)  @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) )  @ k1_numbers)  &  ( (m1_subset_1 @ k35_binop_2)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) )  @ k1_numbers) ) ) ) ) , file(binop_2, k35_binop_2)).
thf(dt_k35_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  ( (v1_relat_1 @  (k35_valued_1 @ A) )  &  ( (v1_funct_1 @  (k35_valued_1 @ A) )  &  (v1_valued_0 @  (k35_valued_1 @ A) ) ) ) ) ) , file(valued_1, k35_valued_1)).
thf(dt_k37_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v3_membered @ B)  &  ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  =>  ( (v1_funct_1 @  ( ( (k37_valued_1 @ A)  @ B)  @ C) )  &  ( (m1_subset_1 @  ( ( (k37_valued_1 @ A)  @ B)  @ C) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ k1_numbers) ) ) ) ) ) , file(valued_1, k37_valued_1)).
thf(dt_k39_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  ( (v1_relat_1 @  (k39_valued_1 @ A) )  &  (v1_funct_1 @  (k39_valued_1 @ A) ) ) ) ) , file(valued_1, k39_valued_1)).
thf(dt_k3_complex1, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (m1_subset_1 @  (k3_complex1 @ A) )  @ k1_numbers) ) ) , file(complex1, k3_complex1)).
thf(dt_k3_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( ( (m2_subset_1 @  (k3_finseq_1 @ A) )  @ k1_numbers)  @ k5_numbers) ) ) , file(finseq_1, k3_finseq_1)).
thf(dt_k3_funcop_1, axiom, $true, file(funcop_1, k3_funcop_1)).
thf(dt_k3_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (m1_subset_1 @ D)  @ A) ) )  =>  ( (m1_subset_1 @  ( ( ( (k3_funct_2 @ A)  @ B)  @ C)  @ D) )  @ B) ) ) , file(funct_2, k3_funct_2)).
thf(dt_k3_lopban_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v2_struct_0 @ B) )  &  ( (v13_algstr_0 @ B)  &  ( (v2_rlvect_1 @ B)  &  ( (v3_rlvect_1 @ B)  &  ( (v4_rlvect_1 @ B)  &  ( (v5_rlvect_1 @ B)  &  ( (v6_rlvect_1 @ B)  &  ( (v7_rlvect_1 @ B)  &  ( (v8_rlvect_1 @ B)  &  (l1_rlvect_1 @ B) ) ) ) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k3_lopban_1 @ A)  @ B) )  &  ( ( ( (v1_funct_2 @  ( (k3_lopban_1 @ A)  @ B) )  @  ( (k2_zfmisc_1 @ k1_numbers)  @  ( (k9_funct_2 @ A)  @  (u1_struct_0 @ B) ) ) )  @  ( (k9_funct_2 @ A)  @  (u1_struct_0 @ B) ) )  &  ( (m1_subset_1 @  ( (k3_lopban_1 @ A)  @ B) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @  ( (k9_funct_2 @ A)  @  (u1_struct_0 @ B) ) ) )  @  ( (k9_funct_2 @ A)  @  (u1_struct_0 @ B) ) ) ) ) ) ) ) ) , file(lopban_1, k3_lopban_1)).
thf(dt_k3_ndiff_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( ~ ( (v7_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  ( (v3_normsp_0 @ A)  &  ( (v4_normsp_0 @ A)  &  ( (v2_normsp_1 @ A)  &  (l1_normsp_1 @ A) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ( ~ ( (v2_struct_0 @ B) )  &  ( ~ ( (v7_struct_0 @ B) )  &  ( (v13_algstr_0 @ B)  &  ( (v2_rlvect_1 @ B)  &  ( (v3_rlvect_1 @ B)  &  ( (v4_rlvect_1 @ B)  &  ( (v5_rlvect_1 @ B)  &  ( (v6_rlvect_1 @ B)  &  ( (v7_rlvect_1 @ B)  &  ( (v8_rlvect_1 @ B)  &  ( (v3_normsp_0 @ B)  &  ( (v4_normsp_0 @ B)  &  ( (v2_normsp_1 @ B)  &  (l1_normsp_1 @ B) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ B) ) ) ) )  &  ( (m1_subset_1 @ D)  @  (u1_struct_0 @ A) ) ) ) )  =>  ( (m1_subset_1 @  ( ( ( (k3_ndiff_1 @ A)  @ B)  @ C)  @ D) )  @  (u1_struct_0 @  ( (k16_lopban_1 @ A)  @ B) ) ) ) ) , file(ndiff_1, k3_ndiff_1)).
thf(dt_k3_numbers, axiom, $true, file(numbers, k3_numbers)).
thf(dt_k3_pdiff_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( (v1_funct_1 @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @ k1_numbers) ) ) ) )  =>  ( (v1_funct_1 @  ( (k3_pdiff_1 @ A)  @ B) )  &  ( (m1_subset_1 @  ( (k3_pdiff_1 @ A)  @ B) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @  (k1_euclid @ np__1) ) ) ) ) ) ) , file(pdiff_1, k3_pdiff_1)).
thf(dt_k3_real_ns1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v1_funct_1 @  (k3_real_ns1 @ A) )  &  ( ( ( (v1_funct_2 @  (k3_real_ns1 @ A) )  @  (k1_euclid @ A) )  @ k1_numbers)  &  ( (m1_subset_1 @  (k3_real_ns1 @ A) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @ k1_numbers) ) ) ) ) ) ) , file(real_ns1, k3_real_ns1)).
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_rlvect_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v2_rlvect_1 @ A)  &  (l1_algstr_0 @ A) )  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) ) ) )  =>  ( (m1_subset_1 @  ( ( (k3_rlvect_1 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ A) ) ) ) , file(rlvect_1, k3_rlvect_1)).
thf(dt_k3_rvsum_1, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  ( (v1_funct_1 @  (k3_rvsum_1 @ A) )  &  ( ( ( (v1_funct_2 @  (k3_rvsum_1 @ A) )  @ k1_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @  (k3_rvsum_1 @ A) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) ) ) ) , file(rvsum_1, k3_rvsum_1)).
thf(dt_k3_square_1, axiom, $true, file(square_1, k3_square_1)).
thf(dt_k3_xcmplx_0, axiom, $true, file(xcmplx_0, k3_xcmplx_0)).
thf(dt_k45_valued_1, 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 @  ( (k45_valued_1 @ A)  @ B) )  &  (v1_funct_1 @  ( (k45_valued_1 @ A)  @ B) ) ) ) ) , file(valued_1, k45_valued_1)).
thf(dt_k4_complex1, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (m1_subset_1 @  (k4_complex1 @ A) )  @ k1_numbers) ) ) , file(complex1, k4_complex1)).
thf(dt_k4_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v1_relat_1 @  (k4_euclid @ A) )  &  ( (v1_funct_1 @  (k4_euclid @ A) )  &  ( (v1_finseq_1 @  (k4_euclid @ A) )  &  (v3_valued_0 @  (k4_euclid @ A) ) ) ) ) ) ) , file(euclid, k4_euclid)).
thf(dt_k4_finseq_2, axiom,  (! [A: $i, B: $i] :  ( (v7_ordinal1 @ A)  =>  ( (m1_finseq_2 @  ( (k4_finseq_2 @ A)  @ B) )  @ B) ) ) , file(finseq_2, k4_finseq_2)).
thf(dt_k4_lopban_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v2_struct_0 @ B) )  &  (l2_struct_0 @ B) )  =>  ( ( ( (m2_funct_2 @  ( (k4_lopban_1 @ A)  @ B) )  @ A)  @  (u1_struct_0 @ B) )  @  ( (k9_funct_2 @ A)  @  (u1_struct_0 @ B) ) ) ) ) , file(lopban_1, k4_lopban_1)).
thf(dt_k4_normsp_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_normsp_0 @ A) )  &  ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ k5_numbers)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @  (u1_struct_0 @ A) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k4_normsp_0 @ A)  @ B) )  &  ( ( ( (v1_funct_2 @  ( (k4_normsp_0 @ A)  @ B) )  @ k5_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @  ( (k4_normsp_0 @ A)  @ B) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k1_numbers) ) ) ) ) ) ) , file(normsp_0, k4_normsp_0)).
thf(dt_k4_numbers, axiom, $true, file(numbers, k4_numbers)).
thf(dt_k4_ordinal1, axiom, $true, file(ordinal1, k4_ordinal1)).
thf(dt_k4_real_ns1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( ~ ( (v2_struct_0 @  (k4_real_ns1 @ A) ) )  &  ( (v1_normsp_1 @  (k4_real_ns1 @ A) )  &  (l1_normsp_1 @  (k4_real_ns1 @ A) ) ) ) ) ) , file(real_ns1, k4_real_ns1)).
thf(dt_k4_relat_1, axiom,  (! [A: $i] :  (v1_relat_1 @  (k4_relat_1 @ A) ) ) , file(relat_1, k4_relat_1)).
thf(dt_k4_rvsum_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v3_valued_0 @ B)  &  (v1_finseq_1 @ B) ) ) ) )  =>  ( (m2_finseq_1 @  ( (k4_rvsum_1 @ A)  @ B) )  @ k1_numbers) ) ) , file(rvsum_1, k4_rvsum_1)).
thf(dt_k4_struct_0, axiom,  (! [A: $i] :  ( (l2_struct_0 @ A)  =>  ( (m1_subset_1 @  (k4_struct_0 @ A) )  @  (u1_struct_0 @ A) ) ) ) , file(struct_0, k4_struct_0)).
thf(dt_k4_xcmplx_0, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) ) ) ) , file(xcmplx_0, k4_xcmplx_0)).
thf(dt_k4_xxreal_1, axiom, $true, file(xxreal_1, k4_xxreal_1)).
thf(dt_k54_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  ( (v1_relat_1 @  (k54_valued_1 @ A) )  &  ( (v1_funct_1 @  (k54_valued_1 @ A) )  &  (v3_valued_0 @  (k54_valued_1 @ A) ) ) ) ) ) , file(valued_1, k54_valued_1)).
thf(dt_k56_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_membered @ B)  &  ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  =>  ( (v1_funct_1 @  ( ( (k56_valued_1 @ A)  @ B)  @ C) )  &  ( (m1_subset_1 @  ( ( (k56_valued_1 @ A)  @ B)  @ C) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ k1_numbers) ) ) ) ) ) , file(valued_1, k56_valued_1)).
thf(dt_k5_algstr_0, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (l2_algstr_0 @ A)  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) ) ) )  =>  ( (m1_subset_1 @  ( ( (k5_algstr_0 @ A)  @ B)  @ C) )  @  (u1_struct_0 @ A) ) ) ) , file(algstr_0, k5_algstr_0)).
thf(dt_k5_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( ( (m2_finseq_2 @  (k5_euclid @ A) )  @ k1_numbers)  @  (k1_euclid @ A) ) ) ) , file(euclid, k5_euclid)).
thf(dt_k5_finseq_1, axiom, $true, file(finseq_1, k5_finseq_1)).
thf(dt_k5_finseq_2, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v7_ordinal1 @ B)  &  ( (m1_subset_1 @ C)  @ A) ) )  =>  ( ( (m2_finseq_2 @  ( ( (k5_finseq_2 @ A)  @ B)  @ C) )  @ A)  @  ( (k4_finseq_2 @ B)  @ A) ) ) ) , file(finseq_2, k5_finseq_2)).
thf(dt_k5_funcop_1, axiom, $true, file(funcop_1, k5_funcop_1)).
thf(dt_k5_lopban_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v2_struct_0 @ B) )  &  ( (v13_algstr_0 @ B)  &  ( (v2_rlvect_1 @ B)  &  ( (v3_rlvect_1 @ B)  &  ( (v4_rlvect_1 @ B)  &  ( (v5_rlvect_1 @ B)  &  ( (v6_rlvect_1 @ B)  &  ( (v7_rlvect_1 @ B)  &  ( (v8_rlvect_1 @ B)  &  (l1_rlvect_1 @ B) ) ) ) ) ) ) ) ) ) )  =>  ( ~ ( (v2_struct_0 @  ( (k5_lopban_1 @ A)  @ B) ) )  &  ( (v13_algstr_0 @  ( (k5_lopban_1 @ A)  @ B) )  &  ( (v2_rlvect_1 @  ( (k5_lopban_1 @ A)  @ B) )  &  ( (v3_rlvect_1 @  ( (k5_lopban_1 @ A)  @ B) )  &  ( (v4_rlvect_1 @  ( (k5_lopban_1 @ A)  @ B) )  &  ( (v5_rlvect_1 @  ( (k5_lopban_1 @ A)  @ B) )  &  ( (v6_rlvect_1 @  ( (k5_lopban_1 @ A)  @ B) )  &  ( (v7_rlvect_1 @  ( (k5_lopban_1 @ A)  @ B) )  &  ( (v8_rlvect_1 @  ( (k5_lopban_1 @ A)  @ B) )  &  (l1_rlvect_1 @  ( (k5_lopban_1 @ A)  @ B) ) ) ) ) ) ) ) ) ) ) ) ) , file(lopban_1, k5_lopban_1)).
thf(dt_k5_numbers, axiom,  ( (m1_subset_1 @ k5_numbers)  @  (k1_zfmisc_1 @ k1_numbers) ) , file(numbers, k5_numbers)).
thf(dt_k5_pdiff_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k5_numbers)  &  ( (m1_finseq_1 @ B)  @ k1_numbers) )  =>  ( (v1_relat_1 @  ( (k5_pdiff_1 @ A)  @ B) )  &  (v1_funct_1 @  ( (k5_pdiff_1 @ A)  @ B) ) ) ) ) , file(pdiff_1, k5_pdiff_1)).
thf(dt_k5_square_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  ( (m1_subset_1 @  (k5_square_1 @ A) )  @ k1_numbers) ) ) , file(square_1, k5_square_1)).
thf(dt_k5_xcmplx_0, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  (v1_xcmplx_0 @  (k5_xcmplx_0 @ A) ) ) ) , file(xcmplx_0, k5_xcmplx_0)).
thf(dt_k6_finseqop, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  &  ( ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) )  &  ( (v1_relat_1 @ C)  &  (v1_funct_1 @ C) ) ) )  =>  ( (v1_relat_1 @  ( ( (k6_finseqop @ A)  @ B)  @ C) )  &  (v1_funct_1 @  ( ( (k6_finseqop @ A)  @ B)  @ C) ) ) ) ) , file(finseqop, k6_finseqop)).
thf(dt_k6_normsp_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  ( (v3_normsp_0 @ A)  &  ( (v4_normsp_0 @ A)  &  ( (v2_normsp_1 @ A)  &  (l1_normsp_1 @ A) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ k5_numbers)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @  (u1_struct_0 @ A) ) ) ) ) ) )  =>  ( (m1_subset_1 @  ( (k6_normsp_1 @ A)  @ B) )  @  (u1_struct_0 @ A) ) ) ) , file(normsp_1, k6_normsp_1)).
thf(dt_k6_numbers, axiom,  ( ( (m2_subset_1 @ k6_numbers)  @ k1_numbers)  @ k5_numbers) , file(numbers, k6_numbers)).
thf(dt_k6_partfun1, axiom,  (! [A: $i] :  ( ( (v1_partfun1 @  (k6_partfun1 @ A) )  @ A)  &  ( (m1_subset_1 @  (k6_partfun1 @ A) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) ) , file(partfun1, k6_partfun1)).
thf(dt_k6_pdiff_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (m1_subset_1 @ A)  @ k5_numbers)  &  ( ( (m1_subset_1 @ B)  @ k5_numbers)  &  ( (m1_subset_1 @ C)  @  (k1_euclid @ A) ) ) )  =>  ( (v1_funct_1 @  ( ( (k6_pdiff_1 @ A)  @ B)  @ C) )  &  ( ( ( (v1_funct_2 @  ( ( (k6_pdiff_1 @ A)  @ B)  @ C) )  @ k1_numbers)  @  (k1_euclid @ A) )  &  ( (m1_subset_1 @  ( ( (k6_pdiff_1 @ A)  @ B)  @ C) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @  (k1_euclid @ A) ) ) ) ) ) ) ) , file(pdiff_1, k6_pdiff_1)).
thf(dt_k6_rvsum_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  =>  ( (m2_finseq_1 @  (k6_rvsum_1 @ A) )  @ k1_numbers) ) ) , file(rvsum_1, k6_rvsum_1)).
thf(dt_k6_square_1, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v1_xreal_0 @  (k6_square_1 @ A) ) ) ) , file(square_1, k6_square_1)).
thf(dt_k6_xcmplx_0, axiom, $true, file(xcmplx_0, k6_xcmplx_0)).
thf(dt_k7_binop_2, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  ( (m1_subset_1 @  (k7_binop_2 @ A) )  @ k1_numbers) ) ) , file(binop_2, k7_binop_2)).
thf(dt_k7_euclid, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v7_ordinal1 @ A)  &  ( ( (m1_subset_1 @ B)  @  (k1_euclid @ A) )  &  ( (m1_subset_1 @ C)  @  (k1_euclid @ A) ) ) )  =>  ( ( (m2_finseq_2 @  ( ( (k7_euclid @ A)  @ B)  @ C) )  @ k1_numbers)  @  (k1_euclid @ A) ) ) ) , file(euclid, k7_euclid)).
thf(dt_k7_finseqop, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A) ) ) ) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ A)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) )  &  ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ A)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( ( ( (k7_finseqop @ A)  @ B)  @ C)  @ D) )  &  ( ( ( (v1_funct_2 @  ( ( ( (k7_finseqop @ A)  @ B)  @ C)  @ D) )  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A)  &  ( (m1_subset_1 @  ( ( ( (k7_finseqop @ A)  @ B)  @ C)  @ D) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A) ) ) ) ) ) ) , file(finseqop, k7_finseqop)).
thf(dt_k7_lopban_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  (l1_rlvect_1 @ A) ) ) ) ) ) ) ) ) )  &  ( ~ ( (v2_struct_0 @ B) )  &  ( (v13_algstr_0 @ B)  &  ( (v2_rlvect_1 @ B)  &  ( (v3_rlvect_1 @ B)  &  ( (v4_rlvect_1 @ B)  &  ( (v5_rlvect_1 @ B)  &  ( (v6_rlvect_1 @ B)  &  ( (v7_rlvect_1 @ B)  &  ( (v8_rlvect_1 @ B)  &  (l1_rlvect_1 @ B) ) ) ) ) ) ) ) ) ) )  =>  ( (m1_subset_1 @  ( (k7_lopban_1 @ A)  @ B) )  @  (k1_zfmisc_1 @  (u1_struct_0 @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) ) ) ) ) ) , file(lopban_1, k7_lopban_1)).
thf(dt_k7_partfun1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) )  =>  ( (m1_subset_1 @  ( ( (k7_partfun1 @ A)  @ B)  @ C) )  @ A) ) ) , file(partfun1, k7_partfun1)).
thf(dt_k7_real_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k1_numbers)  &  (v1_xreal_0 @ B) )  =>  ( (m1_subset_1 @  ( (k7_real_1 @ A)  @ B) )  @ k1_numbers) ) ) , file(real_1, k7_real_1)).
thf(dt_k7_relat_1, axiom, $true, file(relat_1, k7_relat_1)).
thf(dt_k7_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (m1_subset_1 @  ( ( ( (k7_relset_1 @ A)  @ B)  @ C)  @ D) )  @  (k1_zfmisc_1 @ B) ) ) ) , file(relset_1, k7_relset_1)).
thf(dt_k7_square_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  ( (m1_subset_1 @  (k7_square_1 @ A) )  @ k1_numbers) ) ) , file(square_1, k7_square_1)).
thf(dt_k8_euclid, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v7_ordinal1 @ A)  &  ( ( (m1_subset_1 @ B)  @  (k1_euclid @ A) )  &  ( (m1_subset_1 @ C)  @  (k1_euclid @ A) ) ) )  =>  ( ( (m2_finseq_2 @  ( ( (k8_euclid @ A)  @ B)  @ C) )  @ k1_numbers)  @  (k1_euclid @ A) ) ) ) , file(euclid, k8_euclid)).
thf(dt_k8_funcop_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (m1_subset_1 @ C)  @ A) )  =>  ( (v1_funct_1 @  ( ( (k8_funcop_1 @ A)  @ B)  @ C) )  &  ( ( ( (v1_funct_2 @  ( ( (k8_funcop_1 @ A)  @ B)  @ C) )  @ B)  @ A)  &  ( (m1_subset_1 @  ( ( (k8_funcop_1 @ A)  @ B)  @ C) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ A) ) ) ) ) ) ) , file(funcop_1, k8_funcop_1)).
thf(dt_k8_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ~ ( (v1_xboole_0 @ C) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ C)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) )  &  ( (v1_relat_1 @ E)  &  ( ( (v5_relat_1 @ E)  @ B)  &  (v1_funct_1 @ E) ) ) ) )  =>  ( (v1_funct_1 @  ( ( ( ( (k8_funct_2 @ A)  @ B)  @ C)  @ D)  @ E) )  &  ( ( ( (v1_funct_2 @  ( ( ( ( (k8_funct_2 @ A)  @ B)  @ C)  @ D)  @ E) )  @ A)  @ B)  &  ( (m1_subset_1 @  ( ( ( ( (k8_funct_2 @ A)  @ B)  @ C)  @ D)  @ E) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) ) ) , file(funct_2, k8_funct_2)).
thf(dt_k8_lopban_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  (l1_rlvect_1 @ A) ) ) ) ) ) ) ) ) )  &  ( ~ ( (v2_struct_0 @ B) )  &  ( (v13_algstr_0 @ B)  &  ( (v2_rlvect_1 @ B)  &  ( (v3_rlvect_1 @ B)  &  ( (v4_rlvect_1 @ B)  &  ( (v5_rlvect_1 @ B)  &  ( (v6_rlvect_1 @ B)  &  ( (v7_rlvect_1 @ B)  &  ( (v8_rlvect_1 @ B)  &  (l1_rlvect_1 @ B) ) ) ) ) ) ) ) ) ) )  =>  ( ~ ( (v2_struct_0 @  ( (k8_lopban_1 @ A)  @ B) ) )  &  ( (v13_algstr_0 @  ( (k8_lopban_1 @ A)  @ B) )  &  ( (v2_rlvect_1 @  ( (k8_lopban_1 @ A)  @ B) )  &  ( (v3_rlvect_1 @  ( (k8_lopban_1 @ A)  @ B) )  &  ( (v4_rlvect_1 @  ( (k8_lopban_1 @ A)  @ B) )  &  ( (v5_rlvect_1 @  ( (k8_lopban_1 @ A)  @ B) )  &  ( (v6_rlvect_1 @  ( (k8_lopban_1 @ A)  @ B) )  &  ( (v7_rlvect_1 @  ( (k8_lopban_1 @ A)  @ B) )  &  ( (v8_rlvect_1 @  ( (k8_lopban_1 @ A)  @ B) )  &  (l1_rlvect_1 @  ( (k8_lopban_1 @ A)  @ B) ) ) ) ) ) ) ) ) ) ) ) ) , file(lopban_1, k8_lopban_1)).
