% Mizar problem: t42_pdiff_4,pdiff_4,2273,5 include('Axioms/SET010^0.ax'). thf(n0_type, type, np__0: $i). thf(n1_type, type, np__1: $i). thf(n2_type, type, np__2: $i). thf(n3_type, type, np__3: $i). thf(k10_pdiff_1_type, type, k10_pdiff_1: $i > $i > $i > $i > $i). thf(k11_binop_2_type, type, k11_binop_2: $i). thf(k11_finseq_1_type, type, k11_finseq_1: $i > $i > $i > $i). thf(k14_rvsum_1_type, type, k14_rvsum_1: $i > $i > $i). thf(k16_rvsum_1_type, type, k16_rvsum_1: $i > $i). thf(k18_rvsum_1_type, type, k18_rvsum_1: $i > $i). thf(k18_valued_1_type, type, k18_valued_1: $i > $i > $i). thf(k1_card_1_type, type, k1_card_1: $i > $i). thf(k1_euclid_type, type, k1_euclid: $i > $i). thf(k1_euclid_8_type, type, k1_euclid_8: $i > $i > $i > $i). thf(k1_fdiff_1_type, type, k1_fdiff_1: $i > $i > $i). thf(k1_finsop_1_type, type, k1_finsop_1: $i > $i > $i > $i). thf(k1_funct_1_type, type, k1_funct_1: $i > $i > $i). thf(k1_numbers_type, type, k1_numbers: $i). thf(k1_partfun1_type, type, k1_partfun1: $i > $i > $i > $i > $i > $i > $i). thf(k1_pdiff_1_type, type, k1_pdiff_1: $i > $i > $i). thf(k1_square_1_type, type, k1_square_1: $i > $i). thf(k1_valued_1_type, type, k1_valued_1: $i > $i > $i). thf(k1_xboole_0_type, type, k1_xboole_0: $i). thf(k1_zfmisc_1_type, type, k1_zfmisc_1: $i > $i). thf(k22_rvsum_1_type, type, k22_rvsum_1: $i > $i > $i). thf(k24_valued_1_type, type, k24_valued_1: $i > $i > $i). thf(k2_euclid_8_type, type, k2_euclid_8: $i). thf(k2_xcmplx_0_type, type, k2_xcmplx_0: $i > $i > $i). thf(k2_zfmisc_1_type, type, k2_zfmisc_1: $i > $i > $i). thf(k3_euclid_8_type, type, k3_euclid_8: $i). thf(k3_finseq_1_type, type, k3_finseq_1: $i > $i). thf(k3_funcop_1_type, type, k3_funcop_1: $i > $i > $i > $i). thf(k3_funct_2_type, type, k3_funct_2: $i > $i > $i > $i > $i). thf(k3_numbers_type, type, k3_numbers: $i). thf(k3_relat_1_type, type, k3_relat_1: $i > $i > $i). thf(k3_square_1_type, type, k3_square_1: $i > $i). thf(k3_xcmplx_0_type, type, k3_xcmplx_0: $i > $i > $i). thf(k4_euclid_8_type, type, k4_euclid_8: $i). thf(k4_finseq_2_type, type, k4_finseq_2: $i > $i > $i). thf(k4_numbers_type, type, k4_numbers: $i). thf(k4_ordinal1_type, type, k4_ordinal1: $i). thf(k4_pdiff_4_type, type, k4_pdiff_4: $i > $i > $i). thf(k4_xcmplx_0_type, type, k4_xcmplx_0: $i > $i). thf(k5_numbers_type, type, k5_numbers: $i). thf(k5_ordinal1_type, type, k5_ordinal1: $i). thf(k5_pdiff_1_type, type, k5_pdiff_1: $i > $i > $i). thf(k5_pdiff_4_type, type, k5_pdiff_4: $i > $i). thf(k6_pdiff_1_type, type, k6_pdiff_1: $i > $i > $i > $i). thf(k6_pdiff_4_type, type, k6_pdiff_4: $i > $i > $i > $i). thf(k6_xcmplx_0_type, type, k6_xcmplx_0: $i > $i > $i). thf(k7_euclid_type, type, k7_euclid: $i > $i > $i > $i). thf(k7_xcmplx_0_type, type, k7_xcmplx_0: $i > $i > $i). thf(k9_binop_2_type, type, k9_binop_2: $i). thf(k9_euclid_type, type, k9_euclid: $i > $i > $i > $i). 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_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(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(v1_card_1_type, type, v1_card_1: $i > $o). thf(v1_finseq_1_type, type, v1_finseq_1: $i > $o). thf(v1_finset_1_type, type, v1_finset_1: $i > $o). thf(v1_funcop_1_type, type, v1_funcop_1: $i > $o). thf(v1_funct_1_type, type, v1_funct_1: $i > $o). thf(v1_funct_2_type, type, v1_funct_2: $i > $i > $i > $o). thf(v1_int_1_type, type, v1_int_1: $i > $o). thf(v1_membered_type, type, v1_membered: $i > $o). thf(v1_ordinal1_type, type, v1_ordinal1: $i > $o). thf(v1_partfun1_type, type, v1_partfun1: $i > $i > $o). thf(v1_rat_1_type, type, v1_rat_1: $i > $o). thf(v1_relat_1_type, type, v1_relat_1: $i > $o). thf(v1_setfam_1_type, type, v1_setfam_1: $i > $o). thf(v1_valued_0_type, type, v1_valued_0: $i > $o). thf(v1_xboole_0_type, type, v1_xboole_0: $i > $o). thf(v1_xcmplx_0_type, type, v1_xcmplx_0: $i > $o). thf(v1_xreal_0_type, type, v1_xreal_0: $i > $o). thf(v1_xxreal_0_type, type, v1_xxreal_0: $i > $o). thf(v1_zfmisc_1_type, type, v1_zfmisc_1: $i > $o). thf(v2_finseq_1_type, type, v2_finseq_1: $i > $o). thf(v2_funcop_1_type, type, v2_funcop_1: $i > $o). thf(v2_funct_1_type, type, v2_funct_1: $i > $o). thf(v2_membered_type, type, v2_membered: $i > $o). thf(v2_ordinal1_type, type, v2_ordinal1: $i > $o). thf(v2_rcomp_1_type, type, v2_rcomp_1: $i > $o). thf(v2_valued_0_type, type, v2_valued_0: $i > $o). thf(v2_xxreal_0_type, type, v2_xxreal_0: $i > $o). thf(v3_card_1_type, type, v3_card_1: $i > $i > $o). thf(v3_finseq_1_type, type, v3_finseq_1: $i > $o). thf(v3_membered_type, type, v3_membered: $i > $o). thf(v3_ordinal1_type, type, v3_ordinal1: $i > $o). thf(v3_rcomp_1_type, type, v3_rcomp_1: $i > $o). thf(v3_valued_0_type, type, v3_valued_0: $i > $o). thf(v3_valued_2_type, type, v3_valued_2: $i > $o). thf(v3_xxreal_0_type, type, v3_xxreal_0: $i > $o). thf(v4_funct_1_type, type, v4_funct_1: $i > $o). thf(v4_membered_type, type, v4_membered: $i > $o). thf(v4_relat_1_type, type, v4_relat_1: $i > $i > $o). thf(v4_valued_0_type, type, v4_valued_0: $i > $o). thf(v5_membered_type, type, v5_membered: $i > $o). thf(v5_ordinal1_type, type, v5_ordinal1: $i > $o). thf(v5_relat_1_type, type, v5_relat_1: $i > $i > $o). thf(v5_valued_0_type, type, v5_valued_0: $i > $o). thf(v6_membered_type, type, v6_membered: $i > $o). thf(v6_ordinal1_type, type, v6_ordinal1: $i > $o). thf(v6_valued_0_type, type, v6_valued_0: $i > $o). thf(v7_membered_type, type, v7_membered: $i > $o). thf(v7_ordinal1_type, type, v7_ordinal1: $i > $o). thf(v7_valued_0_type, type, v7_valued_0: $i > $o). thf(v8_ordinal1_type, type, v8_ordinal1: $i > $o). thf(v8_valued_0_type, type, v8_valued_0: $i > $o). thf(v9_ordinal1_type, type, v9_ordinal1: $i > $o). 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_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_membered, axiom, (! [A: $i] : ( (v5_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => (v1_int_1 @ B) ) ) ) ) , file(membered, cc10_membered)). thf(cc10_ordinal1, axiom, (! [A: $i] : ( (v6_ordinal1 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v6_ordinal1 @ B) ) ) ) ) , file(ordinal1, cc10_ordinal1)). thf(cc10_valued_0, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & (v1_valued_0 @ A) ) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v1_valued_0 @ B) ) ) ) ) , file(valued_0, cc10_valued_0)). thf(cc11_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_membered, axiom, (! [A: $i] : ( (v6_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => (v7_ordinal1 @ B) ) ) ) ) , file(membered, cc11_membered)). thf(cc11_ordinal1, axiom, (! [A: $i] : ( (v8_ordinal1 @ A) => (v7_ordinal1 @ A) ) ) , file(ordinal1, cc11_ordinal1)). thf(cc11_valued_0, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & (v2_valued_0 @ A) ) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v2_valued_0 @ B) ) ) ) ) , file(valued_0, cc11_valued_0)). thf(cc12_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_membered, axiom, (! [A: $i] : ( (v1_xboole_0 @ A) => (v6_membered @ A) ) ) , file(membered, cc12_membered)). 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(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_membered, axiom, (! [A: $i] : ( (v1_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v1_membered @ B) ) ) ) ) , file(membered, cc13_membered)). 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(cc14_membered, axiom, (! [A: $i] : ( (v2_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v2_membered @ B) ) ) ) ) , file(membered, cc14_membered)). 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(cc15_membered, axiom, (! [A: $i] : ( (v3_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v3_membered @ B) ) ) ) ) , file(membered, cc15_membered)). 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(cc16_membered, axiom, (! [A: $i] : ( (v4_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v4_membered @ B) ) ) ) ) , file(membered, cc16_membered)). 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_0, axiom, (! [A: $i, B: $i] : ( (v1_membered @ B) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => (v1_valued_0 @ C) ) ) ) ) , file(valued_0, cc16_valued_0)). thf(cc17_membered, axiom, (! [A: $i] : ( (v5_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v5_membered @ B) ) ) ) ) , file(membered, cc17_membered)). thf(cc17_ordinal1, axiom, (! [A: $i] : ( ~ ( (v10_ordinal1 @ A) ) => (v1_setfam_1 @ A) ) ) , file(ordinal1, cc17_ordinal1)). thf(cc17_valued_0, axiom, (! [A: $i, B: $i] : ( (v2_membered @ B) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => (v2_valued_0 @ C) ) ) ) ) , file(valued_0, cc17_valued_0)). thf(cc18_membered, axiom, (! [A: $i] : ( (v6_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v6_membered @ B) ) ) ) ) , file(membered, cc18_membered)). thf(cc18_ordinal1, axiom, (! [A: $i] : ( (v10_ordinal1 @ A) => ~ ( (v1_setfam_1 @ A) ) ) ) , file(ordinal1, cc18_ordinal1)). thf(cc18_valued_0, axiom, (! [A: $i, B: $i] : ( (v3_membered @ B) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => (v3_valued_0 @ C) ) ) ) ) , file(valued_0, cc18_valued_0)). thf(cc19_membered, axiom, (! [A: $i] : ( (v1_xboole_0 @ A) => (v7_membered @ A) ) ) , file(membered, cc19_membered)). thf(cc19_ordinal1, axiom, (! [A: $i] : ( (v1_setfam_1 @ A) => ~ ( (v10_ordinal1 @ A) ) ) ) , file(ordinal1, cc19_ordinal1)). thf(cc19_valued_0, axiom, (! [A: $i, B: $i] : ( (v4_membered @ B) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => ( (v5_relat_1 @ C) @ k3_numbers) ) ) ) ) , file(valued_0, cc19_valued_0)). thf(cc1_euclid, axiom, (! [A: $i] : ( (v7_ordinal1 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_euclid @ A) ) => ( (v3_card_1 @ B) @ A) ) ) ) ) , file(euclid, cc1_euclid)). thf(cc1_fcont_3, axiom, (! [A: $i] : ( ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ k1_numbers) ) => ( (v1_xboole_0 @ A) => (v2_rcomp_1 @ A) ) ) ) , file(fcont_3, cc1_fcont_3)). 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_funcop_1, axiom, (! [A: $i] : ( (v4_funct_1 @ A) => (! [B: $i] : ( ( (v1_relat_1 @ B) & ( ( (v5_relat_1 @ B) @ A) & (v1_funct_1 @ B) ) ) => ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v1_funcop_1 @ B) ) ) ) ) ) ) , file(funcop_1, cc1_funcop_1)). thf(cc1_funct_2, axiom, (! [A: $i, B: $i] : (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => ( ( (v1_partfun1 @ C) @ A) => ( ( (v1_funct_2 @ C) @ A) @ B) ) ) ) ) , file(funct_2, cc1_funct_2)). thf(cc1_membered, axiom, (! [A: $i] : ( (v6_membered @ A) => (v5_membered @ A) ) ) , file(membered, cc1_membered)). thf(cc1_nat_1, axiom, (! [A: $i] : ( (v7_ordinal1 @ A) => ( (v3_ordinal1 @ A) & (v7_ordinal1 @ A) ) ) ) , file(nat_1, cc1_nat_1)). thf(cc1_ordinal1, axiom, (! [A: $i] : ( (v3_ordinal1 @ A) => ( (v1_ordinal1 @ A) & (v2_ordinal1 @ A) ) ) ) , file(ordinal1, cc1_ordinal1)). thf(cc1_relset_1, axiom, (! [A: $i, B: $i] : (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => (v1_relat_1 @ C) ) ) ) , file(relset_1, cc1_relset_1)). thf(cc1_valued_0, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & (v4_valued_0 @ A) ) => ( (v1_relat_1 @ A) & ( (v5_relat_1 @ A) @ k4_numbers) ) ) ) , file(valued_0, cc1_valued_0)). thf(cc1_xreal_0, axiom, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => (v1_xreal_0 @ A) ) ) , file(xreal_0, cc1_xreal_0)). thf(cc20_ordinal1, axiom, (! [A: $i] : ( ~ ( (v1_setfam_1 @ A) ) => (v10_ordinal1 @ A) ) ) , file(ordinal1, cc20_ordinal1)). thf(cc20_valued_0, axiom, (! [A: $i, B: $i] : ( (v5_membered @ B) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => ( (v5_relat_1 @ C) @ k4_numbers) ) ) ) ) , file(valued_0, cc20_valued_0)). thf(cc21_valued_0, axiom, (! [A: $i, B: $i] : ( (v6_membered @ B) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => (v4_valued_0 @ C) ) ) ) ) , file(valued_0, cc21_valued_0)). thf(cc22_valued_0, axiom, (! [A: $i] : ( ( (v1_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(cc23_valued_0, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v2_valued_0 @ A) & (v5_valued_0 @ A) ) ) ) => ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v2_valued_0 @ A) & (v7_valued_0 @ A) ) ) ) ) ) , file(valued_0, cc23_valued_0)). thf(cc24_valued_0, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v2_valued_0 @ A) & (v6_valued_0 @ A) ) ) ) => ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v2_valued_0 @ A) & (v8_valued_0 @ A) ) ) ) ) ) , file(valued_0, cc24_valued_0)). thf(cc2_fcont_3, axiom, (! [A: $i] : ( ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ k1_numbers) ) => ( (v1_xboole_0 @ A) => (v3_rcomp_1 @ A) ) ) ) , file(fcont_3, cc2_fcont_3)). 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_funcop_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_funcop_1 @ A) ) ) => ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v2_funcop_1 @ A) ) ) ) ) , file(funcop_1, cc2_funcop_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_membered, axiom, (! [A: $i] : ( (v5_membered @ A) => (v4_membered @ A) ) ) , file(membered, cc2_membered)). 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_valued_0, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v5_relat_1 @ A) @ k4_numbers) ) => ( (v1_relat_1 @ A) & ( (v5_relat_1 @ A) @ k3_numbers) ) ) ) , file(valued_0, cc2_valued_0)). thf(cc2_xreal_0, axiom, (! [A: $i] : ( (v7_ordinal1 @ A) => (v1_xreal_0 @ A) ) ) , file(xreal_0, cc2_xreal_0)). thf(cc30_valued_0, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v5_relat_1 @ A) @ k1_numbers) ) => ( (v1_relat_1 @ A) & (v3_valued_0 @ A) ) ) ) , file(valued_0, cc30_valued_0)). thf(cc31_valued_0, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v5_relat_1 @ A) @ k4_ordinal1) ) => ( (v1_relat_1 @ A) & (v4_valued_0 @ A) ) ) ) , file(valued_0, cc31_valued_0)). 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_funcop_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_xboole_0 @ A) ) ) => ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_funcop_1 @ A) ) ) ) ) , file(funcop_1, cc3_funcop_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_membered, axiom, (! [A: $i] : ( (v4_membered @ A) => (v3_membered @ A) ) ) , file(membered, cc3_membered)). thf(cc3_nat_1, axiom, (! [A: $i] : ( (v7_ordinal1 @ A) => ( (v7_ordinal1 @ A) & ~ ( (v3_xxreal_0 @ A) ) ) ) ) , file(nat_1, cc3_nat_1)). thf(cc3_ordinal1, axiom, (! [A: $i] : ( (v1_xboole_0 @ A) => (v3_ordinal1 @ A) ) ) , file(ordinal1, cc3_ordinal1)). thf(cc3_relset_1, axiom, (! [A: $i, B: $i] : ( (v1_xboole_0 @ A) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => (v1_xboole_0 @ C) ) ) ) ) , file(relset_1, cc3_relset_1)). thf(cc3_valued_0, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v5_relat_1 @ A) @ k4_numbers) ) => ( (v1_relat_1 @ A) & (v3_valued_0 @ A) ) ) ) , file(valued_0, cc3_valued_0)). thf(cc3_xreal_0, axiom, (! [A: $i] : ( (v1_xreal_0 @ A) => (v1_xcmplx_0 @ A) ) ) , file(xreal_0, cc3_xreal_0)). thf(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_membered, axiom, (! [A: $i] : ( (v3_membered @ A) => (v2_membered @ A) ) ) , file(membered, cc4_membered)). 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_valued_0, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v5_relat_1 @ A) @ k3_numbers) ) => ( (v1_relat_1 @ A) & (v3_valued_0 @ A) ) ) ) , file(valued_0, cc4_valued_0)). thf(cc4_xreal_0, axiom, (! [A: $i] : ( (v1_xreal_0 @ A) => (v1_xxreal_0 @ A) ) ) , file(xreal_0, cc4_xreal_0)). thf(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_membered, axiom, (! [A: $i] : ( (v3_membered @ A) => (v1_membered @ A) ) ) , file(membered, cc5_membered)). 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_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(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_membered, axiom, (! [A: $i] : ( (v1_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => (v1_xcmplx_0 @ B) ) ) ) ) , file(membered, cc6_membered)). 