% Mizar problem: t8_pdiff_6,pdiff_6,230,5 
include('Axioms/SET010^0.ax').
thf(n1_type, type, np__1: $i).
thf(g1_normsp_1_type, type, g1_normsp_1: $i > $i > $i > $i > $i > $i).
thf(g1_rlvect_1_type, type, g1_rlvect_1: $i > $i > $i > $i > $i).
thf(k10_binop_2_type, type, k10_binop_2: $i).
thf(k10_funct_2_type, type, k10_funct_2: $i > $i > $i > $i > $i).
thf(k10_lopban_1_type, type, k10_lopban_1: $i > $i > $i).
thf(k10_subset_1_type, type, k10_subset_1: $i > $i > $i).
thf(k15_lopban_1_type, type, k15_lopban_1: $i > $i > $i).
thf(k16_lopban_1_type, type, k16_lopban_1: $i > $i > $i).
thf(k17_lopban_1_type, type, k17_lopban_1: $i > $i > $i > $i > $i).
thf(k1_euclid_type, type, k1_euclid: $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_numbers_type, type, k1_numbers: $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_valued_1_type, type, k1_valued_1: $i > $i > $i).
thf(k1_valued_2_type, type, k1_valued_2: $i > $i).
thf(k1_xboole_0_type, type, k1_xboole_0: $i).
thf(k1_zfmisc_1_type, type, k1_zfmisc_1: $i > $i).
thf(k24_valued_1_type, type, k24_valued_1: $i > $i > $i).
thf(k2_finseq_2_type, type, k2_finseq_2: $i > $i > $i).
thf(k2_funcop_1_type, type, k2_funcop_1: $i > $i > $i).
thf(k2_lopban_1_type, type, k2_lopban_1: $i > $i > $i).
thf(k2_real_ns1_type, type, k2_real_ns1: $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(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_numbers_type, type, k3_numbers: $i).
thf(k3_real_ns1_type, type, k3_real_ns1: $i > $i).
thf(k3_xboole_0_type, type, k3_xboole_0: $i > $i > $i).
thf(k45_valued_1_type, type, k45_valued_1: $i > $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_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_struct_0_type, type, k4_struct_0: $i > $i).
thf(k4_xcmplx_0_type, type, k4_xcmplx_0: $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_2_type, type, k5_finseq_2: $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_ordinal1_type, type, k5_ordinal1: $i).
thf(k5_rsspace_type, type, k5_rsspace: $i > $i > $i).
thf(k6_finseqop_type, type, k6_finseqop: $i > $i > $i > $i).
thf(k6_partfun1_type, type, k6_partfun1: $i > $i).
thf(k6_rsspace_type, type, k6_rsspace: $i > $i > $i).
thf(k6_valued_2_type, type, k6_valued_2: $i > $i).
thf(k78_valued_2_type, type, k78_valued_2: $i > $i > $i > $i > $i).
thf(k7_binop_2_type, type, k7_binop_2: $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_rsspace_type, type, k7_rsspace: $i > $i > $i).
thf(k80_valued_2_type, type, k80_valued_2: $i > $i > $i > $i > $i > $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_integr15_type, type, k8_integr15: $i > $i > $i > $i > $i).
thf(k8_lopban_1_type, type, k8_lopban_1: $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).
thf(k9_funct_2_type, type, k9_funct_2: $i > $i > $i).
thf(k9_subset_1_type, type, k9_subset_1: $i > $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_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_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_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(r1_funct_2_type, type, r1_funct_2: $i > $i > $i > $i > $i > $i > $o).
thf(r1_tarski_type, type, r1_tarski: $i > $i > $o).
thf(r2_tarski_type, type, r2_tarski: $i > $i > $o).
thf(v10_ordinal1_type, type, v10_ordinal1: $i > $o).
thf(v10_valued_2_type, type, v10_valued_2: $i > $o).
thf(v11_valued_2_type, type, v11_valued_2: $i > $o).
thf(v12_valued_2_type, type, v12_valued_2: $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_finseq_1_type, type, v1_finseq_1: $i > $o).
thf(v1_finset_1_type, type, v1_finset_1: $i > $o).
thf(v1_funcop_1_type, type, v1_funcop_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_monoid_0_type, type, v1_monoid_0: $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_setfam_1_type, type, v1_setfam_1: $i > $o).
thf(v1_valued_0_type, type, v1_valued_0: $i > $o).
thf(v1_valued_2_type, type, v1_valued_2: $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_card_1_type, type, v2_card_1: $i > $o).
thf(v2_finseq_1_type, type, v2_finseq_1: $i > $o).
thf(v2_funct_1_type, type, v2_funct_1: $i > $o).
thf(v2_lopban_1_type, type, v2_lopban_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_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_valued_2_type, type, v2_valued_2: $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_finseq_1_type, type, v3_finseq_1: $i > $o).
thf(v3_lopban_1_type, type, v3_lopban_1: $i > $o).
thf(v3_normsp_0_type, type, v3_normsp_0: $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_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(v4_valued_2_type, type, v4_valued_2: $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_rlvect_1_type, type, v5_rlvect_1: $i > $o).
thf(v5_valued_0_type, type, v5_valued_0: $i > $o).
thf(v5_valued_2_type, type, v5_valued_2: $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(v6_valued_2_type, type, v6_valued_2: $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(v7_valued_2_type, type, v7_valued_2: $i > $o).
thf(v8_ordinal1_type, type, v8_ordinal1: $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(v8_valued_2_type, type, v8_valued_2: $i > $o).
thf(v9_ordinal1_type, type, v9_ordinal1: $i > $o).
thf(v9_struct_0_type, type, v9_struct_0: $i > $i > $o).
thf(v9_valued_2_type, type, v9_valued_2: $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(antisymmetry_r2_hidden, axiom,  (! [A: $i, B: $i] :  ( ( (r2_hidden @ A)  @ B)  =>  ~ ( ( (r2_hidden @ B)  @ A) ) ) ) , file(hidden, r2_hidden)).
thf(asymmetry_r2_tarski, axiom,  (! [A: $i, B: $i] :  ( ( (r2_tarski @ A)  @ B)  =>  ~ ( ( (r2_tarski @ B)  @ A) ) ) ) , file(tarski, r2_tarski)).
thf(cc10_card_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_zfmisc_1 @ A) )  =>  ( (v3_card_1 @ A)  @ np__1) ) ) , file(card_1, cc10_card_1)).
thf(cc10_finseq_1, axiom,  (! [A: $i] :  ( (v3_finseq_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_finseq_1 @ B) ) ) ) ) , file(finseq_1, cc10_finseq_1)).
thf(cc10_funct_2, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( ( (m1_funct_2 @ C)  @ A)  @ B)  =>  (v4_funct_1 @ C) ) ) ) , file(funct_2, cc10_funct_2)).
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(cc10_valued_2, axiom,  (! [A: $i] :  ( (v2_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v2_valued_2 @ B) ) ) ) ) , file(valued_2, cc10_valued_2)).
thf(cc11_card_1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_card_1 @ A) )  =>  (! [B: $i] :  ( ( (v3_card_1 @ B)  @ A)  =>  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) , file(card_1, cc11_card_1)).
thf(cc11_finseq_1, axiom,  (! [A: $i] :  ( (v3_finseq_1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v3_finseq_1 @ B) ) ) ) ) , file(finseq_1, cc11_finseq_1)).
thf(cc11_ordinal1, axiom,  (! [A: $i] :  ( (v8_ordinal1 @ A)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc11_ordinal1)).
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(cc11_valued_2, axiom,  (! [A: $i] :  ( (v3_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v3_valued_2 @ B) ) ) ) ) , file(valued_2, cc11_valued_2)).
thf(cc12_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  ( (v5_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) ) ) ) ) , file(finseq_1, cc12_finseq_1)).
thf(cc12_ordinal1, axiom,  (! [A: $i] :  ( (v8_ordinal1 @ A)  =>  (v1_zfmisc_1 @ A) ) ) , file(ordinal1, cc12_ordinal1)).
thf(cc12_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v3_valued_0 @ B) ) ) ) ) , file(valued_0, cc12_valued_0)).
thf(cc12_valued_2, axiom,  (! [A: $i] :  ( (v4_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v4_valued_2 @ B) ) ) ) ) , file(valued_2, cc12_valued_2)).
thf(cc13_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finseq_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) ) , file(finseq_1, cc13_finseq_1)).
thf(cc13_ordinal1, axiom,  (! [A: $i] :  ( ~ ( (v1_zfmisc_1 @ A) )  =>  ~ ( (v8_ordinal1 @ A) ) ) ) , file(ordinal1, cc13_ordinal1)).
thf(cc13_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( (v5_relat_1 @ B)  @ k3_numbers) ) ) ) ) , file(valued_0, cc13_valued_0)).
thf(cc13_valued_2, axiom,  (! [A: $i] :  ( (v5_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v5_valued_2 @ B) ) ) ) ) , file(valued_2, cc13_valued_2)).
thf(cc14_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  ~ ( (v10_ordinal1 @ A) ) ) ) , file(ordinal1, cc14_ordinal1)).
thf(cc14_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( (v5_relat_1 @ B)  @ k4_numbers) ) ) ) ) , file(valued_0, cc14_valued_0)).
thf(cc14_valued_2, axiom,  (! [A: $i] :  ( (v6_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v6_valued_2 @ B) ) ) ) ) , file(valued_2, cc14_valued_2)).
thf(cc15_ordinal1, axiom,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v9_ordinal1 @ A) ) ) ) , file(ordinal1, cc15_ordinal1)).
thf(cc15_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v4_valued_0 @ B) ) ) ) ) , file(valued_0, cc15_valued_0)).
thf(cc15_valued_2, axiom,  (! [A: $i] :  ( (v1_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_valued_0 @ B) ) ) ) ) , file(valued_2, cc15_valued_2)).
thf(cc16_ordinal1, axiom,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v10_ordinal1 @ A) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  ~ ( (v8_ordinal1 @ B) ) ) ) ) ) , file(ordinal1, cc16_ordinal1)).
thf(cc16_valued_2, axiom,  (! [A: $i] :  ( (v2_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v2_valued_0 @ B) ) ) ) ) , file(valued_2, cc16_valued_2)).
thf(cc17_ordinal1, axiom,  (! [A: $i] :  ( ~ ( (v10_ordinal1 @ A) )  =>  (v1_setfam_1 @ A) ) ) , file(ordinal1, cc17_ordinal1)).