thf(dt_k8_pdiff_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (m1_subset_1 @ A)  @ k5_numbers) )  &  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( (m1_subset_1 @ B)  @ k5_numbers) )  &  ( ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @  (k1_euclid @ B) ) ) ) )  &  ( (m1_subset_1 @ D)  @  (k1_euclid @ A) ) ) ) )  =>  ( (v1_funct_1 @  ( ( ( (k8_pdiff_1 @ A)  @ B)  @ C)  @ D) )  &  ( ( ( (v1_funct_2 @  ( ( ( (k8_pdiff_1 @ A)  @ B)  @ C)  @ D) )  @  (k1_euclid @ A) )  @  (k1_euclid @ B) )  &  ( (m1_subset_1 @  ( ( ( (k8_pdiff_1 @ A)  @ B)  @ C)  @ D) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @  (k1_euclid @ B) ) ) ) ) ) ) ) , file(pdiff_1, k8_pdiff_1)).
thf(dt_k8_real_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k1_numbers)  &  (v1_xreal_0 @ B) )  =>  ( (m1_subset_1 @  ( (k8_real_1 @ A)  @ B) )  @ k1_numbers) ) ) , file(real_1, k8_real_1)).
thf(dt_k8_rsspace, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  (l1_rlvect_1 @ A) ) ) ) ) ) ) ) ) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) )  =>  ( (v1_funct_1 @  ( (k8_rsspace @ A)  @ B) )  &  ( ( ( (v1_funct_2 @  ( (k8_rsspace @ A)  @ B) )  @  ( (k2_zfmisc_1 @ B)  @ B) )  @ B)  &  ( (m1_subset_1 @  ( (k8_rsspace @ A)  @ B) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ B) )  @ B) ) ) ) ) ) ) , file(rsspace, k8_rsspace)).
thf(dt_k8_rvsum_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v3_valued_0 @ B)  &  (v1_finseq_1 @ B) ) ) ) )  =>  ( (m2_finseq_1 @  ( (k8_rvsum_1 @ A)  @ B) )  @ k1_numbers) ) ) , file(rvsum_1, k8_rvsum_1)).
thf(dt_k9_binop_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  ( (m1_subset_1 @  ( (k9_binop_2 @ A)  @ B) )  @ k1_numbers) ) ) , file(binop_2, k9_binop_2)).
thf(dt_k9_euclid, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v7_ordinal1 @ A)  &  ( ( (m1_subset_1 @ B)  @  (k1_euclid @ A) )  &  (v1_xreal_0 @ C) ) )  =>  ( ( (m2_finseq_2 @  ( ( (k9_euclid @ A)  @ B)  @ C) )  @ k1_numbers)  @  (k1_euclid @ A) ) ) ) , file(euclid, k9_euclid)).
thf(dt_k9_finseq_1, axiom,  (! [A: $i] :  ( (v1_relat_1 @  (k9_finseq_1 @ A) )  &  (v1_funct_1 @  (k9_finseq_1 @ A) ) ) ) , file(finseq_1, k9_finseq_1)).
thf(dt_k9_funct_2, axiom,  (! [A: $i, B: $i] :  ( ~ ( (v1_xboole_0 @ B) )  =>  ( ( (m1_funct_2 @  ( (k9_funct_2 @ A)  @ B) )  @ A)  @ B) ) ) , file(funct_2, k9_funct_2)).
thf(dt_k9_real_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k1_numbers)  &  (v1_xreal_0 @ B) )  =>  ( (m1_subset_1 @  ( (k9_real_1 @ A)  @ B) )  @ k1_numbers) ) ) , file(real_1, k9_real_1)).
thf(dt_k9_rsspace, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  (l1_rlvect_1 @ A) ) ) ) ) ) ) ) ) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) )  =>  ( (v1_funct_1 @  ( (k9_rsspace @ A)  @ B) )  &  ( ( ( (v1_funct_2 @  ( (k9_rsspace @ A)  @ B) )  @  ( (k2_zfmisc_1 @ k1_numbers)  @ B) )  @ B)  &  ( (m1_subset_1 @  ( (k9_rsspace @ A)  @ B) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ B) )  @ B) ) ) ) ) ) ) , file(rsspace, k9_rsspace)).
thf(dt_k9_xtuple_0, axiom, $true, file(xtuple_0, k9_xtuple_0)).
thf(dt_l1_algstr_0, axiom,  (! [A: $i] :  ( (l1_algstr_0 @ A)  =>  (l1_struct_0 @ A) ) ) , file(algstr_0, l1_algstr_0)).
thf(dt_l1_normsp_0, axiom,  (! [A: $i] :  ( (l1_normsp_0 @ A)  =>  (l1_struct_0 @ A) ) ) , file(normsp_0, l1_normsp_0)).
thf(dt_l1_normsp_1, axiom,  (! [A: $i] :  ( (l1_normsp_1 @ A)  =>  ( (l1_rlvect_1 @ A)  &  (l2_normsp_0 @ A) ) ) ) , file(normsp_1, l1_normsp_1)).
thf(dt_l1_pre_topc, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  (l1_struct_0 @ A) ) ) , file(pre_topc, l1_pre_topc)).
thf(dt_l1_rltopsp1, axiom,  (! [A: $i] :  ( (l1_rltopsp1 @ A)  =>  ( (l1_rlvect_1 @ A)  &  (l1_pre_topc @ A) ) ) ) , file(rltopsp1, l1_rltopsp1)).
thf(dt_l1_rlvect_1, axiom,  (! [A: $i] :  ( (l1_rlvect_1 @ A)  =>  (l2_algstr_0 @ A) ) ) , file(rlvect_1, l1_rlvect_1)).
thf(dt_l1_struct_0, axiom, $true, file(struct_0, l1_struct_0)).
thf(dt_l2_algstr_0, axiom,  (! [A: $i] :  ( (l2_algstr_0 @ A)  =>  ( (l2_struct_0 @ A)  &  (l1_algstr_0 @ A) ) ) ) , file(algstr_0, l2_algstr_0)).
thf(dt_l2_normsp_0, axiom,  (! [A: $i] :  ( (l2_normsp_0 @ A)  =>  ( (l1_normsp_0 @ A)  &  (l2_struct_0 @ A) ) ) ) , file(normsp_0, l2_normsp_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_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_finseq_1 @ B)  @ A)  =>  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) ) ) ) ) , file(finseq_1, m1_finseq_1)).
thf(dt_m1_finseq_2, axiom, $true, file(finseq_2, m1_finseq_2)).
thf(dt_m1_funct_2, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( ( (m1_funct_2 @ C)  @ A)  @ B)  =>  ~ ( (v1_xboole_0 @ C) ) ) ) ) , file(funct_2, m1_funct_2)).
thf(dt_m1_nfcont_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  ( (v3_normsp_0 @ A)  &  ( (v4_normsp_0 @ A)  &  ( (v2_normsp_1 @ A)  &  (l1_normsp_1 @ A) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) ) )  =>  (! [C: $i] :  ( ( ( (m1_nfcont_1 @ C)  @ A)  @ B)  =>  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) ) ) ) ) , file(nfcont_1, m1_nfcont_1)).
thf(dt_m1_rcomp_1, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( ( (m1_rcomp_1 @ B)  @ A)  =>  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ k1_numbers) ) ) ) ) ) , file(rcomp_1, m1_rcomp_1)).
thf(dt_m1_subset_1, axiom, $true, file(subset_1, m1_subset_1)).
thf(dt_m2_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m2_finseq_1 @ B)  @ A)  =>  ( (v1_funct_1 @ B)  &  ( (v1_finseq_1 @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ A) ) ) ) ) ) ) ) , file(finseq_1, m2_finseq_1)).
thf(dt_m2_finseq_2, axiom,  (! [A: $i, B: $i] :  ( ( (m1_finseq_2 @ B)  @ A)  =>  (! [C: $i] :  ( ( ( (m2_finseq_2 @ C)  @ A)  @ B)  =>  ( (m2_finseq_1 @ C)  @ A) ) ) ) ) , file(finseq_2, m2_finseq_2)).
thf(dt_m2_funct_2, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( ( (m1_funct_2 @ C)  @ A)  @ B) )  =>  (! [D: $i] :  ( ( ( ( (m2_funct_2 @ D)  @ A)  @ B)  @ C)  =>  ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) ) ) ) ) , file(funct_2, m2_funct_2)).
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_algstr_0, axiom,  (! [A: $i] :  ( (l1_algstr_0 @ A)  =>  ( (v1_funct_1 @  (u1_algstr_0 @ A) )  &  ( ( ( (v1_funct_2 @  (u1_algstr_0 @ A) )  @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) ) )  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @  (u1_algstr_0 @ A) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ A) ) )  @  (u1_struct_0 @ A) ) ) ) ) ) ) ) , file(algstr_0, u1_algstr_0)).
thf(dt_u1_normsp_0, axiom,  (! [A: $i] :  ( (l1_normsp_0 @ A)  =>  ( (v1_funct_1 @  (u1_normsp_0 @ A) )  &  ( ( ( (v1_funct_2 @  (u1_normsp_0 @ A) )  @  (u1_struct_0 @ A) )  @ k1_numbers)  &  ( (m1_subset_1 @  (u1_normsp_0 @ A) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @ k1_numbers) ) ) ) ) ) ) , file(normsp_0, u1_normsp_0)).
thf(dt_u1_pre_topc, axiom,  (! [A: $i] :  ( (l1_pre_topc @ A)  =>  ( (m1_subset_1 @  (u1_pre_topc @ A) )  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) ) ) ) ) , file(pre_topc, u1_pre_topc)).
thf(dt_u1_rlvect_1, axiom,  (! [A: $i] :  ( (l1_rlvect_1 @ A)  =>  ( (v1_funct_1 @  (u1_rlvect_1 @ A) )  &  ( ( ( (v1_funct_2 @  (u1_rlvect_1 @ A) )  @  ( (k2_zfmisc_1 @ k1_numbers)  @  (u1_struct_0 @ A) ) )  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @  (u1_rlvect_1 @ A) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @  (u1_struct_0 @ A) ) )  @  (u1_struct_0 @ A) ) ) ) ) ) ) ) , file(rlvect_1, u1_rlvect_1)).
thf(dt_u1_struct_0, axiom, $true, file(struct_0, u1_struct_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_algstr_0, axiom,  (? [A: $i] :  (l1_algstr_0 @ A) ) , file(algstr_0, l1_algstr_0)).
thf(existence_l1_normsp_0, axiom,  (? [A: $i] :  (l1_normsp_0 @ A) ) , file(normsp_0, l1_normsp_0)).
thf(existence_l1_normsp_1, axiom,  (? [A: $i] :  (l1_normsp_1 @ A) ) , file(normsp_1, l1_normsp_1)).
thf(existence_l1_pre_topc, axiom,  (? [A: $i] :  (l1_pre_topc @ A) ) , file(pre_topc, l1_pre_topc)).
thf(existence_l1_rltopsp1, axiom,  (? [A: $i] :  (l1_rltopsp1 @ A) ) , file(rltopsp1, l1_rltopsp1)).
thf(existence_l1_rlvect_1, axiom,  (? [A: $i] :  (l1_rlvect_1 @ A) ) , file(rlvect_1, l1_rlvect_1)).
thf(existence_l1_struct_0, axiom,  (? [A: $i] :  (l1_struct_0 @ A) ) , file(struct_0, l1_struct_0)).
thf(existence_l2_algstr_0, axiom,  (? [A: $i] :  (l2_algstr_0 @ A) ) , file(algstr_0, l2_algstr_0)).
thf(existence_l2_normsp_0, axiom,  (? [A: $i] :  (l2_normsp_0 @ A) ) , file(normsp_0, l2_normsp_0)).
thf(existence_l2_struct_0, axiom,  (? [A: $i] :  (l2_struct_0 @ A) ) , file(struct_0, l2_struct_0)).
thf(existence_m1_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m1_finseq_1 @ B)  @ A) ) ) , file(finseq_1, m1_finseq_1)).
thf(existence_m1_finseq_2, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m1_finseq_2 @ B)  @ A) ) ) , file(finseq_2, m1_finseq_2)).
thf(existence_m1_funct_2, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( ( (m1_funct_2 @ C)  @ A)  @ B) ) ) , file(funct_2, m1_funct_2)).
thf(existence_m1_nfcont_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  ( (v3_normsp_0 @ A)  &  ( (v4_normsp_0 @ A)  &  ( (v2_normsp_1 @ A)  &  (l1_normsp_1 @ A) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) ) )  =>  (? [C: $i] :  ( ( (m1_nfcont_1 @ C)  @ A)  @ B) ) ) ) , file(nfcont_1, m1_nfcont_1)).
thf(existence_m1_rcomp_1, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (? [B: $i] :  ( (m1_rcomp_1 @ B)  @ A) ) ) ) , file(rcomp_1, m1_rcomp_1)).
thf(existence_m1_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m1_subset_1 @ B)  @ A) ) ) , file(subset_1, m1_subset_1)).
thf(existence_m2_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m2_finseq_1 @ B)  @ A) ) ) , file(finseq_1, m2_finseq_1)).
thf(existence_m2_finseq_2, axiom,  (! [A: $i, B: $i] :  ( ( (m1_finseq_2 @ B)  @ A)  =>  (? [C: $i] :  ( ( (m2_finseq_2 @ C)  @ A)  @ B) ) ) ) , file(finseq_2, m2_finseq_2)).
thf(existence_m2_funct_2, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( ( (m1_funct_2 @ C)  @ A)  @ B) )  =>  (? [D: $i] :  ( ( ( (m2_funct_2 @ D)  @ A)  @ B)  @ C) ) ) ) , file(funct_2, m2_funct_2)).
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(fc100_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v4_membered @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  (k54_valued_1 @ C) )  &  ( (v1_partfun1 @  (k54_valued_1 @ C) )  @ A) ) ) ) , file(valued_1, fc100_valued_1)).
thf(fc101_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v5_membered @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  (k54_valued_1 @ C) )  &  ( (v1_partfun1 @  (k54_valued_1 @ C) )  @ A) ) ) ) , file(valued_1, fc101_valued_1)).
thf(fc102_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  =>  ( (v1_relat_1 @  (k54_valued_1 @ A) )  &  ( (v1_funct_1 @  (k54_valued_1 @ A) )  &  ( (v3_valued_0 @  (k54_valued_1 @ A) )  &  (v1_finseq_1 @  (k54_valued_1 @ A) ) ) ) ) ) ) , file(valued_1, fc102_valued_1)).
thf(fc108_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v4_relat_1 @ A)  @ k5_numbers) )  =>  (v6_membered @  (k9_xtuple_0 @ A) ) ) ) , file(valued_1, fc108_valued_1)).
thf(fc10_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v3_valued_2 @  (k1_euclid @ A) ) ) ) , file(euclid, fc10_euclid)).
thf(fc10_funct_2, axiom,  (! [A: $i, B: $i] :  (v4_funct_1 @  ( (k1_funct_2 @ A)  @ B) ) ) , file(funct_2, fc10_funct_2)).
thf(fc10_struct_0, axiom,  (! [A: $i] :  ( (l2_struct_0 @ A)  =>  ( (v9_struct_0 @  (k4_struct_0 @ A) )  @ A) ) ) , file(struct_0, fc10_struct_0)).
thf(fc10_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v5_membered @ B) )  &  ( ( ~ ( (v1_xboole_0 @ C) )  &  (v5_membered @ C) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k1_valued_1 @ D)  @ E) )  &  ( (v1_partfun1 @  ( (k1_valued_1 @ D)  @ E) )  @ A) ) ) ) , file(valued_1, fc10_valued_1)).
thf(fc10_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v2_xxreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc10_xreal_0)).
thf(fc111_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  (v1_valued_0 @ B) ) ) )  =>  ( (v1_relat_1 @  (k30_valued_1 @ B) )  &  ( ( (v4_relat_1 @  (k30_valued_1 @ B) )  @ A)  &  ( (v1_funct_1 @  (k30_valued_1 @ B) )  &  (v1_valued_0 @  (k30_valued_1 @ B) ) ) ) ) ) ) , file(valued_1, fc111_valued_1)).
thf(fc112_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  (v1_valued_0 @ B) ) ) )  =>  ( (v1_relat_1 @  (k35_valued_1 @ B) )  &  ( ( (v4_relat_1 @  (k35_valued_1 @ B) )  @ A)  &  ( (v1_funct_1 @  (k35_valued_1 @ B) )  &  (v1_valued_0 @  (k35_valued_1 @ B) ) ) ) ) ) ) , file(valued_1, fc112_valued_1)).
thf(fc113_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  (v1_valued_0 @ B) ) ) )  =>  ( (v1_relat_1 @  (k39_valued_1 @ B) )  &  ( ( (v4_relat_1 @  (k39_valued_1 @ B) )  @ A)  &  (v1_funct_1 @  (k39_valued_1 @ B) ) ) ) ) ) , file(valued_1, fc113_valued_1)).
thf(fc114_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  (v1_valued_0 @ B) ) ) )  =>  ( (v1_relat_1 @  (k54_valued_1 @ B) )  &  ( ( (v4_relat_1 @  (k54_valued_1 @ B) )  @ A)  &  ( (v1_funct_1 @  (k54_valued_1 @ B) )  &  (v3_valued_0 @  (k54_valued_1 @ B) ) ) ) ) ) ) , file(valued_1, fc114_valued_1)).
thf(fc115_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  (v1_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  (k30_valued_1 @ B) )  &  ( (v1_funct_1 @  (k30_valued_1 @ B) )  &  ( ( (v1_partfun1 @  (k30_valued_1 @ B) )  @ A)  &  (v1_valued_0 @  (k30_valued_1 @ B) ) ) ) ) ) ) , file(valued_1, fc115_valued_1)).
thf(fc116_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  (v1_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  (k35_valued_1 @ B) )  &  ( (v1_funct_1 @  (k35_valued_1 @ B) )  &  ( ( (v1_partfun1 @  (k35_valued_1 @ B) )  @ A)  &  (v1_valued_0 @  (k35_valued_1 @ B) ) ) ) ) ) ) , file(valued_1, fc116_valued_1)).
thf(fc117_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  (v1_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  (k39_valued_1 @ B) )  &  ( (v1_funct_1 @  (k39_valued_1 @ B) )  &  ( (v1_partfun1 @  (k39_valued_1 @ B) )  @ A) ) ) ) ) , file(valued_1, fc117_valued_1)).
thf(fc118_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  (v1_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  (k54_valued_1 @ B) )  &  ( (v1_funct_1 @  (k54_valued_1 @ B) )  &  ( ( (v1_partfun1 @  (k54_valued_1 @ B) )  @ A)  &  (v3_valued_0 @  (k54_valued_1 @ B) ) ) ) ) ) ) , file(valued_1, fc118_valued_1)).
thf(fc11_funct_2, axiom,  (! [A: $i] :  ( (v1_relat_1 @  (k4_relat_1 @ A) )  &  ( ( (v4_relat_1 @  (k4_relat_1 @ A) )  @ A)  &  ( (v1_funct_1 @  (k4_relat_1 @ A) )  &  ( (v1_partfun1 @  (k4_relat_1 @ A) )  @ A) ) ) ) ) , file(funct_2, fc11_funct_2)).
thf(fc11_relset_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_relat_1 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (k9_xtuple_0 @ A) ) ) ) )  =>  ~ ( (v1_xboole_0 @  ( (k7_relat_1 @ A)  @ B) ) ) ) ) , file(relset_1, fc11_relset_1)).
thf(fc11_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v6_membered @ B) )  &  ( ( ~ ( (v1_xboole_0 @ C) )  &  (v6_membered @ C) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k1_valued_1 @ D)  @ E) )  &  ( (v1_partfun1 @  ( (k1_valued_1 @ D)  @ E) )  @ A) ) ) ) , file(valued_1, fc11_valued_1)).
thf(fc11_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v2_xxreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc11_xreal_0)).
thf(fc121_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  (v1_valued_0 @ B) ) ) )  &  (v1_xcmplx_0 @ C) )  =>  ( (v1_relat_1 @  ( (k24_valued_1 @ B)  @ C) )  &  ( ( (v4_relat_1 @  ( (k24_valued_1 @ B)  @ C) )  @ A)  &  (v1_funct_1 @  ( (k24_valued_1 @ B)  @ C) ) ) ) ) ) , file(valued_1, fc121_valued_1)).
thf(fc124_valued_1, 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_valued_0 @ B) ) ) ) )  &  (v1_xcmplx_0 @ C) )  =>  ( (v1_relat_1 @  ( (k24_valued_1 @ B)  @ C) )  &  ( (v1_funct_1 @  ( (k24_valued_1 @ B)  @ C) )  &  ( (v1_partfun1 @  ( (k24_valued_1 @ B)  @ C) )  @ A) ) ) ) ) , file(valued_1, fc124_valued_1)).
thf(fc125_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_valued_0 @ B) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v1_funct_1 @ C)  &  (v1_valued_0 @ C) ) ) ) )  =>  ( (v1_relat_1 @  ( (k1_valued_1 @ B)  @ C) )  &  ( ( (v4_relat_1 @  ( (k1_valued_1 @ B)  @ C) )  @ A)  &  (v1_funct_1 @  ( (k1_valued_1 @ B)  @ C) ) ) ) ) ) , file(valued_1, fc125_valued_1)).
thf(fc126_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_valued_0 @ B) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v1_funct_1 @ C)  &  (v1_valued_0 @ C) ) ) ) )  =>  ( (v1_relat_1 @  ( (k45_valued_1 @ B)  @ C) )  &  ( ( (v4_relat_1 @  ( (k45_valued_1 @ B)  @ C) )  @ A)  &  (v1_funct_1 @  ( (k45_valued_1 @ B)  @ C) ) ) ) ) ) , file(valued_1, fc126_valued_1)).