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_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(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_membered, axiom, (! [A: $i] : ( (v2_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => (v1_xxreal_0 @ B) ) ) ) ) , file(membered, cc7_membered)). thf(cc7_ordinal1, axiom, (! [A: $i] : ( (v1_xboole_0 @ A) => (v7_ordinal1 @ A) ) ) , file(ordinal1, cc7_ordinal1)). thf(cc7_valued_0, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & (v4_valued_0 @ A) ) => ( (v1_relat_1 @ A) & ( (v5_relat_1 @ A) @ k3_numbers) ) ) ) , file(valued_0, cc7_valued_0)). thf(cc8_finseq_1, axiom, (! [A: $i] : ( (v1_xboole_0 @ A) => (v3_finseq_1 @ A) ) ) , file(finseq_1, cc8_finseq_1)). thf(cc8_membered, axiom, (! [A: $i] : ( (v3_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => (v1_xreal_0 @ B) ) ) ) ) , file(membered, cc8_membered)). thf(cc8_ordinal1, axiom, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k4_ordinal1) => (v7_ordinal1 @ A) ) ) , file(ordinal1, cc8_ordinal1)). thf(cc8_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(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_membered, axiom, (! [A: $i] : ( (v4_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => (v1_rat_1 @ B) ) ) ) ) , file(membered, cc9_membered)). thf(cc9_ordinal1, axiom, (! [A: $i] : ( (v1_xboole_0 @ A) => (v6_ordinal1 @ A) ) ) , file(ordinal1, cc9_ordinal1)). thf(cc9_valued_0, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & (v1_xboole_0 @ A) ) => ( (v1_relat_1 @ A) & (v4_valued_0 @ A) ) ) ) , file(valued_0, cc9_valued_0)). thf(commutativity_k14_rvsum_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v3_valued_0 @ A) & (v1_finseq_1 @ A) ) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & ( (v3_valued_0 @ B) & (v1_finseq_1 @ B) ) ) ) ) => ( ( (k14_rvsum_1 @ A) @ B) = ( (k14_rvsum_1 @ B) @ A) ) ) ) , file(rvsum_1, k14_rvsum_1)). thf(commutativity_k18_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v1_valued_0 @ B) ) ) ) => ( ( (k18_valued_1 @ A) @ B) = ( (k18_valued_1 @ B) @ A) ) ) ) , file(valued_1, k18_valued_1)). thf(commutativity_k1_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v1_valued_0 @ B) ) ) ) => ( ( (k1_valued_1 @ A) @ B) = ( (k1_valued_1 @ B) @ A) ) ) ) , file(valued_1, k1_valued_1)). thf(commutativity_k22_rvsum_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v3_valued_0 @ A) & (v1_finseq_1 @ A) ) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & ( (v3_valued_0 @ B) & (v1_finseq_1 @ B) ) ) ) ) => ( ( (k22_rvsum_1 @ A) @ B) = ( (k22_rvsum_1 @ B) @ A) ) ) ) , file(rvsum_1, k22_rvsum_1)). thf(commutativity_k2_xcmplx_0, axiom, (! [A: $i, B: $i] : ( ( (v1_xcmplx_0 @ A) & (v1_xcmplx_0 @ B) ) => ( ( (k2_xcmplx_0 @ A) @ B) = ( (k2_xcmplx_0 @ B) @ A) ) ) ) , file(xcmplx_0, k2_xcmplx_0)). thf(commutativity_k3_xcmplx_0, axiom, (! [A: $i, B: $i] : ( ( (v1_xcmplx_0 @ A) & (v1_xcmplx_0 @ B) ) => ( ( (k3_xcmplx_0 @ A) @ B) = ( (k3_xcmplx_0 @ B) @ A) ) ) ) , file(xcmplx_0, k3_xcmplx_0)). thf(commutativity_k7_euclid, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v7_ordinal1 @ A) & ( ( (m1_subset_1 @ B) @ (k1_euclid @ A) ) & ( (m1_subset_1 @ C) @ (k1_euclid @ A) ) ) ) => ( ( ( (k7_euclid @ A) @ B) @ C) = ( ( (k7_euclid @ A) @ C) @ B) ) ) ) , file(euclid, k7_euclid)). thf(d12_pdiff_1, axiom, (! [A: $i] : ( ( (v7_ordinal1 @ A) & ~ ( (v8_ordinal1 @ A) ) ) => (! [B: $i] : ( (v7_ordinal1 @ B) => (! [C: $i] : ( ( (v1_funct_1 @ C) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ (k1_euclid @ A) ) @ k1_numbers) ) ) ) => (! [D: $i] : ( ( ( (m2_finseq_2 @ D) @ k1_numbers) @ (k1_euclid @ A) ) => ( ( ( ( (k10_pdiff_1 @ A) @ B) @ C) @ D) = ( (k1_fdiff_1 @ ( ( ( ( ( (k1_partfun1 @ k1_numbers) @ (k1_euclid @ A) ) @ (k1_euclid @ A) ) @ k1_numbers) @ ( ( (k6_pdiff_1 @ A) @ B) @ D) ) @ C) ) @ ( ( ( (k3_funct_2 @ (k1_euclid @ A) ) @ k1_numbers) @ ( (k1_pdiff_1 @ B) @ A) ) @ D) ) ) ) ) ) ) ) ) ) ) , file(pdiff_1, d12_pdiff_1)). thf(d12_rvsum_1, axiom, (! [A: $i] : ( ( (m2_finseq_1 @ A) @ k1_numbers) => ( (k18_rvsum_1 @ A) = ( ( (k1_finsop_1 @ k1_numbers) @ A) @ k9_binop_2) ) ) ) , file(rvsum_1, d12_rvsum_1)). thf(d16_rvsum_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v3_valued_0 @ A) & (v1_finseq_1 @ A) ) ) ) => (! [B: $i] : ( ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & ( (v3_valued_0 @ B) & (v1_finseq_1 @ B) ) ) ) => ( ( (k22_rvsum_1 @ A) @ B) = (k18_rvsum_1 @ ( (k14_rvsum_1 @ A) @ B) ) ) ) ) ) ) , file(rvsum_1, d16_rvsum_1)). thf(d1_euclid, axiom, (! [A: $i] : ( (v7_ordinal1 @ A) => ( (k1_euclid @ A) = ( (k4_finseq_2 @ A) @ k1_numbers) ) ) ) , file(euclid, d1_euclid)). thf(d1_euclid_8, axiom, (k2_euclid_8 = ( ( (k1_euclid_8 @ np__1) @ k5_numbers) @ k5_numbers) ) , file(euclid_8, d1_euclid_8)). thf(d2_euclid_8, axiom, (k3_euclid_8 = ( ( (k1_euclid_8 @ k5_numbers) @ np__1) @ k5_numbers) ) , file(euclid_8, d2_euclid_8)). thf(d2_xboole_0, axiom, (k1_xboole_0 = (eps @ (^ [A: $i] : (v1_xboole_0 @ A) ) ) ) , file(xboole_0, d2_xboole_0)). thf(d3_euclid_8, axiom, (k4_euclid_8 = ( ( (k1_euclid_8 @ k5_numbers) @ k5_numbers) @ np__1) ) , file(euclid_8, d3_euclid_8)). thf(d7_pdiff_4, axiom, (! [A: $i] : ( ( (v1_funct_1 @ A) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ (k1_euclid @ np__3) ) @ k1_numbers) ) ) ) => (! [B: $i] : ( ( ( (m2_finseq_2 @ B) @ k1_numbers) @ (k1_euclid @ np__3) ) => ( ( (k4_pdiff_4 @ A) @ B) = ( ( (k7_euclid @ np__3) @ ( ( (k7_euclid @ np__3) @ ( ( (k9_euclid @ np__3) @ k2_euclid_8) @ ( ( ( (k10_pdiff_1 @ np__3) @ np__1) @ A) @ B) ) ) @ ( ( (k9_euclid @ np__3) @ k3_euclid_8) @ ( ( ( (k10_pdiff_1 @ np__3) @ np__2) @ A) @ B) ) ) ) @ ( ( (k9_euclid @ np__3) @ k4_euclid_8) @ ( ( ( (k10_pdiff_1 @ np__3) @ np__3) @ A) @ B) ) ) ) ) ) ) ) , file(pdiff_4, d7_pdiff_4)). thf(d8_pdiff_4, axiom, (! [A: $i] : ( ( ( (m2_finseq_2 @ A) @ k1_numbers) @ (k1_euclid @ np__3) ) => ( (k5_pdiff_4 @ A) = ( ( (k1_euclid_8 @ ( (k7_xcmplx_0 @ ( (k1_funct_1 @ A) @ np__1) ) @ (k3_square_1 @ ( (k2_xcmplx_0 @ ( (k2_xcmplx_0 @ (k1_square_1 @ ( (k1_funct_1 @ A) @ np__1) ) ) @ (k1_square_1 @ ( (k1_funct_1 @ A) @ np__2) ) ) ) @ (k1_square_1 @ ( (k1_funct_1 @ A) @ np__3) ) ) ) ) ) @ ( (k7_xcmplx_0 @ ( (k1_funct_1 @ A) @ np__2) ) @ (k3_square_1 @ ( (k2_xcmplx_0 @ ( (k2_xcmplx_0 @ (k1_square_1 @ ( (k1_funct_1 @ A) @ np__1) ) ) @ (k1_square_1 @ ( (k1_funct_1 @ A) @ np__2) ) ) ) @ (k1_square_1 @ ( (k1_funct_1 @ A) @ np__3) ) ) ) ) ) @ ( (k7_xcmplx_0 @ ( (k1_funct_1 @ A) @ np__3) ) @ (k3_square_1 @ ( (k2_xcmplx_0 @ ( (k2_xcmplx_0 @ (k1_square_1 @ ( (k1_funct_1 @ A) @ np__1) ) ) @ (k1_square_1 @ ( (k1_funct_1 @ A) @ np__2) ) ) ) @ (k1_square_1 @ ( (k1_funct_1 @ A) @ np__3) ) ) ) ) ) ) ) ) , file(pdiff_4, d8_pdiff_4)). thf(d9_pdiff_4, axiom, (! [A: $i] : ( ( (v1_funct_1 @ A) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ (k1_euclid @ np__3) ) @ k1_numbers) ) ) ) => (! [B: $i] : ( ( ( (m2_finseq_2 @ B) @ k1_numbers) @ (k1_euclid @ np__3) ) => (! [C: $i] : ( ( ( (m2_finseq_2 @ C) @ k1_numbers) @ (k1_euclid @ np__3) ) => ( ( ( (k6_pdiff_4 @ A) @ B) @ C) = ( (k2_xcmplx_0 @ ( (k2_xcmplx_0 @ ( (k3_xcmplx_0 @ ( ( ( (k10_pdiff_1 @ np__3) @ np__1) @ A) @ B) ) @ ( (k1_funct_1 @ (k5_pdiff_4 @ C) ) @ np__1) ) ) @ ( (k3_xcmplx_0 @ ( ( ( (k10_pdiff_1 @ np__3) @ np__2) @ A) @ B) ) @ ( (k1_funct_1 @ (k5_pdiff_4 @ C) ) @ np__2) ) ) ) @ ( (k3_xcmplx_0 @ ( ( ( (k10_pdiff_1 @ np__3) @ np__3) @ A) @ B) ) @ ( (k1_funct_1 @ (k5_pdiff_4 @ C) ) @ np__3) ) ) ) ) ) ) ) ) ) , file(pdiff_4, d9_pdiff_4)). thf(d9_rvsum_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v3_valued_0 @ A) & (v1_finseq_1 @ A) ) ) ) => (! [B: $i] : ( ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & ( (v3_valued_0 @ B) & (v1_finseq_1 @ B) ) ) ) => ( ( (k14_rvsum_1 @ A) @ B) = ( ( (k3_funcop_1 @ k11_binop_2) @ A) @ B) ) ) ) ) ) , file(rvsum_1, d9_rvsum_1)). thf(dt_k10_pdiff_1, axiom, (! [A: $i, B: $i, C: $i, D: $i] : ( ( ( (v7_ordinal1 @ A) & ~ ( (v8_ordinal1 @ A) ) ) & ( (v7_ordinal1 @ B) & ( ( (v1_funct_1 @ C) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ (k1_euclid @ A) ) @ k1_numbers) ) ) ) & ( (m1_subset_1 @ D) @ (k1_euclid @ A) ) ) ) ) => (v1_xreal_0 @ ( ( ( (k10_pdiff_1 @ A) @ B) @ C) @ D) ) ) ) , file(pdiff_1, k10_pdiff_1)). thf(dt_k11_binop_2, axiom, ( (v1_funct_1 @ k11_binop_2) & ( ( ( (v1_funct_2 @ k11_binop_2) @ ( (k2_zfmisc_1 @ k1_numbers) @ k1_numbers) ) @ k1_numbers) & ( (m1_subset_1 @ k11_binop_2) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ ( (k2_zfmisc_1 @ k1_numbers) @ k1_numbers) ) @ k1_numbers) ) ) ) ) , file(binop_2, k11_binop_2)). thf(dt_k11_finseq_1, axiom, $true, file(finseq_1, k11_finseq_1)). thf(dt_k14_rvsum_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v3_valued_0 @ A) & (v1_finseq_1 @ A) ) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & ( (v3_valued_0 @ B) & (v1_finseq_1 @ B) ) ) ) ) => ( (m2_finseq_1 @ ( (k14_rvsum_1 @ A) @ B) ) @ k1_numbers) ) ) , file(rvsum_1, k14_rvsum_1)). thf(dt_k16_rvsum_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v1_valued_0 @ A) & (v1_finseq_1 @ A) ) ) ) => (v1_xcmplx_0 @ (k16_rvsum_1 @ A) ) ) ) , file(rvsum_1, k16_rvsum_1)). thf(dt_k18_rvsum_1, axiom, (! [A: $i] : ( ( (m1_finseq_1 @ A) @ k1_numbers) => (v1_xreal_0 @ (k18_rvsum_1 @ A) ) ) ) , file(rvsum_1, k18_rvsum_1)). thf(dt_k18_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v1_valued_0 @ B) ) ) ) => ( (v1_relat_1 @ ( (k18_valued_1 @ A) @ B) ) & (v1_funct_1 @ ( (k18_valued_1 @ A) @ B) ) ) ) ) , file(valued_1, k18_valued_1)). thf(dt_k1_card_1, axiom, (! [A: $i] : (v1_card_1 @ (k1_card_1 @ A) ) ) , file(card_1, k1_card_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_euclid_8, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v1_xreal_0 @ A) & ( (v1_xreal_0 @ B) & (v1_xreal_0 @ C) ) ) => ( ( (m2_finseq_2 @ ( ( (k1_euclid_8 @ A) @ B) @ C) ) @ k1_numbers) @ (k1_euclid @ np__3) ) ) ) , file(euclid_8, k1_euclid_8)). thf(dt_k1_fdiff_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_funct_1 @ A) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k1_numbers) @ k1_numbers) ) ) ) & (v1_xreal_0 @ B) ) => (v1_xreal_0 @ ( (k1_fdiff_1 @ A) @ B) ) ) ) , file(fdiff_1, k1_fdiff_1)). thf(dt_k1_finsop_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ~ ( (v1_xboole_0 @ A) ) & ( ( (m1_finseq_1 @ B) @ A) & ( (v1_funct_1 @ C) & ( ( ( (v1_funct_2 @ C) @ ( (k2_zfmisc_1 @ A) @ A) ) @ A) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ A) ) @ A) ) ) ) ) ) ) => ( (m1_subset_1 @ ( ( (k1_finsop_1 @ A) @ B) @ C) ) @ A) ) ) , file(finsop_1, k1_finsop_1)). thf(dt_k1_funct_1, axiom, $true, file(funct_1, k1_funct_1)). thf(dt_k1_numbers, axiom, $true, file(numbers, k1_numbers)). thf(dt_k1_partfun1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ( ( ( (v1_funct_1 @ E) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) & ( (v1_funct_1 @ F) & ( (m1_subset_1 @ F) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ C) @ D) ) ) ) ) => ( (v1_funct_1 @ ( ( ( ( ( (k1_partfun1 @ A) @ B) @ C) @ D) @ E) @ F) ) & ( (m1_subset_1 @ ( ( ( ( ( (k1_partfun1 @ A) @ B) @ C) @ D) @ E) @ F) ) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ D) ) ) ) ) ) , file(partfun1, k1_partfun1)). thf(dt_k1_pdiff_1, axiom, (! [A: $i, B: $i] : ( ( (v7_ordinal1 @ A) & (v7_ordinal1 @ B) ) => ( (v1_funct_1 @ ( (k1_pdiff_1 @ A) @ B) ) & ( ( ( (v1_funct_2 @ ( (k1_pdiff_1 @ A) @ B) ) @ (k1_euclid @ B) ) @ k1_numbers) & ( (m1_subset_1 @ ( (k1_pdiff_1 @ A) @ B) ) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ (k1_euclid @ B) ) @ k1_numbers) ) ) ) ) ) ) , file(pdiff_1, k1_pdiff_1)). thf(dt_k1_square_1, axiom, $true, file(square_1, k1_square_1)). thf(dt_k1_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v1_valued_0 @ B) ) ) ) => ( (v1_relat_1 @ ( (k1_valued_1 @ A) @ B) ) & (v1_funct_1 @ ( (k1_valued_1 @ A) @ B) ) ) ) ) , file(valued_1, k1_valued_1)). thf(dt_k1_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_k22_rvsum_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v3_valued_0 @ A) & (v1_finseq_1 @ A) ) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & ( (v3_valued_0 @ B) & (v1_finseq_1 @ B) ) ) ) ) => (v1_xreal_0 @ ( (k22_rvsum_1 @ A) @ B) ) ) ) , file(rvsum_1, k22_rvsum_1)). thf(dt_k24_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) & (v1_xcmplx_0 @ B) ) => ( (v1_relat_1 @ ( (k24_valued_1 @ A) @ B) ) & (v1_funct_1 @ ( (k24_valued_1 @ A) @ B) ) ) ) ) , file(valued_1, k24_valued_1)). thf(dt_k2_euclid_8, axiom, ( ( (m2_finseq_2 @ k2_euclid_8) @ k1_numbers) @ (k1_euclid @ np__3) ) , file(euclid_8, k2_euclid_8)). thf(dt_k2_xcmplx_0, axiom, $true, file(xcmplx_0, k2_xcmplx_0)). thf(dt_k2_zfmisc_1, axiom, $true, file(zfmisc_1, k2_zfmisc_1)). thf(dt_k3_euclid_8, axiom, ( ( (m2_finseq_2 @ k3_euclid_8) @ k1_numbers) @ (k1_euclid @ np__3) ) , file(euclid_8, k3_euclid_8)). thf(dt_k3_finseq_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_finseq_1 @ A) ) ) => ( (m1_subset_1 @ (k3_finseq_1 @ A) ) @ k4_ordinal1) ) ) , file(finseq_1, k3_finseq_1)). thf(dt_k3_funcop_1, axiom, $true, file(funcop_1, k3_funcop_1)). thf(dt_k3_funct_2, axiom, (! [A: $i, B: $i, C: $i, D: $i] : ( ( ~ ( (v1_xboole_0 @ A) ) & ( ( (v1_funct_1 @ C) & ( ( ( (v1_funct_2 @ C) @ A) @ B) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & ( (m1_subset_1 @ D) @ A) ) ) => ( (m1_subset_1 @ ( ( ( (k3_funct_2 @ A) @ B) @ C) @ D) ) @ B) ) ) , file(funct_2, k3_funct_2)). thf(dt_k3_numbers, axiom, $true, file(numbers, k3_numbers)). thf(dt_k3_relat_1, axiom, (! [A: $i, B: $i] : (v1_relat_1 @ ( (k3_relat_1 @ A) @ B) ) ) , file(relat_1, k3_relat_1)). thf(dt_k3_square_1, axiom, (! [A: $i] : ( (v1_xreal_0 @ A) => (v1_xreal_0 @ (k3_square_1 @ A) ) ) ) , file(square_1, k3_square_1)). thf(dt_k3_xcmplx_0, axiom, $true, file(xcmplx_0, k3_xcmplx_0)). thf(dt_k4_euclid_8, axiom, ( ( (m2_finseq_2 @ k4_euclid_8) @ k1_numbers) @ (k1_euclid @ np__3) ) , file(euclid_8, k4_euclid_8)). 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_numbers, axiom, $true, file(numbers, k4_numbers)). thf(dt_k4_ordinal1, axiom, $true, file(ordinal1, k4_ordinal1)). thf(dt_k4_pdiff_4, axiom, (! [A: $i, B: $i] : ( ( ( (v1_funct_1 @ A) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ (k1_euclid @ np__3) ) @ k1_numbers) ) ) ) & ( (m1_subset_1 @ B) @ (k1_euclid @ np__3) ) ) => ( ( (m2_finseq_2 @ ( (k4_pdiff_4 @ A) @ B) ) @ k1_numbers) @ (k1_euclid @ np__3) ) ) ) , file(pdiff_4, k4_pdiff_4)). thf(dt_k4_xcmplx_0, axiom, (! [A: $i] : ( (v1_xcmplx_0 @ A) => (v1_xcmplx_0 @ (k4_xcmplx_0 @ A) ) ) ) , file(xcmplx_0, k4_xcmplx_0)). thf(dt_k5_numbers, axiom, ( (m1_subset_1 @ k5_numbers) @ k4_ordinal1) , file(numbers, k5_numbers)). thf(dt_k5_ordinal1, axiom, $true, file(ordinal1, k5_ordinal1)). thf(dt_k5_pdiff_1, axiom, (! [A: $i, B: $i] : ( ( (v7_ordinal1 @ A) & ( (m1_finseq_1 @ B) @ k1_numbers) ) => ( (v1_relat_1 @ ( (k5_pdiff_1 @ A) @ B) ) & (v1_funct_1 @ ( (k5_pdiff_1 @ A) @ B) ) ) ) ) , file(pdiff_1, k5_pdiff_1)). thf(dt_k5_pdiff_4, axiom, (! [A: $i] : ( ( (m1_subset_1 @ A) @ (k1_euclid @ np__3) ) => ( ( (m2_finseq_2 @ (k5_pdiff_4 @ A) ) @ k1_numbers) @ (k1_euclid @ np__3) ) ) ) , file(pdiff_4, k5_pdiff_4)). thf(dt_k6_pdiff_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v7_ordinal1 @ A) & ( (v7_ordinal1 @ B) & ( (m1_subset_1 @ C) @ (k1_euclid @ A) ) ) ) => ( (v1_funct_1 @ ( ( (k6_pdiff_1 @ A) @ B) @ C) ) & ( ( ( (v1_funct_2 @ ( ( (k6_pdiff_1 @ A) @ B) @ C) ) @ k1_numbers) @ (k1_euclid @ A) ) & ( (m1_subset_1 @ ( ( (k6_pdiff_1 @ A) @ B) @ C) ) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k1_numbers) @ (k1_euclid @ A) ) ) ) ) ) ) ) , file(pdiff_1, k6_pdiff_1)). thf(dt_k6_pdiff_4, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_funct_1 @ A) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ (k1_euclid @ np__3) ) @ k1_numbers) ) ) ) & ( ( (m1_subset_1 @ B) @ (k1_euclid @ np__3) ) & ( (m1_subset_1 @ C) @ (k1_euclid @ np__3) ) ) ) => (v1_xreal_0 @ ( ( (k6_pdiff_4 @ A) @ B) @ C) ) ) ) , file(pdiff_4, k6_pdiff_4)). thf(dt_k6_xcmplx_0, axiom, $true, file(xcmplx_0, k6_xcmplx_0)). thf(dt_k7_euclid, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v7_ordinal1 @ A) & ( ( (m1_subset_1 @ B) @ (k1_euclid @ A) ) & ( (m1_subset_1 @ C) @ (k1_euclid @ A) ) ) ) => ( ( (m2_finseq_2 @ ( ( (k7_euclid @ A) @ B) @ C) ) @ k1_numbers) @ (k1_euclid @ A) ) ) ) , file(euclid, k7_euclid)). thf(dt_k7_xcmplx_0, axiom, $true, file(xcmplx_0, k7_xcmplx_0)). thf(dt_k9_binop_2, axiom, ( (v1_funct_1 @ k9_binop_2) & ( ( ( (v1_funct_2 @ k9_binop_2) @ ( (k2_zfmisc_1 @ k1_numbers) @ k1_numbers) ) @ k1_numbers) & ( (m1_subset_1 @ k9_binop_2) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ ( (k2_zfmisc_1 @ k1_numbers) @ k1_numbers) ) @ k1_numbers) ) ) ) ) , file(binop_2, k9_binop_2)). thf(dt_k9_euclid, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v7_ordinal1 @ A) & ( ( (m1_subset_1 @ B) @ (k1_euclid @ A) ) & (v1_xreal_0 @ C) ) ) => ( ( (m2_finseq_2 @ ( ( (k9_euclid @ A) @ B) @ C) ) @ k1_numbers) @ (k1_euclid @ A) ) ) ) , file(euclid, k9_euclid)). thf(dt_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_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(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_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(fc10_euclid, axiom, (! [A: $i] : ( (v7_ordinal1 @ A) => (v3_valued_2 @ (k1_euclid @ A) ) ) ) , file(euclid, fc10_euclid)). thf(fc10_funcop_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_funcop_1 @ A) ) ) & ( (v1_relat_1 @ B) & (v1_funct_1 @ B) ) ) => ( (v1_relat_1 @ ( (k3_relat_1 @ B) @ A) ) & (v1_funcop_1 @ ( (k3_relat_1 @ B) @ A) ) ) ) ) , file(funcop_1, fc10_funcop_1)). thf(fc10_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v5_membered @ B) ) & ( ( ~ ( (v1_xboole_0 @ C) ) & (v5_membered @ C) ) & ( ( (v1_funct_1 @ D) & ( ( ( (v1_funct_2 @ D) @ A) @ B) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & ( (v1_funct_1 @ E) & ( ( ( (v1_funct_2 @ E) @ A) @ C) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k1_valued_1 @ D) @ E) ) & ( (v1_partfun1 @ ( (k1_valued_1 @ D) @ E) ) @ A) ) ) ) , file(valued_1, fc10_valued_1)). thf(fc10_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( ~ ( (v2_xxreal_0 @ A) ) & (v1_xreal_0 @ A) ) & ( ~ ( (v2_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => ~ ( (v2_xxreal_0 @ ( (k2_xcmplx_0 @ A) @ B) ) ) ) ) , file(xreal_0, fc10_xreal_0)). thf(fc11_finseq_1, axiom, (! [A: $i, B: $i, C: $i] : (v1_finseq_1 @ ( ( (k11_finseq_1 @ A) @ B) @ C) ) ) , file(finseq_1, fc11_finseq_1)). thf(fc11_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v6_membered @ B) ) & ( ( ~ ( (v1_xboole_0 @ C) ) & (v6_membered @ C) ) & ( ( (v1_funct_1 @ D) & ( ( ( (v1_funct_2 @ D) @ A) @ B) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & ( (v1_funct_1 @ E) & ( ( ( (v1_funct_2 @ E) @ A) @ C) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k1_valued_1 @ D) @ E) ) & ( (v1_partfun1 @ ( (k1_valued_1 @ D) @ E) ) @ A) ) ) ) , file(valued_1, fc11_valued_1)). thf(fc11_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( (v2_xxreal_0 @ A) & (v1_xreal_0 @ A) ) & ( ~ ( (v3_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => (v2_xxreal_0 @ ( (k2_xcmplx_0 @ A) @ B) ) ) ) , file(xreal_0, fc11_xreal_0)). thf(fc121_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_relat_1 @ B) & ( ( (v4_relat_1 @ B) @ A) & ( (v1_funct_1 @ B) & (v1_valued_0 @ B) ) ) ) & (v1_xcmplx_0 @ C) ) => ( (v1_relat_1 @ ( (k24_valued_1 @ B) @ C) ) & ( ( (v4_relat_1 @ ( (k24_valued_1 @ B) @ C) ) @ A) & (v1_funct_1 @ ( (k24_valued_1 @ B) @ C) ) ) ) ) ) , file(valued_1, fc121_valued_1)). thf(fc124_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_relat_1 @ B) & ( ( (v4_relat_1 @ B) @ A) & ( (v1_funct_1 @ B) & ( ( (v1_partfun1 @ B) @ A) & (v1_valued_0 @ B) ) ) ) ) & (v1_xcmplx_0 @ C) ) => ( (v1_relat_1 @ ( (k24_valued_1 @ B) @ C) ) & ( (v1_funct_1 @ ( (k24_valued_1 @ B) @ C) ) & ( (v1_partfun1 @ ( (k24_valued_1 @ B) @ C) ) @ A) ) ) ) ) , file(valued_1, fc124_valued_1)). thf(fc125_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v1_valued_0 @ B) ) ) & ( (v1_relat_1 @ C) & ( ( (v4_relat_1 @ C) @ A) & ( (v1_funct_1 @ C) & (v1_valued_0 @ C) ) ) ) ) => ( (v1_relat_1 @ ( (k1_valued_1 @ B) @ C) ) & ( ( (v4_relat_1 @ ( (k1_valued_1 @ B) @ C) ) @ A) & (v1_funct_1 @ ( (k1_valued_1 @ B) @ C) ) ) ) ) ) , file(valued_1, fc125_valued_1)). thf(fc127_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v1_valued_0 @ B) ) ) & ( (v1_relat_1 @ C) & ( ( (v4_relat_1 @ C) @ A) & ( (v1_funct_1 @ C) & (v1_valued_0 @ C) ) ) ) ) => ( (v1_relat_1 @ ( (k18_valued_1 @ B) @ C) ) & ( ( (v4_relat_1 @ ( (k18_valued_1 @ B) @ C) ) @ A) & (v1_funct_1 @ ( (k18_valued_1 @ B) @ C) ) ) ) ) ) , file(valued_1, fc127_valued_1)). thf(fc129_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_relat_1 @ B) & ( ( (v4_relat_1 @ B) @ A) & ( (v1_funct_1 @ B) & ( ( (v1_partfun1 @ B) @ A) & (v1_valued_0 @ B) ) ) ) ) & ( (v1_relat_1 @ C) & ( ( (v4_relat_1 @ C) @ A) & ( (v1_funct_1 @ C) & ( ( (v1_partfun1 @ C) @ A) & (v1_valued_0 @ C) ) ) ) ) ) => ( (v1_relat_1 @ ( (k1_valued_1 @ B) @ C) ) & ( (v1_funct_1 @ ( (k1_valued_1 @ B) @ C) ) & ( (v1_partfun1 @ ( (k1_valued_1 @ B) @ C) ) @ A) ) ) ) ) , file(valued_1, fc129_valued_1)). thf(fc12_ordinal1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & (v9_ordinal1 @ A) ) & (v1_relat_1 @ B) ) => ( (v1_relat_1 @ ( (k3_relat_1 @ B) @ A) ) & (v9_ordinal1 @ ( (k3_relat_1 @ B) @ A) ) ) ) ) , file(ordinal1, fc12_ordinal1)). thf(fc12_rvsum_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v1_xcmplx_0 @ A) & ( (v1_xcmplx_0 @ B) & (v1_xcmplx_0 @ C) ) ) => (v1_valued_0 @ ( ( (k11_finseq_1 @ A) @ B) @ C) ) ) ) , file(rvsum_1, fc12_rvsum_1)). thf(fc12_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v1_valued_0 @ A) & (v1_finseq_1 @ A) ) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & ( (v1_valued_0 @ B) & (v1_finseq_1 @ B) ) ) ) ) => ( (v1_relat_1 @ ( (k1_valued_1 @ A) @ B) ) & ( (v1_funct_1 @ ( (k1_valued_1 @ A) @ B) ) & (v1_finseq_1 @ ( (k1_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc12_valued_1)). thf(fc12_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( (v2_xxreal_0 @ A) & (v1_xreal_0 @ A) ) & ( ~ ( (v3_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => (v2_xxreal_0 @ ( (k2_xcmplx_0 @ B) @ A) ) ) ) , file(xreal_0, fc12_xreal_0)). thf(fc131_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_relat_1 @ B) & ( ( (v4_relat_1 @ B) @ A) & ( (v1_funct_1 @ B) & ( ( (v1_partfun1 @ B) @ A) & (v1_valued_0 @ B) ) ) ) ) & ( (v1_relat_1 @ C) & ( ( (v4_relat_1 @ C) @ A) & ( (v1_funct_1 @ C) & ( ( (v1_partfun1 @ C) @ A) & (v1_valued_0 @ C) ) ) ) ) ) => ( (v1_relat_1 @ ( (k18_valued_1 @ B) @ C) ) & ( (v1_funct_1 @ ( (k18_valued_1 @ B) @ C) ) & ( (v1_partfun1 @ ( (k18_valued_1 @ B) @ C) ) @ A) ) ) ) ) , file(valued_1, fc131_valued_1)). thf(fc13_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( (v3_xxreal_0 @ A) & (v1_xreal_0 @ A) ) & ( ~ ( (v2_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => (v3_xxreal_0 @ ( (k2_xcmplx_0 @ A) @ B) ) ) ) , file(xreal_0, fc13_xreal_0)). thf(fc14_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( (v3_xxreal_0 @ A) & (v1_xreal_0 @ A) ) & ( ~ ( (v2_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => (v3_xxreal_0 @ ( (k2_xcmplx_0 @ B) @ A) ) ) ) , file(xreal_0, fc14_xreal_0)). thf(fc15_xreal_0, axiom, (! [A: $i] : ( ( ~ ( (v2_xxreal_0 @ A) ) & (v1_xreal_0 @ A) ) => ( (v1_xcmplx_0 @ (k4_xcmplx_0 @ A) ) & ~ ( (v3_xxreal_0 @ (k4_xcmplx_0 @ A) ) ) ) ) ) , file(xreal_0, fc15_xreal_0)). thf(fc16_xreal_0, axiom, (! [A: $i] : ( ( ~ ( (v3_xxreal_0 @ A) ) & (v1_xreal_0 @ A) ) => ( (v1_xcmplx_0 @ (k4_xcmplx_0 @ A) ) & ~ ( (v2_xxreal_0 @ (k4_xcmplx_0 @ A) ) ) ) ) ) , file(xreal_0, fc16_xreal_0)). thf(fc17_rvsum_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v7_ordinal1 @ A) & ( (v7_ordinal1 @ B) & (v7_ordinal1 @ C) ) ) => (v4_valued_0 @ ( ( (k11_finseq_1 @ A) @ B) @ C) ) ) ) , file(rvsum_1, fc17_rvsum_1)). thf(fc17_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( ~ ( (v3_xxreal_0 @ A) ) & (v1_xreal_0 @ A) ) & ( ~ ( (v2_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => ~ ( (v3_xxreal_0 @ ( (k6_xcmplx_0 @ A) @ B) ) ) ) ) , file(xreal_0, fc17_xreal_0)). thf(fc18_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( ~ ( (v3_xxreal_0 @ A) ) & (v1_xreal_0 @ A) ) & ( ~ ( (v2_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => ~ ( (v2_xxreal_0 @ ( (k6_xcmplx_0 @ B) @ A) ) ) ) ) , file(xreal_0, fc18_xreal_0)). thf(fc19_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( (v2_xxreal_0 @ A) & (v1_xreal_0 @ A) ) & ( ~ ( (v2_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => (v2_xxreal_0 @ ( (k6_xcmplx_0 @ A) @ B) ) ) ) , file(xreal_0, fc19_xreal_0)). thf(fc1_euclid, axiom, (! [A: $i] : ( (v7_ordinal1 @ A) => ~ ( (v1_xboole_0 @ (k1_euclid @ A) ) ) ) ) , file(euclid, fc1_euclid)). thf(fc1_nat_1, axiom, (! [A: $i, B: $i] : ( ( (v7_ordinal1 @ A) & (v7_ordinal1 @ B) ) => (v7_ordinal1 @ ( (k2_xcmplx_0 @ A) @ B) ) ) ) , file(nat_1, fc1_nat_1)). thf(fc1_numbers, axiom, ~ ( (v1_xboole_0 @ k1_numbers) ) , file(numbers, fc1_numbers)). thf(fc1_rvsum_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ~ ( (v1_xboole_0 @ A) ) & ( ( (v1_funct_1 @ B) & ( ( ( (v1_funct_2 @ B) @ k1_numbers) @ A) & ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k1_numbers) @ A) ) ) ) ) & ( (v1_relat_1 @ C) & ( (v1_funct_1 @ C) & ( (v3_valued_0 @ C) & (v1_finseq_1 @ C) ) ) ) ) ) => ( (v1_relat_1 @ ( (k3_relat_1 @ C) @ B) ) & (v1_finseq_1 @ ( (k3_relat_1 @ C) @ B) ) ) ) ) , file(rvsum_1, fc1_rvsum_1)). thf(fc1_square_1, axiom, (! [A: $i] : ( (v1_xcmplx_0 @ A) => (v1_xcmplx_0 @ (k1_square_1 @ A) ) ) ) , file(square_1, fc1_square_1)). thf(fc20_finseq_1, axiom, (! [A: $i, B: $i, C: $i] : ~ ( (v1_xboole_0 @ ( ( (k11_finseq_1 @ A) @ B) @ C) ) ) ) , file(finseq_1, fc20_finseq_1)). thf(fc20_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( (v2_xxreal_0 @ A) & (v1_xreal_0 @ A) ) & ( ~ ( (v2_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => (v3_xxreal_0 @ ( (k6_xcmplx_0 @ B) @ A) ) ) ) , file(xreal_0, fc20_xreal_0)). thf(fc21_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( (v3_xxreal_0 @ A) & (v1_xreal_0 @ A) ) & ( ~ ( (v3_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => (v3_xxreal_0 @ ( (k6_xcmplx_0 @ A) @ B) ) ) ) , file(xreal_0, fc21_xreal_0)). thf(fc22_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( (v3_xxreal_0 @ A) & (v1_xreal_0 @ A) ) & ( ~ ( (v3_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => (v2_xxreal_0 @ ( (k6_xcmplx_0 @ B) @ A) ) ) ) , file(xreal_0, fc22_xreal_0)). thf(fc23_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( ~ ( (v2_xxreal_0 @ A) ) & (v1_xreal_0 @ A) ) & ( ~ ( (v3_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => ~ ( (v2_xxreal_0 @ ( (k3_xcmplx_0 @ A) @ B) ) ) ) ) , file(xreal_0, fc23_xreal_0)). thf(fc24_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( ~ ( (v2_xxreal_0 @ A) ) & (v1_xreal_0 @ A) ) & ( ~ ( (v3_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => ~ ( (v2_xxreal_0 @ ( (k3_xcmplx_0 @ B) @ A) ) ) ) ) , file(xreal_0, fc24_xreal_0)). thf(fc25_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( ~ ( (v2_xxreal_0 @ A) ) & (v1_xreal_0 @ A) ) & ( ~ ( (v2_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => ~ ( (v3_xxreal_0 @ ( (k3_xcmplx_0 @ A) @ B) ) ) ) ) , file(xreal_0, fc25_xreal_0)). thf(fc26_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( ~ ( (v3_xxreal_0 @ A) ) & (v1_xreal_0 @ A) ) & ( ~ ( (v3_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => ~ ( (v3_xxreal_0 @ ( (k3_xcmplx_0 @ A) @ B) ) ) ) ) , file(xreal_0, fc26_xreal_0)). thf(fc27_finseq_1, axiom, (! [A: $i, B: $i, C: $i] : ( (v3_card_1 @ ( ( (k11_finseq_1 @ A) @ B) @ C) ) @ np__3) ) , file(finseq_1, fc27_finseq_1)). thf(fc2_nat_1, axiom, (! [A: $i, B: $i] : ( ( (v7_ordinal1 @ A) & (v7_ordinal1 @ B) ) => (v7_ordinal1 @ ( (k3_xcmplx_0 @ A) @ B) ) ) ) , file(nat_1, fc2_nat_1)). thf(fc2_square_1, axiom, (! [A: $i] : ( (v1_xreal_0 @ A) => (v1_xreal_0 @ (k1_square_1 @ A) ) ) ) , file(square_1, fc2_square_1)). thf(fc2_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v1_valued_0 @ B) ) ) ) => ( (v1_relat_1 @ ( (k1_valued_1 @ A) @ B) ) & ( (v1_funct_1 @ ( (k1_valued_1 @ A) @ B) ) & (v1_valued_0 @ ( (k1_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc2_valued_1)). thf(fc30_finseq_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v3_finseq_1 @ A) & ( (v1_relat_1 @ B) & ( ( (v5_relat_1 @ B) @ A) & (v1_funct_1 @ B) ) ) ) => (v1_finseq_1 @ ( (k1_funct_1 @ B) @ C) ) ) ) , file(finseq_1, fc30_finseq_1)). thf(fc31_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( ~ ( (v3_xxreal_0 @ A) ) & (v1_xreal_0 @ A) ) & ( ~ ( (v2_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => ~ ( (v2_xxreal_0 @ ( (k7_xcmplx_0 @ A) @ B) ) ) ) ) , file(xreal_0, fc31_xreal_0)). thf(fc32_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( ~ ( (v3_xxreal_0 @ A) ) & (v1_xreal_0 @ A) ) & ( ~ ( (v2_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => ~ ( (v2_xxreal_0 @ ( (k7_xcmplx_0 @ B) @ A) ) ) ) ) , file(xreal_0, fc32_xreal_0)). thf(fc33_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v1_valued_0 @ B) ) ) ) => ( (v1_relat_1 @ ( (k18_valued_1 @ A) @ B) ) & ( (v1_funct_1 @ ( (k18_valued_1 @ A) @ B) ) & (v1_valued_0 @ ( (k18_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc33_valued_1)). thf(fc33_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( ~ ( (v3_xxreal_0 @ A) ) & (v1_xreal_0 @ A) ) & ( ~ ( (v3_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => ~ ( (v3_xxreal_0 @ ( (k7_xcmplx_0 @ A) @ B) ) ) ) ) , file(xreal_0, fc33_xreal_0)). thf(fc34_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v3_valued_0 @ A) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v3_valued_0 @ B) ) ) ) => ( (v1_relat_1 @ ( (k18_valued_1 @ A) @ B) ) & ( (v1_funct_1 @ ( (k18_valued_1 @ A) @ B) ) & (v3_valued_0 @ ( (k18_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc34_valued_1)). thf(fc34_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( ~ ( (v2_xxreal_0 @ A) ) & (v1_xreal_0 @ A) ) & ( ~ ( (v2_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => ~ ( (v3_xxreal_0 @ ( (k7_xcmplx_0 @ A) @ B) ) ) ) ) , file(xreal_0, fc34_xreal_0)). thf(fc35_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( ( (v5_relat_1 @ A) @ k3_numbers) & (v1_funct_1 @ A) ) ) & ( (v1_relat_1 @ B) & ( ( (v5_relat_1 @ B) @ k3_numbers) & (v1_funct_1 @ B) ) ) ) => ( (v1_relat_1 @ ( (k18_valued_1 @ A) @ B) ) & ( ( (v5_relat_1 @ ( (k18_valued_1 @ A) @ B) ) @ k3_numbers) & (v1_funct_1 @ ( (k18_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc35_valued_1)). thf(fc36_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( ( (v5_relat_1 @ A) @ k4_numbers) & (v1_funct_1 @ A) ) ) & ( (v1_relat_1 @ B) & ( ( (v5_relat_1 @ B) @ k4_numbers) & (v1_funct_1 @ B) ) ) ) => ( (v1_relat_1 @ ( (k18_valued_1 @ A) @ B) ) & ( ( (v5_relat_1 @ ( (k18_valued_1 @ A) @ B) ) @ k4_numbers) & (v1_funct_1 @ ( (k18_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc36_valued_1)). thf(fc37_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v4_valued_0 @ A) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v4_valued_0 @ B) ) ) ) => ( (v1_relat_1 @ ( (k18_valued_1 @ A) @ B) ) & ( (v1_funct_1 @ ( (k18_valued_1 @ A) @ B) ) & (v4_valued_0 @ ( (k18_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc37_valued_1)). thf(fc38_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v1_membered @ B) ) & ( ( ~ ( (v1_xboole_0 @ C) ) & (v1_membered @ C) ) & ( ( (v1_funct_1 @ D) & ( ( ( (v1_funct_2 @ D) @ A) @ B) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & ( (v1_funct_1 @ E) & ( ( ( (v1_funct_2 @ E) @ A) @ C) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k18_valued_1 @ D) @ E) ) & ( (v1_partfun1 @ ( (k18_valued_1 @ D) @ E) ) @ A) ) ) ) , file(valued_1, fc38_valued_1)). thf(fc39_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v3_membered @ B) ) & ( ( ~ ( (v1_xboole_0 @ C) ) & (v3_membered @ C) ) & ( ( (v1_funct_1 @ D) & ( ( ( (v1_funct_2 @ D) @ A) @ B) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & ( (v1_funct_1 @ E) & ( ( ( (v1_funct_2 @ E) @ A) @ C) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k18_valued_1 @ D) @ E) ) & ( (v1_partfun1 @ ( (k18_valued_1 @ D) @ E) ) @ A) ) ) ) , file(valued_1, fc39_valued_1)). thf(fc3_membered, axiom, (v3_membered @ k1_numbers) , file(membered, fc3_membered)). thf(fc3_nat_1, axiom, (! [A: $i, B: $i] : ( ( (v7_ordinal1 @ A) & ( (v7_ordinal1 @ B) & ~ ( (v8_ordinal1 @ B) ) ) ) => ~ ( (v8_ordinal1 @ ( (k2_xcmplx_0 @ A) @ B) ) ) ) ) , file(nat_1, fc3_nat_1)). thf(fc3_numbers, axiom, ~ ( (v1_xboole_0 @ k3_numbers) ) , file(numbers, fc3_numbers)). thf(fc3_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v3_valued_0 @ A) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v3_valued_0 @ B) ) ) ) => ( (v1_relat_1 @ ( (k1_valued_1 @ A) @ B) ) & ( (v1_funct_1 @ ( (k1_valued_1 @ A) @ B) ) & (v3_valued_0 @ ( (k1_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc3_valued_1)). thf(fc3_xreal_0, axiom, (! [A: $i] : ( (v1_xreal_0 @ A) => ( (v1_xcmplx_0 @ (k4_xcmplx_0 @ A) ) & (v1_xreal_0 @ (k4_xcmplx_0 @ A) ) ) ) ) , file(xreal_0, fc3_xreal_0)). thf(fc40_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v4_membered @ B) ) & ( ( ~ ( (v1_xboole_0 @ C) ) & (v4_membered @ C) ) & ( ( (v1_funct_1 @ D) & ( ( ( (v1_funct_2 @ D) @ A) @ B) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & ( (v1_funct_1 @ E) & ( ( ( (v1_funct_2 @ E) @ A) @ C) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k18_valued_1 @ D) @ E) ) & ( (v1_partfun1 @ ( (k18_valued_1 @ D) @ E) ) @ A) ) ) ) , file(valued_1, fc40_valued_1)). thf(fc41_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v5_membered @ B) ) & ( ( ~ ( (v1_xboole_0 @ C) ) & (v5_membered @ C) ) & ( ( (v1_funct_1 @ D) & ( ( ( (v1_funct_2 @ D) @ A) @ B) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & ( (v1_funct_1 @ E) & ( ( ( (v1_funct_2 @ E) @ A) @ C) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k18_valued_1 @ D) @ E) ) & ( (v1_partfun1 @ ( (k18_valued_1 @ D) @ E) ) @ A) ) ) ) , file(valued_1, fc41_valued_1)). thf(fc42_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v6_membered @ B) ) & ( ( ~ ( (v1_xboole_0 @ C) ) & (v6_membered @ C) ) & ( ( (v1_funct_1 @ D) & ( ( ( (v1_funct_2 @ D) @ A) @ B) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & ( (v1_funct_1 @ E) & ( ( ( (v1_funct_2 @ E) @ A) @ C) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k18_valued_1 @ D) @ E) ) & ( (v1_partfun1 @ ( (k18_valued_1 @ D) @ E) ) @ A) ) ) ) , file(valued_1, fc42_valued_1)). thf(fc43_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v1_valued_0 @ A) & (v1_finseq_1 @ A) ) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & ( (v1_valued_0 @ B) & (v1_finseq_1 @ B) ) ) ) ) => ( (v1_relat_1 @ ( (k18_valued_1 @ A) @ B) ) & ( (v1_funct_1 @ ( (k18_valued_1 @ A) @ B) ) & (v1_finseq_1 @ ( (k18_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc43_valued_1)). thf(fc44_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) & (v1_xcmplx_0 @ B) ) => ( (v1_relat_1 @ ( (k24_valued_1 @ A) @ B) ) & ( (v1_funct_1 @ ( (k24_valued_1 @ A) @ B) ) & (v1_valued_0 @ ( (k24_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc44_valued_1)). thf(fc45_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v3_valued_0 @ A) ) ) & (v1_xreal_0 @ B) ) => ( (v1_relat_1 @ ( (k24_valued_1 @ A) @ B) ) & ( (v1_funct_1 @ ( (k24_valued_1 @ A) @ B) ) & (v3_valued_0 @ ( (k24_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc45_valued_1)). thf(fc46_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( ( (v5_relat_1 @ A) @ k3_numbers) & (v1_funct_1 @ A) ) ) & (v1_rat_1 @ B) ) => ( (v1_relat_1 @ ( (k24_valued_1 @ A) @ B) ) & ( ( (v5_relat_1 @ ( (k24_valued_1 @ A) @ B) ) @ k3_numbers) & (v1_funct_1 @ ( (k24_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc46_valued_1)). thf(fc47_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( ( (v5_relat_1 @ A) @ k4_numbers) & (v1_funct_1 @ A) ) ) & (v1_int_1 @ B) ) => ( (v1_relat_1 @ ( (k24_valued_1 @ A) @ B) ) & ( ( (v5_relat_1 @ ( (k24_valued_1 @ A) @ B) ) @ k4_numbers) & (v1_funct_1 @ ( (k24_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc47_valued_1)). thf(fc48_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v4_valued_0 @ A) ) ) & (v7_ordinal1 @ B) ) => ( (v1_relat_1 @ ( (k24_valued_1 @ A) @ B) ) & ( (v1_funct_1 @ ( (k24_valued_1 @ A) @ B) ) & (v4_valued_0 @ ( (k24_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc48_valued_1)). thf(fc49_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v1_membered @ B) ) & ( ( (v1_funct_1 @ C) & ( ( ( (v1_funct_2 @ C) @ A) @ B) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & (v1_xcmplx_0 @ D) ) ) => ( (v1_funct_1 @ ( (k24_valued_1 @ C) @ D) ) & ( (v1_partfun1 @ ( (k24_valued_1 @ C) @ D) ) @ A) ) ) ) , file(valued_1, fc49_valued_1)). thf(fc4_funct_2, axiom, (! [A: $i, B: $i, C: $i, D: $i] : ( ( ( (v1_funct_1 @ C) & ( ( ( (v1_funct_2 @ C) @ A) @ B) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & ( (v1_funct_1 @ D) & ( ( ( (v1_funct_2 @ D) @ A) @ A) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ A) ) ) ) ) ) => ( (v1_funct_1 @ ( (k3_relat_1 @ D) @ C) ) & ( ( (v1_funct_2 @ ( (k3_relat_1 @ D) @ C) ) @ A) @ B) ) ) ) , file(funct_2, fc4_funct_2)). thf(fc4_membered, axiom, (v4_membered @ k3_numbers) , file(membered, fc4_membered)). thf(fc4_nat_1, axiom, (! [A: $i, B: $i] : ( ( (v7_ordinal1 @ A) & ( (v7_ordinal1 @ B) & ~ ( (v8_ordinal1 @ B) ) ) ) => ~ ( (v8_ordinal1 @ ( (k2_xcmplx_0 @ B) @ A) ) ) ) ) , file(nat_1, fc4_nat_1)). thf(fc4_numbers, axiom, ~ ( (v1_xboole_0 @ k4_numbers) ) , file(numbers, fc4_numbers)). thf(fc4_rvsum_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v1_xreal_0 @ A) & ( (v1_xreal_0 @ B) & (v1_xreal_0 @ C) ) ) => (v3_valued_0 @ ( ( (k11_finseq_1 @ A) @ B) @ C) ) ) ) , file(rvsum_1, fc4_rvsum_1)). thf(fc4_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( ( (v5_relat_1 @ A) @ k3_numbers) & (v1_funct_1 @ A) ) ) & ( (v1_relat_1 @ B) & ( ( (v5_relat_1 @ B) @ k3_numbers) & (v1_funct_1 @ B) ) ) ) => ( (v1_relat_1 @ ( (k1_valued_1 @ A) @ B) ) & ( ( (v5_relat_1 @ ( (k1_valued_1 @ A) @ B) ) @ k3_numbers) & (v1_funct_1 @ ( (k1_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc4_valued_1)). thf(fc50_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v3_membered @ B) ) & ( ( (v1_funct_1 @ C) & ( ( ( (v1_funct_2 @ C) @ A) @ B) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & (v1_xreal_0 @ D) ) ) => ( (v1_funct_1 @ ( (k24_valued_1 @ C) @ D) ) & ( (v1_partfun1 @ ( (k24_valued_1 @ C) @ D) ) @ A) ) ) ) , file(valued_1, fc50_valued_1)). thf(fc51_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v4_membered @ B) ) & ( ( (v1_funct_1 @ C) & ( ( ( (v1_funct_2 @ C) @ A) @ B) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & (v1_rat_1 @ D) ) ) => ( (v1_funct_1 @ ( (k24_valued_1 @ C) @ D) ) & ( (v1_partfun1 @ ( (k24_valued_1 @ C) @ D) ) @ A) ) ) ) , file(valued_1, fc51_valued_1)). thf(fc52_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v5_membered @ B) ) & ( ( (v1_funct_1 @ C) & ( ( ( (v1_funct_2 @ C) @ A) @ B) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & (v1_int_1 @ D) ) ) => ( (v1_funct_1 @ ( (k24_valued_1 @ C) @ D) ) & ( (v1_partfun1 @ ( (k24_valued_1 @ C) @ D) ) @ A) ) ) ) , file(valued_1, fc52_valued_1)). thf(fc53_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v6_membered @ B) ) & ( ( (v1_funct_1 @ C) & ( ( ( (v1_funct_2 @ C) @ A) @ B) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & (v7_ordinal1 @ D) ) ) => ( (v1_funct_1 @ ( (k24_valued_1 @ C) @ D) ) & ( (v1_partfun1 @ ( (k24_valued_1 @ C) @ D) ) @ A) ) ) ) , file(valued_1, fc53_valued_1)). thf(fc54_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v1_valued_0 @ A) & (v1_finseq_1 @ A) ) ) ) & (v1_xcmplx_0 @ B) ) => ( (v1_relat_1 @ ( (k24_valued_1 @ A) @ B) ) & ( (v1_funct_1 @ ( (k24_valued_1 @ A) @ B) ) & (v1_finseq_1 @ ( (k24_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc54_valued_1)). thf(fc55_valued_0, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_relat_1 @ B) & (v1_valued_0 @ B) ) ) => ( (v1_relat_1 @ ( (k3_relat_1 @ A) @ B) ) & (v1_valued_0 @ ( (k3_relat_1 @ A) @ B) ) ) ) ) , file(valued_0, fc55_valued_0)). thf(fc56_membered, axiom, (v7_membered @ k1_numbers) , file(membered, fc56_membered)). thf(fc56_valued_0, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_relat_1 @ B) & (v2_valued_0 @ B) ) ) => ( (v1_relat_1 @ ( (k3_relat_1 @ A) @ B) ) & (v2_valued_0 @ ( (k3_relat_1 @ A) @ B) ) ) ) ) , file(valued_0, fc56_valued_0)). thf(fc57_membered, axiom, (v7_membered @ k3_numbers) , file(membered, fc57_membered)). thf(fc57_valued_0, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_relat_1 @ B) & (v3_valued_0 @ B) ) ) => ( (v1_relat_1 @ ( (k3_relat_1 @ A) @ B) ) & (v3_valued_0 @ ( (k3_relat_1 @ A) @ B) ) ) ) ) , file(valued_0, fc57_valued_0)). thf(fc58_membered, axiom, (v7_membered @ k4_numbers) , file(membered, fc58_membered)). thf(fc58_valued_0, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_relat_1 @ B) & ( (v5_relat_1 @ B) @ k3_numbers) ) ) => ( (v1_relat_1 @ ( (k3_relat_1 @ A) @ B) ) & ( (v5_relat_1 @ ( (k3_relat_1 @ A) @ B) ) @ k3_numbers) ) ) ) , file(valued_0, fc58_valued_0)). thf(fc59_membered, axiom, (v7_membered @ k4_ordinal1) , file(membered, fc59_membered)). thf(fc59_valued_0, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_relat_1 @ B) & ( (v5_relat_1 @ B) @ k4_numbers) ) ) => ( (v1_relat_1 @ ( (k3_relat_1 @ A) @ B) ) & ( (v5_relat_1 @ ( (k3_relat_1 @ A) @ B) ) @ k4_numbers) ) ) ) , file(valued_0, fc59_valued_0)). thf(fc5_funct_2, axiom, (! [A: $i, B: $i, C: $i, D: $i] : ( ( ( (v1_funct_1 @ C) & ( ( ( (v1_funct_2 @ C) @ B) @ B) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ B) @ B) ) ) ) ) & ( (v1_funct_1 @ D) & ( ( ( (v1_funct_2 @ D) @ A) @ B) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) ) => ( (v1_funct_1 @ ( (k3_relat_1 @ D) @ C) ) & ( ( (v1_funct_2 @ ( (k3_relat_1 @ D) @ C) ) @ A) @ B) ) ) ) , file(funct_2, fc5_funct_2)). thf(fc5_membered, axiom, (v5_membered @ k4_numbers) , file(membered, fc5_membered)). thf(fc5_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( ( (v5_relat_1 @ A) @ k4_numbers) & (v1_funct_1 @ A) ) ) & ( (v1_relat_1 @ B) & ( ( (v5_relat_1 @ B) @ k4_numbers) & (v1_funct_1 @ B) ) ) ) => ( (v1_relat_1 @ ( (k1_valued_1 @ A) @ B) ) & ( ( (v5_relat_1 @ ( (k1_valued_1 @ A) @ B) ) @ k4_numbers) & (v1_funct_1 @ ( (k1_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc5_valued_1)). thf(fc5_xreal_0, axiom, (! [A: $i, B: $i] : ( ( (v1_xreal_0 @ A) & (v1_xreal_0 @ B) ) => (v1_xreal_0 @ ( (k2_xcmplx_0 @ A) @ B) ) ) ) , file(xreal_0, fc5_xreal_0)). thf(fc60_valued_0, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_relat_1 @ B) & (v4_valued_0 @ B) ) ) => ( (v1_relat_1 @ ( (k3_relat_1 @ A) @ B) ) & (v4_valued_0 @ ( (k3_relat_1 @ A) @ B) ) ) ) ) , file(valued_0, fc60_valued_0)). thf(fc61_valued_0, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) => (v1_xcmplx_0 @ ( (k1_funct_1 @ A) @ B) ) ) ) , file(valued_0, fc61_valued_0)). thf(fc62_valued_0, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v2_valued_0 @ A) ) ) => (v1_xxreal_0 @ ( (k1_funct_1 @ A) @ B) ) ) ) , file(valued_0, fc62_valued_0)). thf(fc63_valued_0, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v3_valued_0 @ A) ) ) => (v1_xreal_0 @ ( (k1_funct_1 @ A) @ B) ) ) ) , file(valued_0, fc63_valued_0)). thf(fc64_valued_0, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( ( (v5_relat_1 @ A) @ k3_numbers) & (v1_funct_1 @ A) ) ) => (v1_rat_1 @ ( (k1_funct_1 @ A) @ B) ) ) ) , file(valued_0, fc64_valued_0)). thf(fc65_valued_0, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( ( (v5_relat_1 @ A) @ k4_numbers) & (v1_funct_1 @ A) ) ) => (v1_int_1 @ ( (k1_funct_1 @ A) @ B) ) ) ) , file(valued_0, fc65_valued_0)). thf(fc66_valued_0, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v4_valued_0 @ A) ) ) => (v7_ordinal1 @ ( (k1_funct_1 @ A) @ B) ) ) ) , file(valued_0, fc66_valued_0)). thf(fc6_funcop_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_relat_1 @ A) & (v1_funct_1 @ A) ) & ( ( (v1_relat_1 @ B) & (v1_funct_1 @ B) ) & ( (v1_relat_1 @ C) & (v1_funct_1 @ C) ) ) ) => ( (v1_relat_1 @ ( ( (k3_funcop_1 @ A) @ B) @ C) ) & (v1_funct_1 @ ( ( (k3_funcop_1 @ A) @ B) @ C) ) ) ) ) , file(funcop_1, fc6_funcop_1)). thf(fc6_membered, axiom, (v6_membered @ k4_ordinal1) , file(membered, fc6_membered)). thf(fc6_numbers, axiom, ~ ( (v1_finset_1 @ k4_numbers) ) , file(numbers, fc6_numbers)). thf(fc6_ordinal1, axiom, ( ~ ( (v1_xboole_0 @ k4_ordinal1) ) & (v3_ordinal1 @ k4_ordinal1) ) , file(ordinal1, fc6_ordinal1)). thf(fc6_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v4_valued_0 @ A) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v4_valued_0 @ B) ) ) ) => ( (v1_relat_1 @ ( (k1_valued_1 @ A) @ B) ) & ( (v1_funct_1 @ ( (k1_valued_1 @ A) @ B) ) & (v4_valued_0 @ ( (k1_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc6_valued_1)). thf(fc6_xreal_0, axiom, (! [A: $i, B: $i] : ( ( (v1_xreal_0 @ A) & (v1_xreal_0 @ B) ) => (v1_xreal_0 @ ( (k3_xcmplx_0 @ A) @ B) ) ) ) , file(xreal_0, fc6_xreal_0)). thf(fc7_numbers, axiom, ~ ( (v1_finset_1 @ k3_numbers) ) , file(numbers, fc7_numbers)). thf(fc7_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v1_membered @ B) ) & ( ( ~ ( (v1_xboole_0 @ C) ) & (v1_membered @ C) ) & ( ( (v1_funct_1 @ D) & ( ( ( (v1_funct_2 @ D) @ A) @ B) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & ( (v1_funct_1 @ E) & ( ( ( (v1_funct_2 @ E) @ A) @ C) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k1_valued_1 @ D) @ E) ) & ( (v1_partfun1 @ ( (k1_valued_1 @ D) @ E) ) @ A) ) ) ) , file(valued_1, fc7_valued_1)). thf(fc7_xreal_0, axiom, (! [A: $i, B: $i] : ( ( (v1_xreal_0 @ A) & (v1_xreal_0 @ B) ) => (v1_xreal_0 @ ( (k6_xcmplx_0 @ A) @ B) ) ) ) , file(xreal_0, fc7_xreal_0)). thf(fc85_valued_0, axiom, (! [A: $i, B: $i] : ( (v1_membered @ B) => (v1_valued_0 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) , file(valued_0, fc85_valued_0)). thf(fc86_valued_0, axiom, (! [A: $i, B: $i] : ( (v2_membered @ B) => (v2_valued_0 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) , file(valued_0, fc86_valued_0)). thf(fc87_valued_0, axiom, (! [A: $i, B: $i] : ( (v3_membered @ B) => (v3_valued_0 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) , file(valued_0, fc87_valued_0)). thf(fc88_valued_0, axiom, (! [A: $i, B: $i] : ( (v4_membered @ B) => ( (v5_relat_1 @ ( (k2_zfmisc_1 @ A) @ B) ) @ k3_numbers) ) ) , file(valued_0, fc88_valued_0)). thf(fc89_valued_0, axiom, (! [A: $i, B: $i] : ( (v5_membered @ B) => ( (v5_relat_1 @ ( (k2_zfmisc_1 @ A) @ B) ) @ k4_numbers) ) ) , file(valued_0, fc89_valued_0)). thf(fc8_euclid, axiom, (! [A: $i, B: $i] : ( (v7_ordinal1 @ A) => (v3_finseq_1 @ ( (k4_finseq_2 @ A) @ B) ) ) ) , file(euclid, fc8_euclid)). thf(fc8_funct_2, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( ~ ( (v1_xboole_0 @ B) ) & ( ( (v1_funct_1 @ D) & ( ( ( (v1_funct_2 @ D) @ A) @ B) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & ( (v1_funct_1 @ E) & ( ( ( (v1_funct_2 @ E) @ B) @ C) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ B) @ C) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k3_relat_1 @ D) @ E) ) & ( ( (v1_funct_2 @ ( (k3_relat_1 @ D) @ E) ) @ A) @ C) ) ) ) , file(funct_2, fc8_funct_2)). thf(fc8_nat_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k4_ordinal1) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k4_ordinal1) ) ) ) ) & ( ~ ( (v1_xboole_0 @ B) ) & ( (v1_funct_1 @ C) & ( ( ( (v1_funct_2 @ C) @ k4_ordinal1) @ B) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ B) ) ) ) ) ) ) => ( (v1_relat_1 @ ( (k3_relat_1 @ A) @ C) ) & ( ( (v4_relat_1 @ ( (k3_relat_1 @ A) @ C) ) @ k4_ordinal1) & ( ( (v5_relat_1 @ ( (k3_relat_1 @ A) @ C) ) @ B) & (v1_funct_1 @ ( (k3_relat_1 @ A) @ C) ) ) ) ) ) ) , file(nat_1, fc8_nat_1)). thf(fc8_numbers, axiom, ~ ( (v1_finset_1 @ k1_numbers) ) , file(numbers, fc8_numbers)). thf(fc8_ordinal1, axiom, (v7_ordinal1 @ k5_ordinal1) , file(ordinal1, fc8_ordinal1)). thf(fc8_rvsum_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v3_valued_0 @ A) & (v1_finseq_1 @ A) ) ) ) => ( (v1_xcmplx_0 @ (k16_rvsum_1 @ A) ) & (v1_xreal_0 @ (k16_rvsum_1 @ A) ) ) ) ) , file(rvsum_1, fc8_rvsum_1)). thf(fc8_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v3_membered @ B) ) & ( ( ~ ( (v1_xboole_0 @ C) ) & (v3_membered @ C) ) & ( ( (v1_funct_1 @ D) & ( ( ( (v1_funct_2 @ D) @ A) @ B) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & ( (v1_funct_1 @ E) & ( ( ( (v1_funct_2 @ E) @ A) @ C) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k1_valued_1 @ D) @ E) ) & ( (v1_partfun1 @ ( (k1_valued_1 @ D) @ E) ) @ A) ) ) ) , file(valued_1, fc8_valued_1)). thf(fc8_xreal_0, axiom, (! [A: $i, B: $i] : ( ( (v1_xreal_0 @ A) & (v1_xreal_0 @ B) ) => (v1_xreal_0 @ ( (k7_xcmplx_0 @ A) @ B) ) ) ) , file(xreal_0, fc8_xreal_0)). thf(fc90_valued_0, axiom, (! [A: $i, B: $i] : ( (v6_membered @ B) => (v4_valued_0 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) , file(valued_0, fc90_valued_0)). thf(fc91_valued_0, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v2_valued_0 @ A) & (v5_valued_0 @ A) ) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & ( (v2_valued_0 @ B) & (v5_valued_0 @ B) ) ) ) ) => ( (v1_relat_1 @ ( (k3_relat_1 @ A) @ B) ) & (v5_valued_0 @ ( (k3_relat_1 @ A) @ B) ) ) ) ) , file(valued_0, fc91_valued_0)). thf(fc92_valued_0, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v2_valued_0 @ A) & (v7_valued_0 @ A) ) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & ( (v2_valued_0 @ B) & (v7_valued_0 @ B) ) ) ) ) => ( (v1_relat_1 @ ( (k3_relat_1 @ A) @ B) ) & (v7_valued_0 @ ( (k3_relat_1 @ A) @ B) ) ) ) ) , file(valued_0, fc92_valued_0)). thf(fc93_valued_0, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v2_valued_0 @ A) & (v6_valued_0 @ A) ) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & ( (v2_valued_0 @ B) & (v6_valued_0 @ B) ) ) ) ) => ( (v1_relat_1 @ ( (k3_relat_1 @ A) @ B) ) & (v5_valued_0 @ ( (k3_relat_1 @ A) @ B) ) ) ) ) , file(valued_0, fc93_valued_0)). thf(fc94_valued_0, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v2_valued_0 @ A) & (v8_valued_0 @ A) ) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & ( (v2_valued_0 @ B) & (v8_valued_0 @ B) ) ) ) ) => ( (v1_relat_1 @ ( (k3_relat_1 @ A) @ B) ) & (v7_valued_0 @ ( (k3_relat_1 @ A) @ B) ) ) ) ) , file(valued_0, fc94_valued_0)). thf(fc95_valued_0, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v2_valued_0 @ A) & (v6_valued_0 @ A) ) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & ( (v2_valued_0 @ B) & (v5_valued_0 @ B) ) ) ) ) => ( (v1_relat_1 @ ( (k3_relat_1 @ A) @ B) ) & (v6_valued_0 @ ( (k3_relat_1 @ A) @ B) ) ) ) ) , file(valued_0, fc95_valued_0)). thf(fc96_valued_0, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v2_valued_0 @ A) & (v6_valued_0 @ A) ) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & ( (v2_valued_0 @ B) & (v5_valued_0 @ B) ) ) ) ) => ( (v1_relat_1 @ ( (k3_relat_1 @ B) @ A) ) & (v6_valued_0 @ ( (k3_relat_1 @ B) @ A) ) ) ) ) , file(valued_0, fc96_valued_0)). thf(fc97_valued_0, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v2_valued_0 @ A) & (v8_valued_0 @ A) ) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & ( (v2_valued_0 @ B) & (v7_valued_0 @ B) ) ) ) ) => ( (v1_relat_1 @ ( (k3_relat_1 @ A) @ B) ) & (v8_valued_0 @ ( (k3_relat_1 @ A) @ B) ) ) ) ) , file(valued_0, fc97_valued_0)). thf(fc98_valued_0, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v2_valued_0 @ A) & (v8_valued_0 @ A) ) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & ( (v2_valued_0 @ B) & (v7_valued_0 @ B) ) ) ) ) => ( (v1_relat_1 @ ( (k3_relat_1 @ B) @ A) ) & (v8_valued_0 @ ( (k3_relat_1 @ B) @ A) ) ) ) ) , file(valued_0, fc98_valued_0)). thf(fc9_euclid, axiom, (! [A: $i] : ( (v7_ordinal1 @ A) => (v3_finseq_1 @ (k1_euclid @ A) ) ) ) , file(euclid, fc9_euclid)). thf(fc9_finseq_1, axiom, (! [A: $i, B: $i, C: $i] : ( (v1_relat_1 @ ( ( (k11_finseq_1 @ A) @ B) @ C) ) & (v1_funct_1 @ ( ( (k11_finseq_1 @ A) @ B) @ C) ) ) ) , file(finseq_1, fc9_finseq_1)). thf(fc9_funcop_1, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_funcop_1 @ A) ) ) => ( (v1_relat_1 @ ( (k1_funct_1 @ A) @ B) ) & (v1_funct_1 @ ( (k1_funct_1 @ A) @ B) ) ) ) ) , file(funcop_1, fc9_funcop_1)). thf(fc9_nat_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k4_ordinal1) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k4_ordinal1) ) ) ) ) & ( ~ ( (v1_xboole_0 @ B) ) & ( (v1_funct_1 @ C) & ( ( ( (v1_funct_2 @ C) @ k4_ordinal1) @ B) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ B) ) ) ) ) ) ) => ( (v1_relat_1 @ ( (k3_relat_1 @ A) @ C) ) & ( (v1_partfun1 @ ( (k3_relat_1 @ A) @ C) ) @ k4_ordinal1) ) ) ) , file(nat_1, fc9_nat_1)). thf(fc9_ordinal1, axiom, (v8_ordinal1 @ k5_ordinal1) , file(ordinal1, fc9_ordinal1)). thf(fc9_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v4_membered @ B) ) & ( ( ~ ( (v1_xboole_0 @ C) ) & (v4_membered @ C) ) & ( ( (v1_funct_1 @ D) & ( ( ( (v1_funct_2 @ D) @ A) @ B) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & ( (v1_funct_1 @ E) & ( ( ( (v1_funct_2 @ E) @ A) @ C) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k1_valued_1 @ D) @ E) ) & ( (v1_partfun1 @ ( (k1_valued_1 @ D) @ E) ) @ A) ) ) ) , file(valued_1, fc9_valued_1)). thf(fc9_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( ~ ( (v3_xxreal_0 @ A) ) & (v1_xreal_0 @ A) ) & ( ~ ( (v3_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => ~ ( (v3_xxreal_0 @ ( (k2_xcmplx_0 @ A) @ B) ) ) ) ) , file(xreal_0, fc9_xreal_0)). thf(involutiveness_k4_xcmplx_0, axiom, (! [A: $i] : ( (v1_xcmplx_0 @ A) => ( (k4_xcmplx_0 @ (k4_xcmplx_0 @ A) ) = A) ) ) , file(xcmplx_0, k4_xcmplx_0)). thf(projectivity_k1_card_1, axiom, (! [A: $i] : ( (k1_card_1 @ (k1_card_1 @ A) ) = (k1_card_1 @ A) ) ) , file(card_1, k1_card_1)). thf(projectivity_k3_finseq_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_finseq_1 @ A) ) ) => ( (k3_finseq_1 @ (k3_finseq_1 @ A) ) = (k3_finseq_1 @ A) ) ) ) , file(finseq_1, k3_finseq_1)). thf(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(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_funcop_1, axiom, (? [A: $i] : ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_funcop_1 @ A) ) ) ) , file(funcop_1, rc1_funcop_1)). thf(rc1_funct_2, axiom, (! [A: $i, B: $i] : (? [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) & ( (v1_relat_1 @ C) & ( ( (v4_relat_1 @ C) @ A) & ( ( (v5_relat_1 @ C) @ B) & ( (v1_funct_1 @ C) & ( ( (v1_funct_2 @ C) @ A) @ B) ) ) ) ) ) ) ) , file(funct_2, rc1_funct_2)). thf(rc1_membered, axiom, (? [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) & (v6_membered @ A) ) ) , file(membered, rc1_membered)). thf(rc1_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_rcomp_1, axiom, (? [A: $i] : ( ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ k1_numbers) ) & ( (v1_membered @ A) & ( (v2_membered @ A) & ( (v3_membered @ A) & (v3_rcomp_1 @ A) ) ) ) ) ) , file(rcomp_1, rc1_rcomp_1)). thf(rc1_relset_1, axiom, (! [A: $i, B: $i] : (? [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) & ( (v1_xboole_0 @ C) & ( (v1_relat_1 @ C) & ( ( (v4_relat_1 @ C) @ A) & ( (v5_relat_1 @ C) @ B) ) ) ) ) ) ) , file(relset_1, rc1_relset_1)). thf(rc1_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_1, axiom, (? [A: $i] : ( (v1_relat_1 @ A) & ( ( (v4_relat_1 @ A) @ k4_ordinal1) & ( (v1_funct_1 @ A) & ( (v1_valued_0 @ A) & ( (v1_finset_1 @ A) & ( (v1_finseq_1 @ A) & (v2_finseq_1 @ A) ) ) ) ) ) ) ) , file(valued_1, rc1_valued_1)). thf(rc1_xreal_0, axiom, (? [A: $i] : (v1_xreal_0 @ A) ) , file(xreal_0, rc1_xreal_0)). 