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_2, axiom,  (! [A: $i] :  ( (v3_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v3_valued_0 @ B) ) ) ) ) , file(valued_2, cc17_valued_2)).
thf(cc18_ordinal1, axiom,  (! [A: $i] :  ( (v10_ordinal1 @ A)  =>  ~ ( (v1_setfam_1 @ A) ) ) ) , file(ordinal1, cc18_ordinal1)).
thf(cc18_valued_2, axiom,  (! [A: $i] :  ( (v4_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  ( (v5_relat_1 @ B)  @ k3_numbers) ) ) ) ) , file(valued_2, cc18_valued_2)).
thf(cc19_ordinal1, axiom,  (! [A: $i] :  ( (v1_setfam_1 @ A)  =>  ~ ( (v10_ordinal1 @ A) ) ) ) , file(ordinal1, cc19_ordinal1)).
thf(cc19_valued_2, axiom,  (! [A: $i] :  ( (v5_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  ( (v5_relat_1 @ B)  @ k4_numbers) ) ) ) ) , file(valued_2, cc19_valued_2)).
thf(cc1_card_1, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(card_1, cc1_card_1)).
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_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_xboole_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v1_finseq_1 @ A) ) ) ) , file(finseq_1, cc1_finseq_1)).
thf(cc1_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_nat_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v3_ordinal1 @ A)  &  (v7_ordinal1 @ A) ) ) ) , file(nat_1, cc1_nat_1)).
thf(cc1_ordinal1, axiom,  (! [A: $i] :  ( (v3_ordinal1 @ A)  =>  ( (v1_ordinal1 @ A)  &  (v2_ordinal1 @ A) ) ) ) , file(ordinal1, cc1_ordinal1)).
thf(cc1_relset_1, axiom,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v1_relat_1 @ C) ) ) ) , file(relset_1, cc1_relset_1)).
thf(cc1_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_valued_2, axiom,  (! [A: $i] :  ( (v6_valued_2 @ A)  =>  (v5_valued_2 @ A) ) ) , file(valued_2, cc1_valued_2)).
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_ordinal1, axiom,  (! [A: $i] :  ( ~ ( (v1_setfam_1 @ A) )  =>  (v10_ordinal1 @ A) ) ) , file(ordinal1, cc20_ordinal1)).
thf(cc20_valued_2, axiom,  (! [A: $i] :  ( (v6_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v4_valued_0 @ B) ) ) ) ) , file(valued_2, cc20_valued_2)).
thf(cc21_valued_2, axiom,  (! [A: $i] :  ( (v1_valued_2 @ A)  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) )  =>  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  (v7_valued_2 @ B) ) ) ) ) ) ) ) , file(valued_2, cc21_valued_2)).
thf(cc22_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v1_zfmisc_1 @ A)  &  (v2_valued_0 @ A) ) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v2_valued_0 @ A)  &  ( (v5_valued_0 @ A)  &  (v6_valued_0 @ A) ) ) ) ) ) ) , file(valued_0, cc22_valued_0)).
thf(cc22_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v12_valued_2 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v11_valued_2 @ A) ) ) ) , file(valued_2, cc22_valued_2)).
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(cc23_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v11_valued_2 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v10_valued_2 @ A) ) ) ) , file(valued_2, cc23_valued_2)).
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(cc24_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v10_valued_2 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v9_valued_2 @ A) ) ) ) , file(valued_2, cc24_valued_2)).
thf(cc25_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v9_valued_2 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v8_valued_2 @ A) ) ) ) , file(valued_2, cc25_valued_2)).
thf(cc26_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v9_valued_2 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v7_valued_2 @ A) ) ) ) , file(valued_2, cc26_valued_2)).
thf(cc27_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_xboole_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v12_valued_2 @ A) ) ) ) , file(valued_2, cc27_valued_2)).
thf(cc28_valued_2, axiom,  (! [A: $i, B: $i] :  ( (v1_valued_2 @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v1_funct_1 @ C)  =>  ( (v1_funct_1 @ C)  &  (v7_valued_2 @ C) ) ) ) ) ) ) , file(valued_2, cc28_valued_2)).
thf(cc29_valued_2, axiom,  (! [A: $i, B: $i] :  ( (v2_valued_2 @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v1_funct_1 @ C)  =>  ( (v1_funct_1 @ C)  &  (v8_valued_2 @ C) ) ) ) ) ) ) , file(valued_2, cc29_valued_2)).
thf(cc2_card_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_card_1 @ A) ) ) , file(card_1, cc2_card_1)).
thf(cc2_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finset_1 @ A) ) ) ) ) , file(finseq_1, cc2_finseq_1)).
thf(cc2_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_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) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (u1_struct_0 @  ( (k16_lopban_1 @ A)  @ B) ) )  =>  ( (v1_relat_1 @ C)  &  (v1_funct_1 @ C) ) ) ) ) ) , file(lopban_1, cc2_lopban_1)).
thf(cc2_nat_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  ~ ( (v3_xxreal_0 @ A) ) ) ) , file(nat_1, cc2_nat_1)).
thf(cc2_ordinal1, axiom,  (! [A: $i] :  ( ( (v1_ordinal1 @ A)  &  (v2_ordinal1 @ A) )  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc2_ordinal1)).
thf(cc2_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_valued_2, axiom,  (! [A: $i] :  ( (v5_valued_2 @ A)  =>  (v4_valued_2 @ A) ) ) , file(valued_2, cc2_valued_2)).
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(cc30_valued_2, axiom,  (! [A: $i, B: $i] :  ( (v3_valued_2 @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v1_funct_1 @ C)  =>  ( (v1_funct_1 @ C)  &  (v9_valued_2 @ C) ) ) ) ) ) ) , file(valued_2, cc30_valued_2)).
thf(cc31_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_ordinal1) )  =>  ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, cc31_valued_0)).
thf(cc31_valued_2, axiom,  (! [A: $i, B: $i] :  ( (v4_valued_2 @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v1_funct_1 @ C)  =>  ( (v1_funct_1 @ C)  &  (v10_valued_2 @ C) ) ) ) ) ) ) , file(valued_2, cc31_valued_2)).
thf(cc32_valued_2, axiom,  (! [A: $i, B: $i] :  ( (v5_valued_2 @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v1_funct_1 @ C)  =>  ( (v1_funct_1 @ C)  &  (v11_valued_2 @ C) ) ) ) ) ) ) , file(valued_2, cc32_valued_2)).
thf(cc33_valued_2, axiom,  (! [A: $i, B: $i] :  ( (v6_valued_2 @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v1_funct_1 @ C)  =>  ( (v1_funct_1 @ C)  &  (v12_valued_2 @ C) ) ) ) ) ) ) , file(valued_2, cc33_valued_2)).
thf(cc34_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v7_valued_2 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_funcop_1 @ A) ) ) ) ) , file(valued_2, cc34_valued_2)).
thf(cc35_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v9_valued_2 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_funcop_1 @ A) ) ) ) ) , file(valued_2, cc35_valued_2)).
thf(cc36_valued_2, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v8_valued_2 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_funcop_1 @ A) ) ) ) ) , file(valued_2, cc36_valued_2)).
thf(cc3_card_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_card_1 @ A) ) ) , file(card_1, cc3_card_1)).
thf(cc3_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_finseq_1 @ B)  @ A)  =>  ( (v5_relat_1 @ B)  @ A) ) ) ) , file(finseq_1, cc3_finseq_1)).
thf(cc3_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_nat_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v7_ordinal1 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) ) ) ) , file(nat_1, cc3_nat_1)).
thf(cc3_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc3_ordinal1)).
thf(cc3_relset_1, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v1_xboole_0 @ C) ) ) ) ) , file(relset_1, cc3_relset_1)).
thf(cc3_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc3_valued_0)).
thf(cc3_valued_2, axiom,  (! [A: $i] :  ( (v4_valued_2 @ A)  =>  (v3_valued_2 @ A) ) ) , file(valued_2, cc3_valued_2)).
thf(cc3_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v1_xcmplx_0 @ A) ) ) , file(xreal_0, cc3_xreal_0)).
thf(cc3_xxreal_0, axiom,  (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) )  =>  ( ~ ( (v8_ordinal1 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc3_xxreal_0)).