thf(fc127_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_valued_0 @ B) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v1_funct_1 @ C)  &  (v1_valued_0 @ C) ) ) ) )  =>  ( (v1_relat_1 @  ( (k18_valued_1 @ B)  @ C) )  &  ( ( (v4_relat_1 @  ( (k18_valued_1 @ B)  @ C) )  @ A)  &  (v1_funct_1 @  ( (k18_valued_1 @ B)  @ C) ) ) ) ) ) , file(valued_1, fc127_valued_1)).
thf(fc129_valued_1, 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_valued_0 @ B) ) ) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v1_funct_1 @ C)  &  ( ( (v1_partfun1 @ C)  @ A)  &  (v1_valued_0 @ C) ) ) ) ) )  =>  ( (v1_relat_1 @  ( (k1_valued_1 @ B)  @ C) )  &  ( (v1_funct_1 @  ( (k1_valued_1 @ B)  @ C) )  &  ( (v1_partfun1 @  ( (k1_valued_1 @ B)  @ C) )  @ A) ) ) ) ) , file(valued_1, fc129_valued_1)).
thf(fc12_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v1_valued_0 @ B)  &  (v1_finseq_1 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k1_valued_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k1_valued_1 @ A)  @ B) )  &  (v1_finseq_1 @  ( (k1_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc12_valued_1)).
thf(fc12_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v2_xxreal_0 @  ( (k2_xcmplx_0 @ B)  @ A) ) ) ) , file(xreal_0, fc12_xreal_0)).
thf(fc130_valued_1, 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_valued_0 @ B) ) ) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v1_funct_1 @ C)  &  ( ( (v1_partfun1 @ C)  @ A)  &  (v1_valued_0 @ C) ) ) ) ) )  =>  ( (v1_relat_1 @  ( (k45_valued_1 @ B)  @ C) )  &  ( (v1_funct_1 @  ( (k45_valued_1 @ B)  @ C) )  &  ( (v1_partfun1 @  ( (k45_valued_1 @ B)  @ C) )  @ A) ) ) ) ) , file(valued_1, fc130_valued_1)).
thf(fc131_valued_1, 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_valued_0 @ B) ) ) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v1_funct_1 @ C)  &  ( ( (v1_partfun1 @ C)  @ A)  &  (v1_valued_0 @ C) ) ) ) ) )  =>  ( (v1_relat_1 @  ( (k18_valued_1 @ B)  @ C) )  &  ( (v1_funct_1 @  ( (k18_valued_1 @ B)  @ C) )  &  ( (v1_partfun1 @  ( (k18_valued_1 @ B)  @ C) )  @ A) ) ) ) ) , file(valued_1, fc131_valued_1)).
thf(fc13_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v3_xxreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc13_xreal_0)).
thf(fc14_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_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_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_struct_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_card_1 @ A)  &  ( ( (v13_struct_0 @ B)  @ A)  &  (l1_struct_0 @ B) ) )  =>  ( (v3_card_1 @  (u1_struct_0 @ B) )  @ A) ) ) , file(struct_0, fc19_struct_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_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ~ ( (v1_xboole_0 @  (k1_euclid @ A) ) ) ) ) , file(euclid, fc1_euclid)).
thf(fc1_fdiff_1, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k5_numbers)  @ k1_numbers)  &  ( ( (v1_fdiff_1 @ A)  @ k6_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k1_numbers) ) ) ) ) )  =>  ( (v1_xboole_0 @  (k1_seq_2 @ A) )  &  (v1_xreal_0 @  (k1_seq_2 @ A) ) ) ) ) , file(fdiff_1, fc1_fdiff_1)).
thf(fc1_funct_2, axiom,  (! [A: $i, B: $i] :  ( ~ ( (v1_xboole_0 @ B) )  =>  ~ ( (v1_xboole_0 @  ( (k1_funct_2 @ A)  @ B) ) ) ) ) , file(funct_2, fc1_funct_2)).
thf(fc1_numbers, axiom,  ~ ( (v1_xboole_0 @ k1_numbers) ) , file(numbers, fc1_numbers)).
thf(fc1_real_ns1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v1_funct_1 @  (k1_real_ns1 @ A) )  &  ( ( ( (v1_funct_2 @  (k1_real_ns1 @ A) )  @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @  (k1_euclid @ A) ) )  @  (k1_euclid @ A) )  &  ( ( (v1_binop_1 @  (k1_real_ns1 @ A) )  @  (k1_euclid @ A) )  &  ( (v2_binop_1 @  (k1_real_ns1 @ A) )  @  (k1_euclid @ A) ) ) ) ) ) ) , file(real_ns1, fc1_real_ns1)).
thf(fc1_seq_4, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k5_numbers)  @ k1_numbers)  &  ( (v2_comseq_2 @ A)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k1_numbers) ) ) ) ) )  =>  ( (v1_funct_1 @  (k54_valued_1 @ A) )  &  ( ( ( (v1_funct_2 @  (k54_valued_1 @ A) )  @ k5_numbers)  @ k1_numbers)  &  (v2_comseq_2 @  (k54_valued_1 @ A) ) ) ) ) ) , file(seq_4, fc1_seq_4)).
thf(fc1_struct_0, axiom,  (! [A: $i] :  ( ( (v2_struct_0 @ A)  &  (l1_struct_0 @ A) )  =>  (v1_xboole_0 @  (u1_struct_0 @ A) ) ) ) , file(struct_0, fc1_struct_0)).
thf(fc1_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) )  =>  (v1_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc1_valued_0)).
thf(fc1_valued_1, axiom,  (! [A: $i] :  ( (v1_rat_1 @ A)  =>  ( (v1_xreal_0 @  (k16_complex1 @ A) )  &  (v1_rat_1 @  (k16_complex1 @ A) ) ) ) ) , file(valued_1, fc1_valued_1)).
thf(fc1_xboole_0, axiom,  (v1_xboole_0 @ k1_xboole_0) , file(xboole_0, fc1_xboole_0)).
thf(fc20_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v3_xxreal_0 @  ( (k6_xcmplx_0 @ B)  @ A) ) ) ) , file(xreal_0, fc20_xreal_0)).
thf(fc21_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v3_xxreal_0 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc21_xreal_0)).
thf(fc22_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v2_xxreal_0 @  ( (k6_xcmplx_0 @ B)  @ A) ) ) ) , file(xreal_0, fc22_xreal_0)).
thf(fc23_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v2_xxreal_0 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc23_xreal_0)).
thf(fc24_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v2_xxreal_0 @  ( (k3_xcmplx_0 @ B)  @ A) ) ) ) ) , file(xreal_0, fc24_xreal_0)).
thf(fc25_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v3_xxreal_0 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc25_xreal_0)).
thf(fc26_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v3_xxreal_0 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc26_xreal_0)).
thf(fc27_xreal_0, axiom,  (! [A: $i] :  ( ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  =>  ( (v1_xcmplx_0 @  (k5_xcmplx_0 @ A) )  &  (v2_xxreal_0 @  (k5_xcmplx_0 @ A) ) ) ) ) , file(xreal_0, fc27_xreal_0)).
thf(fc28_xreal_0, axiom,  (! [A: $i] :  ( ( ~ ( (v2_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  =>  ( (v1_xcmplx_0 @  (k5_xcmplx_0 @ A) )  &  ~ ( (v2_xxreal_0 @  (k5_xcmplx_0 @ A) ) ) ) ) ) , file(xreal_0, fc28_xreal_0)).
thf(fc29_xreal_0, axiom,  (! [A: $i] :  ( ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  =>  ( (v1_xcmplx_0 @  (k5_xcmplx_0 @ A) )  &  (v3_xxreal_0 @  (k5_xcmplx_0 @ A) ) ) ) ) , file(xreal_0, fc29_xreal_0)).
thf(fc2_euclid, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_finseq_1 @ A)  &  (v3_valued_0 @ A) ) ) )  =>  ~ ( (v3_xxreal_0 @  (k12_euclid @ A) ) ) ) ) , file(euclid, fc2_euclid)).
thf(fc2_funct_2, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  ( (k1_funct_2 @ A)  @ A) ) ) ) , file(funct_2, fc2_funct_2)).
thf(fc2_real_ns1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v7_ordinal1 @ A) )  =>  ( ~ ( (v2_struct_0 @  (k4_real_ns1 @ A) ) )  &  ( ~ ( (v7_struct_0 @  (k4_real_ns1 @ A) ) )  &  (v1_normsp_1 @  (k4_real_ns1 @ A) ) ) ) ) ) , file(real_ns1, fc2_real_ns1)).
thf(fc2_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  ~ ( (v1_xboole_0 @  (u1_struct_0 @ A) ) ) ) ) , file(struct_0, fc2_struct_0)).
thf(fc2_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) )  =>  (v2_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc2_valued_0)).
thf(fc2_valued_1, 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_valued_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k1_valued_1 @ A)  @ B) )  &  (v1_valued_0 @  ( (k1_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc2_valued_1)).
thf(fc2_xcmplx_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  (v1_xcmplx_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(xcmplx_0, fc2_xcmplx_0)).
thf(fc30_xreal_0, axiom,  (! [A: $i] :  ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  =>  ( (v1_xcmplx_0 @  (k5_xcmplx_0 @ A) )  &  ~ ( (v3_xxreal_0 @  (k5_xcmplx_0 @ A) ) ) ) ) ) , file(xreal_0, fc30_xreal_0)).
thf(fc31_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) )  =>  (v1_membered @  ( (k7_relat_1 @ A)  @ B) ) ) ) , file(valued_0, fc31_valued_0)).
thf(fc32_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) )  =>  (v2_membered @  ( (k7_relat_1 @ A)  @ B) ) ) ) , file(valued_0, fc32_valued_0)).
thf(fc33_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  (v3_membered @  ( (k7_relat_1 @ A)  @ B) ) ) ) , file(valued_0, fc33_valued_0)).
thf(fc33_valued_1, 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 @  ( (k18_valued_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k18_valued_1 @ A)  @ B) )  &  (v1_valued_0 @  ( (k18_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc33_valued_1)).
thf(fc34_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  =>  (v4_membered @  ( (k7_relat_1 @ A)  @ B) ) ) ) , file(valued_0, fc34_valued_0)).
thf(fc34_valued_1, 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 @  ( (k18_valued_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k18_valued_1 @ A)  @ B) )  &  (v3_valued_0 @  ( (k18_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc34_valued_1)).
thf(fc35_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  (v5_membered @  ( (k7_relat_1 @ A)  @ B) ) ) ) , file(valued_0, fc35_valued_0)).
thf(fc35_valued_1, 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 @  ( (k18_valued_1 @ A)  @ B) )  &  ( ( (v5_relat_1 @  ( (k18_valued_1 @ A)  @ B) )  @ k3_numbers)  &  (v1_funct_1 @  ( (k18_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc35_valued_1)).
thf(fc36_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  (v6_membered @  ( (k7_relat_1 @ A)  @ B) ) ) ) , file(valued_0, fc36_valued_0)).
thf(fc36_valued_1, 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 @  ( (k18_valued_1 @ A)  @ B) )  &  ( ( (v5_relat_1 @  ( (k18_valued_1 @ A)  @ B) )  @ k4_numbers)  &  (v1_funct_1 @  ( (k18_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc36_valued_1)).
thf(fc37_valued_1, 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 @  ( (k18_valued_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k18_valued_1 @ A)  @ B) )  &  (v4_valued_0 @  ( (k18_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc37_valued_1)).
thf(fc38_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v1_membered @ B) )  &  ( ( ~ ( (v1_xboole_0 @ C) )  &  (v1_membered @ C) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k18_valued_1 @ D)  @ E) )  &  ( (v1_partfun1 @  ( (k18_valued_1 @ D)  @ E) )  @ A) ) ) ) , file(valued_1, fc38_valued_1)).
thf(fc39_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v3_membered @ B) )  &  ( ( ~ ( (v1_xboole_0 @ C) )  &  (v3_membered @ C) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k18_valued_1 @ D)  @ E) )  &  ( (v1_partfun1 @  ( (k18_valued_1 @ D)  @ E) )  @ A) ) ) ) , file(valued_1, fc39_valued_1)).
thf(fc3_euclid, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( (m1_subset_1 @ B)  @  (k1_euclid @ A) ) )  =>  (v1_xboole_0 @  (k12_euclid @  ( ( (k8_euclid @ A)  @ B)  @ B) ) ) ) ) , file(euclid, fc3_euclid)).
thf(fc3_funct_2, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_xboole_0 @ B) )  =>  (v1_xboole_0 @  ( (k1_funct_2 @ A)  @ B) ) ) ) , file(funct_2, fc3_funct_2)).
thf(fc3_membered, axiom,  (v3_membered @ k1_numbers) , file(membered, fc3_membered)).
thf(fc3_numbers, axiom,  ~ ( (v1_xboole_0 @ k3_numbers) ) , file(numbers, fc3_numbers)).
thf(fc3_real_ns1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( ~ ( (v2_struct_0 @  (k4_real_ns1 @ A) ) )  &  ( (v13_algstr_0 @  (k4_real_ns1 @ A) )  &  ( (v2_rlvect_1 @  (k4_real_ns1 @ A) )  &  ( (v3_rlvect_1 @  (k4_real_ns1 @ A) )  &  ( (v4_rlvect_1 @  (k4_real_ns1 @ A) )  &  ( (v5_rlvect_1 @  (k4_real_ns1 @ A) )  &  ( (v6_rlvect_1 @  (k4_real_ns1 @ A) )  &  ( (v7_rlvect_1 @  (k4_real_ns1 @ A) )  &  ( (v8_rlvect_1 @  (k4_real_ns1 @ A) )  &  ( (v3_normsp_0 @  (k4_real_ns1 @ A) )  &  ( (v4_normsp_0 @  (k4_real_ns1 @ A) )  &  ( (v1_normsp_1 @  (k4_real_ns1 @ A) )  &  (v2_normsp_1 @  (k4_real_ns1 @ A) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(real_ns1, fc3_real_ns1)).
thf(fc3_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  (v3_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc3_valued_0)).
thf(fc3_valued_1, 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_valued_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k1_valued_1 @ A)  @ B) )  &  (v3_valued_0 @  ( (k1_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc3_valued_1)).
thf(fc3_xcmplx_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  (v1_xcmplx_0 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) , file(xcmplx_0, fc3_xcmplx_0)).
thf(fc3_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  ( (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) )  &  (v1_xreal_0 @  (k4_xcmplx_0 @ A) ) ) ) ) , file(xreal_0, fc3_xreal_0)).
thf(fc40_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v4_membered @ B) )  &  ( ( ~ ( (v1_xboole_0 @ C) )  &  (v4_membered @ C) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k18_valued_1 @ D)  @ E) )  &  ( (v1_partfun1 @  ( (k18_valued_1 @ D)  @ E) )  @ A) ) ) ) , file(valued_1, fc40_valued_1)).
thf(fc41_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v5_membered @ B) )  &  ( ( ~ ( (v1_xboole_0 @ C) )  &  (v5_membered @ C) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k18_valued_1 @ D)  @ E) )  &  ( (v1_partfun1 @  ( (k18_valued_1 @ D)  @ E) )  @ A) ) ) ) , file(valued_1, fc41_valued_1)).
thf(fc42_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v6_membered @ B) )  &  ( ( ~ ( (v1_xboole_0 @ C) )  &  (v6_membered @ C) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k18_valued_1 @ D)  @ E) )  &  ( (v1_partfun1 @  ( (k18_valued_1 @ D)  @ E) )  @ A) ) ) ) , file(valued_1, fc42_valued_1)).
thf(fc43_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v1_valued_0 @ B)  &  (v1_finseq_1 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k18_valued_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k18_valued_1 @ A)  @ B) )  &  (v1_finseq_1 @  ( (k18_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc43_valued_1)).
thf(fc44_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  &  (v1_xcmplx_0 @ B) )  =>  ( (v1_relat_1 @  ( (k24_valued_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k24_valued_1 @ A)  @ B) )  &  (v1_valued_0 @  ( (k24_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc44_valued_1)).
thf(fc45_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_valued_0 @ A) ) )  &  (v1_xreal_0 @ B) )  =>  ( (v1_relat_1 @  ( (k24_valued_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k24_valued_1 @ A)  @ B) )  &  (v3_valued_0 @  ( (k24_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc45_valued_1)).
thf(fc46_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k3_numbers)  &  (v1_funct_1 @ A) ) )  &  (v1_rat_1 @ B) )  =>  ( (v1_relat_1 @  ( (k24_valued_1 @ A)  @ B) )  &  ( ( (v5_relat_1 @  ( (k24_valued_1 @ A)  @ B) )  @ k3_numbers)  &  (v1_funct_1 @  ( (k24_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc46_valued_1)).
thf(fc47_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k4_numbers)  &  (v1_funct_1 @ A) ) )  &  (v1_int_1 @ B) )  =>  ( (v1_relat_1 @  ( (k24_valued_1 @ A)  @ B) )  &  ( ( (v5_relat_1 @  ( (k24_valued_1 @ A)  @ B) )  @ k4_numbers)  &  (v1_funct_1 @  ( (k24_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc47_valued_1)).
thf(fc48_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v4_valued_0 @ A) ) )  &  (v7_ordinal1 @ B) )  =>  ( (v1_relat_1 @  ( (k24_valued_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k24_valued_1 @ A)  @ B) )  &  (v4_valued_0 @  ( (k24_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc48_valued_1)).
thf(fc49_valued_0, axiom,  (! [A: $i] :  ( (v1_membered @ A)  =>  ( (v1_relat_1 @  (k4_relat_1 @ A) )  &  (v1_valued_0 @  (k4_relat_1 @ A) ) ) ) ) , file(valued_0, fc49_valued_0)).
thf(fc49_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v1_membered @ B) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  (v1_xcmplx_0 @ D) ) )  =>  ( (v1_funct_1 @  ( (k24_valued_1 @ C)  @ D) )  &  ( (v1_partfun1 @  ( (k24_valued_1 @ C)  @ D) )  @ A) ) ) ) , file(valued_1, fc49_valued_1)).
thf(fc4_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ A)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k3_relat_1 @ D)  @ C) )  &  ( ( (v1_funct_2 @  ( (k3_relat_1 @ D)  @ C) )  @ A)  @ B) ) ) ) , file(funct_2, fc4_funct_2)).
thf(fc4_membered, axiom,  (v4_membered @ k3_numbers) , file(membered, fc4_membered)).
thf(fc4_numbers, axiom,  ~ ( (v1_xboole_0 @ k4_numbers) ) , file(numbers, fc4_numbers)).
thf(fc4_ordinal1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v5_ordinal1 @ A) ) )  =>  (v3_ordinal1 @  (k9_xtuple_0 @ A) ) ) ) , file(ordinal1, fc4_ordinal1)).
thf(fc4_real_ns1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( ~ ( (v2_struct_0 @  (k4_real_ns1 @ A) ) )  &  ( (v1_normsp_1 @  (k4_real_ns1 @ A) )  &  (v3_lopban_1 @  (k4_real_ns1 @ A) ) ) ) ) ) , file(real_ns1, fc4_real_ns1)).
thf(fc4_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  =>  (v4_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc4_valued_0)).
thf(fc4_valued_1, 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_valued_1 @ A)  @ B) )  &  ( ( (v5_relat_1 @  ( (k1_valued_1 @ A)  @ B) )  @ k3_numbers)  &  (v1_funct_1 @  ( (k1_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc4_valued_1)).
thf(fc4_xcmplx_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  (v1_xcmplx_0 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(xcmplx_0, fc4_xcmplx_0)).
thf(fc4_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  ( (v1_xcmplx_0 @  (k5_xcmplx_0 @ A) )  &  (v1_xreal_0 @  (k5_xcmplx_0 @ A) ) ) ) ) , file(xreal_0, fc4_xreal_0)).
thf(fc50_valued_0, axiom,  (! [A: $i] :  ( (v2_membered @ A)  =>  ( (v1_relat_1 @  (k4_relat_1 @ A) )  &  (v2_valued_0 @  (k4_relat_1 @ A) ) ) ) ) , file(valued_0, fc50_valued_0)).
thf(fc50_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v3_membered @ B) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  (v1_xreal_0 @ D) ) )  =>  ( (v1_funct_1 @  ( (k24_valued_1 @ C)  @ D) )  &  ( (v1_partfun1 @  ( (k24_valued_1 @ C)  @ D) )  @ A) ) ) ) , file(valued_1, fc50_valued_1)).
thf(fc51_valued_0, axiom,  (! [A: $i] :  ( (v3_membered @ A)  =>  ( (v1_relat_1 @  (k4_relat_1 @ A) )  &  (v3_valued_0 @  (k4_relat_1 @ A) ) ) ) ) , file(valued_0, fc51_valued_0)).
thf(fc51_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v4_membered @ B) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  (v1_rat_1 @ D) ) )  =>  ( (v1_funct_1 @  ( (k24_valued_1 @ C)  @ D) )  &  ( (v1_partfun1 @  ( (k24_valued_1 @ C)  @ D) )  @ A) ) ) ) , file(valued_1, fc51_valued_1)).
thf(fc52_valued_0, axiom,  (! [A: $i] :  ( (v4_membered @ A)  =>  ( (v1_relat_1 @  (k4_relat_1 @ A) )  &  ( (v5_relat_1 @  (k4_relat_1 @ A) )  @ k3_numbers) ) ) ) , file(valued_0, fc52_valued_0)).
thf(fc52_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v5_membered @ B) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  (v1_int_1 @ D) ) )  =>  ( (v1_funct_1 @  ( (k24_valued_1 @ C)  @ D) )  &  ( (v1_partfun1 @  ( (k24_valued_1 @ C)  @ D) )  @ A) ) ) ) , file(valued_1, fc52_valued_1)).
thf(fc53_valued_0, axiom,  (! [A: $i] :  ( (v5_membered @ A)  =>  ( (v1_relat_1 @  (k4_relat_1 @ A) )  &  ( (v5_relat_1 @  (k4_relat_1 @ A) )  @ k4_numbers) ) ) ) , file(valued_0, fc53_valued_0)).
thf(fc53_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v6_membered @ B) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  (v7_ordinal1 @ D) ) )  =>  ( (v1_funct_1 @  ( (k24_valued_1 @ C)  @ D) )  &  ( (v1_partfun1 @  ( (k24_valued_1 @ C)  @ D) )  @ A) ) ) ) , file(valued_1, fc53_valued_1)).
thf(fc54_valued_0, axiom,  (! [A: $i] :  ( (v6_membered @ A)  =>  ( (v1_relat_1 @  (k4_relat_1 @ A) )  &  (v4_valued_0 @  (k4_relat_1 @ A) ) ) ) ) , file(valued_0, fc54_valued_0)).
thf(fc54_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  &  (v1_xcmplx_0 @ B) )  =>  ( (v1_relat_1 @  ( (k24_valued_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k24_valued_1 @ A)  @ B) )  &  (v1_finseq_1 @  ( (k24_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc54_valued_1)).
