% Mizar problem: t1_csspace3,csspace3,99,5 include('Axioms/SET010^0.ax'). thf(n1_type, type, 1: $i). thf(k1_funct_1_type, type, k1_funct_1: $i > $i > $i). thf(k1_numbers_type, type, k1_numbers: $i). thf(k1_seq_2_type, type, k1_seq_2: $i > $i). thf(k1_valued_1_type, type, k1_valued_1: $i > $i > $i). thf(k1_xboole_0_type, type, k1_xboole_0: $i). thf(k1_zfmisc_1_type, type, k1_zfmisc_1: $i > $i). thf(k24_valued_1_type, type, k24_valued_1: $i > $i > $i). thf(k2_funcop_1_type, type, k2_funcop_1: $i > $i > $i). thf(k2_numbers_type, type, k2_numbers: $i). thf(k2_valued_1_type, type, k2_valued_1: $i > $i > $i > $i > $i > $i). thf(k2_xcmplx_0_type, type, k2_xcmplx_0: $i > $i > $i). thf(k2_zfmisc_1_type, type, k2_zfmisc_1: $i > $i > $i). thf(k30_valued_1_type, type, k30_valued_1: $i > $i). thf(k31_valued_1_type, type, k31_valued_1: $i > $i > $i > $i). thf(k3_comseq_2_type, type, k3_comseq_2: $i > $i). thf(k3_numbers_type, type, k3_numbers: $i). thf(k45_valued_1_type, type, k45_valued_1: $i > $i > $i). thf(k46_valued_1_type, type, k46_valued_1: $i > $i > $i > $i > $i > $i). thf(k4_numbers_type, type, k4_numbers: $i). thf(k4_ordinal1_type, type, k4_ordinal1: $i). thf(k4_xcmplx_0_type, type, k4_xcmplx_0: $i > $i). thf(k54_valued_1_type, type, k54_valued_1: $i > $i). thf(k55_valued_1_type, type, k55_valued_1: $i > $i > $i > $i). thf(k6_xcmplx_0_type, type, k6_xcmplx_0: $i > $i > $i). thf(k8_funcop_1_type, type, k8_funcop_1: $i > $i > $i > $i). thf(k8_nat_1_type, type, k8_nat_1: $i > $i > $i > $i). thf(k9_complex1_type, type, k9_complex1: $i > $i). thf(k9_xtuple_0_type, type, k9_xtuple_0: $i > $i). thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o). thf(r1_tarski_type, type, r1_tarski: $i > $i > $o). thf(r2_relset_1_type, type, r2_relset_1: $i > $i > $i > $i > $o). thf(r2_tarski_type, type, r2_tarski: $i > $i > $o). thf(v10_ordinal1_type, type, v10_ordinal1: $i > $o). thf(v1_comseq_2_type, type, v1_comseq_2: $i > $o). thf(v1_finset_1_type, type, v1_finset_1: $i > $o). thf(v1_funct_1_type, type, v1_funct_1: $i > $o). thf(v1_funct_2_type, type, v1_funct_2: $i > $i > $i > $o). thf(v1_int_1_type, type, v1_int_1: $i > $o). thf(v1_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_seq_2_type, type, v1_seq_2: $i > $o). thf(v1_setfam_1_type, type, v1_setfam_1: $i > $o). thf(v1_subset_1_type, type, v1_subset_1: $i > $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_comseq_2_type, type, v2_comseq_2: $i > $o). thf(v2_membered_type, type, v2_membered: $i > $o). thf(v2_ordinal1_type, type, v2_ordinal1: $i > $o). thf(v2_seq_2_type, type, v2_seq_2: $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_membered_type, type, v3_membered: $i > $o). thf(v3_ordinal1_type, type, v3_ordinal1: $i > $o). thf(v3_valued_0_type, type, v3_valued_0: $i > $o). thf(v3_xxreal_0_type, type, v3_xxreal_0: $i > $o). thf(v4_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_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_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_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_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_comseq_2, axiom, (! [A: $i] : ( ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k2_numbers) ) ) => ( ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k2_numbers) & (v2_comseq_2 @ A) ) ) => ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k2_numbers) & (v1_comseq_2 @ A) ) ) ) ) ) , file(comseq_2, cc1_comseq_2)). thf(cc1_funct_2, axiom, (! [A: $i, B: $i] : (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => ( ( (v1_partfun1 @ C) @ A) => ( ( (v1_funct_2 @ C) @ A) @ B) ) ) ) ) , file(funct_2, cc1_funct_2)). thf(cc1_membered, axiom, (! [A: $i] : ( (v6_membered @ A) => (v5_membered @ A) ) ) , file(membered, cc1_membered)). thf(cc1_ordinal1, axiom, (! [A: $i] : ( (v3_ordinal1 @ A) => ( (v1_ordinal1 @ A) & (v2_ordinal1 @ A) ) ) ) , file(ordinal1, cc1_ordinal1)). thf(cc1_relset_1, axiom, (! [A: $i, B: $i] : (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => (v1_relat_1 @ C) ) ) ) , file(relset_1, cc1_relset_1)). thf(cc1_seq_2, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v3_valued_0 @ A) & (v1_comseq_2 @ A) ) ) ) => ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v3_valued_0 @ A) & ( (v1_seq_2 @ A) & (v2_seq_2 @ A) ) ) ) ) ) ) , file(seq_2, cc1_seq_2)). thf(cc1_subset_1, axiom, (! [A: $i] : ( (v1_xboole_0 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v1_xboole_0 @ B) ) ) ) ) , file(subset_1, cc1_subset_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_xcmplx_0, axiom, (! [A: $i] : ( (v7_ordinal1 @ A) => (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, cc1_xcmplx_0)). thf(cc1_xreal_0, axiom, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => (v1_xreal_0 @ A) ) ) , file(xreal_0, cc1_xreal_0)). thf(cc20_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(cc28_valued_0, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v5_relat_1 @ A) @ k2_numbers) ) => ( (v1_relat_1 @ A) & (v1_valued_0 @ A) ) ) ) , file(valued_0, cc28_valued_0)). thf(cc2_comseq_2, axiom, (! [A: $i] : ( ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k2_numbers) ) ) => ( ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k2_numbers) & ~ ( (v1_comseq_2 @ A) ) ) ) => ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k2_numbers) & ~ ( (v2_comseq_2 @ A) ) ) ) ) ) ) , file(comseq_2, cc2_comseq_2)). thf(cc2_funct_2, axiom, (! [A: $i, B: $i] : ( (v1_xboole_0 @ A) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => ( ( ( (v1_funct_2 @ C) @ A) @ B) => ( (v1_partfun1 @ C) @ A) ) ) ) ) ) , file(funct_2, cc2_funct_2)). thf(cc2_membered, axiom, (! [A: $i] : ( (v5_membered @ A) => (v4_membered @ A) ) ) , file(membered, cc2_membered)). thf(cc2_ordinal1, axiom, (! [A: $i] : ( ( (v1_ordinal1 @ A) & (v2_ordinal1 @ A) ) => (v3_ordinal1 @ A) ) ) , file(ordinal1, cc2_ordinal1)). thf(cc2_relset_1, axiom, (! [A: $i, B: $i] : (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => ( ( (v4_relat_1 @ C) @ A) & ( (v5_relat_1 @ C) @ B) ) ) ) ) , file(relset_1, cc2_relset_1)). thf(cc2_seq_2, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v3_valued_0 @ A) & ( (v1_seq_2 @ A) & (v2_seq_2 @ A) ) ) ) ) => ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v3_valued_0 @ A) & (v1_comseq_2 @ A) ) ) ) ) ) , file(seq_2, cc2_seq_2)). thf(cc2_subset_1, axiom, (! [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => ( ~ ( ( (v1_subset_1 @ B) @ A) ) => ~ ( (v1_xboole_0 @ B) ) ) ) ) ) ) , file(subset_1, cc2_subset_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_xcmplx_0, axiom, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, cc2_xcmplx_0)). thf(cc2_xreal_0, axiom, (! [A: $i] : ( (v7_ordinal1 @ A) => (v1_xreal_0 @ A) ) ) , file(xreal_0, cc2_xreal_0)). thf(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_funct_2, axiom, (! [A: $i, B: $i] : ( ~ ( (v1_xboole_0 @ B) ) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => ( ( ( (v1_funct_2 @ C) @ A) @ B) => ( (v1_partfun1 @ C) @ A) ) ) ) ) ) , file(funct_2, cc3_funct_2)). thf(cc3_membered, axiom, (! [A: $i] : ( (v4_membered @ A) => (v3_membered @ A) ) ) , file(membered, cc3_membered)). thf(cc3_ordinal1, axiom, (! [A: $i] : ( (v1_xboole_0 @ A) => (v3_ordinal1 @ A) ) ) , file(ordinal1, cc3_ordinal1)). thf(cc3_relset_1, axiom, (! [A: $i, B: $i] : ( (v1_xboole_0 @ A) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => (v1_xboole_0 @ C) ) ) ) ) , file(relset_1, cc3_relset_1)). thf(cc3_subset_1, axiom, (! [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => ( (v1_xboole_0 @ B) => ( (v1_subset_1 @ B) @ A) ) ) ) ) ) , file(subset_1, cc3_subset_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_xcmplx_0, axiom, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k2_numbers) => (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, cc3_xcmplx_0)). thf(cc3_xreal_0, axiom, (! [A: $i] : ( (v1_xreal_0 @ A) => (v1_xcmplx_0 @ A) ) ) , file(xreal_0, cc3_xreal_0)). thf(cc4_funct_2, axiom, (! [A: $i] : (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ A) ) ) => ( ( ( (v1_funct_2 @ B) @ A) @ A) => ( (v1_partfun1 @ B) @ A) ) ) ) ) , file(funct_2, cc4_funct_2)). thf(cc4_membered, axiom, (! [A: $i] : ( (v3_membered @ A) => (v2_membered @ A) ) ) , file(membered, cc4_membered)). thf(cc4_ordinal1, axiom, (! [A: $i] : ( (v1_xboole_0 @ A) => (v5_ordinal1 @ A) ) ) , file(ordinal1, cc4_ordinal1)). thf(cc4_relset_1, axiom, (! [A: $i, B: $i] : ( (v1_xboole_0 @ A) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ B) @ A) ) ) => (v1_xboole_0 @ C) ) ) ) ) , file(relset_1, cc4_relset_1)). thf(cc4_seq_2, axiom, (! [A: $i] : ( ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k1_numbers) ) ) => ( ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k1_numbers) & (v2_comseq_2 @ A) ) ) => ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k1_numbers) & (v1_comseq_2 @ A) ) ) ) ) ) , file(seq_2, cc4_seq_2)). thf(cc4_subset_1, axiom, (! [A: $i] : ( (v1_xboole_0 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => ~ ( ( (v1_subset_1 @ B) @ A) ) ) ) ) ) , file(subset_1, cc4_subset_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_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_ordinal1, axiom, (! [A: $i] : ( (v3_ordinal1 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => (v3_ordinal1 @ B) ) ) ) ) , file(ordinal1, cc5_ordinal1)). thf(cc5_subset_1, axiom, (! [A: $i] : ( (v1_zfmisc_1 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v1_zfmisc_1 @ B) ) ) ) ) , file(subset_1, cc5_subset_1)). 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_membered, axiom, (! [A: $i] : ( (v1_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => (v1_xcmplx_0 @ B) ) ) ) ) , file(membered, cc6_membered)). 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_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_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_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_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_k2_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( (v1_membered @ B) & ( (v1_membered @ C) & ( ( (v1_funct_1 @ D) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) & ( (v1_funct_1 @ E) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) => ( (= @ ( ( ( ( (k2_valued_1 @ A) @ B) @ C) @ D) @ E) ) @ ( ( ( ( (k2_valued_1 @ A) @ B) @ C) @ E) @ D) ) ) ) , file(valued_1, k2_valued_1)). thf(commutativity_k2_xcmplx_0, axiom, (! [A: $i, B: $i] : ( ( (v1_xcmplx_0 @ A) & (v1_xcmplx_0 @ B) ) => ( (= @ ( (k2_xcmplx_0 @ A) @ B) ) @ ( (k2_xcmplx_0 @ B) @ A) ) ) ) , file(xcmplx_0, k2_xcmplx_0)). thf(d12_ordinal1, axiom, (! [A: $i] : ( (v7_ordinal1 @ A) <=> ( (r2_hidden @ A) @ k4_ordinal1) ) ) , file(ordinal1, d12_ordinal1)). thf(d2_xcmplx_0, axiom, (! [A: $i] : ( (v1_xcmplx_0 @ A) <=> ( (r2_hidden @ A) @ k2_numbers) ) ) , file(xcmplx_0, d2_xcmplx_0)). thf(d6_valued_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) => ( (= @ (k30_valued_1 @ A) ) @ ( (k24_valued_1 @ A) @ (k4_xcmplx_0 @ 1) ) ) ) ) , file(valued_1, d6_valued_1)). thf(d9_valued_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) => (! [B: $i] : ( ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v1_valued_0 @ B) ) ) => ( (= @ ( (k45_valued_1 @ A) @ B) ) @ ( (k1_valued_1 @ A) @ (k30_valued_1 @ B) ) ) ) ) ) ) , file(valued_1, d9_valued_1)). thf(dt_k1_funct_1, axiom, $true, file(funct_1, k1_funct_1)). thf(dt_k1_numbers, axiom, $true, file(numbers, k1_numbers)). thf(dt_k1_seq_2, axiom, (! [A: $i] : ( ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k1_numbers) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k1_numbers) ) ) ) ) => (v1_xreal_0 @ (k1_seq_2 @ A) ) ) ) , file(seq_2, k1_seq_2)). thf(dt_k1_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v1_valued_0 @ B) ) ) ) => ( (v1_relat_1 @ ( (k1_valued_1 @ A) @ B) ) & (v1_funct_1 @ ( (k1_valued_1 @ A) @ B) ) ) ) ) , file(valued_1, k1_valued_1)). thf(dt_k1_xboole_0, axiom, $true, file(xboole_0, k1_xboole_0)). thf(dt_k1_zfmisc_1, axiom, $true, file(zfmisc_1, k1_zfmisc_1)). thf(dt_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_funcop_1, axiom, $true, file(funcop_1, k2_funcop_1)). thf(dt_k2_numbers, axiom, $true, file(numbers, k2_numbers)). thf(dt_k2_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( (v1_membered @ B) & ( (v1_membered @ C) & ( ( (v1_funct_1 @ D) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) & ( (v1_funct_1 @ E) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) => ( (v1_funct_1 @ ( ( ( ( (k2_valued_1 @ A) @ B) @ C) @ D) @ E) ) & ( (m1_subset_1 @ ( ( ( ( (k2_valued_1 @ A) @ B) @ C) @ D) @ E) ) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ k2_numbers) ) ) ) ) ) , file(valued_1, k2_valued_1)). thf(dt_k2_xcmplx_0, axiom, $true, file(xcmplx_0, k2_xcmplx_0)). thf(dt_k2_zfmisc_1, axiom, $true, file(zfmisc_1, k2_zfmisc_1)). thf(dt_k30_valued_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) => ( (v1_relat_1 @ (k30_valued_1 @ A) ) & ( (v1_funct_1 @ (k30_valued_1 @ A) ) & (v1_valued_0 @ (k30_valued_1 @ A) ) ) ) ) ) , file(valued_1, k30_valued_1)). thf(dt_k31_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v1_membered @ B) & ( (v1_funct_1 @ C) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) => ( (v1_funct_1 @ ( ( (k31_valued_1 @ A) @ B) @ C) ) & ( (m1_subset_1 @ ( ( (k31_valued_1 @ A) @ B) @ C) ) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ k2_numbers) ) ) ) ) ) , file(valued_1, k31_valued_1)). thf(dt_k3_comseq_2, axiom, (! [A: $i] : ( ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k2_numbers) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k2_numbers) ) ) ) ) => (v1_xcmplx_0 @ (k3_comseq_2 @ A) ) ) ) , file(comseq_2, k3_comseq_2)). thf(dt_k3_numbers, axiom, $true, file(numbers, k3_numbers)). thf(dt_k45_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v1_valued_0 @ B) ) ) ) => ( (v1_relat_1 @ ( (k45_valued_1 @ A) @ B) ) & (v1_funct_1 @ ( (k45_valued_1 @ A) @ B) ) ) ) ) , file(valued_1, k45_valued_1)). thf(dt_k46_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( (v1_membered @ B) & ( (v1_membered @ C) & ( ( (v1_funct_1 @ D) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) & ( (v1_funct_1 @ E) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) => ( (v1_funct_1 @ ( ( ( ( (k46_valued_1 @ A) @ B) @ C) @ D) @ E) ) & ( (m1_subset_1 @ ( ( ( ( (k46_valued_1 @ A) @ B) @ C) @ D) @ E) ) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ k2_numbers) ) ) ) ) ) , file(valued_1, k46_valued_1)). thf(dt_k4_numbers, axiom, $true, file(numbers, k4_numbers)). thf(dt_k4_ordinal1, axiom, $true, file(ordinal1, k4_ordinal1)). 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_k54_valued_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) => ( (v1_relat_1 @ (k54_valued_1 @ A) ) & ( (v1_funct_1 @ (k54_valued_1 @ A) ) & (v3_valued_0 @ (k54_valued_1 @ A) ) ) ) ) ) , file(valued_1, k54_valued_1)). thf(dt_k55_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v1_membered @ B) & ( (v1_funct_1 @ C) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) => ( (v1_funct_1 @ ( ( (k55_valued_1 @ A) @ B) @ C) ) & ( (m1_subset_1 @ ( ( (k55_valued_1 @ A) @ B) @ C) ) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ k1_numbers) ) ) ) ) ) , file(valued_1, k55_valued_1)). thf(dt_k6_xcmplx_0, axiom, $true, file(xcmplx_0, k6_xcmplx_0)). thf(dt_k8_funcop_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ~ ( (v1_xboole_0 @ A) ) & ( (m1_subset_1 @ C) @ A) ) => ( (v1_funct_1 @ ( ( (k8_funcop_1 @ A) @ B) @ C) ) & ( ( ( (v1_funct_2 @ ( ( (k8_funcop_1 @ A) @ B) @ C) ) @ B) @ A) & ( (m1_subset_1 @ ( ( (k8_funcop_1 @ A) @ B) @ C) ) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ B) @ A) ) ) ) ) ) ) , file(funcop_1, k8_funcop_1)). thf(dt_k8_nat_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_funct_1 @ B) & ( ( ( (v1_funct_2 @ B) @ k4_ordinal1) @ A) & ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ A) ) ) ) ) & (v7_ordinal1 @ C) ) => ( (m1_subset_1 @ ( ( (k8_nat_1 @ A) @ B) @ C) ) @ A) ) ) , file(nat_1, k8_nat_1)). thf(dt_k9_complex1, axiom, (! [A: $i] : ( (v1_xcmplx_0 @ A) => (v1_xreal_0 @ (k9_complex1 @ A) ) ) ) , file(complex1, k9_complex1)). thf(dt_k9_xtuple_0, axiom, $true, file(xtuple_0, k9_xtuple_0)). thf(dt_m1_subset_1, axiom, $true, file(subset_1, m1_subset_1)). thf(existence_m1_subset_1, axiom, (! [A: $i] : (? [B: $i] : ( (m1_subset_1 @ B) @ A) ) ) , file(subset_1, m1_subset_1)). thf(fc100_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v4_membered @ B) ) & ( (v1_funct_1 @ C) & ( ( ( (v1_funct_2 @ C) @ A) @ B) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) ) => ( (v1_funct_1 @ (k54_valued_1 @ C) ) & ( (v1_partfun1 @ (k54_valued_1 @ C) ) @ A) ) ) ) , file(valued_1, fc100_valued_1)). thf(fc101_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v5_membered @ B) ) & ( (v1_funct_1 @ C) & ( ( ( (v1_funct_2 @ C) @ A) @ B) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) ) => ( (v1_funct_1 @ (k54_valued_1 @ C) ) & ( (v1_partfun1 @ (k54_valued_1 @ C) ) @ A) ) ) ) , file(valued_1, fc101_valued_1)). thf(fc108_valued_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v4_relat_1 @ A) @ k4_ordinal1) ) => (v6_membered @ (k9_xtuple_0 @ A) ) ) ) , file(valued_1, fc108_valued_1)). thf(fc10_subset_1, axiom, (! [A: $i, B: $i] : ( ( ~ ( (v1_xboole_0 @ A) ) & ~ ( (v1_xboole_0 @ B) ) ) => ~ ( (v1_xboole_0 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) , file(subset_1, fc10_subset_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(fc111_valued_1, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ B) & ( ( (v4_relat_1 @ B) @ A) & ( (v1_funct_1 @ B) & (v1_valued_0 @ B) ) ) ) => ( (v1_relat_1 @ (k30_valued_1 @ B) ) & ( ( (v4_relat_1 @ (k30_valued_1 @ B) ) @ A) & ( (v1_funct_1 @ (k30_valued_1 @ B) ) & (v1_valued_0 @ (k30_valued_1 @ B) ) ) ) ) ) ) , file(valued_1, fc111_valued_1)). thf(fc114_valued_1, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ B) & ( ( (v4_relat_1 @ B) @ A) & ( (v1_funct_1 @ B) & (v1_valued_0 @ B) ) ) ) => ( (v1_relat_1 @ (k54_valued_1 @ B) ) & ( ( (v4_relat_1 @ (k54_valued_1 @ B) ) @ A) & ( (v1_funct_1 @ (k54_valued_1 @ B) ) & (v3_valued_0 @ (k54_valued_1 @ B) ) ) ) ) ) ) , file(valued_1, fc114_valued_1)). thf(fc115_valued_1, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ B) & ( ( (v4_relat_1 @ B) @ A) & ( (v1_funct_1 @ B) & ( ( (v1_partfun1 @ B) @ A) & (v1_valued_0 @ B) ) ) ) ) => ( (v1_relat_1 @ (k30_valued_1 @ B) ) & ( (v1_funct_1 @ (k30_valued_1 @ B) ) & ( ( (v1_partfun1 @ (k30_valued_1 @ B) ) @ A) & (v1_valued_0 @ (k30_valued_1 @ B) ) ) ) ) ) ) , file(valued_1, fc115_valued_1)). thf(fc118_valued_1, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ B) & ( ( (v4_relat_1 @ B) @ A) & ( (v1_funct_1 @ B) & ( ( (v1_partfun1 @ B) @ A) & (v1_valued_0 @ B) ) ) ) ) => ( (v1_relat_1 @ (k54_valued_1 @ B) ) & ( (v1_funct_1 @ (k54_valued_1 @ B) ) & ( ( (v1_partfun1 @ (k54_valued_1 @ B) ) @ A) & (v3_valued_0 @ (k54_valued_1 @ B) ) ) ) ) ) ) , file(valued_1, fc118_valued_1)). thf(fc11_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v6_membered @ B) ) & ( ( ~ ( (v1_xboole_0 @ C) ) & (v6_membered @ C) ) & ( ( (v1_funct_1 @ D) & ( ( ( (v1_funct_2 @ D) @ A) @ B) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & ( (v1_funct_1 @ E) & ( ( ( (v1_funct_2 @ E) @ A) @ C) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k1_valued_1 @ D) @ E) ) & ( (v1_partfun1 @ ( (k1_valued_1 @ D) @ E) ) @ A) ) ) ) , file(valued_1, fc11_valued_1)). thf(fc11_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( (v2_xxreal_0 @ A) & (v1_xreal_0 @ A) ) & ( ~ ( (v3_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => (v2_xxreal_0 @ ( (k2_xcmplx_0 @ A) @ B) ) ) ) , file(xreal_0, fc11_xreal_0)). thf(fc121_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_relat_1 @ B) & ( ( (v4_relat_1 @ B) @ A) & ( (v1_funct_1 @ B) & (v1_valued_0 @ B) ) ) ) & (v1_xcmplx_0 @ C) ) => ( (v1_relat_1 @ ( (k24_valued_1 @ B) @ C) ) & ( ( (v4_relat_1 @ ( (k24_valued_1 @ B) @ C) ) @ A) & (v1_funct_1 @ ( (k24_valued_1 @ B) @ C) ) ) ) ) ) , file(valued_1, fc121_valued_1)). thf(fc124_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_relat_1 @ B) & ( ( (v4_relat_1 @ B) @ A) & ( (v1_funct_1 @ B) & ( ( (v1_partfun1 @ B) @ A) & (v1_valued_0 @ B) ) ) ) ) & (v1_xcmplx_0 @ C) ) => ( (v1_relat_1 @ ( (k24_valued_1 @ B) @ C) ) & ( (v1_funct_1 @ ( (k24_valued_1 @ B) @ C) ) & ( (v1_partfun1 @ ( (k24_valued_1 @ B) @ C) ) @ A) ) ) ) ) , file(valued_1, fc124_valued_1)). thf(fc125_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v1_valued_0 @ B) ) ) & ( (v1_relat_1 @ C) & ( ( (v4_relat_1 @ C) @ A) & ( (v1_funct_1 @ C) & (v1_valued_0 @ C) ) ) ) ) => ( (v1_relat_1 @ ( (k1_valued_1 @ B) @ C) ) & ( ( (v4_relat_1 @ ( (k1_valued_1 @ B) @ C) ) @ A) & (v1_funct_1 @ ( (k1_valued_1 @ B) @ C) ) ) ) ) ) , file(valued_1, fc125_valued_1)). thf(fc126_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v1_valued_0 @ B) ) ) & ( (v1_relat_1 @ C) & ( ( (v4_relat_1 @ C) @ A) & ( (v1_funct_1 @ C) & (v1_valued_0 @ C) ) ) ) ) => ( (v1_relat_1 @ ( (k45_valued_1 @ B) @ C) ) & ( ( (v4_relat_1 @ ( (k45_valued_1 @ B) @ C) ) @ A) & (v1_funct_1 @ ( (k45_valued_1 @ B) @ C) ) ) ) ) ) , file(valued_1, fc126_valued_1)). thf(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_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( (v2_xxreal_0 @ A) & (v1_xreal_0 @ A) ) & ( ~ ( (v3_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => (v2_xxreal_0 @ ( (k2_xcmplx_0 @ B) @ A) ) ) ) , file(xreal_0, fc12_xreal_0)). thf(fc130_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_relat_1 @ B) & ( ( (v4_relat_1 @ B) @ A) & ( (v1_funct_1 @ B) & ( ( (v1_partfun1 @ B) @ A) & (v1_valued_0 @ B) ) ) ) ) & ( (v1_relat_1 @ C) & ( ( (v4_relat_1 @ C) @ A) & ( (v1_funct_1 @ C) & ( ( (v1_partfun1 @ C) @ A) & (v1_valued_0 @ C) ) ) ) ) ) => ( (v1_relat_1 @ ( (k45_valued_1 @ B) @ C) ) & ( (v1_funct_1 @ ( (k45_valued_1 @ B) @ C) ) & ( (v1_partfun1 @ ( (k45_valued_1 @ B) @ C) ) @ A) ) ) ) ) , file(valued_1, fc130_valued_1)). thf(fc13_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( (v3_xxreal_0 @ A) & (v1_xreal_0 @ A) ) & ( ~ ( (v2_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => (v3_xxreal_0 @ ( (k2_xcmplx_0 @ A) @ B) ) ) ) , file(xreal_0, fc13_xreal_0)). thf(fc14_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( (v3_xxreal_0 @ A) & (v1_xreal_0 @ A) ) & ( ~ ( (v2_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => (v3_xxreal_0 @ ( (k2_xcmplx_0 @ B) @ A) ) ) ) , file(xreal_0, fc14_xreal_0)). thf(fc15_xreal_0, axiom, (! [A: $i] : ( ( ~ ( (v2_xxreal_0 @ A) ) & (v1_xreal_0 @ A) ) => ( (v1_xcmplx_0 @ (k4_xcmplx_0 @ A) ) & ~ ( (v3_xxreal_0 @ (k4_xcmplx_0 @ A) ) ) ) ) ) , file(xreal_0, fc15_xreal_0)). thf(fc16_xreal_0, axiom, (! [A: $i] : ( ( ~ ( (v3_xxreal_0 @ A) ) & (v1_xreal_0 @ A) ) => ( (v1_xcmplx_0 @ (k4_xcmplx_0 @ A) ) & ~ ( (v2_xxreal_0 @ (k4_xcmplx_0 @ A) ) ) ) ) ) , file(xreal_0, fc16_xreal_0)). thf(fc17_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( ~ ( (v3_xxreal_0 @ A) ) & (v1_xreal_0 @ A) ) & ( ~ ( (v2_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => ~ ( (v3_xxreal_0 @ ( (k6_xcmplx_0 @ A) @ B) ) ) ) ) , file(xreal_0, fc17_xreal_0)). thf(fc18_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( ~ ( (v3_xxreal_0 @ A) ) & (v1_xreal_0 @ A) ) & ( ~ ( (v2_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => ~ ( (v2_xxreal_0 @ ( (k6_xcmplx_0 @ B) @ A) ) ) ) ) , file(xreal_0, fc18_xreal_0)). thf(fc19_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_membered, axiom, (v1_membered @ k2_numbers) , file(membered, fc1_membered)). thf(fc1_numbers, axiom, ~ ( (v1_xboole_0 @ k1_numbers) ) , file(numbers, fc1_numbers)). thf(fc1_seq_2, axiom, (! [A: $i, B: $i] : ( ( ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k1_numbers) & ( (v2_comseq_2 @ A) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k1_numbers) ) ) ) ) ) & ( (v1_funct_1 @ B) & ( ( ( (v1_funct_2 @ B) @ k4_ordinal1) @ k1_numbers) & ( (v2_comseq_2 @ B) & ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k1_numbers) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k1_valued_1 @ A) @ B) ) & ( ( ( (v1_funct_2 @ ( (k1_valued_1 @ A) @ B) ) @ k4_ordinal1) @ k1_numbers) & (v2_comseq_2 @ ( (k1_valued_1 @ A) @ B) ) ) ) ) ) , file(seq_2, fc1_seq_2)). thf(fc1_subset_1, axiom, (! [A: $i] : ~ ( (v1_xboole_0 @ (k1_zfmisc_1 @ A) ) ) ) , file(subset_1, fc1_subset_1)). thf(fc1_valued_1, axiom, (! [A: $i] : ( (v1_rat_1 @ A) => ( (v1_xreal_0 @ (k9_complex1 @ A) ) & (v1_rat_1 @ (k9_complex1 @ A) ) ) ) ) , file(valued_1, fc1_valued_1)). thf(fc1_xboole_0, axiom, (v1_xboole_0 @ k1_xboole_0) , file(xboole_0, fc1_xboole_0)). thf(fc20_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( (v2_xxreal_0 @ A) & (v1_xreal_0 @ A) ) & ( ~ ( (v2_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => (v3_xxreal_0 @ ( (k6_xcmplx_0 @ B) @ A) ) ) ) , file(xreal_0, fc20_xreal_0)). thf(fc21_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( (v3_xxreal_0 @ A) & (v1_xreal_0 @ A) ) & ( ~ ( (v3_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => (v3_xxreal_0 @ ( (k6_xcmplx_0 @ A) @ B) ) ) ) , file(xreal_0, fc21_xreal_0)). thf(fc22_xreal_0, axiom, (! [A: $i, B: $i] : ( ( ( (v3_xxreal_0 @ A) & (v1_xreal_0 @ A) ) & ( ~ ( (v3_xxreal_0 @ B) ) & (v1_xreal_0 @ B) ) ) => (v2_xxreal_0 @ ( (k6_xcmplx_0 @ B) @ A) ) ) ) , file(xreal_0, fc22_xreal_0)). thf(fc2_numbers, axiom, ~ ( (v1_xboole_0 @ k2_numbers) ) , file(numbers, fc2_numbers)). thf(fc2_seq_2, axiom, (! [A: $i, B: $i] : ( ( (v1_xreal_0 @ A) & ( (v1_funct_1 @ B) & ( ( ( (v1_funct_2 @ B) @ k4_ordinal1) @ k1_numbers) & ( (v2_comseq_2 @ B) & ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k1_numbers) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k24_valued_1 @ B) @ A) ) & ( ( ( (v1_funct_2 @ ( (k24_valued_1 @ B) @ A) ) @ k4_ordinal1) @ k1_numbers) & (v2_comseq_2 @ ( (k24_valued_1 @ B) @ A) ) ) ) ) ) , file(seq_2, fc2_seq_2)). thf(fc2_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v1_valued_0 @ B) ) ) ) => ( (v1_relat_1 @ ( (k1_valued_1 @ A) @ B) ) & ( (v1_funct_1 @ ( (k1_valued_1 @ A) @ B) ) & (v1_valued_0 @ ( (k1_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc2_valued_1)). thf(fc2_xcmplx_0, axiom, (! [A: $i, B: $i] : ( ( (v1_xcmplx_0 @ A) & (v1_xcmplx_0 @ B) ) => (v1_xcmplx_0 @ ( (k2_xcmplx_0 @ A) @ B) ) ) ) , file(xcmplx_0, fc2_xcmplx_0)). thf(fc3_membered, axiom, (v3_membered @ k1_numbers) , file(membered, fc3_membered)). thf(fc3_numbers, axiom, ~ ( (v1_xboole_0 @ k3_numbers) ) , file(numbers, fc3_numbers)). thf(fc3_seq_2, axiom, (! [A: $i] : ( ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k1_numbers) & ( (v2_comseq_2 @ A) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k1_numbers) ) ) ) ) ) => ( (v1_funct_1 @ (k30_valued_1 @ A) ) & ( ( ( (v1_funct_2 @ (k30_valued_1 @ A) ) @ k4_ordinal1) @ k1_numbers) & (v2_comseq_2 @ (k30_valued_1 @ A) ) ) ) ) ) , file(seq_2, fc3_seq_2)). 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(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_comseq_2, axiom, (! [A: $i, B: $i] : ( ( ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k2_numbers) & ( (v2_comseq_2 @ A) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k2_numbers) ) ) ) ) ) & ( (v1_funct_1 @ B) & ( ( ( (v1_funct_2 @ B) @ k4_ordinal1) @ k2_numbers) & ( (v2_comseq_2 @ B) & ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k2_numbers) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k1_valued_1 @ A) @ B) ) & ( ( ( (v1_funct_2 @ ( (k1_valued_1 @ A) @ B) ) @ k4_ordinal1) @ k2_numbers) & (v2_comseq_2 @ ( (k1_valued_1 @ A) @ B) ) ) ) ) ) , file(comseq_2, fc4_comseq_2)). thf(fc4_membered, axiom, (v4_membered @ k3_numbers) , file(membered, fc4_membered)). thf(fc4_numbers, axiom, ~ ( (v1_xboole_0 @ k4_numbers) ) , file(numbers, fc4_numbers)). thf(fc4_ordinal1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v5_ordinal1 @ A) ) ) => (v3_ordinal1 @ (k9_xtuple_0 @ A) ) ) ) , file(ordinal1, fc4_ordinal1)). thf(fc4_seq_2, axiom, (! [A: $i, B: $i] : ( ( ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k1_numbers) & ( (v2_comseq_2 @ A) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k1_numbers) ) ) ) ) ) & ( (v1_funct_1 @ B) & ( ( ( (v1_funct_2 @ B) @ k4_ordinal1) @ k1_numbers) & ( (v2_comseq_2 @ B) & ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k1_numbers) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k45_valued_1 @ A) @ B) ) & ( ( ( (v1_funct_2 @ ( (k45_valued_1 @ A) @ B) ) @ k4_ordinal1) @ k1_numbers) & (v2_comseq_2 @ ( (k45_valued_1 @ A) @ B) ) ) ) ) ) , file(seq_2, fc4_seq_2)). thf(fc4_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( ( (v5_relat_1 @ A) @ k3_numbers) & (v1_funct_1 @ A) ) ) & ( (v1_relat_1 @ B) & ( ( (v5_relat_1 @ B) @ k3_numbers) & (v1_funct_1 @ B) ) ) ) => ( (v1_relat_1 @ ( (k1_valued_1 @ A) @ B) ) & ( ( (v5_relat_1 @ ( (k1_valued_1 @ A) @ B) ) @ k3_numbers) & (v1_funct_1 @ ( (k1_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc4_valued_1)). thf(fc4_xcmplx_0, axiom, (! [A: $i, B: $i] : ( ( (v1_xcmplx_0 @ A) & (v1_xcmplx_0 @ B) ) => (v1_xcmplx_0 @ ( (k6_xcmplx_0 @ A) @ B) ) ) ) , file(xcmplx_0, fc4_xcmplx_0)). thf(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(fc55_membered, axiom, (v7_membered @ k2_numbers) , file(membered, fc55_membered)). thf(fc55_valued_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) => ( (v1_relat_1 @ (k30_valued_1 @ A) ) & ( (v1_funct_1 @ (k30_valued_1 @ A) ) & (v1_valued_0 @ (k30_valued_1 @ A) ) ) ) ) ) , file(valued_1, fc55_valued_1)). thf(fc56_membered, axiom, (v7_membered @ k1_numbers) , file(membered, fc56_membered)). thf(fc56_valued_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v3_valued_0 @ A) ) ) => ( (v1_relat_1 @ (k30_valued_1 @ A) ) & ( (v1_funct_1 @ (k30_valued_1 @ A) ) & ( (v1_valued_0 @ (k30_valued_1 @ A) ) & (v3_valued_0 @ (k30_valued_1 @ A) ) ) ) ) ) ) , file(valued_1, fc56_valued_1)). thf(fc57_membered, axiom, (v7_membered @ k3_numbers) , file(membered, fc57_membered)). thf(fc57_valued_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( ( (v5_relat_1 @ A) @ k3_numbers) & (v1_funct_1 @ A) ) ) => ( (v1_relat_1 @ (k30_valued_1 @ A) ) & ( ( (v5_relat_1 @ (k30_valued_1 @ A) ) @ k3_numbers) & ( (v1_funct_1 @ (k30_valued_1 @ A) ) & (v1_valued_0 @ (k30_valued_1 @ A) ) ) ) ) ) ) , file(valued_1, fc57_valued_1)). thf(fc58_membered, axiom, (v7_membered @ k4_numbers) , file(membered, fc58_membered)). thf(fc58_valued_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( ( (v5_relat_1 @ A) @ k4_numbers) & (v1_funct_1 @ A) ) ) => ( (v1_relat_1 @ (k30_valued_1 @ A) ) & ( ( (v5_relat_1 @ (k30_valued_1 @ A) ) @ k4_numbers) & ( (v1_funct_1 @ (k30_valued_1 @ A) ) & (v1_valued_0 @ (k30_valued_1 @ A) ) ) ) ) ) ) , file(valued_1, fc58_valued_1)). thf(fc59_membered, axiom, (v7_membered @ k4_ordinal1) , file(membered, fc59_membered)). thf(fc59_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v1_membered @ B) ) & ( (v1_funct_1 @ C) & ( ( ( (v1_funct_2 @ C) @ A) @ B) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) ) => ( (v1_funct_1 @ (k30_valued_1 @ C) ) & ( (v1_partfun1 @ (k30_valued_1 @ C) ) @ A) ) ) ) , file(valued_1, fc59_valued_1)). thf(fc5_comseq_2, axiom, (! [A: $i, B: $i] : ( ( ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k2_numbers) & ( (v2_comseq_2 @ A) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k2_numbers) ) ) ) ) ) & (v1_xcmplx_0 @ B) ) => ( (v1_funct_1 @ ( (k24_valued_1 @ A) @ B) ) & ( ( ( (v1_funct_2 @ ( (k24_valued_1 @ A) @ B) ) @ k4_ordinal1) @ k2_numbers) & (v2_comseq_2 @ ( (k24_valued_1 @ A) @ B) ) ) ) ) ) , file(comseq_2, fc5_comseq_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_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v3_membered @ B) ) & ( (v1_funct_1 @ C) & ( ( ( (v1_funct_2 @ C) @ A) @ B) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) ) => ( (v1_funct_1 @ (k30_valued_1 @ C) ) & ( (v1_partfun1 @ (k30_valued_1 @ C) ) @ A) ) ) ) , file(valued_1, fc60_valued_1)). thf(fc61_valued_0, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) => (v1_xcmplx_0 @ ( (k1_funct_1 @ A) @ B) ) ) ) , file(valued_0, fc61_valued_0)). thf(fc61_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v4_membered @ B) ) & ( (v1_funct_1 @ C) & ( ( ( (v1_funct_2 @ C) @ A) @ B) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) ) => ( (v1_funct_1 @ (k30_valued_1 @ C) ) & ( (v1_partfun1 @ (k30_valued_1 @ C) ) @ A) ) ) ) , file(valued_1, fc61_valued_1)). thf(fc62_valued_0, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v2_valued_0 @ A) ) ) => (v1_xxreal_0 @ ( (k1_funct_1 @ A) @ B) ) ) ) , file(valued_0, fc62_valued_0)). thf(fc62_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v5_membered @ B) ) & ( (v1_funct_1 @ C) & ( ( ( (v1_funct_2 @ C) @ A) @ B) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) ) => ( (v1_funct_1 @ (k30_valued_1 @ C) ) & ( (v1_partfun1 @ (k30_valued_1 @ C) ) @ A) ) ) ) , file(valued_1, fc62_valued_1)). thf(fc63_valued_0, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v3_valued_0 @ A) ) ) => (v1_xreal_0 @ ( (k1_funct_1 @ A) @ B) ) ) ) , file(valued_0, fc63_valued_0)). thf(fc64_valued_0, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( ( (v5_relat_1 @ A) @ k3_numbers) & (v1_funct_1 @ A) ) ) => (v1_rat_1 @ ( (k1_funct_1 @ A) @ B) ) ) ) , file(valued_0, fc64_valued_0)). thf(fc65_valued_0, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( ( (v5_relat_1 @ A) @ k4_numbers) & (v1_funct_1 @ A) ) ) => (v1_int_1 @ ( (k1_funct_1 @ A) @ B) ) ) ) , file(valued_0, fc65_valued_0)). thf(fc66_valued_0, axiom, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v4_valued_0 @ A) ) ) => (v7_ordinal1 @ ( (k1_funct_1 @ A) @ B) ) ) ) , file(valued_0, fc66_valued_0)). thf(fc67_valued_0, axiom, (! [A: $i, B: $i] : ( (v1_xcmplx_0 @ B) => (v1_valued_0 @ ( (k2_funcop_1 @ A) @ B) ) ) ) , file(valued_0, fc67_valued_0)). thf(fc68_valued_0, axiom, (! [A: $i, B: $i] : ( (v1_xxreal_0 @ B) => (v2_valued_0 @ ( (k2_funcop_1 @ A) @ B) ) ) ) , file(valued_0, fc68_valued_0)). thf(fc69_valued_0, axiom, (! [A: $i, B: $i] : ( (v1_xreal_0 @ B) => (v3_valued_0 @ ( (k2_funcop_1 @ A) @ B) ) ) ) , file(valued_0, fc69_valued_0)). thf(fc6_comseq_2, axiom, (! [A: $i] : ( ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k2_numbers) & ( (v2_comseq_2 @ A) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k2_numbers) ) ) ) ) ) => ( (v1_funct_1 @ (k30_valued_1 @ A) ) & ( ( ( (v1_funct_2 @ (k30_valued_1 @ A) ) @ k4_ordinal1) @ k2_numbers) & (v2_comseq_2 @ (k30_valued_1 @ A) ) ) ) ) ) , file(comseq_2, fc6_comseq_2)). thf(fc6_membered, axiom, (v6_membered @ k4_ordinal1) , file(membered, fc6_membered)). thf(fc6_numbers, axiom, ~ ( (v1_finset_1 @ k4_numbers) ) , file(numbers, fc6_numbers)). thf(fc6_ordinal1, axiom, ( ~ ( (v1_xboole_0 @ k4_ordinal1) ) & (v3_ordinal1 @ k4_ordinal1) ) , file(ordinal1, fc6_ordinal1)). thf(fc6_seq_2, axiom, (! [A: $i] : ( ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k2_numbers) & ( (v2_comseq_2 @ A) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k2_numbers) ) ) ) ) ) => ( (v1_funct_1 @ (k54_valued_1 @ A) ) & ( ( ( (v1_funct_2 @ (k54_valued_1 @ A) ) @ k4_ordinal1) @ k1_numbers) & (v2_comseq_2 @ (k54_valued_1 @ A) ) ) ) ) ) , file(seq_2, fc6_seq_2)). thf(fc6_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v4_valued_0 @ A) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v4_valued_0 @ B) ) ) ) => ( (v1_relat_1 @ ( (k1_valued_1 @ A) @ B) ) & ( (v1_funct_1 @ ( (k1_valued_1 @ A) @ B) ) & (v4_valued_0 @ ( (k1_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc6_valued_1)). thf(fc6_xcmplx_0, axiom, (! [A: $i] : ( ( ~ ( (v8_ordinal1 @ A) ) & (v1_xcmplx_0 @ A) ) => ( ~ ( (v8_ordinal1 @ (k4_xcmplx_0 @ A) ) ) & (v1_xcmplx_0 @ (k4_xcmplx_0 @ A) ) ) ) ) , file(xcmplx_0, fc6_xcmplx_0)). thf(fc70_valued_0, axiom, (! [A: $i, B: $i] : ( (v1_rat_1 @ B) => ( (v5_relat_1 @ ( (k2_funcop_1 @ A) @ B) ) @ k3_numbers) ) ) , file(valued_0, fc70_valued_0)). thf(fc71_valued_0, axiom, (! [A: $i, B: $i] : ( (v1_int_1 @ B) => ( (v5_relat_1 @ ( (k2_funcop_1 @ A) @ B) ) @ k4_numbers) ) ) , file(valued_0, fc71_valued_0)). thf(fc72_valued_0, axiom, (! [A: $i, B: $i] : ( (v7_ordinal1 @ B) => (v4_valued_0 @ ( (k2_funcop_1 @ A) @ B) ) ) ) , file(valued_0, fc72_valued_0)). thf(fc7_comseq_2, axiom, (! [A: $i, B: $i] : ( ( ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k2_numbers) & ( (v2_comseq_2 @ A) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k2_numbers) ) ) ) ) ) & ( (v1_funct_1 @ B) & ( ( ( (v1_funct_2 @ B) @ k4_ordinal1) @ k2_numbers) & ( (v2_comseq_2 @ B) & ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k2_numbers) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k45_valued_1 @ A) @ B) ) & ( ( ( (v1_funct_2 @ ( (k45_valued_1 @ A) @ B) ) @ k4_ordinal1) @ k2_numbers) & (v2_comseq_2 @ ( (k45_valued_1 @ A) @ B) ) ) ) ) ) , file(comseq_2, fc7_comseq_2)). 