thf(cc4_card_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (v1_finset_1 @ A) ) ) , file(card_1, cc4_card_1)).
thf(cc4_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_xboole_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v1_finseq_1 @ A) ) ) ) , file(finseq_1, cc4_finseq_1)).
thf(cc4_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_nat_1, axiom,  (! [A: $i] :  ( ( (v7_ordinal1 @ A)  &  (v8_ordinal1 @ A) )  =>  ( (v7_ordinal1 @ A)  &  ~ ( (v2_xxreal_0 @ A) ) ) ) ) , file(nat_1, cc4_nat_1)).
thf(cc4_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v5_ordinal1 @ A) ) ) , file(ordinal1, cc4_ordinal1)).
thf(cc4_relset_1, axiom,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ A) ) )  =>  (v1_xboole_0 @ C) ) ) ) ) , file(relset_1, cc4_relset_1)).
thf(cc4_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_valued_2, axiom,  (! [A: $i] :  ( (v3_valued_2 @ A)  =>  (v1_valued_2 @ A) ) ) , file(valued_2, cc4_valued_2)).
thf(cc4_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v1_xxreal_0 @ A) ) ) , file(xreal_0, cc4_xreal_0)).
thf(cc4_xxreal_0, axiom,  (! [A: $i] :  ( ( ~ ( (v8_ordinal1 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) ) )  =>  ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) ) ) ) , file(xxreal_0, cc4_xxreal_0)).
thf(cc5_card_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_finset_1 @ A) ) ) , file(card_1, cc5_card_1)).
thf(cc5_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k4_ordinal1)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) ) ) ) ) , file(finseq_1, cc5_finseq_1)).
thf(cc5_funct_2, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A) ) )  =>  ( ( ( (v1_funct_2 @ B)  @  ( (k2_zfmisc_1 @ A)  @ A) )  @ A)  =>  ( (v1_partfun1 @ B)  @  ( (k2_zfmisc_1 @ A)  @ A) ) ) ) ) ) , file(funct_2, cc5_funct_2)).
thf(cc5_nat_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v8_ordinal1 @ A) ) ) , file(nat_1, cc5_nat_1)).
thf(cc5_ordinal1, axiom,  (! [A: $i] :  ( (v3_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v3_ordinal1 @ B) ) ) ) ) , file(ordinal1, cc5_ordinal1)).
thf(cc5_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_valued_2, axiom,  (! [A: $i] :  ( (v3_valued_2 @ A)  =>  (v2_valued_2 @ A) ) ) , file(valued_2, cc5_valued_2)).
thf(cc5_xxreal_0, axiom,  (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) )  =>  ( ~ ( (v8_ordinal1 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v2_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc5_xxreal_0)).
thf(cc6_card_1, axiom,  (! [A: $i] :  ( ( (v3_ordinal1 @ A)  &  (v1_finset_1 @ A) )  =>  (v7_ordinal1 @ A) ) ) , file(card_1, cc6_card_1)).
thf(cc6_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_finseq_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) , file(finseq_1, cc6_finseq_1)).
thf(cc6_nat_1, axiom,  (! [A: $i] :  ( ~ ( (v8_ordinal1 @ A) )  =>  ~ ( (v1_xboole_0 @ A) ) ) ) , file(nat_1, cc6_nat_1)).
thf(cc6_ordinal1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc6_ordinal1)).
thf(cc6_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_valued_2, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v6_valued_2 @ A) ) ) , file(valued_2, cc6_valued_2)).
thf(cc6_xxreal_0, axiom,  (! [A: $i] :  ( ( ~ ( (v8_ordinal1 @ A) )  &  ( (v1_xxreal_0 @ A)  &  ~ ( (v2_xxreal_0 @ A) ) ) )  =>  ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) ) ) ) , file(xxreal_0, cc6_xxreal_0)).
thf(cc7_card_1, axiom,  (! [A: $i] :  ( ( (v3_card_1 @ A)  @ k5_ordinal1)  =>  (v1_xboole_0 @ A) ) ) , file(card_1, cc7_card_1)).
thf(cc7_finseq_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finseq_1 @ A) ) )  =>  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k4_ordinal1)  &  ( (v1_funct_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) ) , file(finseq_1, cc7_finseq_1)).
thf(cc7_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_valued_2, axiom,  (! [A: $i] :  ( (v1_valued_2 @ A)  =>  (v4_funct_1 @ A) ) ) , file(valued_2, cc7_valued_2)).
thf(cc7_xxreal_0, axiom,  (! [A: $i] :  ( ( (v8_ordinal1 @ A)  &  (v1_xxreal_0 @ A) )  =>  ( (v1_xxreal_0 @ A)  &  ( ~ ( (v2_xxreal_0 @ A) )  &  ~ ( (v3_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc7_xxreal_0)).
thf(cc8_card_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  ( (v3_card_1 @ A)  @ k5_ordinal1) ) ) , file(card_1, cc8_card_1)).
thf(cc8_finseq_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v3_finseq_1 @ A) ) ) , file(finseq_1, cc8_finseq_1)).
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)  @ k5_ordinal1) ) ) ) , 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_valued_2, axiom,  (! [A: $i] :  ( (v2_valued_2 @ A)  =>  (v4_funct_1 @ A) ) ) , file(valued_2, cc8_valued_2)).
thf(cc8_xxreal_0, axiom,  (! [A: $i] :  ( ( (v1_xxreal_0 @ A)  &  ( ~ ( (v2_xxreal_0 @ A) )  &  ~ ( (v3_xxreal_0 @ A) ) ) )  =>  ( (v8_ordinal1 @ A)  &  (v1_xxreal_0 @ A) ) ) ) , file(xxreal_0, cc8_xxreal_0)).
thf(cc9_card_1, axiom,  (! [A: $i] :  ( ( (v3_card_1 @ A)  @ np__1)  =>  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_zfmisc_1 @ A) ) ) ) , file(card_1, cc9_card_1)).
thf(cc9_finseq_1, axiom,  (! [A: $i] :  ( (v3_finseq_1 @ A)  =>  (v4_funct_1 @ A) ) ) , file(finseq_1, cc9_finseq_1)).
thf(cc9_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, cc9_funct_2)).
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)  @ k5_ordinal1)  =>  (v2_struct_0 @ A) ) ) ) , file(struct_0, cc9_struct_0)).
thf(cc9_valued_0, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_xboole_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, cc9_valued_0)).
thf(cc9_valued_2, axiom,  (! [A: $i] :  ( (v1_valued_2 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_valued_2 @ B) ) ) ) ) , file(valued_2, cc9_valued_2)).
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_k3_xboole_0, axiom,  (! [A: $i, B: $i] :  ( ( (k3_xboole_0 @ A)  @ B)  =  ( (k3_xboole_0 @ B)  @ A) ) ) , file(xboole_0, k3_xboole_0)).
thf(commutativity_k9_subset_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @ A) )  =>  ( ( ( (k9_subset_1 @ A)  @ B)  @ C)  =  ( ( (k9_subset_1 @ A)  @ C)  @ B) ) ) ) , file(subset_1, k9_subset_1)).
thf(d10_integr15, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  (! [C: $i] :  ( ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @  (k1_euclid @ A) ) ) ) )  =>  (! [D: $i] :  ( ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @  (k1_euclid @ A) ) ) ) )  =>  ( ( ( ( (k8_integr15 @ A)  @ B)  @ C)  @ D)  =  ( ( ( ( ( (k80_valued_2 @ B)  @ B)  @  (k1_euclid @ A) )  @  (k1_euclid @ A) )  @ C)  @ D) ) ) ) ) ) ) ) ) , file(integr15, d10_integr15)).
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) )  @  ( (k7_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k5_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k6_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_rvsum_1, axiom,  (k10_binop_2 =  ( ( ( (k7_finseqop @ k1_numbers)  @ k9_binop_2)  @  (k6_partfun1 @ k1_numbers) )  @ k7_binop_2) ) , file(rvsum_1, d1_rvsum_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(d46_valued_2, axiom,  (! [A: $i] :  ( (v1_valued_2 @ A)  =>  (! [B: $i] :  ( (v1_valued_2 @ B)  =>  (! [C: $i] :  ( ( (v1_relat_1 @ C)  &  ( ( (v5_relat_1 @ C)  @ A)  &  (v1_funct_1 @ C) ) )  =>  (! [D: $i] :  ( ( (v1_relat_1 @ D)  &  ( ( (v5_relat_1 @ D)  @ B)  &  (v1_funct_1 @ D) ) )  =>  (! [E: $i] :  ( ( (v1_relat_1 @ E)  &  (v1_funct_1 @ E) )  =>  ( (E =  ( ( ( (k78_valued_2 @ A)  @ B)  @ C)  @ D) )  <=>  ( ( (k9_xtuple_0 @ E)  =  ( (k3_xboole_0 @  (k9_xtuple_0 @ C) )  @  (k9_xtuple_0 @ D) ) )  &  (! [F: $i] :  ( ( (r2_hidden @ F)  @  (k9_xtuple_0 @ E) )  =>  ( ( (k1_funct_1 @ E)  @ F)  =  ( (k45_valued_1 @  ( (k1_funct_1 @ C)  @ F) )  @  ( (k1_funct_1 @ D)  @ F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(valued_2, d46_valued_2)).
thf(d4_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (k4_euclid @ A)  =  ( ( (k5_finseq_2 @ k1_numbers)  @ A)  @  ( (k10_subset_1 @ k5_numbers)  @ k1_numbers) ) ) ) ) , file(euclid, d4_euclid)).