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(fc55_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  ( (v1_relat_1 @  (k30_valued_1 @ A) )  &  ( (v1_funct_1 @  (k30_valued_1 @ A) )  &  (v1_valued_0 @  (k30_valued_1 @ A) ) ) ) ) ) , file(valued_1, fc55_valued_1)).
thf(fc56_membered, axiom,  (v7_membered @ k1_numbers) , file(membered, fc56_membered)).
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(fc56_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_valued_0 @ A) ) )  =>  ( (v1_relat_1 @  (k30_valued_1 @ A) )  &  ( (v1_funct_1 @  (k30_valued_1 @ A) )  &  ( (v1_valued_0 @  (k30_valued_1 @ A) )  &  (v3_valued_0 @  (k30_valued_1 @ A) ) ) ) ) ) ) , file(valued_1, fc56_valued_1)).
thf(fc57_membered, axiom,  (v7_membered @ k3_numbers) , file(membered, fc57_membered)).
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(fc57_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k3_numbers)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @  (k30_valued_1 @ A) )  &  ( ( (v5_relat_1 @  (k30_valued_1 @ A) )  @ k3_numbers)  &  ( (v1_funct_1 @  (k30_valued_1 @ A) )  &  (v1_valued_0 @  (k30_valued_1 @ A) ) ) ) ) ) ) , file(valued_1, fc57_valued_1)).
thf(fc58_membered, axiom,  (v7_membered @ k4_numbers) , file(membered, fc58_membered)).
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(fc58_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k4_numbers)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @  (k30_valued_1 @ A) )  &  ( ( (v5_relat_1 @  (k30_valued_1 @ A) )  @ k4_numbers)  &  ( (v1_funct_1 @  (k30_valued_1 @ A) )  &  (v1_valued_0 @  (k30_valued_1 @ A) ) ) ) ) ) ) , file(valued_1, fc58_valued_1)).
thf(fc59_membered, axiom,  (v7_membered @ k4_ordinal1) , file(membered, fc59_membered)).
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(fc59_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v1_membered @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  (k30_valued_1 @ C) )  &  ( (v1_partfun1 @  (k30_valued_1 @ C) )  @ A) ) ) ) , file(valued_1, fc59_valued_1)).
thf(fc5_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( ~ ( (v2_struct_0 @  (k15_euclid @ A) ) )  &  (v5_rltopsp1 @  (k15_euclid @ A) ) ) ) ) , file(euclid, fc5_euclid)).
thf(fc5_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ B)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ B) ) ) ) )  &  ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k3_relat_1 @ D)  @ C) )  &  ( ( (v1_funct_2 @  ( (k3_relat_1 @ D)  @ C) )  @ A)  @ B) ) ) ) , file(funct_2, fc5_funct_2)).
thf(fc5_membered, axiom,  (v5_membered @ k4_numbers) , file(membered, fc5_membered)).
thf(fc5_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  (v5_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc5_valued_0)).
thf(fc5_valued_1, 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_valued_1 @ A)  @ B) )  &  ( ( (v5_relat_1 @  ( (k1_valued_1 @ A)  @ B) )  @ k4_numbers)  &  (v1_funct_1 @  ( (k1_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc5_valued_1)).
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(fc60_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v3_membered @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  (k30_valued_1 @ C) )  &  ( (v1_partfun1 @  (k30_valued_1 @ C) )  @ A) ) ) ) , file(valued_1, fc60_valued_1)).
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(fc61_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v4_membered @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  (k30_valued_1 @ C) )  &  ( (v1_partfun1 @  (k30_valued_1 @ C) )  @ A) ) ) ) , file(valued_1, fc61_valued_1)).
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(fc62_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v5_membered @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  (k30_valued_1 @ C) )  &  ( (v1_partfun1 @  (k30_valued_1 @ C) )  @ A) ) ) ) , file(valued_1, fc62_valued_1)).
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(fc63_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  =>  ( (v1_relat_1 @  (k30_valued_1 @ A) )  &  ( (v1_funct_1 @  (k30_valued_1 @ A) )  &  ( (v1_valued_0 @  (k30_valued_1 @ A) )  &  (v1_finseq_1 @  (k30_valued_1 @ A) ) ) ) ) ) ) , file(valued_1, fc63_valued_1)).
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(fc64_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_valued_0 @ A) ) )  =>  ( (v1_relat_1 @  (k35_valued_1 @ A) )  &  ( (v1_funct_1 @  (k35_valued_1 @ A) )  &  ( (v1_valued_0 @  (k35_valued_1 @ A) )  &  (v3_valued_0 @  (k35_valued_1 @ A) ) ) ) ) ) ) , file(valued_1, fc64_valued_1)).
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(fc65_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k3_numbers)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @  (k35_valued_1 @ A) )  &  ( ( (v5_relat_1 @  (k35_valued_1 @ A) )  @ k3_numbers)  &  ( (v1_funct_1 @  (k35_valued_1 @ A) )  &  (v1_valued_0 @  (k35_valued_1 @ A) ) ) ) ) ) ) , file(valued_1, fc65_valued_1)).
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(fc66_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v1_membered @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  (k35_valued_1 @ C) )  &  ( (v1_partfun1 @  (k35_valued_1 @ C) )  @ A) ) ) ) , file(valued_1, fc66_valued_1)).
thf(fc67_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_xcmplx_0 @ B)  =>  (v1_valued_0 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(valued_0, fc67_valued_0)).
thf(fc67_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v3_membered @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  (k35_valued_1 @ C) )  &  ( (v1_partfun1 @  (k35_valued_1 @ C) )  @ A) ) ) ) , file(valued_1, fc67_valued_1)).
thf(fc68_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_xxreal_0 @ B)  =>  (v2_valued_0 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(valued_0, fc68_valued_0)).
thf(fc68_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v4_membered @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  (k35_valued_1 @ C) )  &  ( (v1_partfun1 @  (k35_valued_1 @ C) )  @ A) ) ) ) , file(valued_1, fc68_valued_1)).
thf(fc69_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_xreal_0 @ B)  =>  (v3_valued_0 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(valued_0, fc69_valued_0)).
thf(fc69_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  =>  ( (v1_relat_1 @  (k35_valued_1 @ A) )  &  ( (v1_funct_1 @  (k35_valued_1 @ A) )  &  ( (v1_valued_0 @  (k35_valued_1 @ A) )  &  (v1_finseq_1 @  (k35_valued_1 @ A) ) ) ) ) ) ) , file(valued_1, fc69_valued_1)).
thf(fc6_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v2_pre_topc @  (k15_euclid @ A) )  &  ( (v13_algstr_0 @  (k15_euclid @ A) )  &  ( (v2_rlvect_1 @  (k15_euclid @ A) )  &  ( (v3_rlvect_1 @  (k15_euclid @ A) )  &  ( (v4_rlvect_1 @  (k15_euclid @ A) )  &  ( (v5_rlvect_1 @  (k15_euclid @ A) )  &  ( (v6_rlvect_1 @  (k15_euclid @ A) )  &  ( (v7_rlvect_1 @  (k15_euclid @ A) )  &  ( (v8_rlvect_1 @  (k15_euclid @ A) )  &  (v5_rltopsp1 @  (k15_euclid @ A) ) ) ) ) ) ) ) ) ) ) ) ) , file(euclid, fc6_euclid)).
thf(fc6_funct_2, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_funct_1 @ B)  &  ( ( (v2_funct_2 @ B)  @ A)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) )  &  ( (v1_funct_1 @ C)  &  ( ( (v2_funct_2 @ C)  @ A)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k3_relat_1 @ C)  @ B) )  &  ( (v2_funct_2 @  ( (k3_relat_1 @ C)  @ B) )  @ A) ) ) ) , file(funct_2, fc6_funct_2)).
thf(fc6_membered, axiom,  (v6_membered @ k4_ordinal1) , file(membered, fc6_membered)).
thf(fc6_numbers, axiom,  ~ ( (v1_finset_1 @ k4_numbers) ) , file(numbers, fc6_numbers)).
thf(fc6_ordinal1, axiom,  ( ~ ( (v1_xboole_0 @ k4_ordinal1) )  &  (v3_ordinal1 @ k4_ordinal1) ) , file(ordinal1, fc6_ordinal1)).
thf(fc6_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v7_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  ~ ( (v1_zfmisc_1 @  (u1_struct_0 @ A) ) ) ) ) , file(struct_0, fc6_struct_0)).
thf(fc6_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  (v6_membered @  (k10_xtuple_0 @ A) ) ) ) , file(valued_0, fc6_valued_0)).
thf(fc6_valued_1, 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_valued_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k1_valued_1 @ A)  @ B) )  &  (v4_valued_0 @  ( (k1_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc6_valued_1)).
thf(fc6_xcmplx_0, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_xcmplx_0 @ A) )  =>  ( ~ ( (v1_xboole_0 @  (k4_xcmplx_0 @ A) ) )  &  (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) ) ) ) ) , file(xcmplx_0, fc6_xcmplx_0)).
thf(fc6_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  (v1_xreal_0 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc6_xreal_0)).
thf(fc70_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_rat_1 @ B)  =>  ( (v5_relat_1 @  ( (k2_funcop_1 @ A)  @ B) )  @ k3_numbers) ) ) , file(valued_0, fc70_valued_0)).
thf(fc70_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  ( (v1_relat_1 @  (k39_valued_1 @ A) )  &  ( (v1_funct_1 @  (k39_valued_1 @ A) )  &  (v1_valued_0 @  (k39_valued_1 @ A) ) ) ) ) ) , file(valued_1, fc70_valued_1)).
thf(fc71_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_int_1 @ B)  =>  ( (v5_relat_1 @  ( (k2_funcop_1 @ A)  @ B) )  @ k4_numbers) ) ) , file(valued_0, fc71_valued_0)).
thf(fc71_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_valued_0 @ A) ) )  =>  ( (v1_relat_1 @  (k39_valued_1 @ A) )  &  ( (v1_funct_1 @  (k39_valued_1 @ A) )  &  (v3_valued_0 @  (k39_valued_1 @ A) ) ) ) ) ) , file(valued_1, fc71_valued_1)).
thf(fc72_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v7_ordinal1 @ B)  =>  (v4_valued_0 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(valued_0, fc72_valued_0)).
thf(fc72_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k3_numbers)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @  (k39_valued_1 @ A) )  &  ( ( (v5_relat_1 @  (k39_valued_1 @ A) )  @ k3_numbers)  &  (v1_funct_1 @  (k39_valued_1 @ A) ) ) ) ) ) , file(valued_1, fc72_valued_1)).
thf(fc73_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k4_numbers)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @  (k39_valued_1 @ A) )  &  ( ( (v5_relat_1 @  (k39_valued_1 @ A) )  @ k4_numbers)  &  (v1_funct_1 @  (k39_valued_1 @ A) ) ) ) ) ) , file(valued_1, fc73_valued_1)).
thf(fc74_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v4_valued_0 @ A) ) )  =>  ( (v1_relat_1 @  (k39_valued_1 @ A) )  &  ( (v1_funct_1 @  (k39_valued_1 @ A) )  &  (v4_valued_0 @  (k39_valued_1 @ A) ) ) ) ) ) , file(valued_1, fc74_valued_1)).
thf(fc75_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v1_membered @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  (k39_valued_1 @ C) )  &  ( (v1_partfun1 @  (k39_valued_1 @ C) )  @ A) ) ) ) , file(valued_1, fc75_valued_1)).
thf(fc76_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v3_membered @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  (k39_valued_1 @ C) )  &  ( (v1_partfun1 @  (k39_valued_1 @ C) )  @ A) ) ) ) , file(valued_1, fc76_valued_1)).
thf(fc77_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v4_membered @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  (k39_valued_1 @ C) )  &  ( (v1_partfun1 @  (k39_valued_1 @ C) )  @ A) ) ) ) , file(valued_1, fc77_valued_1)).
thf(fc78_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v5_membered @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  (k39_valued_1 @ C) )  &  ( (v1_partfun1 @  (k39_valued_1 @ C) )  @ A) ) ) ) , file(valued_1, fc78_valued_1)).
thf(fc79_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v6_membered @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  (k39_valued_1 @ C) )  &  ( (v1_partfun1 @  (k39_valued_1 @ C) )  @ A) ) ) ) , file(valued_1, fc79_valued_1)).
thf(fc7_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v2_monoid_0 @  (k15_euclid @ A) )  &  (v5_rltopsp1 @  (k15_euclid @ A) ) ) ) ) , file(euclid, fc7_euclid)).
thf(fc7_funct_2, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ A)  @ A)  &  ( ( ( (v3_funct_2 @ B)  @ A)  @ A)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) ) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ A)  &  ( ( ( (v3_funct_2 @ C)  @ A)  @ A)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k3_relat_1 @ B)  @ C) )  &  ( ( ( (v1_funct_2 @  ( (k3_relat_1 @ B)  @ C) )  @ A)  @ A)  &  ( ( (v3_funct_2 @  ( (k3_relat_1 @ B)  @ C) )  @ A)  @ A) ) ) ) ) , file(funct_2, fc7_funct_2)).
thf(fc7_numbers, axiom,  ~ ( (v1_finset_1 @ k3_numbers) ) , file(numbers, fc7_numbers)).
thf(fc7_relset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  ( ~ ( (v1_xboole_0 @  (k4_relat_1 @ A) ) )  &  (v1_relat_1 @  (k4_relat_1 @ A) ) ) ) ) , file(relset_1, fc7_relset_1)).
thf(fc7_struct_0, axiom,  (! [A: $i] :  ( ( (v7_struct_0 @ A)  &  (l1_struct_0 @ A) )  =>  (v1_zfmisc_1 @  (u1_struct_0 @ A) ) ) ) , file(struct_0, fc7_struct_0)).
thf(fc7_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v1_membered @ B) )  &  ( ( ~ ( (v1_xboole_0 @ C) )  &  (v1_membered @ C) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k1_valued_1 @ D)  @ E) )  &  ( (v1_partfun1 @  ( (k1_valued_1 @ D)  @ E) )  @ A) ) ) ) , file(valued_1, fc7_valued_1)).
thf(fc7_xcmplx_0, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_xcmplx_0 @ A) )  =>  ( ~ ( (v1_xboole_0 @  (k5_xcmplx_0 @ A) ) )  &  (v1_xcmplx_0 @  (k5_xcmplx_0 @ A) ) ) ) ) , file(xcmplx_0, fc7_xcmplx_0)).
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_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  =>  ( (v1_relat_1 @  (k39_valued_1 @ A) )  &  ( (v1_funct_1 @  (k39_valued_1 @ A) )  &  (v1_finseq_1 @  (k39_valued_1 @ A) ) ) ) ) ) , file(valued_1, fc80_valued_1)).
thf(fc81_valued_1, 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 @  ( (k45_valued_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k45_valued_1 @ A)  @ B) )  &  (v1_valued_0 @  ( (k45_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc81_valued_1)).
thf(fc82_valued_1, 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 @  ( (k45_valued_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k45_valued_1 @ A)  @ B) )  &  (v3_valued_0 @  ( (k45_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc82_valued_1)).
thf(fc83_valued_1, 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 @  ( (k45_valued_1 @ A)  @ B) )  &  ( ( (v5_relat_1 @  ( (k45_valued_1 @ A)  @ B) )  @ k3_numbers)  &  (v1_funct_1 @  ( (k45_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc83_valued_1)).
thf(fc84_valued_1, 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 @  ( (k45_valued_1 @ A)  @ B) )  &  ( ( (v5_relat_1 @  ( (k45_valued_1 @ A)  @ B) )  @ k4_numbers)  &  (v1_funct_1 @  ( (k45_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc84_valued_1)).
thf(fc85_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_membered @ B)  =>  (v1_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc85_valued_0)).
thf(fc85_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v1_membered @ B) )  &  ( ( ~ ( (v1_xboole_0 @ C) )  &  (v1_membered @ C) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k45_valued_1 @ D)  @ E) )  &  ( (v1_partfun1 @  ( (k45_valued_1 @ D)  @ E) )  @ A) ) ) ) , file(valued_1, fc85_valued_1)).
thf(fc86_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v2_membered @ B)  =>  (v2_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc86_valued_0)).
thf(fc86_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v3_membered @ B) )  &  ( ( ~ ( (v1_xboole_0 @ C) )  &  (v3_membered @ C) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k45_valued_1 @ D)  @ E) )  &  ( (v1_partfun1 @  ( (k45_valued_1 @ D)  @ E) )  @ A) ) ) ) , file(valued_1, fc86_valued_1)).
thf(fc87_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v3_membered @ B)  =>  (v3_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc87_valued_0)).
thf(fc87_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v4_membered @ B) )  &  ( ( ~ ( (v1_xboole_0 @ C) )  &  (v4_membered @ C) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k45_valued_1 @ D)  @ E) )  &  ( (v1_partfun1 @  ( (k45_valued_1 @ D)  @ E) )  @ A) ) ) ) , file(valued_1, fc87_valued_1)).
thf(fc88_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v4_membered @ B)  =>  ( (v5_relat_1 @  ( (k2_zfmisc_1 @ A)  @ B) )  @ k3_numbers) ) ) , file(valued_0, fc88_valued_0)).
thf(fc88_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v5_membered @ B) )  &  ( ( ~ ( (v1_xboole_0 @ C) )  &  (v5_membered @ C) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k45_valued_1 @ D)  @ E) )  &  ( (v1_partfun1 @  ( (k45_valued_1 @ D)  @ E) )  @ A) ) ) ) , file(valued_1, fc88_valued_1)).
thf(fc89_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v5_membered @ B)  =>  ( (v5_relat_1 @  ( (k2_zfmisc_1 @ A)  @ B) )  @ k4_numbers) ) ) , file(valued_0, fc89_valued_0)).
thf(fc89_valued_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v1_valued_0 @ B)  &  (v1_finseq_1 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k45_valued_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k45_valued_1 @ A)  @ B) )  &  (v1_finseq_1 @  ( (k45_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc89_valued_1)).
thf(fc8_euclid, axiom,  (! [A: $i, B: $i] :  ( (v7_ordinal1 @ A)  =>  (v3_finseq_1 @  ( (k4_finseq_2 @ A)  @ B) ) ) ) , file(euclid, fc8_euclid)).
thf(fc8_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ B)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ C) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k3_relat_1 @ D)  @ E) )  &  ( ( (v1_funct_2 @  ( (k3_relat_1 @ D)  @ E) )  @ A)  @ C) ) ) ) , file(funct_2, fc8_funct_2)).
thf(fc8_numbers, axiom,  ~ ( (v1_finset_1 @ k1_numbers) ) , file(numbers, fc8_numbers)).
thf(fc8_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) )  @ C) ) )  =>  (v1_relat_1 @  (k9_xtuple_0 @ D) ) ) ) , file(relset_1, fc8_relset_1)).
thf(fc8_struct_0, axiom,  (! [A: $i] :  ( ( (v8_struct_0 @ A)  &  (l1_struct_0 @ A) )  =>  (v1_finset_1 @  (u1_struct_0 @ A) ) ) ) , file(struct_0, fc8_struct_0)).
thf(fc8_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v3_membered @ B) )  &  ( ( ~ ( (v1_xboole_0 @ C) )  &  (v3_membered @ C) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k1_valued_1 @ D)  @ E) )  &  ( (v1_partfun1 @  ( (k1_valued_1 @ D)  @ E) )  @ A) ) ) ) , file(valued_1, fc8_valued_1)).
thf(fc8_xcmplx_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_xcmplx_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_xcmplx_0 @ B) ) )  =>  ~ ( (v1_xboole_0 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xcmplx_0, fc8_xcmplx_0)).
thf(fc90_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v6_membered @ B)  =>  (v4_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc90_valued_0)).
thf(fc91_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v5_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v5_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v5_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc91_valued_0)).
thf(fc92_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v7_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v7_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v7_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc92_valued_0)).
thf(fc93_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v6_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v6_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v5_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc93_valued_0)).
thf(fc94_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v8_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v8_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v7_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc94_valued_0)).
thf(fc95_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v6_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v5_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v6_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc95_valued_0)).
thf(fc96_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v6_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v5_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ B)  @ A) )  &  (v6_valued_0 @  ( (k3_relat_1 @ B)  @ A) ) ) ) ) , file(valued_0, fc96_valued_0)).
thf(fc97_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  (v8_valued_0 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v2_valued_0 @ B)  &  (v7_valued_0 @ B) ) ) ) )  =>  ( (v1_relat_1 @  ( (k3_relat_1 @ A)  @ B) )  &  (v8_valued_0 @  ( (k3_relat_1 @ A)  @ B) ) ) ) ) , file(valued_0, fc97_valued_0)).
thf(fc97_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k3_numbers)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @  (k54_valued_1 @ A) )  &  ( ( (v5_relat_1 @  (k54_valued_1 @ A) )  @ k3_numbers)  &  ( (v1_funct_1 @  (k54_valued_1 @ A) )  &  (v3_valued_0 @  (k54_valued_1 @ A) ) ) ) ) ) ) , file(valued_1, fc97_valued_1)).