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(fc81_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v1_valued_0 @ B) ) ) ) => ( (v1_relat_1 @ ( (k45_valued_1 @ A) @ B) ) & ( (v1_funct_1 @ ( (k45_valued_1 @ A) @ B) ) & (v1_valued_0 @ ( (k45_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc81_valued_1)). thf(fc82_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v3_valued_0 @ A) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v3_valued_0 @ B) ) ) ) => ( (v1_relat_1 @ ( (k45_valued_1 @ A) @ B) ) & ( (v1_funct_1 @ ( (k45_valued_1 @ A) @ B) ) & (v3_valued_0 @ ( (k45_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc82_valued_1)). thf(fc83_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( ( (v5_relat_1 @ A) @ k3_numbers) & (v1_funct_1 @ A) ) ) & ( (v1_relat_1 @ B) & ( ( (v5_relat_1 @ B) @ k3_numbers) & (v1_funct_1 @ B) ) ) ) => ( (v1_relat_1 @ ( (k45_valued_1 @ A) @ B) ) & ( ( (v5_relat_1 @ ( (k45_valued_1 @ A) @ B) ) @ k3_numbers) & (v1_funct_1 @ ( (k45_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc83_valued_1)). thf(fc84_valued_1, axiom, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( ( (v5_relat_1 @ A) @ k4_numbers) & (v1_funct_1 @ A) ) ) & ( (v1_relat_1 @ B) & ( ( (v5_relat_1 @ B) @ k4_numbers) & (v1_funct_1 @ B) ) ) ) => ( (v1_relat_1 @ ( (k45_valued_1 @ A) @ B) ) & ( ( (v5_relat_1 @ ( (k45_valued_1 @ A) @ B) ) @ k4_numbers) & (v1_funct_1 @ ( (k45_valued_1 @ A) @ B) ) ) ) ) ) , file(valued_1, fc84_valued_1)). thf(fc85_valued_0, axiom, (! [A: $i, B: $i] : ( (v1_membered @ B) => (v1_valued_0 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) , file(valued_0, fc85_valued_0)). thf(fc85_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v1_membered @ B) ) & ( ( ~ ( (v1_xboole_0 @ C) ) & (v1_membered @ C) ) & ( ( (v1_funct_1 @ D) & ( ( ( (v1_funct_2 @ D) @ A) @ B) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & ( (v1_funct_1 @ E) & ( ( ( (v1_funct_2 @ E) @ A) @ C) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k45_valued_1 @ D) @ E) ) & ( (v1_partfun1 @ ( (k45_valued_1 @ D) @ E) ) @ A) ) ) ) , file(valued_1, fc85_valued_1)). thf(fc86_valued_0, axiom, (! [A: $i, B: $i] : ( (v2_membered @ B) => (v2_valued_0 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) , file(valued_0, fc86_valued_0)). thf(fc86_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v3_membered @ B) ) & ( ( ~ ( (v1_xboole_0 @ C) ) & (v3_membered @ C) ) & ( ( (v1_funct_1 @ D) & ( ( ( (v1_funct_2 @ D) @ A) @ B) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & ( (v1_funct_1 @ E) & ( ( ( (v1_funct_2 @ E) @ A) @ C) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k45_valued_1 @ D) @ E) ) & ( (v1_partfun1 @ ( (k45_valued_1 @ D) @ E) ) @ A) ) ) ) , file(valued_1, fc86_valued_1)). thf(fc87_valued_0, axiom, (! [A: $i, B: $i] : ( (v3_membered @ B) => (v3_valued_0 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) , file(valued_0, fc87_valued_0)). thf(fc87_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v4_membered @ B) ) & ( ( ~ ( (v1_xboole_0 @ C) ) & (v4_membered @ C) ) & ( ( (v1_funct_1 @ D) & ( ( ( (v1_funct_2 @ D) @ A) @ B) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & ( (v1_funct_1 @ E) & ( ( ( (v1_funct_2 @ E) @ A) @ C) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k45_valued_1 @ D) @ E) ) & ( (v1_partfun1 @ ( (k45_valued_1 @ D) @ E) ) @ A) ) ) ) , file(valued_1, fc87_valued_1)). thf(fc88_valued_0, axiom, (! [A: $i, B: $i] : ( (v4_membered @ B) => ( (v5_relat_1 @ ( (k2_zfmisc_1 @ A) @ B) ) @ k3_numbers) ) ) , file(valued_0, fc88_valued_0)). thf(fc88_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v5_membered @ B) ) & ( ( ~ ( (v1_xboole_0 @ C) ) & (v5_membered @ C) ) & ( ( (v1_funct_1 @ D) & ( ( ( (v1_funct_2 @ D) @ A) @ B) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) & ( (v1_funct_1 @ E) & ( ( ( (v1_funct_2 @ E) @ A) @ C) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k45_valued_1 @ D) @ E) ) & ( (v1_partfun1 @ ( (k45_valued_1 @ D) @ E) ) @ A) ) ) ) , file(valued_1, fc88_valued_1)). thf(fc89_valued_0, axiom, (! [A: $i, B: $i] : ( (v5_membered @ B) => ( (v5_relat_1 @ ( (k2_zfmisc_1 @ A) @ B) ) @ k4_numbers) ) ) , file(valued_0, fc89_valued_0)). thf(fc8_numbers, axiom, ~ ( (v1_finset_1 @ k1_numbers) ) , file(numbers, fc8_numbers)). thf(fc8_relset_1, axiom, (! [A: $i, B: $i, C: $i, D: $i] : ( ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) @ C) ) ) => (v1_relat_1 @ (k9_xtuple_0 @ D) ) ) ) , file(relset_1, fc8_relset_1)). thf(fc8_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(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(fc97_valued_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( ( (v5_relat_1 @ A) @ k3_numbers) & (v1_funct_1 @ A) ) ) => ( (v1_relat_1 @ (k54_valued_1 @ A) ) & ( ( (v5_relat_1 @ (k54_valued_1 @ A) ) @ k3_numbers) & ( (v1_funct_1 @ (k54_valued_1 @ A) ) & (v3_valued_0 @ (k54_valued_1 @ A) ) ) ) ) ) ) , file(valued_1, fc97_valued_1)). thf(fc98_valued_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( ( (v5_relat_1 @ A) @ k4_numbers) & (v1_funct_1 @ A) ) ) => ( (v1_relat_1 @ (k54_valued_1 @ A) ) & ( (v1_funct_1 @ (k54_valued_1 @ A) ) & ( (v3_valued_0 @ (k54_valued_1 @ A) ) & (v4_valued_0 @ (k54_valued_1 @ A) ) ) ) ) ) ) , file(valued_1, fc98_valued_1)). thf(fc99_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( ~ ( (v1_xboole_0 @ B) ) & (v1_membered @ B) ) & ( (v1_funct_1 @ C) & ( ( ( (v1_funct_2 @ C) @ A) @ B) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) ) => ( (v1_funct_1 @ (k54_valued_1 @ C) ) & ( (v1_partfun1 @ (k54_valued_1 @ C) ) @ A) ) ) ) , file(valued_1, fc99_valued_1)). thf(fc9_numbers, axiom, ~ ( (v1_finset_1 @ k2_numbers) ) , file(numbers, fc9_numbers)). 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_k30_valued_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) => ( (= @ (k30_valued_1 @ (k30_valued_1 @ A) ) ) @ A) ) ) , file(valued_1, k30_valued_1)). thf(involutiveness_k31_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v1_membered @ B) & ( (v1_funct_1 @ C) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) => ( (= @ ( ( (k31_valued_1 @ A) @ B) @ ( ( (k31_valued_1 @ A) @ B) @ C) ) ) @ C) ) ) , file(valued_1, k31_valued_1)). thf(involutiveness_k4_xcmplx_0, axiom, (! [A: $i] : ( (v1_xcmplx_0 @ A) => ( (= @ (k4_xcmplx_0 @ (k4_xcmplx_0 @ A) ) ) @ A) ) ) , file(xcmplx_0, k4_xcmplx_0)). thf(projectivity_k54_valued_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) => ( (= @ (k54_valued_1 @ (k54_valued_1 @ A) ) ) @ (k54_valued_1 @ A) ) ) ) , file(valued_1, k54_valued_1)). thf(projectivity_k55_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v1_membered @ B) & ( (v1_funct_1 @ C) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) => ( (= @ ( ( (k55_valued_1 @ A) @ B) @ ( ( (k55_valued_1 @ A) @ B) @ C) ) ) @ ( ( (k55_valued_1 @ A) @ B) @ C) ) ) ) , file(valued_1, k55_valued_1)). thf(projectivity_k9_complex1, axiom, (! [A: $i] : ( (v1_xcmplx_0 @ A) => ( (= @ (k9_complex1 @ (k9_complex1 @ A) ) ) @ (k9_complex1 @ A) ) ) ) , file(complex1, k9_complex1)). thf(rc10_ordinal1, axiom, (? [A: $i] : (v8_ordinal1 @ A) ) , file(ordinal1, rc10_ordinal1)). thf(rc11_ordinal1, axiom, (? [A: $i] : ~ ( (v8_ordinal1 @ A) ) ) , file(ordinal1, rc11_ordinal1)). thf(rc12_ordinal1, axiom, (? [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) & ~ ( (v10_ordinal1 @ A) ) ) ) , file(ordinal1, rc12_ordinal1)). 