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_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(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 @ k10_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) )  @  ( (k7_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k5_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k6_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) ) ) ) ) ) ) , file(lopban_1, d7_lopban_1)).
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_tarski @ 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_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_binop_2, axiom,  ( (v1_funct_1 @ k10_binop_2)  &  ( ( ( (v1_funct_2 @ k10_binop_2)  @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) )  @ k1_numbers)  &  ( (m1_subset_1 @ k10_binop_2)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) )  @ k1_numbers) ) ) ) ) , file(binop_2, k10_binop_2)).
thf(dt_k10_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 @  ( ( ( (k10_funct_2 @ A)  @ B)  @ C)  @ D) )  @ B) ) ) , file(funct_2, k10_funct_2)).
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_subset_1, axiom,  (! [A: $i, B: $i] :  ( (m1_subset_1 @  ( (k10_subset_1 @ A)  @ B) )  @ B) ) , file(subset_1, k10_subset_1)).
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_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_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_k1_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (m1_finseq_2 @  (k1_euclid @ A) )  @ k1_numbers) ) ) , file(euclid, k1_euclid)).
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_numbers, axiom, $true, file(numbers, k1_numbers)).
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_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_valued_2, axiom, $true, file(valued_2, k1_valued_2)).
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_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_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_funcop_1, axiom, $true, file(funcop_1, k2_funcop_1)).
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_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_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_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_numbers, axiom, $true, file(numbers, k3_numbers)).
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_xboole_0, axiom, $true, file(xboole_0, k3_xboole_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_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_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_struct_0, axiom,  (! [A: $i] :  ( (l2_struct_0 @ A)  =>  ( (m1_subset_1 @  (k4_struct_0 @ A) )  @  (u1_struct_0 @ A) ) ) ) , file(struct_0, k4_struct_0)).
thf(dt_k4_xcmplx_0, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) ) ) ) , file(xcmplx_0, k4_xcmplx_0)).
thf(dt_k5_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_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_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)  @ k4_ordinal1) , file(numbers, k5_numbers)).
thf(dt_k5_ordinal1, axiom, $true, file(ordinal1, k5_ordinal1)).
thf(dt_k5_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 @  ( (k5_rsspace @ A)  @ B) )  &  ( ( ( (v1_funct_2 @  ( (k5_rsspace @ A)  @ B) )  @  ( (k2_zfmisc_1 @ B)  @ B) )  @ B)  &  ( (m1_subset_1 @  ( (k5_rsspace @ A)  @ B) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ B) )  @ B) ) ) ) ) ) ) , file(rsspace, k5_rsspace)).
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_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_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 @  ( (k6_rsspace @ A)  @ B) )  &  ( ( ( (v1_funct_2 @  ( (k6_rsspace @ A)  @ B) )  @  ( (k2_zfmisc_1 @ k1_numbers)  @ B) )  @ B)  &  ( (m1_subset_1 @  ( (k6_rsspace @ A)  @ B) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ B) )  @ B) ) ) ) ) ) ) , file(rsspace, k6_rsspace)).
thf(dt_k6_valued_2, axiom, $true, file(valued_2, k6_valued_2)).
thf(dt_k78_valued_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v1_valued_2 @ A)  &  ( (v1_valued_2 @ B)  &  ( ( (v1_relat_1 @ C)  &  ( ( (v5_relat_1 @ C)  @ A)  &  (v1_funct_1 @ C) ) )  &  ( (v1_relat_1 @ D)  &  ( ( (v5_relat_1 @ D)  @ B)  &  (v1_funct_1 @ D) ) ) ) ) )  =>  ( (v1_relat_1 @  ( ( ( (k78_valued_2 @ A)  @ B)  @ C)  @ D) )  &  (v1_funct_1 @  ( ( ( (k78_valued_2 @ A)  @ B)  @ C)  @ D) ) ) ) ) , file(valued_2, k78_valued_2)).
thf(dt_k7_binop_2, axiom,  ( (v1_funct_1 @ k7_binop_2)  &  ( ( ( (v1_funct_2 @ k7_binop_2)  @ k1_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ k7_binop_2)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) ) , file(binop_2, k7_binop_2)).
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_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 @  ( (k7_rsspace @ A)  @ B) )  @ B) ) ) , file(rsspace, k7_rsspace)).
thf(dt_k80_valued_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] :  ( ( (v3_valued_2 @ C)  &  ( (v3_valued_2 @ D)  &  ( ( (v1_funct_1 @ E)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) )  &  ( (v1_funct_1 @ F)  &  ( (m1_subset_1 @ F)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ D) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( ( ( ( ( (k80_valued_2 @ A)  @ B)  @ C)  @ D)  @ E)  @ F) )  &  ( (m1_subset_1 @  ( ( ( ( ( (k80_valued_2 @ A)  @ B)  @ C)  @ D)  @ E)  @ F) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k3_xboole_0 @ A)  @ B) )  @  (k6_valued_2 @  ( (k3_xboole_0 @  (k1_valued_2 @ C) )  @  (k1_valued_2 @ D) ) ) ) ) ) ) ) ) , file(valued_2, k80_valued_2)).
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_integr15, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v7_ordinal1 @ A)  &  ( ( (v1_funct_1 @ C)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @  (k1_euclid @ A) ) ) ) )  &  ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @  (k1_euclid @ A) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( ( ( (k8_integr15 @ A)  @ B)  @ C)  @ D) )  &  ( (m1_subset_1 @  ( ( ( (k8_integr15 @ A)  @ B)  @ C)  @ D) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @  (k1_euclid @ A) ) ) ) ) ) ) , file(integr15, k8_integr15)).
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_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,  ( (v1_funct_1 @ k9_binop_2)  &  ( ( ( (v1_funct_2 @ k9_binop_2)  @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) )  @ k1_numbers)  &  ( (m1_subset_1 @ k9_binop_2)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) )  @ k1_numbers) ) ) ) ) , file(binop_2, k9_binop_2)).
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_subset_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @ A) )  =>  ( (m1_subset_1 @  ( ( (k9_subset_1 @ A)  @ B)  @ C) )  @  (k1_zfmisc_1 @ A) ) ) ) , file(subset_1, k9_subset_1)).
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_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_subset_1, axiom, $true, file(subset_1, m1_subset_1)).
thf(dt_m2_finseq_1, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m2_finseq_1 @ B)  @ A)  =>  ( (v1_funct_1 @ B)  &  ( (v1_finseq_1 @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ A) ) ) ) ) ) ) ) , file(finseq_1, m2_finseq_1)).
thf(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_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_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_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_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(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_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) ) )  &  ( (v13_algstr_0 @  ( (k16_lopban_1 @ A)  @ B) )  &  ( (v2_rlvect_1 @  ( (k16_lopban_1 @ A)  @ B) )  &  ( (v3_rlvect_1 @  ( (k16_lopban_1 @ A)  @ B) )  &  ( (v4_rlvect_1 @  ( (k16_lopban_1 @ A)  @ B) )  &  ( (v5_rlvect_1 @  ( (k16_lopban_1 @ A)  @ B) )  &  ( (v6_rlvect_1 @  ( (k16_lopban_1 @ A)  @ B) )  &  ( (v7_rlvect_1 @  ( (k16_lopban_1 @ A)  @ B) )  &  ( (v8_rlvect_1 @  ( (k16_lopban_1 @ A)  @ B) )  &  ( (v3_normsp_0 @  ( (k16_lopban_1 @ A)  @ B) )  &  ( (v4_normsp_0 @  ( (k16_lopban_1 @ A)  @ B) )  &  (v2_normsp_1 @  ( (k16_lopban_1 @ A)  @ B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(lopban_1, fc10_lopban_1)).
thf(fc10_nat_1, axiom,  (! [A: $i, B: $i] :  ( (v3_ordinal1 @ A)  =>  (v5_ordinal1 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(nat_1, fc10_nat_1)).
thf(fc10_struct_0, axiom,  (! [A: $i] :  ( (l2_struct_0 @ A)  =>  ( (v9_struct_0 @  (k4_struct_0 @ A) )  @ A) ) ) , file(struct_0, fc10_struct_0)).