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(fc98_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k4_numbers)  &  (v1_funct_1 @ A) ) )  =>  ( (v1_relat_1 @  (k54_valued_1 @ A) )  &  ( (v1_funct_1 @  (k54_valued_1 @ A) )  &  ( (v3_valued_0 @  (k54_valued_1 @ A) )  &  (v4_valued_0 @  (k54_valued_1 @ A) ) ) ) ) ) ) , file(valued_1, fc98_valued_1)).
thf(fc99_valued_0, axiom,  (! [A: $i] :  ( (v2_membered @ A)  =>  ( (v1_funct_1 @  (k4_relat_1 @ A) )  &  ( ( ( (v1_funct_2 @  (k4_relat_1 @ A) )  @ A)  @ A)  &  (v5_valued_0 @  (k4_relat_1 @ A) ) ) ) ) ) , file(valued_0, fc99_valued_0)).
thf(fc99_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v1_membered @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) )  =>  ( (v1_funct_1 @  (k54_valued_1 @ C) )  &  ( (v1_partfun1 @  (k54_valued_1 @ C) )  @ A) ) ) ) , file(valued_1, fc99_valued_1)).
thf(fc9_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v3_finseq_1 @  (k1_euclid @ A) ) ) ) , file(euclid, fc9_euclid)).
thf(fc9_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @  ( (k2_zfmisc_1 @ B)  @ C) ) ) )  =>  (v1_relat_1 @  (k10_xtuple_0 @ D) ) ) ) , file(relset_1, fc9_relset_1)).
thf(fc9_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v8_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  ~ ( (v1_finset_1 @  (u1_struct_0 @ A) ) ) ) ) , file(struct_0, fc9_struct_0)).
thf(fc9_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v4_membered @ B) )  &  ( ( ~ ( (v1_xboole_0 @ C) )  &  (v4_membered @ C) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k1_valued_1 @ D)  @ E) )  &  ( (v1_partfun1 @  ( (k1_valued_1 @ D)  @ E) )  @ A) ) ) ) , file(valued_1, fc9_valued_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_normsp_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( (m1_subset_1 @ B)  @ A)  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A) ) ) ) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @  ( (k2_zfmisc_1 @ k1_numbers)  @ A) )  @ A)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ A) )  @ A) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ k1_numbers)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ k1_numbers) ) ) ) ) ) ) )  =>  (! [F: $i, G: $i, H: $i, I: $i, J: $i] :  ( ( ( ( ( ( (g1_normsp_1 @ A)  @ B)  @ C)  @ D)  @ E)  =  ( ( ( ( (g1_normsp_1 @ F)  @ G)  @ H)  @ I)  @ J) )  =>  ( (A = F)  &  ( (B = G)  &  ( (C = H)  &  ( (D = I)  &  (E = J) ) ) ) ) ) ) ) ) , file(normsp_1, g1_normsp_1)).
thf(free_g1_rltopsp1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( (m1_subset_1 @ B)  @ A)  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A) ) ) ) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @  ( (k2_zfmisc_1 @ k1_numbers)  @ A) )  @ A)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ A) )  @ A) ) ) ) )  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  (k1_zfmisc_1 @ A) ) ) ) ) )  =>  (! [F: $i, G: $i, H: $i, I: $i, J: $i] :  ( ( ( ( ( ( (g1_rltopsp1 @ A)  @ B)  @ C)  @ D)  @ E)  =  ( ( ( ( (g1_rltopsp1 @ F)  @ G)  @ H)  @ I)  @ J) )  =>  ( (A = F)  &  ( (B = G)  &  ( (C = H)  &  ( (D = I)  &  (E = J) ) ) ) ) ) ) ) ) , file(rltopsp1, g1_rltopsp1)).
thf(free_g1_rlvect_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (m1_subset_1 @ B)  @ A)  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A) ) ) ) )  &  ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @  ( (k2_zfmisc_1 @ k1_numbers)  @ A) )  @ A)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ A) )  @ A) ) ) ) ) ) )  =>  (! [E: $i, F: $i, G: $i, H: $i] :  ( ( ( ( ( (g1_rlvect_1 @ A)  @ B)  @ C)  @ D)  =  ( ( ( (g1_rlvect_1 @ E)  @ F)  @ G)  @ H) )  =>  ( (A = E)  &  ( (B = F)  &  ( (C = G)  &  (D = H) ) ) ) ) ) ) ) , file(rlvect_1, g1_rlvect_1)).
thf(ie1_euclid, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( (v1_xreal_0 @ A)  &  ( (v1_xreal_0 @ B)  &  ( (v7_ordinal1 @ C)  &  ( ( (m1_subset_1 @ D)  @  (u1_struct_0 @  (k15_euclid @ C) ) )  &  ( (v1_relat_1 @ E)  &  ( (v1_funct_1 @ E)  &  ( (v1_finseq_1 @ E)  &  (v3_valued_0 @ E) ) ) ) ) ) ) )  =>  ( ( (A = B)  &  (D = E) )  =>  ( ( ( (k1_rlvect_1 @  (k15_euclid @ C) )  @ D)  @ A)  =  ( (k10_rvsum_1 @ E)  @ B) ) ) ) ) , file(euclid, ie1_euclid)).
thf(ie1_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (m1_subset_1 @ D)  @ A) ) ) )  =>  ( ( ( (k7_partfun1 @ B)  @ C)  @ D)  =  ( ( ( (k3_funct_2 @ A)  @ B)  @ C)  @ D) ) ) ) , file(funct_2, ie1_funct_2)).
thf(ie2_euclid, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( (v7_ordinal1 @ A)  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @  (k15_euclid @ A) ) )  &  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @  (k15_euclid @ A) ) )  &  ( ( (v1_relat_1 @ D)  &  ( (v1_funct_1 @ D)  &  ( (v1_finseq_1 @ D)  &  (v3_valued_0 @ D) ) ) )  &  ( (v1_relat_1 @ E)  &  ( (v1_funct_1 @ E)  &  ( (v1_finseq_1 @ E)  &  (v3_valued_0 @ E) ) ) ) ) ) ) )  =>  ( ( (B = D)  &  (C = E) )  =>  ( ( ( (k3_rlvect_1 @  (k15_euclid @ A) )  @ B)  @ C)  =  ( (k4_rvsum_1 @ D)  @ E) ) ) ) ) , file(euclid, ie2_euclid)).
thf(ie4_euclid, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( (v7_ordinal1 @ A)  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @  (k15_euclid @ A) ) )  &  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @  (k15_euclid @ A) ) )  &  ( ( (v1_relat_1 @ D)  &  ( (v1_funct_1 @ D)  &  ( (v1_finseq_1 @ D)  &  (v3_valued_0 @ D) ) ) )  &  ( (v1_relat_1 @ E)  &  ( (v1_funct_1 @ E)  &  ( (v1_finseq_1 @ E)  &  (v3_valued_0 @ E) ) ) ) ) ) ) )  =>  ( ( (B = D)  &  (C = E) )  =>  ( ( ( (k5_algstr_0 @  (k15_euclid @ A) )  @ B)  @ C)  =  ( (k8_rvsum_1 @ D)  @ E) ) ) ) ) , file(euclid, ie4_euclid)).
thf(involutiveness_k1_real_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  ( (k1_real_1 @  (k1_real_1 @ A) )  = A) ) ) , file(real_1, k1_real_1)).
thf(involutiveness_k2_real_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  ( (k2_real_1 @  (k2_real_1 @ A) )  = A) ) ) , file(real_1, k2_real_1)).
thf(involutiveness_k30_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  ( (k30_valued_1 @  (k30_valued_1 @ A) )  = A) ) ) , file(valued_1, k30_valued_1)).
thf(involutiveness_k35_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  ( (k35_valued_1 @  (k35_valued_1 @ A) )  = A) ) ) , file(valued_1, k35_valued_1)).
thf(involutiveness_k37_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v3_membered @ B)  &  ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  =>  ( ( ( (k37_valued_1 @ A)  @ B)  @  ( ( (k37_valued_1 @ A)  @ B)  @ C) )  = C) ) ) , file(valued_1, k37_valued_1)).
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(involutiveness_k5_xcmplx_0, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (k5_xcmplx_0 @  (k5_xcmplx_0 @ A) )  = A) ) ) , file(xcmplx_0, k5_xcmplx_0)).
thf(involutiveness_k6_rvsum_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  =>  ( (k6_rvsum_1 @  (k6_rvsum_1 @ A) )  = A) ) ) , file(rvsum_1, k6_rvsum_1)).
thf(involutiveness_k7_binop_2, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  ( (k7_binop_2 @  (k7_binop_2 @ A) )  = A) ) ) , file(binop_2, k7_binop_2)).
thf(l11_cfdiff_2, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ k1_numbers)  =>  ( (m1_subset_1 @  ( (k10_finseq_1 @ A)  @ B) )  @  (u1_struct_0 @  (k4_real_ns1 @ np__2) ) ) ) ) ) ) , file(cfdiff_2, l11_cfdiff_2)).
thf(l12_cfdiff_2, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ k1_numbers)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @ k1_numbers)  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @ k1_numbers)  =>  (! [E: $i] :  ( ( (m1_subset_1 @ E)  @  (u1_struct_0 @  (k4_real_ns1 @ np__2) ) )  =>  (! [F: $i] :  ( ( (m1_subset_1 @ F)  @  (u1_struct_0 @  (k4_real_ns1 @ np__2) ) )  =>  ( ( (E =  ( (k10_finseq_1 @ A)  @ B) )  &  (F =  ( (k10_finseq_1 @ C)  @ D) ) )  =>  ( ( ( ( (k3_rlvect_1 @  (k4_real_ns1 @ np__2) )  @ E)  @ F)  =  ( (k10_finseq_1 @  ( (k7_real_1 @ A)  @ C) )  @  ( (k7_real_1 @ B)  @ D) ) )  &  ( ( ( (k5_algstr_0 @  (k4_real_ns1 @ np__2) )  @ E)  @ F)  =  ( (k10_finseq_1 @  ( (k9_real_1 @ A)  @ C) )  @  ( (k9_real_1 @ B)  @ D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(cfdiff_2, l12_cfdiff_2)).
thf(l13_cfdiff_2, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ k1_numbers)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @ k1_numbers)  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @  (u1_struct_0 @  (k4_real_ns1 @ np__2) ) )  =>  ( (D =  ( (k10_finseq_1 @ A)  @ B) )  =>  ( ( ( (k1_rlvect_1 @  (k4_real_ns1 @ np__2) )  @ D)  @ C)  =  ( (k10_finseq_1 @  ( (k8_real_1 @ C)  @ A) )  @  ( (k8_real_1 @ C)  @ B) ) ) ) ) ) ) ) ) ) ) ) , file(cfdiff_2, l13_cfdiff_2)).
thf(l14_cfdiff_2, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ np__2) )  @ k1_numbers) ) ) )  =>  (! [B: $i] :  ( ( ( (m2_finseq_2 @ B)  @ k1_numbers)  @  (k1_euclid @ np__2) )  =>  ( ( (r2_hidden @ B)  @  ( (k1_relset_1 @  (k1_euclid @ np__2) )  @ A) )  =>  ( ( (k1_funct_1 @  ( (k3_pdiff_1 @ np__2)  @ A) )  @ B)  =  ( (k12_finseq_1 @ k1_numbers)  @  ( (k1_seq_1 @ A)  @ B) ) ) ) ) ) ) ) , file(cfdiff_2, l14_cfdiff_2)).
thf(l22_cfdiff_2, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @  (k4_real_ns1 @ np__2) ) )  =>  ( (B =  ( (k10_finseq_1 @ A)  @ k6_numbers) )  =>  ( ( (k1_normsp_0 @  (k4_real_ns1 @ np__2) )  @ B)  =  (k18_complex1 @ A) ) ) ) ) ) ) , file(cfdiff_2, l22_cfdiff_2)).
thf(l23_cfdiff_2, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @  (k4_real_ns1 @ np__2) ) )  =>  ( (B =  ( (k10_finseq_1 @ k6_numbers)  @ A) )  =>  ( ( (k1_normsp_0 @  (k4_real_ns1 @ np__2) )  @ B)  =  (k18_complex1 @ A) ) ) ) ) ) ) , file(cfdiff_2, l23_cfdiff_2)).
thf(l24_cfdiff_2, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @  (k4_real_ns1 @ np__1) ) )  =>  ( (B =  ( (k12_finseq_1 @ k1_numbers)  @ A) )  =>  ( ( (k1_normsp_0 @  (k4_real_ns1 @ np__1) )  @ B)  =  (k18_complex1 @ A) ) ) ) ) ) ) , file(cfdiff_2, l24_cfdiff_2)).
thf(l8_cfdiff_2, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ k1_numbers)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @  (k4_real_ns1 @ np__1) ) )  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @  (u1_struct_0 @  (k4_real_ns1 @ np__1) ) )  =>  ( ( (C =  ( (k12_finseq_1 @ k1_numbers)  @ A) )  &  (D =  ( (k12_finseq_1 @ k1_numbers)  @ B) ) )  =>  ( ( ( ( (k3_rlvect_1 @  (k4_real_ns1 @ np__1) )  @ C)  @ D)  =  ( (k12_finseq_1 @ k1_numbers)  @  ( (k7_real_1 @ A)  @ B) ) )  &  ( ( ( (k5_algstr_0 @  (k4_real_ns1 @ np__1) )  @ C)  @ D)  =  ( (k12_finseq_1 @ k1_numbers)  @  ( (k9_real_1 @ A)  @ B) ) ) ) ) ) ) ) ) ) ) ) ) , file(cfdiff_2, l8_cfdiff_2)).
thf(l9_cfdiff_2, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ k1_numbers)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @ k1_numbers)  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @ k1_numbers)  =>  (! [E: $i] :  ( ( ( (m2_finseq_2 @ E)  @ k1_numbers)  @  (k1_euclid @ np__2) )  =>  (! [F: $i] :  ( ( ( (m2_finseq_2 @ F)  @ k1_numbers)  @  (k1_euclid @ np__2) )  =>  ( ( (E =  ( (k10_finseq_1 @ A)  @ B) )  &  (F =  ( (k10_finseq_1 @ C)  @ D) ) )  =>  ( ( ( ( (k7_euclid @ np__2)  @ E)  @ F)  =  ( (k10_finseq_1 @  ( (k7_real_1 @ A)  @ C) )  @  ( (k7_real_1 @ B)  @ D) ) )  &  ( ( ( (k8_euclid @ np__2)  @ E)  @ F)  =  ( (k10_finseq_1 @  ( (k9_real_1 @ A)  @ C) )  @  ( (k9_real_1 @ B)  @ D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(cfdiff_2, l9_cfdiff_2)).
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_k17_complex1, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (k17_complex1 @  (k17_complex1 @ A) )  =  (k17_complex1 @ A) ) ) ) , file(complex1, k17_complex1)).
thf(projectivity_k18_complex1, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (k18_complex1 @  (k18_complex1 @ A) )  =  (k18_complex1 @ A) ) ) ) , file(complex1, k18_complex1)).
thf(projectivity_k1_card_1, axiom,  (! [A: $i] :  ( (k1_card_1 @  (k1_card_1 @ A) )  =  (k1_card_1 @ A) ) ) , file(card_1, k1_card_1)).
thf(projectivity_k3_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (k3_finseq_1 @  (k3_finseq_1 @ A) )  =  (k3_finseq_1 @ A) ) ) ) , file(finseq_1, k3_finseq_1)).
thf(projectivity_k54_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  ( (k54_valued_1 @  (k54_valued_1 @ A) )  =  (k54_valued_1 @ A) ) ) ) , file(valued_1, k54_valued_1)).
thf(projectivity_k56_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_membered @ B)  &  ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  =>  ( ( ( (k56_valued_1 @ A)  @ B)  @  ( ( (k56_valued_1 @ A)  @ B)  @ C) )  =  ( ( (k56_valued_1 @ A)  @ B)  @ C) ) ) ) , file(valued_1, k56_valued_1)).
thf(rc17_struct_0, axiom,  (! [A: $i] :  ( (l2_struct_0 @ A)  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (v9_struct_0 @ B)  @ A) ) ) ) ) , file(struct_0, rc17_struct_0)).
thf(rc19_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v7_struct_0 @ A) )  &  (l2_struct_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ~ ( ( (v9_struct_0 @ B)  @ A) ) ) ) ) ) , file(struct_0, rc19_struct_0)).
thf(rc1_fdiff_1, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k1_numbers) ) )  &  ( (v1_relat_1 @ A)  &  ( (v2_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( ( (v5_relat_1 @ A)  @ k1_numbers)  &  ( (v1_funct_1 @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_partfun1 @ A)  @ k5_numbers)  &  ( ( ( (v1_funct_2 @ A)  @ k5_numbers)  @ k1_numbers)  &  ( (v1_valued_0 @ A)  &  ( (v2_valued_0 @ A)  &  ( (v3_valued_0 @ A)  &  ( (v1_fdiff_1 @ A)  @ k6_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(fdiff_1, rc1_fdiff_1)).
thf(rc1_funct_2, axiom,  (! [A: $i, B: $i] :  (? [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( ( (v5_relat_1 @ C)  @ B)  &  ( (v1_funct_1 @ C)  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) ) ) ) ) ) ) ) , file(funct_2, rc1_funct_2)).
thf(rc1_membered, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v6_membered @ A) ) ) , file(membered, rc1_membered)).
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_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_valued_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) ) ) , file(valued_1, rc1_valued_1)).
thf(rc1_xboole_0, axiom,  (? [A: $i] :  (v1_xboole_0 @ A) ) , file(xboole_0, rc1_xboole_0)).
thf(rc1_xcmplx_0, axiom,  (? [A: $i] :  (v1_xcmplx_0 @ A) ) , file(xcmplx_0, rc1_xcmplx_0)).
thf(rc1_xreal_0, axiom,  (? [A: $i] :  (v1_xreal_0 @ A) ) , file(xreal_0, rc1_xreal_0)).
thf(rc1_xxreal_0, axiom,  (? [A: $i] :  (v1_xxreal_0 @ A) ) , file(xxreal_0, rc1_xxreal_0)).
thf(rc20_struct_0, axiom,  (? [A: $i] :  ( (l2_struct_0 @ A)  &  ( ~ ( (v2_struct_0 @ A) )  &  (v7_struct_0 @ A) ) ) ) , file(struct_0, rc20_struct_0)).
thf(rc21_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_zfmisc_1 @ B) ) ) ) ) ) , file(struct_0, rc21_struct_0)).
thf(rc22_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v7_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ~ ( (v1_zfmisc_1 @ B) ) ) ) ) ) , file(struct_0, rc22_struct_0)).
thf(rc23_struct_0, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (? [B: $i] :  ( (l1_struct_0 @ B)  &  ( (v13_struct_0 @ B)  @ A) ) ) ) ) , file(struct_0, rc23_struct_0)).
thf(rc2_fdiff_1, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k1_numbers)  &  ( ( (v5_relat_1 @ A)  @ k1_numbers)  &  ( (v1_funct_1 @ A)  &  ( (v1_valued_0 @ A)  &  ( (v2_valued_0 @ A)  &  ( (v3_valued_0 @ A)  &  (v2_fdiff_1 @ A) ) ) ) ) ) ) ) ) ) , file(fdiff_1, rc2_fdiff_1)).
thf(rc2_funct_2, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  ( ( ( (v1_funct_2 @ B)  @ A)  @ A)  &  ( ( (v3_funct_2 @ B)  @ A)  @ A) ) ) ) ) ) ) ) ) ) , file(funct_2, rc2_funct_2)).
thf(rc2_membered, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v6_membered @ A) ) ) , file(membered, rc2_membered)).
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_valued_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ~ ( (v1_xboole_0 @ A) ) ) ) ) ) , file(valued_1, rc2_valued_1)).
thf(rc2_xboole_0, axiom,  (? [A: $i] :  ~ ( (v1_xboole_0 @ A) ) ) , file(xboole_0, rc2_xboole_0)).
thf(rc2_xcmplx_0, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, rc2_xcmplx_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_fdiff_1, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k1_numbers)  &  ( ( (v5_relat_1 @ A)  @ k1_numbers)  &  ( (v1_funct_1 @ A)  &  ( (v1_valued_0 @ A)  &  ( (v2_valued_0 @ A)  &  ( (v3_valued_0 @ A)  &  (v3_fdiff_1 @ A) ) ) ) ) ) ) ) ) ) , file(fdiff_1, rc3_fdiff_1)).
thf(rc3_membered, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v6_membered @ A)  &  (v7_membered @ A) ) ) ) , file(membered, rc3_membered)).
