% Mizar problem: t3_pdiff_6,pdiff_6,91,5 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_lopban_1_type, type, k10_lopban_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(k1_euclid_type, type, k1_euclid: $i > $i). thf(k1_funct_2_type, type, k1_funct_2: $i > $i > $i). thf(k1_numbers_type, type, k1_numbers: $i). thf(k1_xboole_0_type, type, k1_xboole_0: $i). thf(k1_zfmisc_1_type, type, k1_zfmisc_1: $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_zfmisc_1_type, type, k2_zfmisc_1: $i > $i > $i). thf(k3_lopban_1_type, type, k3_lopban_1: $i > $i > $i). thf(k3_ndiff_1_type, type, k3_ndiff_1: $i > $i > $i > $i > $i). thf(k3_numbers_type, type, k3_numbers: $i). thf(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_struct_0_type, type, k4_struct_0: $i > $i). thf(k5_lopban_1_type, type, k5_lopban_1: $i > $i > $i). thf(k5_ordinal1_type, type, k5_ordinal1: $i). thf(k5_rsspace_type, type, k5_rsspace: $i > $i > $i). thf(k6_rsspace_type, type, k6_rsspace: $i > $i > $i). thf(k7_lopban_1_type, type, k7_lopban_1: $i > $i > $i). thf(k7_rsspace_type, type, k7_rsspace: $i > $i > $i). thf(k8_funcop_1_type, type, k8_funcop_1: $i > $i > $i > $i). thf(k8_lopban_1_type, type, k8_lopban_1: $i > $i > $i). thf(k8_pdiff_1_type, type, k8_pdiff_1: $i > $i > $i > $i > $i). thf(k9_funct_2_type, type, k9_funct_2: $i > $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_pdiff_1_type, type, r1_pdiff_1: $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(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_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_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_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_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(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(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(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(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(d8_pdiff_1, axiom, (! [A: $i] : ( ( (v7_ordinal1 @ A) & ~ ( (v8_ordinal1 @ A) ) ) => (! [B: $i] : ( ( (v7_ordinal1 @ B) & ~ ( (v8_ordinal1 @ B) ) ) => (! [C: $i] : ( ( (v1_funct_1 @ C) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ (k1_euclid @ A) ) @ (k1_euclid @ B) ) ) ) ) => (! [D: $i] : ( ( ( (m2_finseq_2 @ D) @ k1_numbers) @ (k1_euclid @ A) ) => ( ( ( ( (r1_pdiff_1 @ A) @ B) @ C) @ D) => (! [E: $i] : ( ( (v1_funct_1 @ E) & ( ( ( (v1_funct_2 @ E) @ (k1_euclid @ A) ) @ (k1_euclid @ B) ) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ (k1_euclid @ A) ) @ (k1_euclid @ B) ) ) ) ) ) => ( (E = ( ( ( (k8_pdiff_1 @ A) @ B) @ C) @ D) ) <=> (? [F: $i] : ( ( (v1_funct_1 @ F) & ( (m1_subset_1 @ F) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ (u1_struct_0 @ (k4_real_ns1 @ A) ) ) @ (u1_struct_0 @ (k4_real_ns1 @ B) ) ) ) ) ) & (? [G: $i] : ( ( (m1_subset_1 @ G) @ (u1_struct_0 @ (k4_real_ns1 @ A) ) ) & ( (C = F) & ( (D = G) & (E = ( ( ( (k3_ndiff_1 @ (k4_real_ns1 @ A) ) @ (k4_real_ns1 @ B) ) @ F) @ G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(pdiff_1, d8_pdiff_1)). thf(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_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_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_k1_euclid, axiom, (! [A: $i] : ( (v7_ordinal1 @ A) => ( (m1_finseq_2 @ (k1_euclid @ A) ) @ k1_numbers) ) ) , file(euclid, k1_euclid)). 