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_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)  &  ( (v3_lopban_1 @ B)  &  (l1_normsp_1 @ B) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ~ ( (v2_struct_0 @  ( (k16_lopban_1 @ A)  @ B) ) )  &  (v3_lopban_1 @  ( (k16_lopban_1 @ A)  @ B) ) ) ) ) , file(lopban_1, fc11_lopban_1)).
thf(fc12_card_1, axiom,  (! [A: $i] :  ( ~ ( (v1_finset_1 @ A) )  =>  ~ ( (v1_finset_1 @  (k1_zfmisc_1 @ A) ) ) ) ) , file(card_1, fc12_card_1)).
thf(fc13_card_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_finset_1 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  ~ ( (v1_finset_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) ) , file(card_1, fc13_card_1)).
thf(fc13_rvsum_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( (v1_relat_1 @  ( (k2_finseq_2 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k2_finseq_2 @ A)  @ B) )  &  ( (v1_valued_0 @  ( (k2_finseq_2 @ A)  @ B) )  &  (v1_finseq_1 @  ( (k2_finseq_2 @ A)  @ B) ) ) ) ) ) ) , file(rvsum_1, fc13_rvsum_1)).
thf(fc13_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) )  &  (v1_relat_1 @ B) )  =>  (v1_valued_0 @  ( (k3_xboole_0 @ A)  @ B) ) ) ) , file(valued_0, fc13_valued_0)).
thf(fc14_card_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_finset_1 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  ~ ( (v1_finset_1 @  ( (k2_zfmisc_1 @ B)  @ A) ) ) ) ) , file(card_1, fc14_card_1)).
thf(fc14_valued_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v1_valued_2 @ C)  &  ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_1 @ D)  @ B) )  &  (v1_funct_1 @  ( (k1_funct_1 @ D)  @ B) ) ) ) ) , file(valued_2, fc14_valued_2)).
thf(fc15_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) )  &  (v1_relat_1 @ B) )  =>  (v2_valued_0 @  ( (k3_xboole_0 @ A)  @ B) ) ) ) , file(valued_0, fc15_valued_0)).
thf(fc15_valued_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v2_valued_2 @ C)  &  ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_1 @ D)  @ B) )  &  (v1_funct_1 @  ( (k1_funct_1 @ D)  @ B) ) ) ) ) , file(valued_2, fc15_valued_2)).
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_valued_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v1_valued_2 @ C)  &  ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) )  =>  (v1_valued_0 @  ( (k1_funct_1 @ D)  @ B) ) ) ) , file(valued_2, fc16_valued_2)).
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_card_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_card_1 @ A)  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v3_card_1 @ B)  @ A) ) ) )  =>  ( (v3_card_1 @  (k9_xtuple_0 @ B) )  @ A) ) ) , file(card_1, fc17_card_1)).
thf(fc17_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  &  (v1_relat_1 @ B) )  =>  (v3_valued_0 @  ( (k3_xboole_0 @ A)  @ B) ) ) ) , file(valued_0, fc17_valued_0)).
thf(fc17_valued_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v2_valued_2 @ C)  &  ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) )  =>  (v2_valued_0 @  ( (k1_funct_1 @ D)  @ B) ) ) ) , file(valued_2, fc17_valued_2)).
thf(fc18_valued_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v3_valued_2 @ C)  &  ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) )  =>  (v3_valued_0 @  ( (k1_funct_1 @ D)  @ B) ) ) ) , file(valued_2, fc18_valued_2)).
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_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  &  (v1_relat_1 @ B) )  =>  ( (v5_relat_1 @  ( (k3_xboole_0 @ A)  @ B) )  @ k3_numbers) ) ) , file(valued_0, fc19_valued_0)).
thf(fc19_valued_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v4_valued_2 @ C)  &  ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) )  =>  ( (v5_relat_1 @  ( (k1_funct_1 @ D)  @ B) )  @ k3_numbers) ) ) , file(valued_2, fc19_valued_2)).
thf(fc1_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ~ ( (v1_xboole_0 @  (k1_euclid @ A) ) ) ) ) , file(euclid, fc1_euclid)).
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_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) )  &  ( (v1_rlvect_1 @  ( (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) ) ) ) ) ) ) ) ) ) ) ) ) , file(lopban_1, fc1_lopban_1)).
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_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_xboole_0, axiom,  (v1_xboole_0 @ k1_xboole_0) , file(xboole_0, fc1_xboole_0)).
thf(fc20_valued_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v5_valued_2 @ C)  &  ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) )  =>  ( (v5_relat_1 @  ( (k1_funct_1 @ D)  @ B) )  @ k4_numbers) ) ) , file(valued_2, fc20_valued_2)).
thf(fc21_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  &  (v1_relat_1 @ B) )  =>  ( (v5_relat_1 @  ( (k3_xboole_0 @ A)  @ B) )  @ k4_numbers) ) ) , file(valued_0, fc21_valued_0)).
thf(fc21_valued_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (v6_valued_2 @ C)  &  ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) )  =>  (v4_valued_0 @  ( (k1_funct_1 @ D)  @ B) ) ) ) , file(valued_2, fc21_valued_2)).
thf(fc23_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  &  (v1_relat_1 @ B) )  =>  (v4_valued_0 @  ( (k3_xboole_0 @ A)  @ B) ) ) ) , file(valued_0, fc23_valued_0)).
thf(fc2_funct_2, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  ( (k1_funct_2 @ A)  @ A) ) ) ) , file(funct_2, fc2_funct_2)).
thf(fc2_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) )  &  (v1_monoid_0 @  ( (k5_lopban_1 @ A)  @ B) ) ) ) ) ) ) ) ) ) ) ) ) , file(lopban_1, fc2_lopban_1)).
thf(fc2_real_ns1, axiom,  (! [A: $i] :  ( ( (v7_ordinal1 @ A)  &  ~ ( (v8_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_relset_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( (v4_relat_1 @ B)  @ A) )  &  (v1_relat_1 @ C) )  =>  ( (v4_relat_1 @  ( (k3_xboole_0 @ B)  @ C) )  @ A) ) ) , file(relset_1, fc2_relset_1)).
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(fc30_finseq_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (v3_finseq_1 @ A)  &  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  (v1_funct_1 @ B) ) ) )  =>  (v1_finseq_1 @  ( (k1_funct_1 @ B)  @ C) ) ) ) , file(finseq_1, fc30_finseq_1)).
thf(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_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) ) ) ) ) ) ) ) ) ) )  =>  ( ~ ( (v1_xboole_0 @  ( (k7_lopban_1 @ A)  @ B) ) )  &  (v4_funct_1 @  ( (k7_lopban_1 @ A)  @ B) ) ) ) ) , file(lopban_1, fc3_lopban_1)).
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_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_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v7_valued_2 @ A) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_1 @ A)  @ B) )  &  (v1_funct_1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) ) , file(valued_2, fc40_valued_2)).
thf(fc41_valued_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v8_valued_2 @ A) ) )  =>  ( (v1_relat_1 @  ( (k1_funct_1 @ A)  @ B) )  &  (v1_funct_1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) ) , file(valued_2, fc41_valued_2)).
thf(fc42_valued_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v7_valued_2 @ A) ) )  =>  (v1_valued_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_2, fc42_valued_2)).
thf(fc43_valued_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v8_valued_2 @ A) ) )  =>  (v2_valued_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_2, fc43_valued_2)).
thf(fc44_valued_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v9_valued_2 @ A) ) )  =>  (v3_valued_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_2, fc44_valued_2)).
thf(fc45_valued_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v10_valued_2 @ A) ) )  =>  ( (v5_relat_1 @  ( (k1_funct_1 @ A)  @ B) )  @ k3_numbers) ) ) , file(valued_2, fc45_valued_2)).
thf(fc46_valued_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v11_valued_2 @ A) ) )  =>  ( (v5_relat_1 @  ( (k1_funct_1 @ A)  @ B) )  @ k4_numbers) ) ) , file(valued_2, fc46_valued_2)).
thf(fc47_valued_2, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v12_valued_2 @ A) ) )  =>  (v4_valued_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_2, fc47_valued_2)).
thf(fc4_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) ) ) ) ) ) ) ) ) ) )  =>  ( (v13_algstr_0 @  ( ( ( (g1_rlvect_1 @  ( (k7_lopban_1 @ A)  @ B) )  @  ( (k7_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k5_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k6_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) ) )  &  ( (v1_rlvect_1 @  ( ( ( (g1_rlvect_1 @  ( (k7_lopban_1 @ A)  @ B) )  @  ( (k7_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k5_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k6_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) ) )  &  ( (v2_rlvect_1 @  ( ( ( (g1_rlvect_1 @  ( (k7_lopban_1 @ A)  @ B) )  @  ( (k7_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k5_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k6_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) ) )  &  ( (v3_rlvect_1 @  ( ( ( (g1_rlvect_1 @  ( (k7_lopban_1 @ A)  @ B) )  @  ( (k7_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k5_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k6_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) ) )  &  ( (v4_rlvect_1 @  ( ( ( (g1_rlvect_1 @  ( (k7_lopban_1 @ A)  @ B) )  @  ( (k7_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k5_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k6_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) ) )  &  ( (v5_rlvect_1 @  ( ( ( (g1_rlvect_1 @  ( (k7_lopban_1 @ A)  @ B) )  @  ( (k7_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k5_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k6_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) ) )  &  ( (v6_rlvect_1 @  ( ( ( (g1_rlvect_1 @  ( (k7_lopban_1 @ A)  @ B) )  @  ( (k7_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k5_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k6_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) ) )  &  ( (v7_rlvect_1 @  ( ( ( (g1_rlvect_1 @  ( (k7_lopban_1 @ A)  @ B) )  @  ( (k7_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k5_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k6_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) ) )  &  (v8_rlvect_1 @  ( ( ( (g1_rlvect_1 @  ( (k7_lopban_1 @ A)  @ B) )  @  ( (k7_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k5_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) )  @  ( (k6_rsspace @  ( (k5_lopban_1 @  (u1_struct_0 @ A) )  @ B) )  @  ( (k7_lopban_1 @ A)  @ B) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(lopban_1, fc4_lopban_1)).
thf(fc4_numbers, axiom,  ~ ( (v1_xboole_0 @ k4_numbers) ) , file(numbers, fc4_numbers)).