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_valued_0, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k5_numbers) ) )  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( ( (v5_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ( ( (v1_partfun1 @ A)  @ k5_numbers)  &  ( ( ( (v1_funct_2 @ A)  @ k5_numbers)  @ k5_numbers)  &  ( (v1_valued_0 @ A)  &  ( (v2_valued_0 @ A)  &  ( (v3_valued_0 @ A)  &  ( (v4_valued_0 @ A)  &  (v5_valued_0 @ A) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(valued_0, rc3_valued_0)).
thf(rc3_valued_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_finset_1 @ A) ) ) ) ) ) , file(valued_1, rc3_valued_1)).
thf(rc3_xreal_0, axiom,  (? [A: $i] :  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc3_xreal_0)).
thf(rc3_xxreal_0, axiom,  (? [A: $i] :  ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) ) ) , file(xxreal_0, rc3_xxreal_0)).
thf(rc4_ordinal1, axiom,  (? [A: $i] :  (v7_ordinal1 @ A) ) , file(ordinal1, rc4_ordinal1)).
thf(rc4_struct_0, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_struct_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  (u1_struct_0 @ A) ) )  &  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) , file(struct_0, rc4_struct_0)).
thf(rc4_valued_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  ( (v3_card_1 @ A)  @ np__1) ) ) ) ) ) , file(valued_1, rc4_valued_1)).
thf(rc4_xreal_0, axiom,  (? [A: $i] :  ( (v1_xboole_0 @ A)  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc4_xreal_0)).
thf(rc4_xxreal_0, axiom,  (? [A: $i] :  ( (v1_xboole_0 @ A)  &  (v1_xxreal_0 @ A) ) ) , file(xxreal_0, rc4_xxreal_0)).
thf(rc5_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v7_ordinal1 @ A) ) ) , file(ordinal1, rc5_ordinal1)).
thf(rc5_valued_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( ( (v5_relat_1 @ B)  @ k3_numbers)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  ( (v1_valued_0 @ B)  &  ( (v2_valued_0 @ B)  &  ( (v3_valued_0 @ B)  &  (v4_valued_0 @ B) ) ) ) ) ) ) ) ) ) ) , file(valued_1, rc5_valued_1)).
thf(rc6_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(redefinition_k10_rvsum_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  &  (v1_xreal_0 @ B) )  =>  ( ( (k10_rvsum_1 @ A)  @ B)  =  ( (k24_valued_1 @ A)  @ B) ) ) ) , file(rvsum_1, k10_rvsum_1)).
thf(redefinition_k11_binop_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  ( ( (k11_binop_2 @ A)  @ B)  =  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) , file(binop_2, k11_binop_2)).
thf(redefinition_k11_pdiff_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (m1_subset_1 @ A)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ B)  @ k5_numbers)  &  ( ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ A) )  @ k1_numbers) ) ) )  &  ( (m1_subset_1 @ D)  @  (k1_euclid @ A) ) ) ) )  =>  ( ( ( ( (k11_pdiff_1 @ A)  @ B)  @ C)  @ D)  =  ( ( ( (k10_pdiff_1 @ A)  @ B)  @ C)  @ D) ) ) ) , file(pdiff_1, k11_pdiff_1)).
thf(redefinition_k12_finseq_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (m1_subset_1 @ B)  @ A) )  =>  ( ( (k12_finseq_1 @ A)  @ B)  =  (k5_finseq_1 @ B) ) ) ) , file(finseq_1, k12_finseq_1)).
thf(redefinition_k12_rvsum_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  =>  ( (k12_rvsum_1 @ A)  =  (k39_valued_1 @ A) ) ) ) , file(rvsum_1, k12_rvsum_1)).
thf(redefinition_k17_complex1, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (k17_complex1 @ A)  =  (k16_complex1 @ A) ) ) ) , file(complex1, k17_complex1)).
thf(redefinition_k17_lopban_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  ( (v3_normsp_0 @ A)  &  ( (v4_normsp_0 @ A)  &  ( (v2_normsp_1 @ A)  &  (l1_normsp_1 @ A) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ( ~ ( (v2_struct_0 @ B) )  &  ( (v13_algstr_0 @ B)  &  ( (v2_rlvect_1 @ B)  &  ( (v3_rlvect_1 @ B)  &  ( (v4_rlvect_1 @ B)  &  ( (v5_rlvect_1 @ B)  &  ( (v6_rlvect_1 @ B)  &  ( (v7_rlvect_1 @ B)  &  ( (v8_rlvect_1 @ B)  &  ( (v3_normsp_0 @ B)  &  ( (v4_normsp_0 @ B)  &  ( (v2_normsp_1 @ B)  &  (l1_normsp_1 @ B) ) ) ) ) ) ) ) ) ) ) ) )  &  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @  ( (k16_lopban_1 @ A)  @ B) ) )  &  ( (m1_subset_1 @ D)  @  (u1_struct_0 @ A) ) ) ) )  =>  ( ( ( ( (k17_lopban_1 @ A)  @ B)  @ C)  @ D)  =  ( (k1_funct_1 @ C)  @ D) ) ) ) , file(lopban_1, k17_lopban_1)).
thf(redefinition_k18_complex1, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (k18_complex1 @ A)  =  (k16_complex1 @ A) ) ) ) , file(complex1, k18_complex1)).
thf(redefinition_k18_rvsum_1, axiom,  (! [A: $i] :  ( ( (m1_finseq_1 @ A)  @ k1_numbers)  =>  ( (k18_rvsum_1 @ A)  =  (k16_rvsum_1 @ A) ) ) ) , file(rvsum_1, k18_rvsum_1)).
thf(redefinition_k19_euclid, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  ( ( (k19_euclid @ A)  @ B)  =  ( (k10_finseq_1 @ A)  @ B) ) ) ) , file(euclid, k19_euclid)).
thf(redefinition_k1_finseq_7, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (m1_finseq_1 @ B)  @ A)  &  ( (v7_ordinal1 @ C)  &  ( (m1_subset_1 @ D)  @ A) ) ) )  =>  ( ( ( ( (k1_finseq_7 @ A)  @ B)  @ C)  @ D)  =  ( ( (k2_funct_7 @ B)  @ C)  @ D) ) ) ) , file(finseq_7, k1_finseq_7)).
thf(redefinition_k1_normsp_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_struct_0 @ A) )  &  ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ k5_numbers)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @  (u1_struct_0 @ A) ) ) ) ) )  &  ( (m1_subset_1 @ C)  @ k5_numbers) ) )  =>  ( ( ( (k1_normsp_1 @ A)  @ B)  @ C)  =  ( (k1_funct_1 @ B)  @ C) ) ) ) , file(normsp_1, k1_normsp_1)).
thf(redefinition_k1_partfun1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] :  ( ( ( (v1_funct_1 @ E)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  &  ( (v1_funct_1 @ F)  &  ( (m1_subset_1 @ F)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ C)  @ D) ) ) ) )  =>  ( ( ( ( ( ( (k1_partfun1 @ A)  @ B)  @ C)  @ D)  @ E)  @ F)  =  ( (k3_relat_1 @ E)  @ F) ) ) ) , file(partfun1, k1_partfun1)).
thf(redefinition_k1_real_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  ( (k1_real_1 @ A)  =  (k4_xcmplx_0 @ A) ) ) ) , file(real_1, k1_real_1)).
thf(redefinition_k1_relset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  =>  ( ( (k1_relset_1 @ A)  @ B)  =  (k9_xtuple_0 @ B) ) ) ) , file(relset_1, k1_relset_1)).
thf(redefinition_k1_rvsum_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  ( (k1_rvsum_1 @ A)  =  (k10_xtuple_0 @ A) ) ) ) , file(rvsum_1, k1_rvsum_1)).
thf(redefinition_k1_seq_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_valued_0 @ A) ) )  =>  ( ( (k1_seq_1 @ A)  @ B)  =  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(seq_1, k1_seq_1)).
thf(redefinition_k20_valued_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( (v3_membered @ B)  &  ( (v3_membered @ C)  &  ( ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  &  ( (v1_funct_1 @ E)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) )  =>  ( ( ( ( ( (k20_valued_1 @ A)  @ B)  @ C)  @ D)  @ E)  =  ( (k18_valued_1 @ D)  @ E) ) ) ) , file(valued_1, k20_valued_1)).
thf(redefinition_k2_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (k2_finseq_1 @ A)  =  (k1_finseq_1 @ A) ) ) ) , file(finseq_1, k2_finseq_1)).
thf(redefinition_k2_finseq_4, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (m1_subset_1 @ B)  @ A)  &  ( (m1_subset_1 @ C)  @ A) ) )  =>  ( ( ( (k2_finseq_4 @ A)  @ B)  @ C)  =  ( (k10_finseq_1 @ B)  @ C) ) ) ) , file(finseq_4, k2_finseq_4)).
thf(redefinition_k2_rcomp_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v1_xxreal_0 @ B) )  =>  ( ( (k2_rcomp_1 @ A)  @ B)  =  ( (k4_xxreal_1 @ A)  @ B) ) ) ) , file(rcomp_1, k2_rcomp_1)).
thf(redefinition_k2_real_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  ( (k2_real_1 @ A)  =  (k5_xcmplx_0 @ A) ) ) ) , file(real_1, k2_real_1)).
thf(redefinition_k2_relset_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) )  =>  ( ( (k2_relset_1 @ A)  @ B)  =  (k10_xtuple_0 @ B) ) ) ) , file(relset_1, k2_relset_1)).
thf(redefinition_k2_seq_2, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k5_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k1_numbers) ) ) ) )  =>  ( (k2_seq_2 @ A)  =  (k1_seq_2 @ A) ) ) ) , file(seq_2, k2_seq_2)).
thf(redefinition_k37_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v3_membered @ B)  &  ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  =>  ( ( ( (k37_valued_1 @ A)  @ B)  @ C)  =  (k35_valued_1 @ C) ) ) ) , file(valued_1, k37_valued_1)).
thf(redefinition_k3_complex1, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (k3_complex1 @ A)  =  (k1_complex1 @ A) ) ) ) , file(complex1, k3_complex1)).
thf(redefinition_k3_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (k3_finseq_1 @ A)  =  (k1_card_1 @ A) ) ) ) , file(finseq_1, k3_finseq_1)).
thf(redefinition_k3_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (m1_subset_1 @ D)  @ A) ) )  =>  ( ( ( ( (k3_funct_2 @ A)  @ B)  @ C)  @ D)  =  ( (k1_funct_1 @ C)  @ D) ) ) ) , file(funct_2, k3_funct_2)).
thf(redefinition_k3_rlvect_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v2_rlvect_1 @ A)  &  (l1_algstr_0 @ A) )  &  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ C)  @  (u1_struct_0 @ A) ) ) )  =>  ( ( ( (k3_rlvect_1 @ A)  @ B)  @ C)  =  ( ( (k1_algstr_0 @ A)  @ B)  @ C) ) ) ) , file(rlvect_1, k3_rlvect_1)).
thf(redefinition_k4_complex1, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (k4_complex1 @ A)  =  (k2_complex1 @ A) ) ) ) , file(complex1, k4_complex1)).
thf(redefinition_k4_normsp_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ A) )  &  (l1_normsp_0 @ A) )  &  ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ k5_numbers)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @  (u1_struct_0 @ A) ) ) ) ) ) )  =>  ( ( (k4_normsp_0 @ A)  @ B)  =  ( (k2_normsp_0 @ A)  @ B) ) ) ) , file(normsp_0, k4_normsp_0)).
thf(redefinition_k4_rvsum_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v3_valued_0 @ B)  &  (v1_finseq_1 @ B) ) ) ) )  =>  ( ( (k4_rvsum_1 @ A)  @ B)  =  ( (k1_valued_1 @ A)  @ B) ) ) ) , file(rvsum_1, k4_rvsum_1)).
thf(redefinition_k56_valued_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_membered @ B)  &  ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  =>  ( ( ( (k56_valued_1 @ A)  @ B)  @ C)  =  (k54_valued_1 @ C) ) ) ) , file(valued_1, k56_valued_1)).
thf(redefinition_k5_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (k5_euclid @ A)  =  (k4_euclid @ A) ) ) ) , file(euclid, k5_euclid)).
thf(redefinition_k5_finseq_2, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (v7_ordinal1 @ B)  &  ( (m1_subset_1 @ C)  @ A) ) )  =>  ( ( ( (k5_finseq_2 @ A)  @ B)  @ C)  =  ( (k2_finseq_2 @ B)  @ C) ) ) ) , file(finseq_2, k5_finseq_2)).
thf(redefinition_k5_numbers, axiom,  (k5_numbers = k4_ordinal1) , file(numbers, k5_numbers)).
thf(redefinition_k5_square_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  ( (k5_square_1 @ A)  =  (k3_square_1 @ A) ) ) ) , file(square_1, k5_square_1)).
thf(redefinition_k6_numbers, axiom,  (k6_numbers = k1_xboole_0) , file(numbers, k6_numbers)).
thf(redefinition_k6_partfun1, axiom,  (! [A: $i] :  ( (k6_partfun1 @ A)  =  (k4_relat_1 @ A) ) ) , file(partfun1, k6_partfun1)).
thf(redefinition_k6_pdiff_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (m1_subset_1 @ A)  @ k5_numbers)  &  ( ( (m1_subset_1 @ B)  @ k5_numbers)  &  ( (m1_subset_1 @ C)  @  (k1_euclid @ A) ) ) )  =>  ( ( ( (k6_pdiff_1 @ A)  @ B)  @ C)  =  ( (k5_pdiff_1 @ B)  @ C) ) ) ) , file(pdiff_1, k6_pdiff_1)).
thf(redefinition_k6_rvsum_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  =>  ( (k6_rvsum_1 @ A)  =  (k30_valued_1 @ A) ) ) ) , file(rvsum_1, k6_rvsum_1)).
thf(redefinition_k7_binop_2, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  ( (k7_binop_2 @ A)  =  (k4_xcmplx_0 @ A) ) ) ) , file(binop_2, k7_binop_2)).
thf(redefinition_k7_euclid, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v7_ordinal1 @ A)  &  ( ( (m1_subset_1 @ B)  @  (k1_euclid @ A) )  &  ( (m1_subset_1 @ C)  @  (k1_euclid @ A) ) ) )  =>  ( ( ( (k7_euclid @ A)  @ B)  @ C)  =  ( (k1_valued_1 @ B)  @ C) ) ) ) , file(euclid, k7_euclid)).
thf(redefinition_k7_finseqop, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A) ) ) ) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ A)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) )  &  ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ A)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) ) ) ) )  =>  ( ( ( ( (k7_finseqop @ A)  @ B)  @ C)  @ D)  =  ( ( (k6_finseqop @ B)  @ C)  @ D) ) ) ) , file(finseqop, k7_finseqop)).
thf(redefinition_k7_real_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k1_numbers)  &  (v1_xreal_0 @ B) )  =>  ( ( (k7_real_1 @ A)  @ B)  =  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(real_1, k7_real_1)).
thf(redefinition_k7_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( ( ( (k7_relset_1 @ A)  @ B)  @ C)  @ D)  =  ( (k7_relat_1 @ C)  @ D) ) ) ) , file(relset_1, k7_relset_1)).
thf(redefinition_k7_square_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  ( (k7_square_1 @ A)  =  (k6_square_1 @ A) ) ) ) , file(square_1, k7_square_1)).
thf(redefinition_k8_euclid, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v7_ordinal1 @ A)  &  ( ( (m1_subset_1 @ B)  @  (k1_euclid @ A) )  &  ( (m1_subset_1 @ C)  @  (k1_euclid @ A) ) ) )  =>  ( ( ( (k8_euclid @ A)  @ B)  @ C)  =  ( (k45_valued_1 @ B)  @ C) ) ) ) , file(euclid, k8_euclid)).
thf(redefinition_k8_funcop_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( (m1_subset_1 @ C)  @ A) )  =>  ( ( ( (k8_funcop_1 @ A)  @ B)  @ C)  =  ( (k2_funcop_1 @ B)  @ C) ) ) ) , file(funcop_1, k8_funcop_1)).
thf(redefinition_k8_real_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k1_numbers)  &  (v1_xreal_0 @ B) )  =>  ( ( (k8_real_1 @ A)  @ B)  =  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) , file(real_1, k8_real_1)).
thf(redefinition_k8_rvsum_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v3_valued_0 @ B)  &  (v1_finseq_1 @ B) ) ) ) )  =>  ( ( (k8_rvsum_1 @ A)  @ B)  =  ( (k45_valued_1 @ A)  @ B) ) ) ) , file(rvsum_1, k8_rvsum_1)).
thf(redefinition_k9_binop_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  ( ( (k9_binop_2 @ A)  @ B)  =  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(binop_2, k9_binop_2)).
thf(redefinition_k9_euclid, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v7_ordinal1 @ A)  &  ( ( (m1_subset_1 @ B)  @  (k1_euclid @ A) )  &  (v1_xreal_0 @ C) ) )  =>  ( ( ( (k9_euclid @ A)  @ B)  @ C)  =  ( (k24_valued_1 @ B)  @ C) ) ) ) , file(euclid, k9_euclid)).
thf(redefinition_k9_finseq_1, axiom,  (! [A: $i] :  ( (k9_finseq_1 @ A)  =  (k5_finseq_1 @ A) ) ) , file(finseq_1, k9_finseq_1)).
thf(redefinition_k9_funct_2, axiom,  (! [A: $i, B: $i] :  ( ~ ( (v1_xboole_0 @ B) )  =>  ( ( (k9_funct_2 @ A)  @ B)  =  ( (k1_funct_2 @ A)  @ B) ) ) ) , file(funct_2, k9_funct_2)).
thf(redefinition_k9_real_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k1_numbers)  &  (v1_xreal_0 @ B) )  =>  ( ( (k9_real_1 @ A)  @ B)  =  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(real_1, k9_real_1)).
thf(redefinition_m2_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m2_finseq_1 @ B)  @ A)  <=>  ( (m1_finseq_1 @ B)  @ A) ) ) ) , file(finseq_1, m2_finseq_1)).
thf(redefinition_m2_finseq_2, axiom,  (! [A: $i, B: $i] :  ( ( (m1_finseq_2 @ B)  @ A)  =>  (! [C: $i] :  ( ( ( (m2_finseq_2 @ C)  @ A)  @ B)  <=>  ( (m1_subset_1 @ C)  @ B) ) ) ) ) , file(finseq_2, m2_finseq_2)).
thf(redefinition_m2_funct_2, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( ( (m1_funct_2 @ C)  @ A)  @ B) )  =>  (! [D: $i] :  ( ( ( ( (m2_funct_2 @ D)  @ A)  @ B)  @ C)  <=>  ( (m1_subset_1 @ D)  @ C) ) ) ) ) , file(funct_2, m2_funct_2)).
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(redefinition_r1_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( ~ ( (v1_xboole_0 @ D) )  &  ( ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ B)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ F)  &  ( ( ( (v1_funct_2 @ F)  @ C)  @ D)  &  ( (m1_subset_1 @ F)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ C)  @ D) ) ) ) ) ) ) )  =>  ( ( ( ( ( ( (r1_funct_2 @ A)  @ B)  @ C)  @ D)  @ E)  @ F)  <=>  (E = F) ) ) ) , file(funct_2, r1_funct_2)).
thf(redefinition_r2_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  =>  ( ( ( ( (r2_relset_1 @ A)  @ B)  @ C)  @ D)  <=>  (C = D) ) ) ) , file(relset_1, r2_relset_1)).
thf(reflexivity_r1_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( ~ ( (v1_xboole_0 @ D) )  &  ( ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ B)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ F)  &  ( ( ( (v1_funct_2 @ F)  @ C)  @ D)  &  ( (m1_subset_1 @ F)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ C)  @ D) ) ) ) ) ) ) )  =>  ( ( ( ( ( (r1_funct_2 @ A)  @ B)  @ C)  @ D)  @ E)  @ E) ) ) , file(funct_2, r1_funct_2)).
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(reflexivity_r2_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  =>  ( ( ( (r2_relset_1 @ A)  @ B)  @ C)  @ C) ) ) , file(relset_1, r2_relset_1)).
thf(rqLessOrEqual__r1_xxreal_0__r0_r0, axiom,  ( (r1_xxreal_0 @ np__0)  @ np__0) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_r0)).
thf(rqLessOrEqual__r1_xxreal_0__r0_r1, axiom,  ( (r1_xxreal_0 @ np__0)  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r0_r2, axiom,  ( (r1_xxreal_0 @ np__0)  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r0_r3, axiom,  ( (r1_xxreal_0 @ np__0)  @ np__3) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_r3)).
thf(rqLessOrEqual__r1_xxreal_0__r0_rm1, axiom,  ~ ( ( (r1_xxreal_0 @ np__0)  @  (k4_xcmplx_0 @ np__1) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__r0_rm2, axiom,  ~ ( ( (r1_xxreal_0 @ np__0)  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__r0_rm3, axiom,  ~ ( ( (r1_xxreal_0 @ np__0)  @  (k4_xcmplx_0 @ np__3) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_rm3)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r0, axiom,  ~ ( ( (r1_xxreal_0 @ np__1)  @ np__0) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r0)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r1, axiom,  ( (r1_xxreal_0 @ np__1)  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r2, axiom,  ( (r1_xxreal_0 @ np__1)  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r3, axiom,  ( (r1_xxreal_0 @ np__1)  @ np__3) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r3)).
thf(rqLessOrEqual__r1_xxreal_0__r1_rm1, axiom,  ~ ( ( (r1_xxreal_0 @ np__1)  @  (k4_xcmplx_0 @ np__1) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__r1_rm2, axiom,  ~ ( ( (r1_xxreal_0 @ np__1)  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__r1_rm3, axiom,  ~ ( ( (r1_xxreal_0 @ np__1)  @  (k4_xcmplx_0 @ np__3) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_rm3)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r0, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @ np__0) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_r0)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r1, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r2, axiom,  ( (r1_xxreal_0 @ np__2)  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r3, axiom,  ( (r1_xxreal_0 @ np__2)  @ np__3) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_r3)).
thf(rqLessOrEqual__r1_xxreal_0__r2_rm1, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @  (k4_xcmplx_0 @ np__1) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__r2_rm2, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__r2_rm3, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @  (k4_xcmplx_0 @ np__3) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_rm3)).
thf(rqLessOrEqual__r1_xxreal_0__r3_r0, axiom,  ~ ( ( (r1_xxreal_0 @ np__3)  @ np__0) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_r0)).
thf(rqLessOrEqual__r1_xxreal_0__r3_r1, axiom,  ~ ( ( (r1_xxreal_0 @ np__3)  @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r3_r2, axiom,  ~ ( ( (r1_xxreal_0 @ np__3)  @ np__2) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r3_r3, axiom,  ( (r1_xxreal_0 @ np__3)  @ np__3) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_r3)).
thf(rqLessOrEqual__r1_xxreal_0__r3_rm1, axiom,  ~ ( ( (r1_xxreal_0 @ np__3)  @  (k4_xcmplx_0 @ np__1) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__r3_rm2, axiom,  ~ ( ( (r1_xxreal_0 @ np__3)  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__r3_rm3, axiom,  ~ ( ( (r1_xxreal_0 @ np__3)  @  (k4_xcmplx_0 @ np__3) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_rm3)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_r0, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @ np__0) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_r0)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_r1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_r1)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_r2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_r2)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_r3, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @ np__3) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_r3)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_rm1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_rm2, axiom,  ~ ( ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_rm3, axiom,  ~ ( ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__3) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_rm3)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_r0, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @ np__0) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_r0)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_r1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_r1)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_r2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_r2)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_r3, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @ np__3) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_r3)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_rm1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_rm2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_rm3, axiom,  ~ ( ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__3) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_rm3)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_r0, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @ np__0) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_r0)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_r1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_r1)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_r2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_r2)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_r3, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @ np__3) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_r3)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_rm1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_rm2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_rm3, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_rm3)).
thf(rqRealAdd__k2_xcmplx_0__r0_r0_r0, axiom,  ( ( (k2_xcmplx_0 @ np__0)  @ np__0)  = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r0_r0)).
thf(rqRealAdd__k2_xcmplx_0__r0_r1_r1, axiom,  ( ( (k2_xcmplx_0 @ np__0)  @ np__1)  = np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r1_r1)).
thf(rqRealAdd__k2_xcmplx_0__r0_r2_r2, axiom,  ( ( (k2_xcmplx_0 @ np__0)  @ np__2)  = np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r2_r2)).