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_membered, axiom, (? [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) & (v6_membered @ A) ) ) , file(membered, rc2_membered)). 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_1, axiom, (? [A: $i] : ( (v1_relat_1 @ A) & ( ( (v4_relat_1 @ A) @ k4_ordinal1) & ( (v1_funct_1 @ A) & ~ ( (v1_xboole_0 @ A) ) ) ) ) ) , file(valued_1, rc2_valued_1)). thf(rc2_xreal_0, axiom, (? [A: $i] : (v1_xreal_0 @ A) ) , file(xreal_0, rc2_xreal_0)). 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_membered, axiom, (? [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) & ( (v6_membered @ A) & (v7_membered @ A) ) ) ) , file(membered, rc3_membered)). 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_valued_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) ) ) ) ) ) , file(valued_1, rc3_valued_1)). 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(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_funcop_1, axiom, (! [A: $i, B: $i] : ( ~ ( (v1_xboole_0 @ B) ) => (? [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_partfun1 @ C) @ A) ) ) ) ) ) ) ) ) , file(funcop_1, rc4_funcop_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_valued_1, axiom, (? [A: $i] : ( (v1_relat_1 @ A) & ( ( (v4_relat_1 @ A) @ k4_ordinal1) & ( (v1_funct_1 @ A) & ( (v1_finset_1 @ A) & ( (v3_card_1 @ A) @ np__1) ) ) ) ) ) , file(valued_1, rc4_valued_1)). thf(rc4_xreal_0, axiom, (? [A: $i] : ( (v1_xcmplx_0 @ A) & ( (v1_xxreal_0 @ A) & ( (v3_xxreal_0 @ A) & (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc4_xreal_0)). 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_valued_1, axiom, (! [A: $i] : (? [B: $i] : ( (v1_relat_1 @ B) & ( ( (v4_relat_1 @ B) @ A) & ( ( (v5_relat_1 @ B) @ k3_numbers) & ( (v1_funct_1 @ B) & ( ( (v1_partfun1 @ B) @ A) & ( (v1_valued_0 @ B) & ( (v2_valued_0 @ B) & ( (v3_valued_0 @ B) & (v4_valued_0 @ B) ) ) ) ) ) ) ) ) ) ) , file(valued_1, rc5_valued_1)). thf(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(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_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_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_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_k14_rvsum_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v3_valued_0 @ A) & (v1_finseq_1 @ A) ) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & ( (v3_valued_0 @ B) & (v1_finseq_1 @ B) ) ) ) ) => ( ( (k14_rvsum_1 @ A) @ B) = ( (k18_valued_1 @ A) @ B) ) ) ) , file(rvsum_1, k14_rvsum_1)). thf(redefinition_k18_rvsum_1, axiom, (! [A: $i] : ( ( (m1_finseq_1 @ A) @ k1_numbers) => ( (k18_rvsum_1 @ A) = (k16_rvsum_1 @ A) ) ) ) , file(rvsum_1, k18_rvsum_1)). thf(redefinition_k1_euclid_8, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v1_xreal_0 @ A) & ( (v1_xreal_0 @ B) & (v1_xreal_0 @ C) ) ) => ( ( ( (k1_euclid_8 @ A) @ B) @ C) = ( ( (k11_finseq_1 @ A) @ B) @ C) ) ) ) , file(euclid_8, k1_euclid_8)). thf(redefinition_k1_partfun1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ( ( ( (v1_funct_1 @ E) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) & ( (v1_funct_1 @ F) & ( (m1_subset_1 @ F) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ C) @ D) ) ) ) ) => ( ( ( ( ( ( (k1_partfun1 @ A) @ B) @ C) @ D) @ E) @ F) = ( (k3_relat_1 @ E) @ F) ) ) ) , file(partfun1, k1_partfun1)). thf(redefinition_k3_finseq_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_finseq_1 @ A) ) ) => ( (k3_finseq_1 @ A) = (k1_card_1 @ A) ) ) ) , file(finseq_1, k3_finseq_1)). thf(redefinition_k3_funct_2, axiom, (! [A: $i, B: $i, C: $i, D: $i] : ( ( ~ ( (v1_xboole_0 @ A) ) & ( ( (v1_funct_1 @ C) & ( ( ( (v1_funct_2 @ C) @ A) @ B) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & ( (m1_subset_1 @ D) @ A) ) ) => ( ( ( ( (k3_funct_2 @ A) @ B) @ C) @ D) = ( (k1_funct_1 @ C) @ D) ) ) ) , file(funct_2, k3_funct_2)). thf(redefinition_k5_numbers, axiom, (k5_numbers = k5_ordinal1) , file(numbers, k5_numbers)). thf(redefinition_k6_pdiff_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v7_ordinal1 @ A) & ( (v7_ordinal1 @ B) & ( (m1_subset_1 @ C) @ (k1_euclid @ A) ) ) ) => ( ( ( (k6_pdiff_1 @ A) @ B) @ C) = ( (k5_pdiff_1 @ B) @ C) ) ) ) , file(pdiff_1, k6_pdiff_1)). thf(redefinition_k7_euclid, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v7_ordinal1 @ A) & ( ( (m1_subset_1 @ B) @ (k1_euclid @ A) ) & ( (m1_subset_1 @ C) @ (k1_euclid @ A) ) ) ) => ( ( ( (k7_euclid @ A) @ B) @ C) = ( (k1_valued_1 @ B) @ C) ) ) ) , file(euclid, k7_euclid)). thf(redefinition_k9_euclid, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v7_ordinal1 @ A) & ( ( (m1_subset_1 @ B) @ (k1_euclid @ A) ) & (v1_xreal_0 @ C) ) ) => ( ( ( (k9_euclid @ A) @ B) @ C) = ( (k24_valued_1 @ B) @ C) ) ) ) , file(euclid, k9_euclid)). thf(redefinition_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_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(rqRealAdd__k2_xcmplx_0__r0_r0_r0, axiom, ( ( (k2_xcmplx_0 @ np__0) @ np__0) = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r0_r0)). thf(rqRealAdd__k2_xcmplx_0__r0_r1_r1, axiom, ( ( (k2_xcmplx_0 @ np__0) @ np__1) = np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r1_r1)). thf(rqRealAdd__k2_xcmplx_0__r0_r2_r2, axiom, ( ( (k2_xcmplx_0 @ np__0) @ np__2) = np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r2_r2)). thf(rqRealAdd__k2_xcmplx_0__r0_r3_r3, axiom, ( ( (k2_xcmplx_0 @ np__0) @ np__3) = np__3) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r3_r3)). thf(rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, axiom, ( ( (k2_xcmplx_0 @ np__0) @ (k4_xcmplx_0 @ np__1) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1)). thf(rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, axiom, ( ( (k2_xcmplx_0 @ np__0) @ (k4_xcmplx_0 @ np__2) ) = (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2)). thf(rqRealAdd__k2_xcmplx_0__r0_rm3_rm3, axiom, ( ( (k2_xcmplx_0 @ np__0) @ (k4_xcmplx_0 @ np__3) ) = (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm3_rm3)). thf(rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, axiom, ( ( (k2_xcmplx_0 @ np__0) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2)). thf(rqRealAdd__k2_xcmplx_0__r0_rn2d3_rn2d3, axiom, ( ( (k2_xcmplx_0 @ np__0) @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) = ( (k7_xcmplx_0 @ np__2) @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rn2d3_rn2d3)). thf(rqRealAdd__k2_xcmplx_0__r0_rn3d2_rn3d2, axiom, ( ( (k2_xcmplx_0 @ np__0) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rn3d2_rn3d2)). thf(rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, axiom, ( ( (k2_xcmplx_0 @ np__0) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2)). thf(rqRealAdd__k2_xcmplx_0__r0_rnm1d3_rnm1d3, axiom, ( ( (k2_xcmplx_0 @ np__0) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rnm1d3_rnm1d3)). thf(rqRealAdd__k2_xcmplx_0__r0_rnm2d3_rnm2d3, axiom, ( ( (k2_xcmplx_0 @ np__0) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rnm2d3_rnm2d3)). thf(rqRealAdd__k2_xcmplx_0__r1_r0_r1, axiom, ( ( (k2_xcmplx_0 @ np__1) @ np__0) = np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r0_r1)). thf(rqRealAdd__k2_xcmplx_0__r1_r1_r2, axiom, ( ( (k2_xcmplx_0 @ np__1) @ np__1) = np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r1_r2)). thf(rqRealAdd__k2_xcmplx_0__r1_r2_r3, axiom, ( ( (k2_xcmplx_0 @ np__1) @ np__2) = np__3) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r2_r3)). thf(rqRealAdd__k2_xcmplx_0__r1_rm1_r0, axiom, ( ( (k2_xcmplx_0 @ np__1) @ (k4_xcmplx_0 @ np__1) ) = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm1_r0)). thf(rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, axiom, ( ( (k2_xcmplx_0 @ np__1) @ (k4_xcmplx_0 @ np__2) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1)). thf(rqRealAdd__k2_xcmplx_0__r1_rm3_rm2, axiom, ( ( (k2_xcmplx_0 @ np__1) @ (k4_xcmplx_0 @ np__3) ) = (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm3_rm2)). thf(rqRealAdd__k2_xcmplx_0__r1_rn1d2_rn3d2, axiom, ( ( (k2_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rn1d2_rn3d2)). thf(rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, axiom, ( ( (k2_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2)). thf(rqRealAdd__k2_xcmplx_0__r1_rnm1d3_rn2d3, axiom, ( ( (k2_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = ( (k7_xcmplx_0 @ np__2) @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rnm1d3_rn2d3)). thf(rqRealAdd__k2_xcmplx_0__r1_rnm2d3_rn1d3, axiom, ( ( (k2_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) = ( (k7_xcmplx_0 @ np__1) @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rnm2d3_rn1d3)). thf(rqRealAdd__k2_xcmplx_0__r2_r0_r2, axiom, ( ( (k2_xcmplx_0 @ np__2) @ np__0) = np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_r0_r2)). thf(rqRealAdd__k2_xcmplx_0__r2_r1_r3, axiom, ( ( (k2_xcmplx_0 @ np__2) @ np__1) = np__3) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_r1_r3)). thf(rqRealAdd__k2_xcmplx_0__r2_rm1_r1, axiom, ( ( (k2_xcmplx_0 @ np__2) @ (k4_xcmplx_0 @ np__1) ) = np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm1_r1)). thf(rqRealAdd__k2_xcmplx_0__r2_rm2_r0, axiom, ( ( (k2_xcmplx_0 @ np__2) @ (k4_xcmplx_0 @ np__2) ) = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm2_r0)). thf(rqRealAdd__k2_xcmplx_0__r2_rm3_rm1, axiom, ( ( (k2_xcmplx_0 @ np__2) @ (k4_xcmplx_0 @ np__3) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm3_rm1)). thf(rqRealAdd__k2_xcmplx_0__r2_rnm1d2_rn3d2, axiom, ( ( (k2_xcmplx_0 @ np__2) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rnm1d2_rn3d2)). thf(rqRealAdd__k2_xcmplx_0__r2_rnm3d2_rn1d2, axiom, ( ( (k2_xcmplx_0 @ np__2) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rnm3d2_rn1d2)). thf(rqRealAdd__k2_xcmplx_0__r3_r0_r3, axiom, ( ( (k2_xcmplx_0 @ np__3) @ np__0) = np__3) , file(arithm, rqRealAdd__k2_xcmplx_0__r3_r0_r3)). thf(rqRealAdd__k2_xcmplx_0__r3_rm1_r2, axiom, ( ( (k2_xcmplx_0 @ np__3) @ (k4_xcmplx_0 @ np__1) ) = np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r3_rm1_r2)). thf(rqRealAdd__k2_xcmplx_0__r3_rm2_r1, axiom, ( ( (k2_xcmplx_0 @ np__3) @ (k4_xcmplx_0 @ np__2) ) = np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r3_rm2_r1)). thf(rqRealAdd__k2_xcmplx_0__r3_rm3_r0, axiom, ( ( (k2_xcmplx_0 @ np__3) @ (k4_xcmplx_0 @ np__3) ) = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r3_rm3_r0)). thf(rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, axiom, ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__0) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1)). thf(rqRealAdd__k2_xcmplx_0__rm1_r1_r0, axiom, ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__1) = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r1_r0)). thf(rqRealAdd__k2_xcmplx_0__rm1_r2_r1, axiom, ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) = np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r2_r1)). thf(rqRealAdd__k2_xcmplx_0__rm1_r3_r2, axiom, ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) = np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r3_r2)). thf(rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, axiom, ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ (k4_xcmplx_0 @ np__1) ) = (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2)). thf(rqRealAdd__k2_xcmplx_0__rm1_rm2_rm3, axiom, ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ (k4_xcmplx_0 @ np__2) ) = (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_rm2_rm3)). thf(rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, axiom, ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2)). thf(rqRealAdd__k2_xcmplx_0__rm1_rn2d3_rnm1d3, axiom, ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_rn2d3_rnm1d3)). thf(rqRealAdd__k2_xcmplx_0__rm1_rn3d2_rn1d2, axiom, ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_rn3d2_rn1d2)). thf(rqRealAdd__k2_xcmplx_0__rm1_rnm1d2_rnm3d2, axiom, ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_rnm1d2_rnm3d2)). thf(rqRealAdd__k2_xcmplx_0__rm2_r0_rm2, axiom, ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__0) = (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r0_rm2)). thf(rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, axiom, ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__1) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1)). thf(rqRealAdd__k2_xcmplx_0__rm2_r2_r0, axiom, ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__2) = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r2_r0)). thf(rqRealAdd__k2_xcmplx_0__rm2_r3_r1, axiom, ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) = np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r3_r1)). thf(rqRealAdd__k2_xcmplx_0__rm2_rm1_rm3, axiom, ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ (k4_xcmplx_0 @ np__1) ) = (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_rm1_rm3)). thf(rqRealAdd__k2_xcmplx_0__rm2_rn1d2_rnm3d2, axiom, ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_rn1d2_rnm3d2)). thf(rqRealAdd__k2_xcmplx_0__rm2_rn3d2_rnm1d2, axiom, ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_rn3d2_rnm1d2)). thf(rqRealAdd__k2_xcmplx_0__rm3_r1_rm2, axiom, ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__1) = (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm3_r1_rm2)). thf(rqRealAdd__k2_xcmplx_0__rm3_r2_rm1, axiom, ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm3_r2_rm1)). thf(rqRealAdd__k2_xcmplx_0__rm3_r3_r0, axiom, ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__3) = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm3_r3_r0)). thf(rqRealAdd__k2_xcmplx_0__rm3_rn3d2_rnm3d2, axiom, ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm3_rn3d2_rnm3d2)). thf(rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ np__0) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2)). thf(rqRealAdd__k2_xcmplx_0__rn1d2_r1_rn3d2, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ np__1) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rn1d2_r1_rn3d2)). thf(rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ (k4_xcmplx_0 @ np__1) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2)). thf(rqRealAdd__k2_xcmplx_0__rn1d2_rm2_rnm3d2, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ (k4_xcmplx_0 @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rn1d2_rm2_rnm3d2)). thf(rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1)). thf(rqRealAdd__k2_xcmplx_0__rn1d2_rn3d2_r2, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__rn1d2_rn3d2_r2)). thf(rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0)). thf(rqRealAdd__k2_xcmplx_0__rn1d2_rnm3d2_rm1, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rn1d2_rnm3d2_rm1)). thf(rqRealAdd__k2_xcmplx_0__rn1d3_rn1d3_rn2d3, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) = ( (k7_xcmplx_0 @ np__2) @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rn1d3_rn1d3_rn2d3)). thf(rqRealAdd__k2_xcmplx_0__rn1d3_rn2d3_r1, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) = np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__rn1d3_rn2d3_r1)). thf(rqRealAdd__k2_xcmplx_0__rn1d3_rnm1d3_r0, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rn1d3_rnm1d3_r0)). thf(rqRealAdd__k2_xcmplx_0__rn1d3_rnm2d3_rnm1d3, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rn1d3_rnm2d3_rnm1d3)). thf(rqRealAdd__k2_xcmplx_0__rn2d3_r0_rn2d3, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) @ np__0) = ( (k7_xcmplx_0 @ np__2) @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rn2d3_r0_rn2d3)). thf(rqRealAdd__k2_xcmplx_0__rn2d3_rn1d3_r1, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) = np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__rn2d3_rn1d3_r1)). thf(rqRealAdd__k2_xcmplx_0__rn2d3_rnm1d3_rn1d3, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = ( (k7_xcmplx_0 @ np__1) @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rn2d3_rnm1d3_rn1d3)). thf(rqRealAdd__k2_xcmplx_0__rn2d3_rnm2d3_r0, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rn2d3_rnm2d3_r0)). thf(rqRealAdd__k2_xcmplx_0__rn3d2_r0_rn3d2, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ np__0) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rn3d2_r0_rn3d2)). thf(rqRealAdd__k2_xcmplx_0__rn3d2_rm1_rn1d2, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ (k4_xcmplx_0 @ np__1) ) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rn3d2_rm1_rn1d2)). thf(rqRealAdd__k2_xcmplx_0__rn3d2_rm2_rnm1d2, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ (k4_xcmplx_0 @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rn3d2_rm2_rnm1d2)). thf(rqRealAdd__k2_xcmplx_0__rn3d2_rn1d2_r2, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__rn3d2_rn1d2_r2)). thf(rqRealAdd__k2_xcmplx_0__rn3d2_rn3d2_r3, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = np__3) , file(arithm, rqRealAdd__k2_xcmplx_0__rn3d2_rn3d2_r3)). thf(rqRealAdd__k2_xcmplx_0__rn3d2_rnm1d2_r1, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__rn3d2_rnm1d2_r1)). thf(rqRealAdd__k2_xcmplx_0__rn3d2_rnm3d2_r0, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rn3d2_rnm3d2_r0)). thf(rqRealAdd__k2_xcmplx_0__rnm1d2_r0_rnm1d2, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ np__0) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d2_r0_rnm1d2)). thf(rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ np__1) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2)). thf(rqRealAdd__k2_xcmplx_0__rnm1d2_r2_rn3d2, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ np__2) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d2_r2_rn3d2)). thf(rqRealAdd__k2_xcmplx_0__rnm1d2_rm1_rnm3d2, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ (k4_xcmplx_0 @ np__1) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d2_rm1_rnm3d2)). thf(rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0)). thf(rqRealAdd__k2_xcmplx_0__rnm1d2_rn3d2_r1, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d2_rn3d2_r1)). thf(rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1)). thf(rqRealAdd__k2_xcmplx_0__rnm1d2_rnm3d2_rm2, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm3d2_rm2)). thf(rqRealAdd__k2_xcmplx_0__rnm1d3_r0_rnm1d3, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) @ np__0) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d3_r0_rnm1d3)). thf(rqRealAdd__k2_xcmplx_0__rnm1d3_r1_rn2d3, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) @ np__1) = ( (k7_xcmplx_0 @ np__2) @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d3_r1_rn2d3)). thf(rqRealAdd__k2_xcmplx_0__rnm1d3_rn1d3_r0, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d3_rn1d3_r0)). thf(rqRealAdd__k2_xcmplx_0__rnm1d3_rn2d3_rn1d3, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) = ( (k7_xcmplx_0 @ np__1) @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d3_rn2d3_rn1d3)). thf(rqRealAdd__k2_xcmplx_0__rnm1d3_rnm1d3_rnm2d3, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d3_rnm1d3_rnm2d3)). thf(rqRealAdd__k2_xcmplx_0__rnm1d3_rnm2d3_rm1, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d3_rnm2d3_rm1)). thf(rqRealAdd__k2_xcmplx_0__rnm2d3_r0_rnm2d3, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) @ np__0) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm2d3_r0_rnm2d3)). thf(rqRealAdd__k2_xcmplx_0__rnm2d3_r1_rn1d3, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) @ np__1) = ( (k7_xcmplx_0 @ np__1) @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm2d3_r1_rn1d3)). thf(rqRealAdd__k2_xcmplx_0__rnm2d3_rn2d3_r0, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm2d3_rn2d3_r0)). thf(rqRealAdd__k2_xcmplx_0__rnm2d3_rnm1d3_rm1, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm2d3_rnm1d3_rm1)). thf(rqRealAdd__k2_xcmplx_0__rnm3d2_r1_rnm1d2, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) @ np__1) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm3d2_r1_rnm1d2)). thf(rqRealAdd__k2_xcmplx_0__rnm3d2_r2_rn1d2, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) @ np__2) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm3d2_r2_rn1d2)). thf(rqRealAdd__k2_xcmplx_0__rnm3d2_rn1d2_rm1, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm3d2_rn1d2_rm1)). thf(rqRealAdd__k2_xcmplx_0__rnm3d2_rn3d2_r0, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm3d2_rn3d2_r0)). thf(rqRealAdd__k2_xcmplx_0__rnm3d2_rnm3d2_rm3, axiom, ( ( (k2_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm3d2_rnm3d2_rm3)). thf(rqRealDiff__k6_xcmplx_0__r0_r0_r0, axiom, ( ( (k6_xcmplx_0 @ np__0) @ np__0) = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r0_r0)). thf(rqRealDiff__k6_xcmplx_0__r0_r1_rm1, axiom, ( ( (k6_xcmplx_0 @ np__0) @ np__1) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r1_rm1)). thf(rqRealDiff__k6_xcmplx_0__r0_r2_rm2, axiom, ( ( (k6_xcmplx_0 @ np__0) @ np__2) = (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r2_rm2)). thf(rqRealDiff__k6_xcmplx_0__r0_r3_rm3, axiom, ( ( (k6_xcmplx_0 @ np__0) @ np__3) = (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r3_rm3)). thf(rqRealDiff__k6_xcmplx_0__r0_rm1_r1, axiom, ( ( (k6_xcmplx_0 @ np__0) @ (k4_xcmplx_0 @ np__1) ) = np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm1_r1)). thf(rqRealDiff__k6_xcmplx_0__r0_rm2_r2, axiom, ( ( (k6_xcmplx_0 @ np__0) @ (k4_xcmplx_0 @ np__2) ) = np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm2_r2)). thf(rqRealDiff__k6_xcmplx_0__r0_rm3_r3, axiom, ( ( (k6_xcmplx_0 @ np__0) @ (k4_xcmplx_0 @ np__3) ) = np__3) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm3_r3)). thf(rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, axiom, ( ( (k6_xcmplx_0 @ np__0) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2)). thf(rqRealDiff__k6_xcmplx_0__r0_rn1d3_rnm1d3, axiom, ( ( (k6_xcmplx_0 @ np__0) @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rn1d3_rnm1d3)). thf(rqRealDiff__k6_xcmplx_0__r0_rn2d3_rnm2d3, axiom, ( ( (k6_xcmplx_0 @ np__0) @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rn2d3_rnm2d3)). thf(rqRealDiff__k6_xcmplx_0__r0_rn3d2_rnm3d2, axiom, ( ( (k6_xcmplx_0 @ np__0) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rn3d2_rnm3d2)). thf(rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, axiom, ( ( (k6_xcmplx_0 @ np__0) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2)). thf(rqRealDiff__k6_xcmplx_0__r0_rnm1d3_rn1d3, axiom, ( ( (k6_xcmplx_0 @ np__0) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = ( (k7_xcmplx_0 @ np__1) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rnm1d3_rn1d3)). thf(rqRealDiff__k6_xcmplx_0__r0_rnm2d3_rn2d3, axiom, ( ( (k6_xcmplx_0 @ np__0) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) = ( (k7_xcmplx_0 @ np__2) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rnm2d3_rn2d3)). thf(rqRealDiff__k6_xcmplx_0__r0_rnm3d2_rn3d2, axiom, ( ( (k6_xcmplx_0 @ np__0) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rnm3d2_rn3d2)). thf(rqRealDiff__k6_xcmplx_0__r1_r0_r1, axiom, ( ( (k6_xcmplx_0 @ np__1) @ np__0) = np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r0_r1)). thf(rqRealDiff__k6_xcmplx_0__r1_r1_r0, axiom, ( ( (k6_xcmplx_0 @ np__1) @ np__1) = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r1_r0)). thf(rqRealDiff__k6_xcmplx_0__r1_r2_rm1, axiom, ( ( (k6_xcmplx_0 @ np__1) @ np__2) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r2_rm1)). thf(rqRealDiff__k6_xcmplx_0__r1_r3_rm2, axiom, ( ( (k6_xcmplx_0 @ np__1) @ np__3) = (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r3_rm2)). thf(rqRealDiff__k6_xcmplx_0__r1_rm1_r2, axiom, ( ( (k6_xcmplx_0 @ np__1) @ (k4_xcmplx_0 @ np__1) ) = np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_rm1_r2)). thf(rqRealDiff__k6_xcmplx_0__r1_rm2_r3, axiom, ( ( (k6_xcmplx_0 @ np__1) @ (k4_xcmplx_0 @ np__2) ) = np__3) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_rm2_r3)). thf(rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, axiom, ( ( (k6_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2)). thf(rqRealDiff__k6_xcmplx_0__r1_rn1d3_rn2d3, axiom, ( ( (k6_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) = ( (k7_xcmplx_0 @ np__2) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_rn1d3_rn2d3)). thf(rqRealDiff__k6_xcmplx_0__r1_rn2d3_rn1d3, axiom, ( ( (k6_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) = ( (k7_xcmplx_0 @ np__1) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_rn2d3_rn1d3)). thf(rqRealDiff__k6_xcmplx_0__r1_rn3d2_rnm1d2, axiom, ( ( (k6_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_rn3d2_rnm1d2)). thf(rqRealDiff__k6_xcmplx_0__r1_rnm1d2_rn3d2, axiom, ( ( (k6_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_rnm1d2_rn3d2)). thf(rqRealDiff__k6_xcmplx_0__r2_r0_r2, axiom, ( ( (k6_xcmplx_0 @ np__2) @ np__0) = np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r0_r2)). thf(rqRealDiff__k6_xcmplx_0__r2_r1_r1, axiom, ( ( (k6_xcmplx_0 @ np__2) @ np__1) = np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r1_r1)). thf(rqRealDiff__k6_xcmplx_0__r2_r2_r0, axiom, ( ( (k6_xcmplx_0 @ np__2) @ np__2) = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r2_r0)). thf(rqRealDiff__k6_xcmplx_0__r2_r3_rm1, axiom, ( ( (k6_xcmplx_0 @ np__2) @ np__3) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r3_rm1)). thf(rqRealDiff__k6_xcmplx_0__r2_rm1_r3, axiom, ( ( (k6_xcmplx_0 @ np__2) @ (k4_xcmplx_0 @ np__1) ) = np__3) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_rm1_r3)). thf(rqRealDiff__k6_xcmplx_0__r2_rn1d2_rn3d2, axiom, ( ( (k6_xcmplx_0 @ np__2) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_rn1d2_rn3d2)). thf(rqRealDiff__k6_xcmplx_0__r2_rn3d2_rn1d2, axiom, ( ( (k6_xcmplx_0 @ np__2) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_rn3d2_rn1d2)). thf(rqRealDiff__k6_xcmplx_0__r3_r0_r3, axiom, ( ( (k6_xcmplx_0 @ np__3) @ np__0) = np__3) , file(arithm, rqRealDiff__k6_xcmplx_0__r3_r0_r3)). thf(rqRealDiff__k6_xcmplx_0__r3_r1_r2, axiom, ( ( (k6_xcmplx_0 @ np__3) @ np__1) = np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r3_r1_r2)). thf(rqRealDiff__k6_xcmplx_0__r3_r2_r1, axiom, ( ( (k6_xcmplx_0 @ np__3) @ np__2) = np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r3_r2_r1)). thf(rqRealDiff__k6_xcmplx_0__r3_r3_r0, axiom, ( ( (k6_xcmplx_0 @ np__3) @ np__3) = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r3_r3_r0)). thf(rqRealDiff__k6_xcmplx_0__r3_rn3d2_rn3d2, axiom, ( ( (k6_xcmplx_0 @ np__3) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r3_rn3d2_rn3d2)). thf(rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__0) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1)). thf(rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__1) = (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2)). thf(rqRealDiff__k6_xcmplx_0__rm1_r2_rm3, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) = (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r2_rm3)). thf(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ (k4_xcmplx_0 @ np__1) ) = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0)). thf(rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ (k4_xcmplx_0 @ np__2) ) = np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1)). thf(rqRealDiff__k6_xcmplx_0__rm1_rm3_r2, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ (k4_xcmplx_0 @ np__3) ) = np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm3_r2)). thf(rqRealDiff__k6_xcmplx_0__rm1_rn1d2_rnm3d2, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rn1d2_rnm3d2)). thf(rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2)). thf(rqRealDiff__k6_xcmplx_0__rm1_rnm1d3_rnm2d3, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rnm1d3_rnm2d3)). thf(rqRealDiff__k6_xcmplx_0__rm1_rnm2d3_rnm1d3, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rnm2d3_rnm1d3)). thf(rqRealDiff__k6_xcmplx_0__rm1_rnm3d2_rn1d2, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rnm3d2_rn1d2)). thf(rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__0) = (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2)). thf(rqRealDiff__k6_xcmplx_0__rm2_r1_rm3, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__1) = (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_r1_rm3)). thf(rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ (k4_xcmplx_0 @ np__1) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1)). thf(rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ (k4_xcmplx_0 @ np__2) ) = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0)). thf(rqRealDiff__k6_xcmplx_0__rm2_rm3_r1, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ (k4_xcmplx_0 @ np__3) ) = np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm3_r1)). thf(rqRealDiff__k6_xcmplx_0__rm2_rnm1d2_rnm3d2, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rnm1d2_rnm3d2)). thf(rqRealDiff__k6_xcmplx_0__rm2_rnm3d2_rnm1d2, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rnm3d2_rnm1d2)). thf(rqRealDiff__k6_xcmplx_0__rm3_r0_rm3, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__0) = (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm3_r0_rm3)). thf(rqRealDiff__k6_xcmplx_0__rm3_rm1_rm2, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ (k4_xcmplx_0 @ np__1) ) = (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm3_rm1_rm2)). thf(rqRealDiff__k6_xcmplx_0__rm3_rm2_rm1, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ (k4_xcmplx_0 @ np__2) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm3_rm2_rm1)). thf(rqRealDiff__k6_xcmplx_0__rm3_rm3_r0, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ (k4_xcmplx_0 @ np__3) ) = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm3_rm3_r0)). thf(rqRealDiff__k6_xcmplx_0__rm3_rnm3d2_rnm3d2, axiom, ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm3_rnm3d2_rnm3d2)). thf(rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ np__0) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2)). thf(rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ np__1) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2)). thf(rqRealDiff__k6_xcmplx_0__rn1d2_r2_rnm3d2, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ np__2) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rn1d2_r2_rnm3d2)). thf(rqRealDiff__k6_xcmplx_0__rn1d2_rm1_rn3d2, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ (k4_xcmplx_0 @ np__1) ) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rn1d2_rm1_rn3d2)). thf(rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0)). thf(rqRealDiff__k6_xcmplx_0__rn1d2_rn3d2_rm1, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rn1d2_rn3d2_rm1)). thf(rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1)). thf(rqRealDiff__k6_xcmplx_0__rn1d2_rnm3d2_r2, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__rn1d2_rnm3d2_r2)). thf(rqRealDiff__k6_xcmplx_0__rn1d3_r0_rn1d3, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) @ np__0) = ( (k7_xcmplx_0 @ np__1) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rn1d3_r0_rn1d3)). thf(rqRealDiff__k6_xcmplx_0__rn1d3_r1_rnm2d3, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) @ np__1) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rn1d3_r1_rnm2d3)). thf(rqRealDiff__k6_xcmplx_0__rn1d3_rn1d3_r0, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rn1d3_rn1d3_r0)). thf(rqRealDiff__k6_xcmplx_0__rn1d3_rn2d3_rnm1d3, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rn1d3_rn2d3_rnm1d3)). thf(rqRealDiff__k6_xcmplx_0__rn1d3_rnm1d3_rn2d3, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = ( (k7_xcmplx_0 @ np__2) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rn1d3_rnm1d3_rn2d3)). thf(rqRealDiff__k6_xcmplx_0__rn1d3_rnm2d3_r1, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) = np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__rn1d3_rnm2d3_r1)). thf(rqRealDiff__k6_xcmplx_0__rn2d3_r0_rn2d3, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) @ np__0) = ( (k7_xcmplx_0 @ np__2) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rn2d3_r0_rn2d3)). thf(rqRealDiff__k6_xcmplx_0__rn2d3_r1_rnm1d3, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) @ np__1) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rn2d3_r1_rnm1d3)). thf(rqRealDiff__k6_xcmplx_0__rn2d3_rn1d3_rn1d3, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) = ( (k7_xcmplx_0 @ np__1) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rn2d3_rn1d3_rn1d3)). thf(rqRealDiff__k6_xcmplx_0__rn2d3_rn2d3_r0, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rn2d3_rn2d3_r0)). thf(rqRealDiff__k6_xcmplx_0__rn2d3_rnm1d3_r1, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__rn2d3_rnm1d3_r1)). thf(rqRealDiff__k6_xcmplx_0__rn3d2_r0_rn3d2, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ np__0) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rn3d2_r0_rn3d2)). thf(rqRealDiff__k6_xcmplx_0__rn3d2_r1_rn1d2, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ np__1) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rn3d2_r1_rn1d2)). thf(rqRealDiff__k6_xcmplx_0__rn3d2_r2_rnm1d2, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ np__2) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rn3d2_r2_rnm1d2)). thf(rqRealDiff__k6_xcmplx_0__rn3d2_r3_rnm3d2, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ np__3) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rn3d2_r3_rnm3d2)). thf(rqRealDiff__k6_xcmplx_0__rn3d2_rn1d2_r1, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__rn3d2_rn1d2_r1)). thf(rqRealDiff__k6_xcmplx_0__rn3d2_rn3d2_r0, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rn3d2_rn3d2_r0)). thf(rqRealDiff__k6_xcmplx_0__rn3d2_rnm1d2_r2, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__rn3d2_rnm1d2_r2)). thf(rqRealDiff__k6_xcmplx_0__rn3d2_rnm3d2_r3, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = np__3) , file(arithm, rqRealDiff__k6_xcmplx_0__rn3d2_rnm3d2_r3)). thf(rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ np__0) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2)). thf(rqRealDiff__k6_xcmplx_0__rnm1d2_r1_rnm3d2, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ np__1) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d2_r1_rnm3d2)). thf(rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ (k4_xcmplx_0 @ np__1) ) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2)). thf(rqRealDiff__k6_xcmplx_0__rnm1d2_rm2_rn3d2, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ (k4_xcmplx_0 @ np__2) ) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d2_rm2_rn3d2)). thf(rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1)). thf(rqRealDiff__k6_xcmplx_0__rnm1d2_rn3d2_rm2, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d2_rn3d2_rm2)). thf(rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0)). thf(rqRealDiff__k6_xcmplx_0__rnm1d2_rnm3d2_r1, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm3d2_r1)). thf(rqRealDiff__k6_xcmplx_0__rnm1d3_r0_rnm1d3, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) @ np__0) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d3_r0_rnm1d3)). thf(rqRealDiff__k6_xcmplx_0__rnm1d3_rm1_rn2d3, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) @ (k4_xcmplx_0 @ np__1) ) = ( (k7_xcmplx_0 @ np__2) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d3_rm1_rn2d3)). thf(rqRealDiff__k6_xcmplx_0__rnm1d3_rn1d3_rnm2d3, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d3_rn1d3_rnm2d3)). thf(rqRealDiff__k6_xcmplx_0__rnm1d3_rn2d3_rm1, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d3_rn2d3_rm1)). thf(rqRealDiff__k6_xcmplx_0__rnm1d3_rnm1d3_r0, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d3_rnm1d3_r0)). thf(rqRealDiff__k6_xcmplx_0__rnm1d3_rnm2d3_rn1d3, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) = ( (k7_xcmplx_0 @ np__1) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d3_rnm2d3_rn1d3)). thf(rqRealDiff__k6_xcmplx_0__rnm2d3_r0_rnm2d3, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) @ np__0) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm2d3_r0_rnm2d3)). thf(rqRealDiff__k6_xcmplx_0__rnm2d3_rm1_rn1d3, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) @ (k4_xcmplx_0 @ np__1) ) = ( (k7_xcmplx_0 @ np__1) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm2d3_rm1_rn1d3)). thf(rqRealDiff__k6_xcmplx_0__rnm2d3_rn1d3_rm1, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm2d3_rn1d3_rm1)). thf(rqRealDiff__k6_xcmplx_0__rnm2d3_rnm1d3_rnm1d3, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm2d3_rnm1d3_rnm1d3)). thf(rqRealDiff__k6_xcmplx_0__rnm2d3_rnm2d3_r0, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm2d3_rnm2d3_r0)). thf(rqRealDiff__k6_xcmplx_0__rnm3d2_r0_rnm3d2, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) @ np__0) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm3d2_r0_rnm3d2)). thf(rqRealDiff__k6_xcmplx_0__rnm3d2_rm1_rnm1d2, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) @ (k4_xcmplx_0 @ np__1) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm3d2_rm1_rnm1d2)). thf(rqRealDiff__k6_xcmplx_0__rnm3d2_rm2_rn1d2, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) @ (k4_xcmplx_0 @ np__2) ) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm3d2_rm2_rn1d2)). thf(rqRealDiff__k6_xcmplx_0__rnm3d2_rm3_rn3d2, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) @ (k4_xcmplx_0 @ np__3) ) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm3d2_rm3_rn3d2)). thf(rqRealDiff__k6_xcmplx_0__rnm3d2_rn1d2_rm2, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm3d2_rn1d2_rm2)). thf(rqRealDiff__k6_xcmplx_0__rnm3d2_rn3d2_rm3, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm3d2_rn3d2_rm3)). thf(rqRealDiff__k6_xcmplx_0__rnm3d2_rnm1d2_rm1, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm3d2_rnm1d2_rm1)). thf(rqRealDiff__k6_xcmplx_0__rnm3d2_rnm3d2_r0, axiom, ( ( (k6_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm3d2_rnm3d2_r0)). thf(rqRealDiv__k7_xcmplx_0__r1_r1_r1, axiom, ( ( (k7_xcmplx_0 @ np__1) @ np__1) = np__1) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_r1_r1)). thf(rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, axiom, ( ( (k7_xcmplx_0 @ np__1) @ np__2) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2)). thf(rqRealDiv__k7_xcmplx_0__r1_r3_rn1d3, axiom, ( ( (k7_xcmplx_0 @ np__1) @ np__3) = ( (k7_xcmplx_0 @ np__1) @ np__3) ) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_r3_rn1d3)). thf(rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, axiom, ( ( (k7_xcmplx_0 @ np__1) @ (k4_xcmplx_0 @ np__1) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1)). thf(rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, axiom, ( ( (k7_xcmplx_0 @ np__1) @ (k4_xcmplx_0 @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2)). thf(rqRealDiv__k7_xcmplx_0__r1_rm3_rnm1d3, axiom, ( ( (k7_xcmplx_0 @ np__1) @ (k4_xcmplx_0 @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_rm3_rnm1d3)). thf(rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, axiom, ( ( (k7_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = np__2) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2)). thf(rqRealDiv__k7_xcmplx_0__r1_rn1d3_r3, axiom, ( ( (k7_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) = np__3) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_rn1d3_r3)). thf(rqRealDiv__k7_xcmplx_0__r1_rn2d3_rn3d2, axiom, ( ( (k7_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_rn2d3_rn3d2)). thf(rqRealDiv__k7_xcmplx_0__r1_rn3d2_rn2d3, axiom, ( ( (k7_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = ( (k7_xcmplx_0 @ np__2) @ np__3) ) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_rn3d2_rn2d3)). thf(rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, axiom, ( ( (k7_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2)). thf(rqRealDiv__k7_xcmplx_0__r1_rnm1d3_rm3, axiom, ( ( (k7_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_rnm1d3_rm3)). thf(rqRealDiv__k7_xcmplx_0__r1_rnm2d3_rnm3d2, axiom, ( ( (k7_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_rnm2d3_rnm3d2)). thf(rqRealDiv__k7_xcmplx_0__r1_rnm3d2_rnm2d3, axiom, ( ( (k7_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_rnm3d2_rnm2d3)). thf(rqRealDiv__k7_xcmplx_0__r2_r1_r2, axiom, ( ( (k7_xcmplx_0 @ np__2) @ np__1) = np__2) , file(arithm, rqRealDiv__k7_xcmplx_0__r2_r1_r2)). thf(rqRealDiv__k7_xcmplx_0__r2_r2_r1, axiom, ( ( (k7_xcmplx_0 @ np__2) @ np__2) = np__1) , file(arithm, rqRealDiv__k7_xcmplx_0__r2_r2_r1)). thf(rqRealDiv__k7_xcmplx_0__r2_r3_rn2d3, axiom, ( ( (k7_xcmplx_0 @ np__2) @ np__3) = ( (k7_xcmplx_0 @ np__2) @ np__3) ) , file(arithm, rqRealDiv__k7_xcmplx_0__r2_r3_rn2d3)). thf(rqRealDiv__k7_xcmplx_0__r3_r2_rn3d2, axiom, ( ( (k7_xcmplx_0 @ np__3) @ np__2) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealDiv__k7_xcmplx_0__r3_r2_rn3d2)). thf(rqRealDiv__k7_xcmplx_0__r3_r3_r1, axiom, ( ( (k7_xcmplx_0 @ np__3) @ np__3) = np__1) , file(arithm, rqRealDiv__k7_xcmplx_0__r3_r3_r1)). thf(rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, axiom, ( ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__1) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1)). thf(rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, axiom, ( ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2)). thf(rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, axiom, ( ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__2) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1)). thf(rqRealMult__k3_xcmplx_0__r0_r0_r0, axiom, ( ( (k3_xcmplx_0 @ np__0) @ np__0) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_r0_r0)). thf(rqRealMult__k3_xcmplx_0__r0_r1_r0, axiom, ( ( (k3_xcmplx_0 @ np__0) @ np__1) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_r1_r0)). thf(rqRealMult__k3_xcmplx_0__r0_r2_r0, axiom, ( ( (k3_xcmplx_0 @ np__0) @ np__2) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_r2_r0)). thf(rqRealMult__k3_xcmplx_0__r0_r3_r0, axiom, ( ( (k3_xcmplx_0 @ np__0) @ np__3) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_r3_r0)). thf(rqRealMult__k3_xcmplx_0__r0_rm2_r0, axiom, ( ( (k3_xcmplx_0 @ np__0) @ (k4_xcmplx_0 @ np__2) ) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_rm2_r0)). thf(rqRealMult__k3_xcmplx_0__r0_rm3_r0, axiom, ( ( (k3_xcmplx_0 @ np__0) @ (k4_xcmplx_0 @ np__3) ) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_rm3_r0)). thf(rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, axiom, ( ( (k3_xcmplx_0 @ np__0) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0)). thf(rqRealMult__k3_xcmplx_0__r0_rn1d3_r0, axiom, ( ( (k3_xcmplx_0 @ np__0) @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_rn1d3_r0)). thf(rqRealMult__k3_xcmplx_0__r0_rn2d3_r0, axiom, ( ( (k3_xcmplx_0 @ np__0) @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_rn2d3_r0)). thf(rqRealMult__k3_xcmplx_0__r0_rn3d2_r0, axiom, ( ( (k3_xcmplx_0 @ np__0) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_rn3d2_r0)). thf(rqRealMult__k3_xcmplx_0__r0_rnm1d3_r0, axiom, ( ( (k3_xcmplx_0 @ np__0) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_rnm1d3_r0)). thf(rqRealMult__k3_xcmplx_0__r0_rnm2d3_r0, axiom, ( ( (k3_xcmplx_0 @ np__0) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_rnm2d3_r0)). thf(rqRealMult__k3_xcmplx_0__r1_r0_r0, axiom, ( ( (k3_xcmplx_0 @ np__1) @ np__0) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r1_r0_r0)). thf(rqRealMult__k3_xcmplx_0__r1_r1_r1, axiom, ( ( (k3_xcmplx_0 @ np__1) @ np__1) = np__1) , file(arithm, rqRealMult__k3_xcmplx_0__r1_r1_r1)). thf(rqRealMult__k3_xcmplx_0__r1_r2_r2, axiom, ( ( (k3_xcmplx_0 @ np__1) @ np__2) = np__2) , file(arithm, rqRealMult__k3_xcmplx_0__r1_r2_r2)). thf(rqRealMult__k3_xcmplx_0__r1_r3_r3, axiom, ( ( (k3_xcmplx_0 @ np__1) @ np__3) = np__3) , file(arithm, rqRealMult__k3_xcmplx_0__r1_r3_r3)). thf(rqRealMult__k3_xcmplx_0__r1_rm2_rm2, axiom, ( ( (k3_xcmplx_0 @ np__1) @ (k4_xcmplx_0 @ np__2) ) = (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__r1_rm2_rm2)). thf(rqRealMult__k3_xcmplx_0__r1_rm3_rm3, axiom, ( ( (k3_xcmplx_0 @ np__1) @ (k4_xcmplx_0 @ np__3) ) = (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__r1_rm3_rm3)). thf(rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2, axiom, ( ( (k3_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2)). thf(rqRealMult__k3_xcmplx_0__r1_rn1d3_rn1d3, axiom, ( ( (k3_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) = ( (k7_xcmplx_0 @ np__1) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__r1_rn1d3_rn1d3)). thf(rqRealMult__k3_xcmplx_0__r1_rn2d3_rn2d3, axiom, ( ( (k3_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) = ( (k7_xcmplx_0 @ np__2) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__r1_rn2d3_rn2d3)). thf(rqRealMult__k3_xcmplx_0__r1_rn3d2_rn3d2, axiom, ( ( (k3_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__r1_rn3d2_rn3d2)). thf(rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, axiom, ( ( (k3_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2)). thf(rqRealMult__k3_xcmplx_0__r1_rnm1d3_rnm1d3, axiom, ( ( (k3_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__r1_rnm1d3_rnm1d3)). thf(rqRealMult__k3_xcmplx_0__r1_rnm2d3_rnm2d3, axiom, ( ( (k3_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__r1_rnm2d3_rnm2d3)). thf(rqRealMult__k3_xcmplx_0__r1_rnm3d2_rnm3d2, axiom, ( ( (k3_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__r1_rnm3d2_rnm3d2)). thf(rqRealMult__k3_xcmplx_0__r2_r0_r0, axiom, ( ( (k3_xcmplx_0 @ np__2) @ np__0) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r2_r0_r0)). thf(rqRealMult__k3_xcmplx_0__r2_r1_r2, axiom, ( ( (k3_xcmplx_0 @ np__2) @ np__1) = np__2) , file(arithm, rqRealMult__k3_xcmplx_0__r2_r1_r2)). thf(rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, axiom, ( ( (k3_xcmplx_0 @ np__2) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = np__1) , file(arithm, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1)). thf(rqRealMult__k3_xcmplx_0__r2_rn1d3_rn2d3, axiom, ( ( (k3_xcmplx_0 @ np__2) @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) = ( (k7_xcmplx_0 @ np__2) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__r2_rn1d3_rn2d3)). thf(rqRealMult__k3_xcmplx_0__r2_rn3d2_r3, axiom, ( ( (k3_xcmplx_0 @ np__2) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = np__3) , file(arithm, rqRealMult__k3_xcmplx_0__r2_rn3d2_r3)). thf(rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, axiom, ( ( (k3_xcmplx_0 @ np__2) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1)). thf(rqRealMult__k3_xcmplx_0__r2_rnm1d3_rnm2d3, axiom, ( ( (k3_xcmplx_0 @ np__2) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__r2_rnm1d3_rnm2d3)). thf(rqRealMult__k3_xcmplx_0__r2_rnm3d2_rm3, axiom, ( ( (k3_xcmplx_0 @ np__2) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__r2_rnm3d2_rm3)). thf(rqRealMult__k3_xcmplx_0__r3_r0_r0, axiom, ( ( (k3_xcmplx_0 @ np__3) @ np__0) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r3_r0_r0)). thf(rqRealMult__k3_xcmplx_0__r3_r1_r3, axiom, ( ( (k3_xcmplx_0 @ np__3) @ np__1) = np__3) , file(arithm, rqRealMult__k3_xcmplx_0__r3_r1_r3)). thf(rqRealMult__k3_xcmplx_0__r3_rn1d2_rn3d2, axiom, ( ( (k3_xcmplx_0 @ np__3) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__r3_rn1d2_rn3d2)). thf(rqRealMult__k3_xcmplx_0__r3_rn1d3_r1, axiom, ( ( (k3_xcmplx_0 @ np__3) @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) = np__1) , file(arithm, rqRealMult__k3_xcmplx_0__r3_rn1d3_r1)). thf(rqRealMult__k3_xcmplx_0__r3_rn2d3_r2, axiom, ( ( (k3_xcmplx_0 @ np__3) @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) = np__2) , file(arithm, rqRealMult__k3_xcmplx_0__r3_rn2d3_r2)). thf(rqRealMult__k3_xcmplx_0__r3_rnm1d2_rnm3d2, axiom, ( ( (k3_xcmplx_0 @ np__3) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__r3_rnm1d2_rnm3d2)). thf(rqRealMult__k3_xcmplx_0__r3_rnm1d3_rm1, axiom, ( ( (k3_xcmplx_0 @ np__3) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealMult__k3_xcmplx_0__r3_rnm1d3_rm1)). thf(rqRealMult__k3_xcmplx_0__r3_rnm2d3_rm2, axiom, ( ( (k3_xcmplx_0 @ np__3) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) = (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__r3_rnm2d3_rm2)). thf(rqRealMult__k3_xcmplx_0__rm2_r0_r0, axiom, ( ( (k3_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__0) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__rm2_r0_r0)). thf(rqRealMult__k3_xcmplx_0__rm2_r1_rm2, axiom, ( ( (k3_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__1) = (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rm2_r1_rm2)). thf(rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, axiom, ( ( (k3_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1)). thf(rqRealMult__k3_xcmplx_0__rm2_rn1d3_rnm2d3, axiom, ( ( (k3_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rm2_rn1d3_rnm2d3)). thf(rqRealMult__k3_xcmplx_0__rm2_rn3d2_rm3, axiom, ( ( (k3_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rm2_rn3d2_rm3)). thf(rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, axiom, ( ( (k3_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = np__1) , file(arithm, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1)). thf(rqRealMult__k3_xcmplx_0__rm2_rnm1d3_rn2d3, axiom, ( ( (k3_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = ( (k7_xcmplx_0 @ np__2) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rm2_rnm1d3_rn2d3)). thf(rqRealMult__k3_xcmplx_0__rm2_rnm3d2_r3, axiom, ( ( (k3_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = np__3) , file(arithm, rqRealMult__k3_xcmplx_0__rm2_rnm3d2_r3)). thf(rqRealMult__k3_xcmplx_0__rm3_r0_r0, axiom, ( ( (k3_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__0) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__rm3_r0_r0)). thf(rqRealMult__k3_xcmplx_0__rm3_r1_rm3, axiom, ( ( (k3_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__1) = (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rm3_r1_rm3)). thf(rqRealMult__k3_xcmplx_0__rm3_rn1d2_rnm3d2, axiom, ( ( (k3_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rm3_rn1d2_rnm3d2)). thf(rqRealMult__k3_xcmplx_0__rm3_rn1d3_rm1, axiom, ( ( (k3_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealMult__k3_xcmplx_0__rm3_rn1d3_rm1)). thf(rqRealMult__k3_xcmplx_0__rm3_rn2d3_rm2, axiom, ( ( (k3_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) = (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rm3_rn2d3_rm2)). thf(rqRealMult__k3_xcmplx_0__rm3_rnm1d2_rn3d2, axiom, ( ( (k3_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rm3_rnm1d2_rn3d2)). thf(rqRealMult__k3_xcmplx_0__rm3_rnm1d3_r1, axiom, ( ( (k3_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = np__1) , file(arithm, rqRealMult__k3_xcmplx_0__rm3_rnm1d3_r1)). thf(rqRealMult__k3_xcmplx_0__rm3_rnm2d3_r2, axiom, ( ( (k3_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) = np__2) , file(arithm, rqRealMult__k3_xcmplx_0__rm3_rnm2d3_r2)). thf(rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ np__0) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0)). thf(rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ np__1) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2)). thf(rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ np__2) = np__1) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1)). thf(rqRealMult__k3_xcmplx_0__rn1d2_r3_rn3d2, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ np__3) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_r3_rn3d2)). thf(rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ (k4_xcmplx_0 @ np__2) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1)). thf(rqRealMult__k3_xcmplx_0__rn1d2_rm3_rnm3d2, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ (k4_xcmplx_0 @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_rm3_rnm3d2)). thf(rqRealMult__k3_xcmplx_0__rn1d2_rn2d3_rn1d3, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) = ( (k7_xcmplx_0 @ np__1) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_rn2d3_rn1d3)). thf(rqRealMult__k3_xcmplx_0__rn1d2_rnm2d3_rnm1d3, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_rnm2d3_rnm1d3)). thf(rqRealMult__k3_xcmplx_0__rn1d3_r0_r0, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) @ np__0) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d3_r0_r0)). thf(rqRealMult__k3_xcmplx_0__rn1d3_r1_rn1d3, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) @ np__1) = ( (k7_xcmplx_0 @ np__1) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d3_r1_rn1d3)). thf(rqRealMult__k3_xcmplx_0__rn1d3_r2_rn2d3, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) @ np__2) = ( (k7_xcmplx_0 @ np__2) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d3_r2_rn2d3)). thf(rqRealMult__k3_xcmplx_0__rn1d3_r3_r1, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) @ np__3) = np__1) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d3_r3_r1)). thf(rqRealMult__k3_xcmplx_0__rn1d3_rm2_rnm2d3, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) @ (k4_xcmplx_0 @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d3_rm2_rnm2d3)). thf(rqRealMult__k3_xcmplx_0__rn1d3_rm3_rm1, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) @ (k4_xcmplx_0 @ np__3) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d3_rm3_rm1)). thf(rqRealMult__k3_xcmplx_0__rn1d3_rn3d2_rn1d2, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d3_rn3d2_rn1d2)). thf(rqRealMult__k3_xcmplx_0__rn1d3_rnm3d2_rnm1d2, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d3_rnm3d2_rnm1d2)). thf(rqRealMult__k3_xcmplx_0__rn2d3_r0_r0, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) @ np__0) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__rn2d3_r0_r0)). thf(rqRealMult__k3_xcmplx_0__rn2d3_r1_rn2d3, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) @ np__1) = ( (k7_xcmplx_0 @ np__2) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn2d3_r1_rn2d3)). thf(rqRealMult__k3_xcmplx_0__rn2d3_r3_r2, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) @ np__3) = np__2) , file(arithm, rqRealMult__k3_xcmplx_0__rn2d3_r3_r2)). thf(rqRealMult__k3_xcmplx_0__rn2d3_rm3_rm2, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) @ (k4_xcmplx_0 @ np__3) ) = (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn2d3_rm3_rm2)). thf(rqRealMult__k3_xcmplx_0__rn2d3_rn1d2_rn1d3, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = ( (k7_xcmplx_0 @ np__1) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn2d3_rn1d2_rn1d3)). thf(rqRealMult__k3_xcmplx_0__rn2d3_rn3d2_r1, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = np__1) , file(arithm, rqRealMult__k3_xcmplx_0__rn2d3_rn3d2_r1)). thf(rqRealMult__k3_xcmplx_0__rn2d3_rnm1d2_rnm1d3, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn2d3_rnm1d2_rnm1d3)). thf(rqRealMult__k3_xcmplx_0__rn2d3_rnm3d2_rm1, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn2d3_rnm3d2_rm1)). thf(rqRealMult__k3_xcmplx_0__rn3d2_r0_r0, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ np__0) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__rn3d2_r0_r0)). thf(rqRealMult__k3_xcmplx_0__rn3d2_r1_rn3d2, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ np__1) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn3d2_r1_rn3d2)). thf(rqRealMult__k3_xcmplx_0__rn3d2_r2_r3, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ np__2) = np__3) , file(arithm, rqRealMult__k3_xcmplx_0__rn3d2_r2_r3)). thf(rqRealMult__k3_xcmplx_0__rn3d2_rm2_rm3, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ (k4_xcmplx_0 @ np__2) ) = (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn3d2_rm2_rm3)). thf(rqRealMult__k3_xcmplx_0__rn3d2_rn1d3_rn1d2, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn3d2_rn1d3_rn1d2)). thf(rqRealMult__k3_xcmplx_0__rn3d2_rn2d3_r1, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) = np__1) , file(arithm, rqRealMult__k3_xcmplx_0__rn3d2_rn2d3_r1)). thf(rqRealMult__k3_xcmplx_0__rn3d2_rnm1d3_rnm1d2, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn3d2_rnm1d3_rnm1d2)). thf(rqRealMult__k3_xcmplx_0__rn3d2_rnm2d3_rm1, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn3d2_rnm2d3_rm1)). thf(rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ np__1) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2)). thf(rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ np__2) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1)). thf(rqRealMult__k3_xcmplx_0__rnm1d2_r3_rnm3d2, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ np__3) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm1d2_r3_rnm3d2)). thf(rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ (k4_xcmplx_0 @ np__2) ) = np__1) , file(arithm, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1)). thf(rqRealMult__k3_xcmplx_0__rnm1d2_rm3_rn3d2, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ (k4_xcmplx_0 @ np__3) ) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm1d2_rm3_rn3d2)). thf(rqRealMult__k3_xcmplx_0__rnm1d2_rn2d3_rnm1d3, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm1d2_rn2d3_rnm1d3)). thf(rqRealMult__k3_xcmplx_0__rnm1d2_rnm2d3_rn1d3, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) = ( (k7_xcmplx_0 @ np__1) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm1d2_rnm2d3_rn1d3)). thf(rqRealMult__k3_xcmplx_0__rnm1d3_r0_r0, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) @ np__0) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__rnm1d3_r0_r0)). thf(rqRealMult__k3_xcmplx_0__rnm1d3_r1_rnm1d3, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) @ np__1) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm1d3_r1_rnm1d3)). thf(rqRealMult__k3_xcmplx_0__rnm1d3_r2_rnm2d3, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) @ np__2) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm1d3_r2_rnm2d3)). thf(rqRealMult__k3_xcmplx_0__rnm1d3_r3_rm1, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) @ np__3) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm1d3_r3_rm1)). thf(rqRealMult__k3_xcmplx_0__rnm1d3_rm2_rn2d3, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) @ (k4_xcmplx_0 @ np__2) ) = ( (k7_xcmplx_0 @ np__2) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm1d3_rm2_rn2d3)). thf(rqRealMult__k3_xcmplx_0__rnm1d3_rm3_r1, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) @ (k4_xcmplx_0 @ np__3) ) = np__1) , file(arithm, rqRealMult__k3_xcmplx_0__rnm1d3_rm3_r1)). thf(rqRealMult__k3_xcmplx_0__rnm1d3_rn3d2_rnm1d2, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm1d3_rn3d2_rnm1d2)). thf(rqRealMult__k3_xcmplx_0__rnm1d3_rnm3d2_rn1d2, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm1d3_rnm3d2_rn1d2)). thf(rqRealMult__k3_xcmplx_0__rnm2d3_r0_r0, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) @ np__0) = np__0) , file(arithm, rqRealMult__k3_xcmplx_0__rnm2d3_r0_r0)). thf(rqRealMult__k3_xcmplx_0__rnm2d3_r1_rnm2d3, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) @ np__1) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm2d3_r1_rnm2d3)). thf(rqRealMult__k3_xcmplx_0__rnm2d3_r3_rm2, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) @ np__3) = (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm2d3_r3_rm2)). thf(rqRealMult__k3_xcmplx_0__rnm2d3_rm3_r2, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) @ (k4_xcmplx_0 @ np__3) ) = np__2) , file(arithm, rqRealMult__k3_xcmplx_0__rnm2d3_rm3_r2)). thf(rqRealMult__k3_xcmplx_0__rnm2d3_rn1d2_rnm1d3, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm2d3_rn1d2_rnm1d3)). thf(rqRealMult__k3_xcmplx_0__rnm2d3_rn3d2_rm1, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm2d3_rn3d2_rm1)). thf(rqRealMult__k3_xcmplx_0__rnm2d3_rnm1d2_rn1d3, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = ( (k7_xcmplx_0 @ np__1) @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm2d3_rnm1d2_rn1d3)). thf(rqRealMult__k3_xcmplx_0__rnm2d3_rnm3d2_r1, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = np__1) , file(arithm, rqRealMult__k3_xcmplx_0__rnm2d3_rnm3d2_r1)). thf(rqRealMult__k3_xcmplx_0__rnm3d2_r1_rnm3d2, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) @ np__1) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm3d2_r1_rnm3d2)). thf(rqRealMult__k3_xcmplx_0__rnm3d2_r2_rm3, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) @ np__2) = (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm3d2_r2_rm3)). thf(rqRealMult__k3_xcmplx_0__rnm3d2_rm2_r3, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) @ (k4_xcmplx_0 @ np__2) ) = np__3) , file(arithm, rqRealMult__k3_xcmplx_0__rnm3d2_rm2_r3)). thf(rqRealMult__k3_xcmplx_0__rnm3d2_rn1d3_rnm1d2, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm3d2_rn1d3_rnm1d2)). thf(rqRealMult__k3_xcmplx_0__rnm3d2_rn2d3_rm1, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm3d2_rn2d3_rm1)). thf(rqRealMult__k3_xcmplx_0__rnm3d2_rnm1d3_rn1d2, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm3d2_rnm1d3_rn1d2)). thf(rqRealMult__k3_xcmplx_0__rnm3d2_rnm2d3_r1, axiom, ( ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) = np__1) , file(arithm, rqRealMult__k3_xcmplx_0__rnm3d2_rnm2d3_r1)). thf(rqRealNeg__k4_xcmplx_0__r0_r0, axiom, ( (k4_xcmplx_0 @ np__0) = np__0) , file(arithm, rqRealNeg__k4_xcmplx_0__r0_r0)). thf(rqRealNeg__k4_xcmplx_0__r1_rm1, axiom, ( (k4_xcmplx_0 @ np__1) = (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r1_rm1)). thf(rqRealNeg__k4_xcmplx_0__r2_rm2, axiom, ( (k4_xcmplx_0 @ np__2) = (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r2_rm2)). thf(rqRealNeg__k4_xcmplx_0__r3_rm3, axiom, ( (k4_xcmplx_0 @ np__3) = (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r3_rm3)). thf(rqRealNeg__k4_xcmplx_0__rm1_r1, axiom, ( (k4_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) = np__1) , file(arithm, rqRealNeg__k4_xcmplx_0__rm1_r1)). thf(rqRealNeg__k4_xcmplx_0__rm2_r2, axiom, ( (k4_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) = np__2) , file(arithm, rqRealNeg__k4_xcmplx_0__rm2_r2)). thf(rqRealNeg__k4_xcmplx_0__rm3_r3, axiom, ( (k4_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) = np__3) , file(arithm, rqRealNeg__k4_xcmplx_0__rm3_r3)). thf(rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, axiom, ( (k4_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) , file(arithm, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2)). thf(rqRealNeg__k4_xcmplx_0__rn1d3_rnm1d3, axiom, ( (k4_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) , file(arithm, rqRealNeg__k4_xcmplx_0__rn1d3_rnm1d3)). thf(rqRealNeg__k4_xcmplx_0__rn2d3_rnm2d3, axiom, ( (k4_xcmplx_0 @ ( (k7_xcmplx_0 @ np__2) @ np__3) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) , file(arithm, rqRealNeg__k4_xcmplx_0__rn2d3_rnm2d3)). thf(rqRealNeg__k4_xcmplx_0__rn3d2_rnm3d2, axiom, ( (k4_xcmplx_0 @ ( (k7_xcmplx_0 @ np__3) @ np__2) ) = ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) , file(arithm, rqRealNeg__k4_xcmplx_0__rn3d2_rnm3d2)). thf(rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, axiom, ( (k4_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) = ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2)). thf(rqRealNeg__k4_xcmplx_0__rnm1d3_rn1d3, axiom, ( (k4_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__3) ) = ( (k7_xcmplx_0 @ np__1) @ np__3) ) , file(arithm, rqRealNeg__k4_xcmplx_0__rnm1d3_rn1d3)). thf(rqRealNeg__k4_xcmplx_0__rnm2d3_rn2d3, axiom, ( (k4_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__3) ) = ( (k7_xcmplx_0 @ np__2) @ np__3) ) , file(arithm, rqRealNeg__k4_xcmplx_0__rnm2d3_rn2d3)). thf(rqRealNeg__k4_xcmplx_0__rnm3d2_rn3d2, axiom, ( (k4_xcmplx_0 @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__3) ) @ np__2) ) = ( (k7_xcmplx_0 @ np__3) @ np__2) ) , file(arithm, rqRealNeg__k4_xcmplx_0__rnm3d2_rn3d2)). thf(spc0_boole, axiom, (v1_xboole_0 @ np__0) , file(boole, spc0_boole)). thf(spc0_numerals, axiom, ( (m1_subset_1 @ np__0) @ k4_ordinal1) , file(numerals, spc0_numerals)). thf(spc1_arithm, axiom, (! [A: $i, B: $i] : ( ( (v1_xcmplx_0 @ A) & (v1_xcmplx_0 @ B) ) => ( ( (k2_xcmplx_0 @ A) @ (k4_xcmplx_0 @ B) ) = ( (k6_xcmplx_0 @ A) @ B) ) ) ) , file(arithm, spc1_arithm)). thf(spc1_boole, axiom, ~ ( (v1_xboole_0 @ np__1) ) , file(boole, spc1_boole)). thf(spc1_numerals, axiom, ( (v2_xxreal_0 @ np__1) & ( (m1_subset_1 @ np__1) @ k4_ordinal1) ) , file(numerals, spc1_numerals)). thf(spc2_arithm, axiom, (! [A: $i] : ( (v1_xcmplx_0 @ A) => ( ( (k3_xcmplx_0 @ A) @ (k4_xcmplx_0 @ np__1) ) = (k4_xcmplx_0 @ A) ) ) ) , file(arithm, spc2_arithm)). thf(spc2_boole, axiom, ~ ( (v1_xboole_0 @ np__2) ) , file(boole, spc2_boole)). thf(spc2_numerals, axiom, ( (v2_xxreal_0 @ np__2) & ( (m1_subset_1 @ np__2) @ k4_ordinal1) ) , file(numerals, spc2_numerals)). thf(spc3_boole, axiom, ~ ( (v1_xboole_0 @ np__3) ) , file(boole, spc3_boole)). thf(spc3_numerals, axiom, ( (v2_xxreal_0 @ np__3) & ( (m1_subset_1 @ np__3) @ k4_ordinal1) ) , file(numerals, spc3_numerals)). thf(spc4_arithm, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v1_xcmplx_0 @ A) & ( (v1_xcmplx_0 @ B) & (v1_xcmplx_0 @ C) ) ) => ( ( (k3_xcmplx_0 @ A) @ ( (k7_xcmplx_0 @ B) @ C) ) = ( (k7_xcmplx_0 @ ( (k3_xcmplx_0 @ A) @ B) ) @ C) ) ) ) , file(arithm, spc4_arithm)). thf(spc5_arithm, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v1_xcmplx_0 @ A) & ( (v1_xcmplx_0 @ B) & (v1_xcmplx_0 @ C) ) ) => ( ( (k3_xcmplx_0 @ ( (k2_xcmplx_0 @ A) @ B) ) @ C) = ( (k2_xcmplx_0 @ ( (k3_xcmplx_0 @ A) @ C) ) @ ( (k3_xcmplx_0 @ B) @ C) ) ) ) ) , file(arithm, spc5_arithm)). thf(spc6_arithm, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v1_xcmplx_0 @ A) & ( (v1_xcmplx_0 @ B) & (v1_xcmplx_0 @ C) ) ) => ( ( (k2_xcmplx_0 @ ( (k2_xcmplx_0 @ A) @ B) ) @ C) = ( (k2_xcmplx_0 @ A) @ ( (k2_xcmplx_0 @ B) @ C) ) ) ) ) , file(arithm, spc6_arithm)). thf(spc7_arithm, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v1_xcmplx_0 @ A) & ( (v1_xcmplx_0 @ B) & (v1_xcmplx_0 @ C) ) ) => ( ( (k3_xcmplx_0 @ ( (k3_xcmplx_0 @ A) @ B) ) @ C) = ( (k3_xcmplx_0 @ A) @ ( (k3_xcmplx_0 @ B) @ C) ) ) ) ) , file(arithm, spc6_arithm)). thf(spc8_arithm, axiom, (! [A: $i, B: $i] : ( ( (v1_xcmplx_0 @ A) & (v1_xcmplx_0 @ B) ) => ( ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ A) ) @ (k4_xcmplx_0 @ B) ) = (k4_xcmplx_0 @ ( (k2_xcmplx_0 @ A) @ B) ) ) ) ) , file(arithm, spc8_arithm)). thf(spc9_arithm, axiom, (! [A: $i, B: $i] : ( ( (v1_xcmplx_0 @ A) & (v1_xcmplx_0 @ B) ) => ( ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ A) ) @ (k4_xcmplx_0 @ B) ) = ( (k6_xcmplx_0 @ B) @ A) ) ) ) , file(arithm, spc9_arithm)). thf(t1_arithm, axiom, (! [A: $i] : ( (v1_xcmplx_0 @ A) => ( ( (k2_xcmplx_0 @ A) @ k5_numbers) = A) ) ) , file(arithm, t1_arithm)). thf(t1_euclid_8, axiom, (! [A: $i] : ( ( ( (m2_finseq_2 @ A) @ k1_numbers) @ (k1_euclid @ np__3) ) => (A = ( ( (k1_euclid_8 @ ( (k1_funct_1 @ A) @ np__1) ) @ ( (k1_funct_1 @ A) @ np__2) ) @ ( (k1_funct_1 @ A) @ np__3) ) ) ) ) , file(euclid_8, t1_euclid_8)). 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(t28_euclid_5, axiom, (! [A: $i] : ( ( (m2_finseq_1 @ A) @ k1_numbers) => (! [B: $i] : ( ( (m2_finseq_1 @ B) @ k1_numbers) => ( ( ( (k3_finseq_1 @ A) = np__3) & ( (k3_finseq_1 @ B) = np__3) ) => ( ( (k14_rvsum_1 @ A) @ B) = ( ( (k11_finseq_1 @ ( (k3_xcmplx_0 @ ( (k1_funct_1 @ A) @ np__1) ) @ ( (k1_funct_1 @ B) @ np__1) ) ) @ ( (k3_xcmplx_0 @ ( (k1_funct_1 @ A) @ np__2) ) @ ( (k1_funct_1 @ B) @ np__2) ) ) @ ( (k3_xcmplx_0 @ ( (k1_funct_1 @ A) @ np__3) ) @ ( (k1_funct_1 @ B) @ np__3) ) ) ) ) ) ) ) ) , file(euclid_5, t28_euclid_5)). thf(t2_arithm, axiom, (! [A: $i] : ( (v1_xcmplx_0 @ A) => ( ( (k3_xcmplx_0 @ A) @ k5_numbers) = k5_numbers) ) ) , file(arithm, t2_arithm)). 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(t34_pdiff_4, axiom, (! [A: $i] : ( ( ( (m2_finseq_2 @ A) @ k1_numbers) @ (k1_euclid @ np__3) ) => (! [B: $i] : ( ( (v1_funct_1 @ B) & ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ (k1_euclid @ np__3) ) @ k1_numbers) ) ) ) => ( ( (k4_pdiff_4 @ B) @ A) = ( ( (k1_euclid_8 @ ( ( ( (k10_pdiff_1 @ np__3) @ np__1) @ B) @ A) ) @ ( ( ( (k10_pdiff_1 @ np__3) @ np__2) @ B) @ A) ) @ ( ( ( (k10_pdiff_1 @ np__3) @ np__3) @ B) @ A) ) ) ) ) ) ) , file(pdiff_4, t34_pdiff_4)). thf(t3_arithm, axiom, (! [A: $i] : ( (v1_xcmplx_0 @ A) => ( ( (k3_xcmplx_0 @ np__1) @ A) = A) ) ) , file(arithm, t3_arithm)). 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(t45_finseq_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_finseq_1 @ A) ) ) => (! [B: $i] : (! [C: $i] : (! [D: $i] : ( (A = ( ( (k11_finseq_1 @ B) @ C) @ D) ) <=> ( ( (k3_finseq_1 @ A) = np__3) & ( ( ( (k1_funct_1 @ A) @ np__1) = B) & ( ( ( (k1_funct_1 @ A) @ np__2) = C) & ( ( (k1_funct_1 @ A) @ np__3) = D) ) ) ) ) ) ) ) ) ) , file(finseq_1, t45_finseq_1)). thf(t4_arithm, axiom, (! [A: $i] : ( (v1_xcmplx_0 @ A) => ( ( (k6_xcmplx_0 @ A) @ k5_numbers) = A) ) ) , file(arithm, t4_arithm)). 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_arithm, axiom, (! [A: $i] : ( (v1_xcmplx_0 @ A) => ( ( (k7_xcmplx_0 @ k5_numbers) @ A) = k5_numbers) ) ) , file(arithm, t5_arithm)). 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_arithm, axiom, (! [A: $i] : ( (v1_xcmplx_0 @ A) => ( ( (k7_xcmplx_0 @ A) @ np__1) = A) ) ) , file(arithm, t6_arithm)). thf(t6_boole, axiom, (! [A: $i] : ( (v1_xboole_0 @ A) => (A = k1_xboole_0) ) ) , file(boole, t6_boole)). thf(t78_rvsum_1, axiom, (! [A: $i] : ( (v1_xreal_0 @ A) => (! [B: $i] : ( (v1_xreal_0 @ B) => (! [C: $i] : ( (v1_xreal_0 @ C) => ( (k16_rvsum_1 @ ( ( (k11_finseq_1 @ A) @ B) @ C) ) = ( (k2_xcmplx_0 @ ( (k2_xcmplx_0 @ A) @ B) ) @ C) ) ) ) ) ) ) ) , file(rvsum_1, t78_rvsum_1)). 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(t42_pdiff_4, conjecture, (! [A: $i] : ( ( ( (m2_finseq_2 @ A) @ k1_numbers) @ (k1_euclid @ np__3) ) => (! [B: $i] : ( ( ( (m2_finseq_2 @ B) @ k1_numbers) @ (k1_euclid @ np__3) ) => (! [C: $i] : ( ( (v1_funct_1 @ C) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ (k1_euclid @ np__3) ) @ k1_numbers) ) ) ) => ( ( ( (k6_pdiff_4 @ C) @ A) @ B) = ( (k22_rvsum_1 @ ( (k4_pdiff_4 @ C) @ A) ) @ (k5_pdiff_4 @ B) ) ) ) ) ) ) ) ) , file(pdiff_4, t42_pdiff_4)).