thf(fc4_ordinal1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v5_ordinal1 @ A) ) )  =>  (v3_ordinal1 @  (k9_xtuple_0 @ A) ) ) ) , file(ordinal1, fc4_ordinal1)).
thf(fc4_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(fc5_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) )  &  ( (v1_rlvect_1 @  ( (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) ) ) ) ) ) ) ) ) ) ) ) ) , file(lopban_1, fc5_lopban_1)).
thf(fc5_relset_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( (v5_relat_1 @ B)  @ A) )  &  (v1_relat_1 @ C) )  =>  ( (v5_relat_1 @  ( (k3_xboole_0 @ B)  @ C) )  @ A) ) ) , file(relset_1, fc5_relset_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(fc62_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_valued_0 @ A) ) )  =>  (v1_xxreal_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc62_valued_0)).
thf(fc63_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_valued_0 @ A) ) )  =>  (v1_xreal_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc63_valued_0)).
thf(fc64_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k3_numbers)  &  (v1_funct_1 @ A) ) )  =>  (v1_rat_1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc64_valued_0)).
thf(fc65_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k4_numbers)  &  (v1_funct_1 @ A) ) )  =>  (v1_int_1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc65_valued_0)).
thf(fc66_valued_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v4_valued_0 @ A) ) )  =>  (v7_ordinal1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc66_valued_0)).
thf(fc67_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_xcmplx_0 @ B)  =>  (v1_valued_0 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(valued_0, fc67_valued_0)).
thf(fc68_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_xxreal_0 @ B)  =>  (v2_valued_0 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(valued_0, fc68_valued_0)).
thf(fc69_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_xreal_0 @ B)  =>  (v3_valued_0 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(valued_0, fc69_valued_0)).
thf(fc6_card_1, axiom,  (v1_card_1 @ k4_ordinal1) , file(card_1, fc6_card_1)).
thf(fc6_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) )  &  (v1_monoid_0 @  ( (k8_lopban_1 @ A)  @ B) ) ) ) ) ) ) ) ) ) ) ) ) , file(lopban_1, fc6_lopban_1)).
thf(fc6_numbers, axiom,  ~ ( (v1_finset_1 @ k4_numbers) ) , file(numbers, fc6_numbers)).
thf(fc6_ordinal1, axiom,  ( ~ ( (v1_xboole_0 @ k4_ordinal1) )  &  (v3_ordinal1 @ k4_ordinal1) ) , file(ordinal1, fc6_ordinal1)).
thf(fc6_rvsum_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  (v1_xreal_0 @ B) )  =>  ( (v1_relat_1 @  ( (k2_finseq_2 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k2_finseq_2 @ A)  @ B) )  &  ( (v3_valued_0 @  ( (k2_finseq_2 @ A)  @ B) )  &  (v1_finseq_1 @  ( (k2_finseq_2 @ A)  @ B) ) ) ) ) ) ) , file(rvsum_1, fc6_rvsum_1)).
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_2, axiom,  (! [A: $i] :  (v3_valued_2 @  (k6_valued_2 @ A) ) ) , file(valued_2, fc6_valued_2)).
thf(fc70_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_rat_1 @ B)  =>  ( (v5_relat_1 @  ( (k2_funcop_1 @ A)  @ B) )  @ k3_numbers) ) ) , file(valued_0, fc70_valued_0)).
thf(fc71_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v1_int_1 @ B)  =>  ( (v5_relat_1 @  ( (k2_funcop_1 @ A)  @ B) )  @ k4_numbers) ) ) , file(valued_0, fc71_valued_0)).
thf(fc72_valued_0, axiom,  (! [A: $i, B: $i] :  ( (v7_ordinal1 @ B)  =>  (v4_valued_0 @  ( (k2_funcop_1 @ A)  @ B) ) ) ) , file(valued_0, fc72_valued_0)).
thf(fc7_card_1, axiom,  (v2_card_1 @ k4_ordinal1) , file(card_1, fc7_card_1)).
thf(fc7_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_xboole_0 @  ( (k10_lopban_1 @ A)  @ B) ) ) ) ) , file(lopban_1, fc7_lopban_1)).
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(fc8_euclid, axiom,  (! [A: $i, B: $i] :  ( (v7_ordinal1 @ A)  =>  (v3_finseq_1 @  ( (k4_finseq_2 @ A)  @ B) ) ) ) , file(euclid, fc8_euclid)).
thf(fc8_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) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( (v13_algstr_0 @  ( ( ( (g1_rlvect_1 @  ( (k10_lopban_1 @ A)  @ B) )  @  ( (k7_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k5_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k6_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) ) )  &  ( (v1_rlvect_1 @  ( ( ( (g1_rlvect_1 @  ( (k10_lopban_1 @ A)  @ B) )  @  ( (k7_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k5_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k6_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) ) )  &  ( (v2_rlvect_1 @  ( ( ( (g1_rlvect_1 @  ( (k10_lopban_1 @ A)  @ B) )  @  ( (k7_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k5_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k6_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) ) )  &  ( (v3_rlvect_1 @  ( ( ( (g1_rlvect_1 @  ( (k10_lopban_1 @ A)  @ B) )  @  ( (k7_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k5_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k6_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) ) )  &  ( (v4_rlvect_1 @  ( ( ( (g1_rlvect_1 @  ( (k10_lopban_1 @ A)  @ B) )  @  ( (k7_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k5_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k6_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) ) )  &  ( (v5_rlvect_1 @  ( ( ( (g1_rlvect_1 @  ( (k10_lopban_1 @ A)  @ B) )  @  ( (k7_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k5_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k6_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) ) )  &  ( (v6_rlvect_1 @  ( ( ( (g1_rlvect_1 @  ( (k10_lopban_1 @ A)  @ B) )  @  ( (k7_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k5_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k6_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) ) )  &  ( (v7_rlvect_1 @  ( ( ( (g1_rlvect_1 @  ( (k10_lopban_1 @ A)  @ B) )  @  ( (k7_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k5_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k6_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) ) )  &  (v8_rlvect_1 @  ( ( ( (g1_rlvect_1 @  ( (k10_lopban_1 @ A)  @ B) )  @  ( (k7_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k5_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) )  @  ( (k6_rsspace @  ( (k8_lopban_1 @ A)  @ B) )  @  ( (k10_lopban_1 @ A)  @ B) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(lopban_1, fc8_lopban_1)).
thf(fc8_numbers, axiom,  ~ ( (v1_finset_1 @ k1_numbers) ) , file(numbers, fc8_numbers)).
thf(fc8_ordinal1, axiom,  (v7_ordinal1 @ k5_ordinal1) , file(ordinal1, fc8_ordinal1)).
thf(fc8_relset_1, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) )  @ C) ) )  =>  (v1_relat_1 @  (k9_xtuple_0 @ D) ) ) ) , file(relset_1, fc8_relset_1)).
thf(fc8_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(fc9_card_1, axiom,  ~ ( (v1_finset_1 @ k4_ordinal1) ) , file(card_1, fc9_card_1)).
thf(fc9_euclid, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v3_finseq_1 @  (k1_euclid @ A) ) ) ) , file(euclid, fc9_euclid)).
thf(fc9_ordinal1, axiom,  (v8_ordinal1 @ k5_ordinal1) , file(ordinal1, fc9_ordinal1)).
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(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_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(idempotence_k3_xboole_0, axiom,  (! [A: $i, B: $i] :  ( ( (k3_xboole_0 @ A)  @ A)  = A) ) , file(xboole_0, k3_xboole_0)).
thf(idempotence_k9_subset_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @ A) )  =>  ( ( ( (k9_subset_1 @ A)  @ B)  @ B)  = B) ) ) , file(subset_1, k9_subset_1)).
thf(ie1_funct_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (m1_subset_1 @ D)  @ A) ) ) )  =>  ( ( ( (k7_partfun1 @ B)  @ C)  @ D)  =  ( ( ( (k3_funct_2 @ A)  @ B)  @ C)  @ D) ) ) ) , file(funct_2, ie1_funct_2)).
thf(involutiveness_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_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(rc10_ordinal1, axiom,  (? [A: $i] :  (v8_ordinal1 @ A) ) , file(ordinal1, rc10_ordinal1)).
thf(rc11_finseq_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k4_ordinal1)  &  ( (v1_funct_1 @ A)  &  ( (v2_funct_1 @ A)  &  ( (v1_finset_1 @ A)  &  ( (v1_finseq_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) ) ) ) , file(finseq_1, rc11_finseq_1)).
thf(rc11_ordinal1, axiom,  (? [A: $i] :  ~ ( (v8_ordinal1 @ A) ) ) , file(ordinal1, rc11_ordinal1)).
thf(rc12_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_finseq_1 @ B)  @ A)  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k4_ordinal1)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v2_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v1_finseq_1 @ B)  &  (v2_finseq_1 @ B) ) ) ) ) ) ) ) ) ) ) , file(finseq_1, rc12_finseq_1)).
thf(rc12_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v10_ordinal1 @ A) ) ) ) , file(ordinal1, rc12_ordinal1)).
thf(rc13_finseq_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k4_ordinal1)  &  ( (v1_funct_1 @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_finset_1 @ A)  &  ( (v4_valued_0 @ A)  &  ( (v1_finseq_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) ) ) ) ) , file(finseq_1, rc13_finseq_1)).