thf(rqRealAdd__k2_xcmplx_0__r0_r3_r3, axiom,  ( ( (k2_xcmplx_0 @ np__0)  @ np__3)  = np__3) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r3_r3)).
thf(rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, axiom,  ( ( (k2_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__1) )  =  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1)).
thf(rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, axiom,  ( ( (k2_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__2) )  =  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2)).
thf(rqRealAdd__k2_xcmplx_0__r0_rm3_rm3, axiom,  ( ( (k2_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__3) )  =  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm3_rm3)).
thf(rqRealAdd__k2_xcmplx_0__r1_r0_r1, axiom,  ( ( (k2_xcmplx_0 @ np__1)  @ np__0)  = np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r0_r1)).
thf(rqRealAdd__k2_xcmplx_0__r1_r1_r2, axiom,  ( ( (k2_xcmplx_0 @ np__1)  @ np__1)  = np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r1_r2)).
thf(rqRealAdd__k2_xcmplx_0__r1_r2_r3, axiom,  ( ( (k2_xcmplx_0 @ np__1)  @ np__2)  = np__3) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r2_r3)).
thf(rqRealAdd__k2_xcmplx_0__r1_rm1_r0, axiom,  ( ( (k2_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__1) )  = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm1_r0)).
thf(rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, axiom,  ( ( (k2_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__2) )  =  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1)).
thf(rqRealAdd__k2_xcmplx_0__r1_rm3_rm2, axiom,  ( ( (k2_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__3) )  =  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm3_rm2)).
thf(rqRealAdd__k2_xcmplx_0__r2_r0_r2, axiom,  ( ( (k2_xcmplx_0 @ np__2)  @ np__0)  = np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_r0_r2)).
thf(rqRealAdd__k2_xcmplx_0__r2_r1_r3, axiom,  ( ( (k2_xcmplx_0 @ np__2)  @ np__1)  = np__3) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_r1_r3)).
thf(rqRealAdd__k2_xcmplx_0__r2_rm1_r1, axiom,  ( ( (k2_xcmplx_0 @ np__2)  @  (k4_xcmplx_0 @ np__1) )  = np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm1_r1)).
thf(rqRealAdd__k2_xcmplx_0__r2_rm2_r0, axiom,  ( ( (k2_xcmplx_0 @ np__2)  @  (k4_xcmplx_0 @ np__2) )  = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm2_r0)).
thf(rqRealAdd__k2_xcmplx_0__r2_rm3_rm1, axiom,  ( ( (k2_xcmplx_0 @ np__2)  @  (k4_xcmplx_0 @ np__3) )  =  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm3_rm1)).
thf(rqRealAdd__k2_xcmplx_0__r3_r0_r3, axiom,  ( ( (k2_xcmplx_0 @ np__3)  @ np__0)  = np__3) , file(arithm, rqRealAdd__k2_xcmplx_0__r3_r0_r3)).
thf(rqRealAdd__k2_xcmplx_0__r3_rm1_r2, axiom,  ( ( (k2_xcmplx_0 @ np__3)  @  (k4_xcmplx_0 @ np__1) )  = np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r3_rm1_r2)).
thf(rqRealAdd__k2_xcmplx_0__r3_rm2_r1, axiom,  ( ( (k2_xcmplx_0 @ np__3)  @  (k4_xcmplx_0 @ np__2) )  = np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r3_rm2_r1)).
thf(rqRealAdd__k2_xcmplx_0__r3_rm3_r0, axiom,  ( ( (k2_xcmplx_0 @ np__3)  @  (k4_xcmplx_0 @ np__3) )  = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r3_rm3_r0)).
thf(rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, axiom,  ( ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__0)  =  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1)).
thf(rqRealAdd__k2_xcmplx_0__rm1_r1_r0, axiom,  ( ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__1)  = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r1_r0)).
thf(rqRealAdd__k2_xcmplx_0__rm1_r2_r1, axiom,  ( ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2)  = np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r2_r1)).
thf(rqRealAdd__k2_xcmplx_0__rm1_r3_r2, axiom,  ( ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__3)  = np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r3_r2)).
thf(rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, axiom,  ( ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__1) )  =  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2)).
thf(rqRealAdd__k2_xcmplx_0__rm1_rm2_rm3, axiom,  ( ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__2) )  =  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_rm2_rm3)).
thf(rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, axiom,  ( ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__1)  =  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1)).
thf(rqRealAdd__k2_xcmplx_0__rm2_r2_r0, axiom,  ( ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__2)  = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r2_r0)).
thf(rqRealAdd__k2_xcmplx_0__rm2_r3_r1, axiom,  ( ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__3)  = np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r3_r1)).
thf(rqRealAdd__k2_xcmplx_0__rm2_rm1_rm3, axiom,  ( ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__1) )  =  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_rm1_rm3)).
thf(rqRealAdd__k2_xcmplx_0__rm3_r1_rm2, axiom,  ( ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @ np__1)  =  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm3_r1_rm2)).
thf(rqRealAdd__k2_xcmplx_0__rm3_r2_rm1, axiom,  ( ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @ np__2)  =  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm3_r2_rm1)).
thf(rqRealAdd__k2_xcmplx_0__rm3_r3_r0, axiom,  ( ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @ np__3)  = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm3_r3_r0)).
thf(rqRealDiff__k6_xcmplx_0__r0_r0_r0, axiom,  ( ( (k6_xcmplx_0 @ np__0)  @ np__0)  = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r0_r0)).
thf(rqRealDiff__k6_xcmplx_0__r0_r1_rm1, axiom,  ( ( (k6_xcmplx_0 @ np__0)  @ np__1)  =  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r1_rm1)).
thf(rqRealDiff__k6_xcmplx_0__r0_r2_rm2, axiom,  ( ( (k6_xcmplx_0 @ np__0)  @ np__2)  =  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r2_rm2)).
thf(rqRealDiff__k6_xcmplx_0__r0_r3_rm3, axiom,  ( ( (k6_xcmplx_0 @ np__0)  @ np__3)  =  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r3_rm3)).
thf(rqRealDiff__k6_xcmplx_0__r0_rm1_r1, axiom,  ( ( (k6_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__1) )  = np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm1_r1)).
thf(rqRealDiff__k6_xcmplx_0__r0_rm2_r2, axiom,  ( ( (k6_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__2) )  = np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm2_r2)).
thf(rqRealDiff__k6_xcmplx_0__r0_rm3_r3, axiom,  ( ( (k6_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__3) )  = np__3) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm3_r3)).
thf(rqRealDiff__k6_xcmplx_0__r1_r0_r1, axiom,  ( ( (k6_xcmplx_0 @ np__1)  @ np__0)  = np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r0_r1)).
thf(rqRealDiff__k6_xcmplx_0__r1_r1_r0, axiom,  ( ( (k6_xcmplx_0 @ np__1)  @ np__1)  = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r1_r0)).
thf(rqRealDiff__k6_xcmplx_0__r1_r2_rm1, axiom,  ( ( (k6_xcmplx_0 @ np__1)  @ np__2)  =  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r2_rm1)).
thf(rqRealDiff__k6_xcmplx_0__r1_r3_rm2, axiom,  ( ( (k6_xcmplx_0 @ np__1)  @ np__3)  =  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r3_rm2)).
thf(rqRealDiff__k6_xcmplx_0__r1_rm1_r2, axiom,  ( ( (k6_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__1) )  = np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_rm1_r2)).
thf(rqRealDiff__k6_xcmplx_0__r1_rm2_r3, axiom,  ( ( (k6_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__2) )  = np__3) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_rm2_r3)).
thf(rqRealDiff__k6_xcmplx_0__r2_r0_r2, axiom,  ( ( (k6_xcmplx_0 @ np__2)  @ np__0)  = np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r0_r2)).
thf(rqRealDiff__k6_xcmplx_0__r2_r1_r1, axiom,  ( ( (k6_xcmplx_0 @ np__2)  @ np__1)  = np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r1_r1)).
thf(rqRealDiff__k6_xcmplx_0__r2_r2_r0, axiom,  ( ( (k6_xcmplx_0 @ np__2)  @ np__2)  = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r2_r0)).
thf(rqRealDiff__k6_xcmplx_0__r2_r3_rm1, axiom,  ( ( (k6_xcmplx_0 @ np__2)  @ np__3)  =  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r3_rm1)).
thf(rqRealDiff__k6_xcmplx_0__r2_rm1_r3, axiom,  ( ( (k6_xcmplx_0 @ np__2)  @  (k4_xcmplx_0 @ np__1) )  = np__3) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_rm1_r3)).
thf(rqRealDiff__k6_xcmplx_0__r3_r0_r3, axiom,  ( ( (k6_xcmplx_0 @ np__3)  @ np__0)  = np__3) , file(arithm, rqRealDiff__k6_xcmplx_0__r3_r0_r3)).
thf(rqRealDiff__k6_xcmplx_0__r3_r1_r2, axiom,  ( ( (k6_xcmplx_0 @ np__3)  @ np__1)  = np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r3_r1_r2)).
thf(rqRealDiff__k6_xcmplx_0__r3_r2_r1, axiom,  ( ( (k6_xcmplx_0 @ np__3)  @ np__2)  = np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r3_r2_r1)).
thf(rqRealDiff__k6_xcmplx_0__r3_r3_r0, axiom,  ( ( (k6_xcmplx_0 @ np__3)  @ np__3)  = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r3_r3_r0)).
thf(rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, axiom,  ( ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__0)  =  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1)).
thf(rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, axiom,  ( ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__1)  =  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2)).
thf(rqRealDiff__k6_xcmplx_0__rm1_r2_rm3, axiom,  ( ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2)  =  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r2_rm3)).
thf(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, axiom,  ( ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__1) )  = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0)).
thf(rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, axiom,  ( ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__2) )  = np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1)).
thf(rqRealDiff__k6_xcmplx_0__rm1_rm3_r2, axiom,  ( ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__3) )  = np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm3_r2)).
thf(rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, axiom,  ( ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__0)  =  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2)).
thf(rqRealDiff__k6_xcmplx_0__rm2_r1_rm3, axiom,  ( ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__1)  =  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_r1_rm3)).
thf(rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, axiom,  ( ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__1) )  =  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1)).
thf(rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, axiom,  ( ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__2) )  = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0)).
thf(rqRealDiff__k6_xcmplx_0__rm2_rm3_r1, axiom,  ( ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__3) )  = np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm3_r1)).
thf(rqRealDiff__k6_xcmplx_0__rm3_r0_rm3, axiom,  ( ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @ np__0)  =  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm3_r0_rm3)).
thf(rqRealDiff__k6_xcmplx_0__rm3_rm1_rm2, axiom,  ( ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__1) )  =  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm3_rm1_rm2)).
thf(rqRealDiff__k6_xcmplx_0__rm3_rm2_rm1, axiom,  ( ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__2) )  =  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm3_rm2_rm1)).
thf(rqRealDiff__k6_xcmplx_0__rm3_rm3_r0, axiom,  ( ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__3) )  = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm3_rm3_r0)).
thf(rqRealMult__k3_xcmplx_0__r0_r0_r0, axiom,  ( ( (k3_xcmplx_0 @ np__0)  @ np__0)  = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_r0_r0)).
thf(rqRealMult__k3_xcmplx_0__r0_r1_r0, axiom,  ( ( (k3_xcmplx_0 @ np__0)  @ np__1)  = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_r1_r0)).
thf(rqRealMult__k3_xcmplx_0__r0_r2_r0, axiom,  ( ( (k3_xcmplx_0 @ np__0)  @ np__2)  = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_r2_r0)).
thf(rqRealMult__k3_xcmplx_0__r0_r3_r0, axiom,  ( ( (k3_xcmplx_0 @ np__0)  @ np__3)  = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_r3_r0)).
thf(rqRealMult__k3_xcmplx_0__r0_rm2_r0, axiom,  ( ( (k3_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__2) )  = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_rm2_r0)).
thf(rqRealMult__k3_xcmplx_0__r0_rm3_r0, axiom,  ( ( (k3_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__3) )  = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_rm3_r0)).
thf(rqRealMult__k3_xcmplx_0__r1_r0_r0, axiom,  ( ( (k3_xcmplx_0 @ np__1)  @ np__0)  = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r1_r0_r0)).
thf(rqRealMult__k3_xcmplx_0__r1_r1_r1, axiom,  ( ( (k3_xcmplx_0 @ np__1)  @ np__1)  = np__1) , file(arithm, rqRealMult__k3_xcmplx_0__r1_r1_r1)).
thf(rqRealMult__k3_xcmplx_0__r1_r2_r2, axiom,  ( ( (k3_xcmplx_0 @ np__1)  @ np__2)  = np__2) , file(arithm, rqRealMult__k3_xcmplx_0__r1_r2_r2)).
thf(rqRealMult__k3_xcmplx_0__r1_r3_r3, axiom,  ( ( (k3_xcmplx_0 @ np__1)  @ np__3)  = np__3) , file(arithm, rqRealMult__k3_xcmplx_0__r1_r3_r3)).
thf(rqRealMult__k3_xcmplx_0__r1_rm2_rm2, axiom,  ( ( (k3_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__2) )  =  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__r1_rm2_rm2)).
thf(rqRealMult__k3_xcmplx_0__r1_rm3_rm3, axiom,  ( ( (k3_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__3) )  =  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__r1_rm3_rm3)).
thf(rqRealMult__k3_xcmplx_0__r2_r0_r0, axiom,  ( ( (k3_xcmplx_0 @ np__2)  @ np__0)  = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r2_r0_r0)).
thf(rqRealMult__k3_xcmplx_0__r2_r1_r2, axiom,  ( ( (k3_xcmplx_0 @ np__2)  @ np__1)  = np__2) , file(arithm, rqRealMult__k3_xcmplx_0__r2_r1_r2)).
thf(rqRealMult__k3_xcmplx_0__r3_r0_r0, axiom,  ( ( (k3_xcmplx_0 @ np__3)  @ np__0)  = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r3_r0_r0)).
thf(rqRealMult__k3_xcmplx_0__r3_r1_r3, axiom,  ( ( (k3_xcmplx_0 @ np__3)  @ np__1)  = np__3) , file(arithm, rqRealMult__k3_xcmplx_0__r3_r1_r3)).
thf(rqRealMult__k3_xcmplx_0__rm2_r0_r0, axiom,  ( ( (k3_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__0)  = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__rm2_r0_r0)).
thf(rqRealMult__k3_xcmplx_0__rm2_r1_rm2, axiom,  ( ( (k3_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__1)  =  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rm2_r1_rm2)).
thf(rqRealMult__k3_xcmplx_0__rm3_r0_r0, axiom,  ( ( (k3_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @ np__0)  = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__rm3_r0_r0)).
thf(rqRealMult__k3_xcmplx_0__rm3_r1_rm3, axiom,  ( ( (k3_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @ np__1)  =  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rm3_r1_rm3)).
thf(rqRealNeg__k4_xcmplx_0__r0_r0, axiom,  ( (k4_xcmplx_0 @ np__0)  = np__0) , file(arithm, rqRealNeg__k4_xcmplx_0__r0_r0)).
thf(rqRealNeg__k4_xcmplx_0__r1_rm1, axiom,  ( (k4_xcmplx_0 @ np__1)  =  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r1_rm1)).
thf(rqRealNeg__k4_xcmplx_0__r2_rm2, axiom,  ( (k4_xcmplx_0 @ np__2)  =  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r2_rm2)).
thf(rqRealNeg__k4_xcmplx_0__r3_rm3, axiom,  ( (k4_xcmplx_0 @ np__3)  =  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r3_rm3)).
thf(rqRealNeg__k4_xcmplx_0__rm1_r1, axiom,  ( (k4_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  = np__1) , file(arithm, rqRealNeg__k4_xcmplx_0__rm1_r1)).
thf(rqRealNeg__k4_xcmplx_0__rm2_r2, axiom,  ( (k4_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  = np__2) , file(arithm, rqRealNeg__k4_xcmplx_0__rm2_r2)).
thf(rqRealNeg__k4_xcmplx_0__rm3_r3, axiom,  ( (k4_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  = np__3) , file(arithm, rqRealNeg__k4_xcmplx_0__rm3_r3)).
thf(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(spc10_arithm, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( ( (k3_xcmplx_0 @  (k5_xcmplx_0 @ A) )  @  (k5_xcmplx_0 @ B) )  =  (k5_xcmplx_0 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) ) , file(arithm, spc10_arithm)).
thf(spc1_arithm, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( ( (k2_xcmplx_0 @ A)  @  (k4_xcmplx_0 @ B) )  =  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(arithm, spc1_arithm)).
thf(spc1_boole, axiom,  ~ ( (v1_xboole_0 @ np__1) ) , file(boole, spc1_boole)).
thf(spc1_numerals, axiom,  ( ( (v2_xxreal_0 @ np__1)  &  ( ( (m2_subset_1 @ np__1)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ np__1)  @ k5_numbers)  &  ( (m1_subset_1 @ np__1)  @ k1_numbers) ) ) , file(numerals, spc1_numerals)).
thf(spc2_arithm, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( ( (k3_xcmplx_0 @ A)  @  (k4_xcmplx_0 @ np__1) )  =  (k4_xcmplx_0 @ A) ) ) ) , file(arithm, spc2_arithm)).
thf(spc2_boole, axiom,  ~ ( (v1_xboole_0 @ np__2) ) , file(boole, spc2_boole)).
thf(spc2_numerals, axiom,  ( ( (v2_xxreal_0 @ np__2)  &  ( ( (m2_subset_1 @ np__2)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ np__2)  @ k5_numbers)  &  ( (m1_subset_1 @ np__2)  @ k1_numbers) ) ) , file(numerals, spc2_numerals)).
thf(spc3_boole, axiom,  ~ ( (v1_xboole_0 @ np__3) ) , file(boole, spc3_boole)).
thf(spc3_numerals, axiom,  ( ( (v2_xxreal_0 @ np__3)  &  ( ( (m2_subset_1 @ np__3)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ np__3)  @ k5_numbers)  &  ( (m1_subset_1 @ np__3)  @ k1_numbers) ) ) , file(numerals, spc3_numerals)).
thf(spc5_arithm, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_xcmplx_0 @ A)  &  ( (v1_xcmplx_0 @ B)  &  (v1_xcmplx_0 @ C) ) )  =>  ( ( (k3_xcmplx_0 @  ( (k2_xcmplx_0 @ A)  @ B) )  @ C)  =  ( (k2_xcmplx_0 @  ( (k3_xcmplx_0 @ A)  @ C) )  @  ( (k3_xcmplx_0 @ B)  @ C) ) ) ) ) , file(arithm, spc5_arithm)).
thf(spc6_arithm, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_xcmplx_0 @ A)  &  ( (v1_xcmplx_0 @ B)  &  (v1_xcmplx_0 @ C) ) )  =>  ( ( (k2_xcmplx_0 @  ( (k2_xcmplx_0 @ A)  @ B) )  @ C)  =  ( (k2_xcmplx_0 @ A)  @  ( (k2_xcmplx_0 @ B)  @ C) ) ) ) ) , file(arithm, spc6_arithm)).
thf(spc7_arithm, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_xcmplx_0 @ A)  &  ( (v1_xcmplx_0 @ B)  &  (v1_xcmplx_0 @ C) ) )  =>  ( ( (k3_xcmplx_0 @  ( (k3_xcmplx_0 @ A)  @ B) )  @ C)  =  ( (k3_xcmplx_0 @ A)  @  ( (k3_xcmplx_0 @ B)  @ C) ) ) ) ) , file(arithm, spc6_arithm)).
thf(spc8_arithm, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ A) )  @  (k4_xcmplx_0 @ B) )  =  (k4_xcmplx_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) ) , file(arithm, spc8_arithm)).
thf(spc9_arithm, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ A) )  @  (k4_xcmplx_0 @ B) )  =  ( (k6_xcmplx_0 @ B)  @ A) ) ) ) , file(arithm, spc9_arithm)).
thf(symmetry_r1_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] :  ( ( ~ ( (v1_xboole_0 @ B) )  &  ( ~ ( (v1_xboole_0 @ D) )  &  ( ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ B)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ F)  &  ( ( ( (v1_funct_2 @ F)  @ C)  @ D)  &  ( (m1_subset_1 @ F)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ C)  @ D) ) ) ) ) ) ) )  =>  ( ( ( ( ( ( (r1_funct_2 @ A)  @ B)  @ C)  @ D)  @ E)  @ F)  =>  ( ( ( ( ( (r1_funct_2 @ A)  @ B)  @ C)  @ D)  @ F)  @ E) ) ) ) , file(funct_2, r1_funct_2)).
thf(symmetry_r2_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  =>  ( ( ( ( (r2_relset_1 @ A)  @ B)  @ C)  @ D)  =>  ( ( ( (r2_relset_1 @ A)  @ B)  @ D)  @ C) ) ) ) , file(relset_1, r2_relset_1)).
thf(t101_finseq_2, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @ A)  =>  ( (r2_hidden @  ( (k10_finseq_1 @ B)  @ C) )  @  ( (k4_finseq_2 @ np__2)  @ A) ) ) ) ) ) ) ) , file(finseq_2, t101_finseq_2)).
thf(t108_funct_2, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ~ ( (v1_xboole_0 @ C) )  =>  (! [D: $i] :  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ B)  @ C)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ C) ) ) ) )  =>  (! [E: $i] :  ( ( (v1_funct_1 @ E)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ C)  @ A) ) ) )  =>  (! [F: $i] :  ( ( (m1_subset_1 @ F)  @ B)  =>  ( ( (r1_tarski @  ( (k2_relset_1 @ C)  @ D) )  @  ( (k1_relset_1 @ C)  @ E) )  =>  ( (B = k1_xboole_0)  |  ( ( (k1_funct_1 @  ( ( ( ( (k8_funct_2 @ B)  @ A)  @ C)  @ D)  @ E) )  @ F)  =  ( (k1_funct_1 @ E)  @  ( (k1_funct_1 @ D)  @ F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(funct_2, t108_funct_2)).
thf(t109_funct_2, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ~ ( (v1_xboole_0 @ C) )  =>  (! [D: $i] :  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ B)  @ C)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ C) ) ) ) )  =>  (! [E: $i] :  ( ( (v1_funct_1 @ E)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ C)  @ A) ) ) )  =>  (! [F: $i] :  ( ( (m1_subset_1 @ F)  @ B)  =>  ( ( (r1_tarski @  ( (k2_relset_1 @ C)  @ D) )  @  ( (k1_relset_1 @ C)  @ E) )  =>  ( (B = k1_xboole_0)  |  ( ( (k1_funct_1 @  ( ( ( ( (k8_funct_2 @ B)  @ A)  @ C)  @ D)  @ E) )  @ F)  =  ( ( (k7_partfun1 @ A)  @ E)  @  ( (k1_funct_1 @ D)  @ F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(funct_2, t109_funct_2)).
thf(t10_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  (! [B: $i] :  ( ( (k1_funct_1 @  (k35_valued_1 @ A) )  @ B)  =  (k5_xcmplx_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, t10_valued_1)).
thf(t13_finseq_7, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @ A)  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @ A)  =>  ( ( ( ( (k1_finseq_7 @ A)  @  ( ( (k2_finseq_4 @ A)  @ B)  @ C) )  @ np__1)  @ D)  =  ( ( (k2_finseq_4 @ A)  @ D)  @ C) ) ) ) ) ) ) ) ) ) , file(finseq_7, t13_finseq_7)).
thf(t13_funct_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  (v1_funct_1 @ C) )  =>  ( ( (r2_hidden @ A)  @  (k9_xtuple_0 @ B) )  =>  ( ( (k1_funct_1 @  ( (k3_relat_1 @ B)  @ C) )  @ A)  =  ( (k1_funct_1 @ C)  @  ( (k1_funct_1 @ B)  @ A) ) ) ) ) ) ) ) ) , file(funct_1, t13_funct_1)).
thf(t13_rvsum_1, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (k4_rvsum_1 @  (k9_finseq_1 @ A) )  @  (k9_finseq_1 @ B) )  =  ( (k12_finseq_1 @ k1_numbers)  @  ( (k9_binop_2 @ A)  @ B) ) ) ) ) ) ) , file(rvsum_1, t13_rvsum_1)).
thf(t14_finseq_7, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @ A)  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @ A)  =>  ( ( ( ( (k1_finseq_7 @ A)  @  ( ( (k2_finseq_4 @ A)  @ B)  @ C) )  @ np__2)  @ D)  =  ( ( (k2_finseq_4 @ A)  @ B)  @ D) ) ) ) ) ) ) ) ) ) , file(finseq_7, t14_finseq_7)).
thf(t18_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  (! [B: $i] :  ( ( (k1_funct_1 @  (k54_valued_1 @ A) )  @ B)  =  (k17_complex1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, t18_valued_1)).