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_xboole_0, axiom, $true, file(xboole_0, k1_xboole_0)). thf(dt_k1_zfmisc_1, axiom, $true, file(zfmisc_1, k1_zfmisc_1)). thf(dt_k2_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_zfmisc_1, axiom, $true, file(zfmisc_1, k2_zfmisc_1)). thf(dt_k3_lopban_1, axiom, (! [A: $i, B: $i] : ( ( ~ ( (v1_xboole_0 @ A) ) & ( ~ ( (v2_struct_0 @ B) ) & ( (v13_algstr_0 @ B) & ( (v2_rlvect_1 @ B) & ( (v3_rlvect_1 @ B) & ( (v4_rlvect_1 @ B) & ( (v5_rlvect_1 @ B) & ( (v6_rlvect_1 @ B) & ( (v7_rlvect_1 @ B) & ( (v8_rlvect_1 @ B) & (l1_rlvect_1 @ B) ) ) ) ) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k3_lopban_1 @ A) @ B) ) & ( ( ( (v1_funct_2 @ ( (k3_lopban_1 @ A) @ B) ) @ ( (k2_zfmisc_1 @ k1_numbers) @ ( (k9_funct_2 @ A) @ (u1_struct_0 @ B) ) ) ) @ ( (k9_funct_2 @ A) @ (u1_struct_0 @ B) ) ) & ( (m1_subset_1 @ ( (k3_lopban_1 @ A) @ B) ) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ ( (k2_zfmisc_1 @ k1_numbers) @ ( (k9_funct_2 @ A) @ (u1_struct_0 @ B) ) ) ) @ ( (k9_funct_2 @ A) @ (u1_struct_0 @ B) ) ) ) ) ) ) ) ) , file(lopban_1, k3_lopban_1)). thf(dt_k3_ndiff_1, axiom, (! [A: $i, B: $i, C: $i, D: $i] : ( ( ( ~ ( (v2_struct_0 @ A) ) & ( (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 @ C) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ (u1_struct_0 @ A) ) @ (u1_struct_0 @ B) ) ) ) ) & ( (m1_subset_1 @ D) @ (u1_struct_0 @ A) ) ) ) ) => ( (m1_subset_1 @ ( ( ( (k3_ndiff_1 @ A) @ B) @ C) @ D) ) @ (u1_struct_0 @ ( (k16_lopban_1 @ A) @ B) ) ) ) ) , file(ndiff_1, k3_ndiff_1)). thf(dt_k3_numbers, axiom, $true, file(numbers, k3_numbers)). thf(dt_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_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_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_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_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_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_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_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_lopban_1, axiom, (! [A: $i, B: $i] : ( ( ( ~ ( (v2_struct_0 @ A) ) & ( (v13_algstr_0 @ A) & ( (v2_rlvect_1 @ A) & ( (v3_rlvect_1 @ A) & ( (v4_rlvect_1 @ A) & ( (v5_rlvect_1 @ A) & ( (v6_rlvect_1 @ A) & ( (v7_rlvect_1 @ A) & ( (v8_rlvect_1 @ A) & (l1_rlvect_1 @ A) ) ) ) ) ) ) ) ) ) & ( ~ ( (v2_struct_0 @ B) ) & ( (v13_algstr_0 @ B) & ( (v2_rlvect_1 @ B) & ( (v3_rlvect_1 @ B) & ( (v4_rlvect_1 @ B) & ( (v5_rlvect_1 @ B) & ( (v6_rlvect_1 @ B) & ( (v7_rlvect_1 @ B) & ( (v8_rlvect_1 @ B) & (l1_rlvect_1 @ B) ) ) ) ) ) ) ) ) ) ) => ( ~ ( (v2_struct_0 @ ( (k8_lopban_1 @ A) @ B) ) ) & ( (v13_algstr_0 @ ( (k8_lopban_1 @ A) @ B) ) & ( (v2_rlvect_1 @ ( (k8_lopban_1 @ A) @ B) ) & ( (v3_rlvect_1 @ ( (k8_lopban_1 @ A) @ B) ) & ( (v4_rlvect_1 @ ( (k8_lopban_1 @ A) @ B) ) & ( (v5_rlvect_1 @ ( (k8_lopban_1 @ A) @ B) ) & ( (v6_rlvect_1 @ ( (k8_lopban_1 @ A) @ B) ) & ( (v7_rlvect_1 @ ( (k8_lopban_1 @ A) @ B) ) & ( (v8_rlvect_1 @ ( (k8_lopban_1 @ A) @ B) ) & (l1_rlvect_1 @ ( (k8_lopban_1 @ A) @ B) ) ) ) ) ) ) ) ) ) ) ) ) , file(lopban_1, k8_lopban_1)). thf(dt_k8_pdiff_1, axiom, (! [A: $i, B: $i, C: $i, D: $i] : ( ( ( (v7_ordinal1 @ A) & ~ ( (v8_ordinal1 @ A) ) ) & ( ( (v7_ordinal1 @ B) & ~ ( (v8_ordinal1 @ B) ) ) & ( ( (v1_funct_1 @ C) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ (k1_euclid @ A) ) @ (k1_euclid @ B) ) ) ) ) & ( (m1_subset_1 @ D) @ (k1_euclid @ A) ) ) ) ) => ( (v1_funct_1 @ ( ( ( (k8_pdiff_1 @ A) @ B) @ C) @ D) ) & ( ( ( (v1_funct_2 @ ( ( ( (k8_pdiff_1 @ A) @ B) @ C) @ D) ) @ (k1_euclid @ A) ) @ (k1_euclid @ B) ) & ( (m1_subset_1 @ ( ( ( (k8_pdiff_1 @ A) @ B) @ C) @ D) ) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ (k1_euclid @ A) ) @ (k1_euclid @ B) ) ) ) ) ) ) ) , file(pdiff_1, k8_pdiff_1)). thf(dt_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_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_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(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(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(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_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(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_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(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(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_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(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_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(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_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_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(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_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_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(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_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_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_r2_tarski, axiom, (! [A: $i, B: $i] : ( ( (r2_tarski @ A) @ B) <=> ( (r2_hidden @ A) @ B) ) ) , file(tarski, r2_tarski)). thf(reflexivity_r1_tarski, axiom, (! [A: $i, B: $i] : ( (r1_tarski @ A) @ A) ) , file(tarski, r1_tarski)). thf(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(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_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(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_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(t3_pdiff_6, conjecture, (! [A: $i] : ( ( (v7_ordinal1 @ A) & ~ ( (v8_ordinal1 @ A) ) ) => (! [B: $i] : ( ( (v7_ordinal1 @ B) & ~ ( (v8_ordinal1 @ B) ) ) => (! [C: $i] : ( ( (v1_funct_1 @ C) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ (k1_euclid @ B) ) @ (k1_euclid @ A) ) ) ) ) => (! [D: $i] : ( ( (v1_funct_1 @ D) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ (u1_struct_0 @ (k4_real_ns1 @ B) ) ) @ (u1_struct_0 @ (k4_real_ns1 @ A) ) ) ) ) ) => (! [E: $i] : ( ( ( (m2_finseq_2 @ E) @ k1_numbers) @ (k1_euclid @ B) ) => (! [F: $i] : ( ( (m1_subset_1 @ F) @ (u1_struct_0 @ (k4_real_ns1 @ B) ) ) => ( ( (C = D) & ( (E = F) & ( ( ( (r1_pdiff_1 @ B) @ A) @ C) @ E) ) ) => ( ( ( ( (k8_pdiff_1 @ B) @ A) @ C) @ E) = ( ( ( (k3_ndiff_1 @ (k4_real_ns1 @ B) ) @ (k4_real_ns1 @ A) ) @ D) @ F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(pdiff_6, t3_pdiff_6)).