thf(rc13_ordinal1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  (v9_ordinal1 @ A) ) ) , file(ordinal1, rc13_ordinal1)).
thf(rc14_ordinal1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ~ ( (v9_ordinal1 @ A) ) ) ) , file(ordinal1, rc14_ordinal1)).
thf(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_card_1, axiom,  (? [A: $i] :  (v1_card_1 @ A) ) , file(card_1, rc1_card_1)).
thf(rc1_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) ) ) ) ) , file(finseq_1, rc1_finseq_1)).
thf(rc1_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_lopban_1, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_struct_0 @ 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) ) ) ) ) ) ) ) ) ) )  =>  (? [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ B) ) ) )  &  ( ~ ( (v1_xboole_0 @ C) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ A) )  &  ( ( (v5_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( (v1_partfun1 @ C)  @  (u1_struct_0 @ A) )  &  ( ( ( (v1_funct_2 @ C)  @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ B) )  &  ( ( ( (v13_vectsp_1 @ C)  @ A)  @ B)  &  ( ( (v1_lopban_1 @ C)  @ A)  @ B) ) ) ) ) ) ) ) ) ) ) ) ) , file(lopban_1, rc1_lopban_1)).
thf(rc1_nat_1, axiom,  (? [A: $i] :  (v7_ordinal1 @ A) ) , file(nat_1, rc1_nat_1)).
thf(rc1_ordinal1, axiom,  (? [A: $i] :  ( (v1_ordinal1 @ A)  &  (v2_ordinal1 @ A) ) ) , file(ordinal1, rc1_ordinal1)).
thf(rc1_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_rvsum_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k4_ordinal1)  &  ( (v1_funct_1 @ B)  &  ( (v4_valued_0 @ B)  &  ( (v1_finset_1 @ B)  &  ( ( (v3_card_1 @ B)  @ A)  &  ( (v1_finseq_1 @ B)  &  (v2_finseq_1 @ B) ) ) ) ) ) ) ) ) ) ) , file(rvsum_1, rc1_rvsum_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_2, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v6_valued_2 @ A) ) ) , file(valued_2, rc1_valued_2)).
thf(rc1_xboole_0, axiom,  (? [A: $i] :  (v1_xboole_0 @ A) ) , file(xboole_0, rc1_xboole_0)).
thf(rc1_xreal_0, axiom,  (? [A: $i] :  (v1_xreal_0 @ A) ) , file(xreal_0, rc1_xreal_0)).
thf(rc1_xxreal_0, axiom,  (? [A: $i] :  (v1_xxreal_0 @ A) ) , file(xxreal_0, rc1_xxreal_0)).
thf(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_card_1, axiom,  (? [A: $i] :  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  ( (v3_ordinal1 @ A)  &  ( (v1_finset_1 @ A)  &  (v1_card_1 @ A) ) ) ) ) ) , file(card_1, rc2_card_1)).
thf(rc2_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_finseq_1 @ B)  @ A)  &  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_xboole_0 @ B)  &  ( (v1_finset_1 @ B)  &  (v1_finseq_1 @ B) ) ) ) ) ) ) ) ) , file(finseq_1, rc2_finseq_1)).
thf(rc2_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) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ B) ) ) )  &  ( ~ ( (v1_xboole_0 @ C) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @  (u1_struct_0 @ A) )  &  ( ( (v5_relat_1 @ C)  @  (u1_struct_0 @ B) )  &  ( (v1_funct_1 @ C)  &  ( ( (v1_partfun1 @ C)  @  (u1_struct_0 @ A) )  &  ( ( ( (v1_funct_2 @ C)  @  (u1_struct_0 @ A) )  @  (u1_struct_0 @ B) )  &  ( ( ( (v13_vectsp_1 @ C)  @ A)  @ B)  &  ( ( ( (v1_lopban_1 @ C)  @ A)  @ B)  &  ( ( (v2_lopban_1 @ C)  @ A)  @ B) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(lopban_1, rc2_lopban_1)).
thf(rc2_nat_1, axiom,  (? [A: $i] :  ( (v7_ordinal1 @ A)  &  (v8_ordinal1 @ A) ) ) , file(nat_1, rc2_nat_1)).
thf(rc2_ordinal1, axiom,  (? [A: $i] :  (v3_ordinal1 @ A) ) , file(ordinal1, rc2_ordinal1)).
thf(rc2_rvsum_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k4_ordinal1)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  ( (v1_finset_1 @ A)  &  ( (v1_finseq_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) ) ) ) , file(rvsum_1, rc2_rvsum_1)).
thf(rc2_valued_2, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v12_valued_2 @ A) ) ) ) , file(valued_2, rc2_valued_2)).
thf(rc2_xboole_0, axiom,  (? [A: $i] :  ~ ( (v1_xboole_0 @ A) ) ) , file(xboole_0, rc2_xboole_0)).
thf(rc2_xreal_0, axiom,  (? [A: $i] :  (v1_xreal_0 @ A) ) , file(xreal_0, rc2_xreal_0)).
thf(rc2_xxreal_0, axiom,  (? [A: $i] :  (v1_xxreal_0 @ A) ) , file(xxreal_0, rc2_xxreal_0)).
thf(rc3_card_1, axiom,  (? [A: $i] :  ~ ( (v1_finset_1 @ A) ) ) , file(card_1, rc3_card_1)).
thf(rc3_finseq_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) , file(finseq_1, rc3_finseq_1)).
thf(rc3_nat_1, axiom,  (? [A: $i] :  ( (v7_ordinal1 @ A)  &  ~ ( (v8_ordinal1 @ A) ) ) ) , file(nat_1, rc3_nat_1)).
thf(rc3_ordinal1, axiom,  (? [A: $i] :  (v3_ordinal1 @ A) ) , file(ordinal1, rc3_ordinal1)).
thf(rc3_rvsum_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k4_ordinal1)  &  ( (v1_funct_1 @ A)  &  ( (v1_valued_0 @ A)  &  ( (v3_valued_0 @ A)  &  ( (v1_finset_1 @ A)  &  ( (v1_finseq_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) ) ) ) ) , file(rvsum_1, rc3_rvsum_1)).
thf(rc3_valued_0, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k4_ordinal1)  @ k4_ordinal1) ) )  &  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k4_ordinal1)  &  ( ( (v5_relat_1 @ A)  @ k4_ordinal1)  &  ( (v1_funct_1 @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_partfun1 @ A)  @ k4_ordinal1)  &  ( ( ( (v1_funct_2 @ A)  @ k4_ordinal1)  @ k4_ordinal1)  &  ( (v1_valued_0 @ A)  &  ( (v2_valued_0 @ A)  &  ( (v3_valued_0 @ A)  &  ( (v4_valued_0 @ A)  &  (v5_valued_0 @ A) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(valued_0, rc3_valued_0)).
thf(rc3_xreal_0, axiom,  (? [A: $i] :  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc3_xreal_0)).
thf(rc3_xxreal_0, axiom,  (? [A: $i] :  ( (v1_xxreal_0 @ A)  &  (v2_xxreal_0 @ A) ) ) , file(xxreal_0, rc3_xxreal_0)).
thf(rc4_card_1, axiom,  (? [A: $i] :  ( (v7_ordinal1 @ A)  &  ~ ( (v8_ordinal1 @ A) ) ) ) , file(card_1, rc4_card_1)).
thf(rc4_finseq_1, axiom,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k4_ordinal1)  &  ( (v1_funct_1 @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_finset_1 @ A)  &  ( (v1_finseq_1 @ A)  &  (v2_finseq_1 @ A) ) ) ) ) ) ) ) , file(finseq_1, rc4_finseq_1)).
thf(rc4_nat_1, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k1_numbers) )  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v3_ordinal1 @ A) ) ) ) , file(nat_1, rc4_nat_1)).
thf(rc4_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  (v3_ordinal1 @ A) ) ) ) ) , file(ordinal1, rc4_ordinal1)).
thf(rc4_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_xreal_0, axiom,  (? [A: $i] :  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc4_xreal_0)).
thf(rc4_xxreal_0, axiom,  (? [A: $i] :  ( (v1_xxreal_0 @ A)  &  (v3_xxreal_0 @ A) ) ) , file(xxreal_0, rc4_xxreal_0)).
thf(rc5_card_1, axiom,  (? [A: $i] :  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  ( (v3_ordinal1 @ A)  &  ( (v7_ordinal1 @ A)  &  ( ~ ( (v8_ordinal1 @ A) )  &  (v1_card_1 @ A) ) ) ) ) ) ) , file(card_1, rc5_card_1)).
thf(rc5_nat_1, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  &  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  ( (v3_ordinal1 @ A)  &  ( (v7_ordinal1 @ A)  &  ( ~ ( (v8_ordinal1 @ A) )  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v1_xreal_0 @ A)  &  ( (v1_finset_1 @ A)  &  (v1_card_1 @ A) ) ) ) ) ) ) ) ) ) ) ) , file(nat_1, rc5_nat_1)).
thf(rc5_ordinal1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  (v5_ordinal1 @ B) ) ) ) ) ) , file(ordinal1, rc5_ordinal1)).
thf(rc5_xreal_0, axiom,  (? [A: $i] :  ( (v8_ordinal1 @ A)  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc5_xreal_0)).