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_rcomp_1, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  (! [C: $i] :  ( (v1_xreal_0 @ C)  =>  ( ( (r2_hidden @ A)  @  ( (k2_rcomp_1 @  ( (k6_xcmplx_0 @ B)  @ C) )  @  ( (k2_xcmplx_0 @ B)  @ C) ) )  <=>  ~ ( ( (r1_xxreal_0 @ C)  @  (k18_complex1 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) ) ) ) ) ) ) ) , file(rcomp_1, t1_rcomp_1)).
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_real_ns1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @  (k4_real_ns1 @ A) ) )  =>  (! [C: $i] :  ( ( ( (m2_finseq_2 @ C)  @ k1_numbers)  @  (k1_euclid @ A) )  =>  ( (B = C)  =>  ( ( (k1_normsp_0 @  (k4_real_ns1 @ A) )  @ B)  =  (k12_euclid @ C) ) ) ) ) ) ) ) ) , file(real_ns1, t1_real_ns1)).
thf(t1_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (r2_hidden @ A)  @ B)  =>  ( (m1_subset_1 @ A)  @ B) ) ) ) , file(subset, t1_subset)).
thf(t20_rvsum_1, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  ( (k6_rvsum_1 @  (k9_finseq_1 @ A) )  =  ( (k12_finseq_1 @ k1_numbers)  @  (k7_binop_2 @ A) ) ) ) ) , file(rvsum_1, t20_rvsum_1)).
thf(t22_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (u1_struct_0 @  (k15_euclid @ A) )  =  (k1_euclid @ A) ) ) ) , file(euclid, t22_euclid)).
thf(t27_relat_1, axiom,  (! [A: $i] :  ( (v1_relat_1 @ A)  =>  (! [B: $i] :  ( (v1_relat_1 @ B)  =>  ( ( (r1_tarski @  (k10_xtuple_0 @ A) )  @  (k9_xtuple_0 @ B) )  =>  ( (k9_xtuple_0 @  ( (k3_relat_1 @ A)  @ B) )  =  (k9_xtuple_0 @ A) ) ) ) ) ) ) , file(relat_1, t27_relat_1)).
thf(t2_absvalue, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  ( (A = k6_numbers)  <=>  ( (k18_complex1 @ A)  = k6_numbers) ) ) ) , file(absvalue, t2_absvalue)).
thf(t2_arithm, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( ( (k3_xcmplx_0 @ A)  @ k6_numbers)  = k6_numbers) ) ) , file(arithm, t2_arithm)).
thf(t2_pdiff_1, axiom,  ( ( (v1_funct_1 @  (k2_funct_1 @  ( (k1_pdiff_1 @ np__1)  @ np__1) ) )  &  ( ( ( (v1_funct_2 @  (k2_funct_1 @  ( (k1_pdiff_1 @ np__1)  @ np__1) ) )  @ k1_numbers)  @  (k1_euclid @ np__1) )  &  ( (m1_subset_1 @  (k2_funct_1 @  ( (k1_pdiff_1 @ np__1)  @ np__1) ) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @  (k1_euclid @ np__1) ) ) ) ) )  &  ( (v2_funct_1 @  (k2_funct_1 @  ( (k1_pdiff_1 @ np__1)  @ np__1) ) )  &  ( ( (k9_xtuple_0 @  (k2_funct_1 @  ( (k1_pdiff_1 @ np__1)  @ np__1) ) )  = k1_numbers)  &  ( ( (k10_xtuple_0 @  (k2_funct_1 @  ( (k1_pdiff_1 @ np__1)  @ np__1) ) )  =  (k1_euclid @ np__1) )  &  (? [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k1_numbers)  @  (k1_euclid @ np__1) )  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @  (k1_euclid @ np__1) ) ) ) ) )  &  ( ( ( (v3_funct_2 @ A)  @ k1_numbers)  @  (k1_euclid @ np__1) )  &  ( (k2_funct_1 @  ( (k1_pdiff_1 @ np__1)  @ np__1) )  = A) ) ) ) ) ) ) ) , file(pdiff_1, t2_pdiff_1)).
thf(t2_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( ( (r1_xxreal_0 @ A)  @ B)  &  (v3_xxreal_0 @ B) )  =>  (v3_xxreal_0 @ A) ) ) ) ) ) , file(real, t2_real)).
thf(t2_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ A)  @ B)  =>  ( (v1_xboole_0 @ B)  |  ( (r2_hidden @ A)  @ B) ) ) ) ) , file(subset, t2_subset)).
thf(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(t31_jgraph_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (u1_struct_0 @  (k15_euclid @ np__2) ) )  =>  ( (r1_xxreal_0 @  (k12_euclid @ A) )  @  ( (k7_real_1 @  (k18_complex1 @  (k17_euclid @ A) ) )  @  (k18_complex1 @  (k18_euclid @ A) ) ) ) ) ) , file(jgraph_1, t31_jgraph_1)).
thf(t3_arithm, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( ( (k3_xcmplx_0 @ np__1)  @ A)  = A) ) ) , file(arithm, t3_arithm)).
thf(t3_cfdiff_2, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k5_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k1_numbers) ) ) ) )  =>  ( ( ( (v2_comseq_2 @ A)  &  ( (k2_seq_2 @ A)  = k6_numbers) )  =>  ( (v2_comseq_2 @  ( ( (k56_valued_1 @ k5_numbers)  @ k1_numbers)  @ A) )  &  ( (k2_seq_2 @  ( ( (k56_valued_1 @ k5_numbers)  @ k1_numbers)  @ A) )  = k6_numbers) ) )  &  ( ( (v2_comseq_2 @  ( ( (k56_valued_1 @ k5_numbers)  @ k1_numbers)  @ A) )  &  ( (k2_seq_2 @  ( ( (k56_valued_1 @ k5_numbers)  @ k1_numbers)  @ A) )  = k6_numbers) )  =>  ( (v2_comseq_2 @ A)  &  ( (k2_seq_2 @ A)  = k6_numbers) ) ) ) ) ) , file(cfdiff_2, t3_cfdiff_2)).
thf(t3_funct_3, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) )  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  (v1_funct_1 @ C) )  =>  ( ( ( (r1_tarski @ A)  @  (k9_xtuple_0 @ B) )  &  ( (r1_tarski @  ( (k7_relat_1 @ B)  @ A) )  @  (k9_xtuple_0 @ C) ) )  =>  ( (r1_tarski @ A)  @  (k9_xtuple_0 @  ( (k3_relat_1 @ B)  @ C) ) ) ) ) ) ) ) ) , file(funct_3, t3_funct_3)).
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_real_ns1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @  (k4_real_ns1 @ A) ) )  =>  (! [C: $i] :  ( ( ( (m2_finseq_2 @ C)  @ k1_numbers)  @  (k1_euclid @ A) )  =>  (! [D: $i] :  ( (v1_xreal_0 @ D)  =>  ( (B = C)  =>  ( ( ( (k1_rlvect_1 @  (k4_real_ns1 @ A) )  @ B)  @ D)  =  ( ( (k9_euclid @ A)  @ C)  @ D) ) ) ) ) ) ) ) ) ) ) , file(real_ns1, t3_real_ns1)).
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_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( (v1_funct_1 @ C)  &  (v1_finseq_1 @ C) ) )  =>  ( (C =  ( (k10_finseq_1 @ A)  @ B) )  <=>  ( ( (k3_finseq_1 @ C)  = np__2)  &  ( ( ( (k1_funct_1 @ C)  @ np__1)  = A)  &  ( ( (k1_funct_1 @ C)  @ np__2)  = B) ) ) ) ) ) ) ) , file(finseq_1, t44_finseq_1)).
thf(t47_rvsum_1, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (k10_rvsum_1 @  (k9_finseq_1 @ B) )  @ A)  =  ( (k12_finseq_1 @ k1_numbers)  @  ( (k11_binop_2 @ A)  @ B) ) ) ) ) ) ) , file(rvsum_1, t47_rvsum_1)).
thf(t4_arithm, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( ( (k6_xcmplx_0 @ A)  @ k6_numbers)  = A) ) ) , file(arithm, t4_arithm)).
thf(t4_cfdiff_2, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  ( (v3_normsp_0 @ A)  &  ( (v4_normsp_0 @ A)  &  ( (v2_normsp_1 @ A)  &  (l1_normsp_1 @ A) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B: $i] :  ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ k5_numbers)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @  (u1_struct_0 @ A) ) ) ) ) )  =>  ( ( ( ( (v3_normsp_1 @ B)  @ A)  &  ( ( (k6_normsp_1 @ A)  @ B)  =  (k4_struct_0 @ A) ) )  =>  ( (v2_comseq_2 @  ( (k4_normsp_0 @ A)  @ B) )  &  ( (k2_seq_2 @  ( (k4_normsp_0 @ A)  @ B) )  = k6_numbers) ) )  &  ( ( (v2_comseq_2 @  ( (k4_normsp_0 @ A)  @ B) )  &  ( (k2_seq_2 @  ( (k4_normsp_0 @ A)  @ B) )  = k6_numbers) )  =>  ( ( (v3_normsp_1 @ B)  @ A)  &  ( ( (k6_normsp_1 @ A)  @ B)  =  (k4_struct_0 @ A) ) ) ) ) ) ) ) ) , file(cfdiff_2, t4_cfdiff_2)).
thf(t4_nfcont_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  ( (v3_normsp_0 @ A)  &  ( (v4_normsp_0 @ A)  &  ( (v2_normsp_1 @ A)  &  (l1_normsp_1 @ A) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @ A) )  =>  (! [C: $i] :  ( ( ( (m1_nfcont_1 @ C)  @ A)  @ B)  =>  ( (r2_hidden @ B)  @ C) ) ) ) ) ) ) , file(nfcont_1, t4_nfcont_1)).
thf(t4_partfun1, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( ( (v5_relat_1 @ C)  @ A)  &  (v1_funct_1 @ C) ) )  =>  ( ( (r2_hidden @ B)  @  (k9_xtuple_0 @ C) )  =>  ( (r2_hidden @  ( (k1_funct_1 @ C)  @ B) )  @ A) ) ) ) ) ) , file(partfun1, t4_partfun1)).
thf(t4_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ( (r1_xxreal_0 @ A)  @ B)  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v2_xxreal_0 @ A) ) ) ) ) ) ) ) , file(real, t4_real)).
thf(t4_subset, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( ( (r2_hidden @ A)  @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ C) ) )  =>  ( (m1_subset_1 @ A)  @ C) ) ) ) ) , file(subset, t4_subset)).
thf(t54_euclid, axiom,  ( (k4_struct_0 @  (k15_euclid @ np__2) )  =  ( (k19_euclid @ k6_numbers)  @ k6_numbers) ) , file(euclid, t54_euclid)).
thf(t5_funct_2, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  (! [D: $i] :  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  =>  ( ( (r2_hidden @ C)  @ A)  =>  ( (B = k1_xboole_0)  |  ( (r2_hidden @  ( (k1_funct_1 @ D)  @ C) )  @ B) ) ) ) ) ) ) ) , file(funct_2, t5_funct_2)).
thf(t5_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (r1_xxreal_0 @ A)  @ B)  =>  ( (v1_xboole_0 @ B)  |  ( (v3_xxreal_0 @ A)  |  (v2_xxreal_0 @ B) ) ) ) ) ) ) ) , file(real, t5_real)).
thf(t5_real_ns1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (u1_struct_0 @  (k4_real_ns1 @ A) ) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @  (k4_real_ns1 @ A) ) )  =>  (! [D: $i] :  ( ( ( (m2_finseq_2 @ D)  @ k1_numbers)  @  (k1_euclid @ A) )  =>  (! [E: $i] :  ( ( ( (m2_finseq_2 @ E)  @ k1_numbers)  @  (k1_euclid @ A) )  =>  ( ( (B = D)  &  (C = E) )  =>  ( ( ( (k5_algstr_0 @  (k4_real_ns1 @ A) )  @ B)  @ C)  =  ( ( (k8_euclid @ A)  @ D)  @ E) ) ) ) ) ) ) ) ) ) ) ) ) , file(real_ns1, t5_real_ns1)).
thf(t5_seq_1, axiom,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k5_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ k1_numbers) ) ) ) )  =>  ( (v2_relat_1 @ A)  <=>  (! [B: $i] :  ( ( ( (m2_subset_1 @ B)  @ k1_numbers)  @ k5_numbers)  =>  ~ ( ( ( (k1_seq_1 @ A)  @ B)  = k6_numbers) ) ) ) ) ) ) , file(seq_1, t5_seq_1)).
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(t5_valued_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_valued_0 @ B) ) )  =>  (! [C: $i] :  ( ( (k1_funct_1 @  ( (k18_valued_1 @ A)  @ B) )  @ C)  =  ( (k3_xcmplx_0 @  ( (k1_funct_1 @ A)  @ C) )  @  ( (k1_funct_1 @ B)  @ C) ) ) ) ) ) ) ) , file(valued_1, t5_valued_1)).
thf(t63_funct_2, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  =>  (! [D: $i] :  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  =>  ( (! [E: $i] :  ( ( (m1_subset_1 @ E)  @ A)  =>  ( ( (k1_funct_1 @ C)  @ E)  =  ( (k1_funct_1 @ D)  @ E) ) ) )  =>  ( ( ( (r2_relset_1 @ A)  @ B)  @ C)  @ D) ) ) ) ) ) ) ) , file(funct_2, t63_funct_2)).
thf(t65_complex1, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  (! [B: $i] :  ( (v1_xcmplx_0 @ B)  =>  ( (k17_complex1 @  ( (k3_xcmplx_0 @ A)  @ B) )  =  ( (k8_real_1 @  (k17_complex1 @ A) )  @  (k17_complex1 @ B) ) ) ) ) ) ) , file(complex1, t65_complex1)).
thf(t65_funct_2, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  (! [D: $i] :  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  =>  (! [E: $i] :  ~ ( ( ( (r2_hidden @ E)  @  ( ( ( (k7_relset_1 @ A)  @ B)  @ D)  @ C) )  &  (! [F: $i] :  ( ( (m1_subset_1 @ F)  @ A)  =>  ~ ( ( ( (r2_hidden @ F)  @ C)  &  (E =  ( (k1_funct_1 @ D)  @ F) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(funct_2, t65_funct_2)).
thf(t66_complex1, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (k17_complex1 @  (k5_xcmplx_0 @ A) )  =  (k2_real_1 @  (k17_complex1 @ A) ) ) ) ) , file(complex1, t66_complex1)).
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(t70_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (k4_struct_0 @  (k15_euclid @ A) )  =  (k5_euclid @ A) ) ) ) , file(euclid, t70_euclid)).
thf(t77_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  (! [D: $i] :  ( ( ( (k10_finseq_1 @ A)  @ B)  =  ( (k10_finseq_1 @ C)  @ D) )  =>  ( (A = C)  &  (B = D) ) ) ) ) ) ) , file(finseq_1, t77_finseq_1)).
thf(t7_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( ( (r2_hidden @ A)  @ B)  &  (v1_xboole_0 @ B) ) ) ) ) , file(boole, t7_boole)).
thf(t7_ndiff_1, axiom,  (! [A: $i] :  ( ( ~ ( (v2_struct_0 @ A) )  &  ( (v13_algstr_0 @ A)  &  ( (v2_rlvect_1 @ A)  &  ( (v3_rlvect_1 @ A)  &  ( (v4_rlvect_1 @ A)  &  ( (v5_rlvect_1 @ A)  &  ( (v6_rlvect_1 @ A)  &  ( (v7_rlvect_1 @ A)  &  ( (v8_rlvect_1 @ A)  &  ( (v3_normsp_0 @ A)  &  ( (v4_normsp_0 @ A)  &  ( (v2_normsp_1 @ A)  &  (l1_normsp_1 @ A) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [B: $i] :  ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ k5_numbers)  @  (u1_struct_0 @ A) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @  (u1_struct_0 @ A) ) ) ) ) )  =>  ( ( ( (v12_struct_0 @ B)  @ k5_numbers)  @ A)  <=>  (! [C: $i] :  ( ( ( (m2_subset_1 @ C)  @ k1_numbers)  @ k5_numbers)  =>  ~ ( ( ( ( (k1_normsp_1 @ A)  @ B)  @ C)  =  (k4_struct_0 @ A) ) ) ) ) ) ) ) ) ) , file(ndiff_1, t7_ndiff_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(t97_finseq_2, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( ( (v3_card_1 @ B)  @ np__1)  &  ( (m2_finseq_1 @ B)  @ A) )  =>  (? [C: $i] :  ( ( (m1_subset_1 @ C)  @ A)  &  (B =  ( (k12_finseq_1 @ A)  @ C) ) ) ) ) ) ) ) , file(finseq_2, t97_finseq_2)).
thf(s3_funct_2, axiom,  (! [A: $i > $i > $o] :  (! [B: $i] :  (! [C: $i] :  ( ( ~ ( (v1_xboole_0 @ C) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  ( (! [D: $i] :  ( ( (m1_subset_1 @ D)  @ C)  =>  (? [E: $i] :  ( ( (m1_subset_1 @ E)  @ B)  &  ( (A @ D)  @ E) ) ) ) )  =>  (? [D: $i] :  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ C)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ C)  @ B) ) ) ) )  &  (! [E: $i] :  ( ( (m1_subset_1 @ E)  @ C)  =>  ( (A @ E)  @  ( ( ( (k3_funct_2 @ C)  @ B)  @ D)  @ E) ) ) ) ) ) ) ) ) ) ) , file(funct_2, s3_funct_2)).
thf(s4_funct_2, axiom,  (! [A: $i > $i] :  (! [B: $i] :  (! [C: $i] :  ( ( ~ ( (v1_xboole_0 @ C) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  (! [D: $i] :  ( (m1_subset_1 @  (A @ D) )  @ B) ) ) )  =>  (? [E: $i] :  ( ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ C)  @ B)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ C)  @ B) ) ) ) )  &  (! [F: $i] :  ( ( (m1_subset_1 @ F)  @ C)  =>  ( ( ( ( (k3_funct_2 @ C)  @ B)  @ E)  @ F)  =  (A @ F) ) ) ) ) ) ) ) ) ) , file(funct_2, s4_funct_2)).
thf(t5_cfdiff_2, conjecture,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ np__2) )  @ k1_numbers) ) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ k1_numbers)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @ k1_numbers)  =>  (! [D: $i] :  ( ( ( (m2_finseq_2 @ D)  @ k1_numbers)  @  (k1_euclid @ np__2) )  =>  ( ( (D =  ( (k10_finseq_1 @ B)  @ C) )  &  ( ( ( (r1_pdiff_1 @ np__2)  @ np__1)  @  ( (k3_pdiff_1 @ np__2)  @ A) )  @ D) )  =>  ( ( ( ( (r3_pdiff_1 @ np__2)  @ np__1)  @ A)  @ D)  &  ( ( ( ( (r3_pdiff_1 @ np__2)  @ np__2)  @ A)  @ D)  &  ( ( ( (k12_finseq_1 @ k1_numbers)  @  ( ( ( (k11_pdiff_1 @ np__2)  @ np__1)  @ A)  @ D) )  =  ( (k1_funct_1 @  ( ( ( (k8_pdiff_1 @ np__2)  @ np__1)  @  ( (k3_pdiff_1 @ np__2)  @ A) )  @ D) )  @  ( (k10_finseq_1 @ np__1)  @ k6_numbers) ) )  &  ( ( (k12_finseq_1 @ k1_numbers)  @  ( ( ( (k11_pdiff_1 @ np__2)  @ np__2)  @ A)  @ D) )  =  ( (k1_funct_1 @  ( ( ( (k8_pdiff_1 @ np__2)  @ np__1)  @  ( (k3_pdiff_1 @ np__2)  @ A) )  @ D) )  @  ( (k10_finseq_1 @ k6_numbers)  @ np__1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(cfdiff_2, t5_cfdiff_2)).