thf(rc5_xxreal_0, axiom,  (? [A: $i] :  ( (v8_ordinal1 @ A)  &  (v1_xxreal_0 @ A) ) ) , file(xxreal_0, rc5_xxreal_0)).
thf(rc6_card_1, axiom,  (! [A: $i] :  ( ~ ( (v1_finset_1 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( (v1_finset_1 @ B) ) ) ) ) ) , file(card_1, rc6_card_1)).
thf(rc6_finseq_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_finseq_1 @ B)  @ A)  &  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k4_ordinal1)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (v1_finset_1 @ B)  &  ( (v1_finseq_1 @ B)  &  (v2_finseq_1 @ B) ) ) ) ) ) ) ) ) ) ) ) , file(finseq_1, rc6_finseq_1)).
thf(rc6_ordinal1, axiom,  (? [A: $i] :  (v7_ordinal1 @ A) ) , file(ordinal1, rc6_ordinal1)).
thf(rc6_valued_0, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  (v4_valued_0 @ B) ) ) ) ) ) ) , file(valued_0, rc6_valued_0)).
thf(rc7_card_1, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (? [B: $i] :  ( (v3_card_1 @ B)  @ A) ) ) ) , file(card_1, rc7_card_1)).
thf(rc7_finseq_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k4_ordinal1)  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( ( (v3_card_1 @ B)  @ A)  &  ( (v1_finseq_1 @ B)  &  (v2_finseq_1 @ B) ) ) ) ) ) ) ) ) ) , file(finseq_1, rc7_finseq_1)).
thf(rc7_ordinal1, axiom,  (? [A: $i] :  (v7_ordinal1 @ A) ) , file(ordinal1, rc7_ordinal1)).
thf(rc8_card_1, axiom,  (! [A: $i] :  ( (v1_card_1 @ A)  =>  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v3_card_1 @ B)  @ A) ) ) ) ) ) , file(card_1, rc8_card_1)).
thf(rc8_finseq_1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v3_finseq_1 @ A) ) ) , file(finseq_1, rc8_finseq_1)).
thf(rc8_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v7_ordinal1 @ A) ) ) , file(ordinal1, rc8_ordinal1)).
thf(rc9_card_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( (v3_card_1 @ B)  @ np__1) ) ) ) ) , file(card_1, rc9_card_1)).
thf(rc9_finseq_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ k4_ordinal1)  &  ( ( (v5_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( (v1_finset_1 @ B)  &  ( (v1_finseq_1 @ B)  &  (v2_finseq_1 @ B) ) ) ) ) ) ) ) ) , file(finseq_1, rc9_finseq_1)).
thf(rc9_ordinal1, axiom,  (? [A: $i] :  (v8_ordinal1 @ A) ) , file(ordinal1, rc9_ordinal1)).
thf(rd1_nat_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( ( (k10_subset_1 @ A)  @ k4_ordinal1)  = A) ) ) , file(nat_1, rd1_nat_1)).
thf(rd1_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  ( ( (k10_subset_1 @ A)  @ k1_numbers)  = A) ) ) , file(xreal_0, rd1_xreal_0)).
thf(redefinition_k10_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) ) ) ) ) ) )  =>  ( ( ( ( (k10_funct_2 @ A)  @ B)  @ C)  @ D)  =  ( ( (k7_partfun1 @ B)  @ C)  @ D) ) ) ) , file(funct_2, k10_funct_2)).
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_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_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_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 = k5_ordinal1) , file(numbers, k5_numbers)).
thf(redefinition_k6_partfun1, axiom,  (! [A: $i] :  ( (k6_partfun1 @ A)  =  (k4_relat_1 @ A) ) ) , file(partfun1, k6_partfun1)).
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_k80_valued_2, axiom,  (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] :  ( ( (v3_valued_2 @ C)  &  ( (v3_valued_2 @ D)  &  ( ( (v1_funct_1 @ E)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) )  &  ( (v1_funct_1 @ F)  &  ( (m1_subset_1 @ F)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ D) ) ) ) ) ) )  =>  ( ( ( ( ( ( (k80_valued_2 @ A)  @ B)  @ C)  @ D)  @ E)  @ F)  =  ( ( ( (k78_valued_2 @ C)  @ D)  @ E)  @ F) ) ) ) , file(valued_2, k80_valued_2)).
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_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_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_subset_1, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @ A) )  =>  ( ( ( (k9_subset_1 @ A)  @ B)  @ C)  =  ( (k3_xboole_0 @ B)  @ C) ) ) ) , file(subset_1, k9_subset_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_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_tarski, axiom,  (! [A: $i, B: $i] :  ( ( (r2_tarski @ A)  @ B)  <=>  ( (r2_hidden @ A)  @ B) ) ) , file(tarski, r2_tarski)).
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(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__rm1_r1, axiom,  ( (k4_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  = np__1) , file(arithm, rqRealNeg__k4_xcmplx_0__rm1_r1)).
thf(spc1_boole, axiom,  ~ ( (v1_xboole_0 @ np__1) ) , file(boole, spc1_boole)).
thf(spc1_numerals, axiom,  ( (v2_xxreal_0 @ np__1)  &  ( (m1_subset_1 @ np__1)  @ k4_ordinal1) ) , file(numerals, spc1_numerals)).
thf(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(t1_numerals, axiom,  ( (m1_subset_1 @ k1_xboole_0)  @ k4_ordinal1) , file(numerals, t1_numerals)).
thf(t1_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (r2_tarski @ A)  @ B)  =>  ( (m1_subset_1 @ A)  @ B) ) ) ) , file(subset, t1_subset)).
thf(t2_boole, axiom,  (! [A: $i] :  ( ( (k3_xboole_0 @ A)  @ k1_xboole_0)  = k1_xboole_0) ) , file(boole, t2_boole)).
thf(t2_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ A)  @ B)  =>  ( (v1_xboole_0 @ B)  |  ( (r2_tarski @ A)  @ B) ) ) ) ) , file(subset, t2_subset)).
thf(t3_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ B) )  <=>  ( (r1_tarski @ A)  @ B) ) ) ) , file(subset, t3_subset)).
thf(t40_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)  @  (u1_struct_0 @  ( (k16_lopban_1 @ A)  @ B) ) )  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @  (u1_struct_0 @  ( (k16_lopban_1 @ A)  @ B) ) )  =>  (! [E: $i] :  ( ( (m1_subset_1 @ E)  @  (u1_struct_0 @  ( (k16_lopban_1 @ A)  @ B) ) )  =>  ( (E =  ( ( (k5_algstr_0 @  ( (k16_lopban_1 @ A)  @ B) )  @ C)  @ D) )  <=>  (! [F: $i] :  ( ( (m1_subset_1 @ F)  @  (u1_struct_0 @ A) )  =>  ( ( ( ( (k17_lopban_1 @ A)  @ B)  @ E)  @ F)  =  ( ( (k5_algstr_0 @ B)  @  ( ( ( (k17_lopban_1 @ A)  @ B)  @ C)  @ F) )  @  ( ( ( (k17_lopban_1 @ A)  @ B)  @ D)  @ F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(lopban_1, t40_lopban_1)).
thf(t4_subset, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( ( (r2_tarski @ A)  @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ C) ) )  =>  ( (m1_subset_1 @ A)  @ C) ) ) ) ) , file(subset, t4_subset)).
thf(t5_real_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_subset, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ~ ( ( ( (r2_tarski @ A)  @ B)  &  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ C) )  &  (v1_xboole_0 @ C) ) ) ) ) ) ) , file(subset, t5_subset)).
thf(t6_boole, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (A = k1_xboole_0) ) ) , file(boole, t6_boole)).
thf(t7_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( ( (r2_tarski @ A)  @ B)  &  (v1_xboole_0 @ B) ) ) ) ) , file(boole, t7_boole)).
thf(t8_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( (v1_xboole_0 @ A)  &  ( ~ ( (A = B) )  &  (v1_xboole_0 @ B) ) ) ) ) ) , file(boole, t8_boole)).
thf(t8_pdiff_6, conjecture,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (! [B: $i] :  ( (v7_ordinal1 @ B)  =>  (! [C: $i] :  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @  (k1_euclid @ B) )  @  (k1_euclid @ A) )  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ B) )  @  (k1_euclid @ A) ) ) ) ) )  =>  (! [D: $i] :  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @  (k1_euclid @ B) )  @  (k1_euclid @ A) )  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @  (k1_euclid @ B) )  @  (k1_euclid @ A) ) ) ) ) )  =>  (! [E: $i] :  ( ( (m1_subset_1 @ E)  @  (u1_struct_0 @  ( (k16_lopban_1 @  (k4_real_ns1 @ B) )  @  (k4_real_ns1 @ A) ) ) )  =>  (! [F: $i] :  ( ( (m1_subset_1 @ F)  @  (u1_struct_0 @  ( (k16_lopban_1 @  (k4_real_ns1 @ B) )  @  (k4_real_ns1 @ A) ) ) )  =>  ( ( (C = E)  &  (D = F) )  =>  ( ( ( ( (k8_integr15 @ A)  @  (k1_euclid @ B) )  @ C)  @ D)  =  ( ( (k5_algstr_0 @  ( (k16_lopban_1 @  (k4_real_ns1 @ B) )  @  (k4_real_ns1 @ A) ) )  @ E)  @ F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(pdiff_6, t8_pdiff_6)).