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_comseq_2, axiom, (? [A: $i] : ( ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k2_numbers) ) ) & ( (v1_relat_1 @ A) & ( ( (v4_relat_1 @ A) @ k4_ordinal1) & ( ( (v5_relat_1 @ A) @ k2_numbers) & ( (v1_funct_1 @ A) & ( ~ ( (v1_xboole_0 @ A) ) & ( ( (v1_partfun1 @ A) @ k4_ordinal1) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k2_numbers) & ( (v1_valued_0 @ A) & (v1_comseq_2 @ A) ) ) ) ) ) ) ) ) ) ) , file(comseq_2, rc1_comseq_2)). thf(rc1_funct_2, axiom, (! [A: $i, B: $i] : (? [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) & ( (v1_relat_1 @ C) & ( ( (v4_relat_1 @ C) @ A) & ( ( (v5_relat_1 @ C) @ B) & ( (v1_funct_1 @ C) & ( ( (v1_funct_2 @ C) @ A) @ B) ) ) ) ) ) ) ) , file(funct_2, rc1_funct_2)). thf(rc1_membered, axiom, (? [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) & (v6_membered @ A) ) ) , file(membered, rc1_membered)). thf(rc1_ordinal1, axiom, (? [A: $i] : ( (v1_ordinal1 @ A) & (v2_ordinal1 @ A) ) ) , file(ordinal1, rc1_ordinal1)). thf(rc1_relset_1, axiom, (! [A: $i, B: $i] : (? [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) & ( (v1_xboole_0 @ C) & ( (v1_relat_1 @ C) & ( ( (v4_relat_1 @ C) @ A) & ( (v5_relat_1 @ C) @ B) ) ) ) ) ) ) , file(relset_1, rc1_relset_1)). thf(rc1_subset_1, axiom, (! [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) => (? [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) & ~ ( (v1_xboole_0 @ B) ) ) ) ) ) , file(subset_1, rc1_subset_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_xboole_0, axiom, (? [A: $i] : (v1_xboole_0 @ A) ) , file(xboole_0, rc1_xboole_0)). thf(rc1_xcmplx_0, axiom, (? [A: $i] : (v1_xcmplx_0 @ A) ) , file(xcmplx_0, rc1_xcmplx_0)). thf(rc1_xreal_0, axiom, (? [A: $i] : (v1_xreal_0 @ A) ) , file(xreal_0, rc1_xreal_0)). thf(rc2_comseq_2, axiom, (? [A: $i] : ( ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k2_numbers) ) ) & ( (v1_relat_1 @ A) & ( ( (v4_relat_1 @ A) @ k4_ordinal1) & ( ( (v5_relat_1 @ A) @ k2_numbers) & ( (v1_funct_1 @ A) & ( ~ ( (v1_xboole_0 @ A) ) & ( ( (v1_partfun1 @ A) @ k4_ordinal1) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k2_numbers) & ( (v1_valued_0 @ A) & (v2_comseq_2 @ A) ) ) ) ) ) ) ) ) ) ) , file(comseq_2, rc2_comseq_2)). thf(rc2_membered, axiom, (? [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) & (v6_membered @ A) ) ) , file(membered, rc2_membered)). thf(rc2_ordinal1, axiom, (? [A: $i] : (v3_ordinal1 @ A) ) , file(ordinal1, rc2_ordinal1)). thf(rc2_subset_1, axiom, (! [A: $i] : (? [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) & (v1_xboole_0 @ B) ) ) ) , file(subset_1, rc2_subset_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_xboole_0, axiom, (? [A: $i] : ~ ( (v1_xboole_0 @ A) ) ) , file(xboole_0, rc2_xboole_0)). thf(rc2_xcmplx_0, axiom, (? [A: $i] : (v1_xcmplx_0 @ A) ) , file(xcmplx_0, rc2_xcmplx_0)). thf(rc2_xreal_0, axiom, (? [A: $i] : (v1_xreal_0 @ A) ) , file(xreal_0, rc2_xreal_0)). thf(rc3_membered, axiom, (? [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) & ( (v6_membered @ A) & (v7_membered @ A) ) ) ) , file(membered, rc3_membered)). thf(rc3_ordinal1, axiom, (? [A: $i] : (v3_ordinal1 @ A) ) , file(ordinal1, rc3_ordinal1)). thf(rc3_subset_1, axiom, (! [A: $i] : (? [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) & ~ ( ( (v1_subset_1 @ B) @ A) ) ) ) ) , file(subset_1, rc3_subset_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_xcmplx_0, axiom, (? [A: $i] : ( (v8_ordinal1 @ A) & (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, rc3_xcmplx_0)). thf(rc3_xreal_0, axiom, (? [A: $i] : ( (v1_xcmplx_0 @ A) & ( (v1_xxreal_0 @ A) & ( (v2_xxreal_0 @ A) & (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc3_xreal_0)). thf(rc4_ordinal1, axiom, (? [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) & ( (v1_ordinal1 @ A) & ( (v2_ordinal1 @ A) & (v3_ordinal1 @ A) ) ) ) ) , file(ordinal1, rc4_ordinal1)). thf(rc4_subset_1, axiom, (! [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) => (? [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) & ( (v1_subset_1 @ B) @ A) ) ) ) ) , file(subset_1, rc4_subset_1)). thf(rc4_xcmplx_0, axiom, (? [A: $i] : ( ~ ( (v8_ordinal1 @ A) ) & (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, rc4_xcmplx_0)). thf(rc4_xreal_0, axiom, (? [A: $i] : ( (v1_xcmplx_0 @ A) & ( (v1_xxreal_0 @ A) & ( (v3_xxreal_0 @ A) & (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc4_xreal_0)). thf(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_subset_1, axiom, (! [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) => (? [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) & ( ~ ( (v1_xboole_0 @ B) ) & (v1_zfmisc_1 @ B) ) ) ) ) ) , file(subset_1, rc5_subset_1)). 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_xcmplx_0, axiom, (? [A: $i] : ( ~ ( (v8_ordinal1 @ A) ) & (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, rc5_xcmplx_0)). 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_ordinal1, axiom, (? [A: $i] : (v7_ordinal1 @ A) ) , file(ordinal1, rc6_ordinal1)). thf(rc6_subset_1, axiom, (! [A: $i] : ( ~ ( (v1_zfmisc_1 @ A) ) => (? [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) & ~ ( (v1_zfmisc_1 @ B) ) ) ) ) ) , file(subset_1, rc6_subset_1)). thf(rc6_valued_0, axiom, (! [A: $i] : (? [B: $i] : ( (v1_relat_1 @ B) & ( ( (v4_relat_1 @ B) @ A) & ( (v1_funct_1 @ B) & ( ( (v1_partfun1 @ B) @ A) & (v4_valued_0 @ B) ) ) ) ) ) ) , file(valued_0, rc6_valued_0)). thf(rc7_ordinal1, axiom, (? [A: $i] : (v7_ordinal1 @ A) ) , file(ordinal1, rc7_ordinal1)). thf(rc8_ordinal1, axiom, (? [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) & (v7_ordinal1 @ A) ) ) , file(ordinal1, rc8_ordinal1)). thf(rc9_ordinal1, axiom, (? [A: $i] : (v8_ordinal1 @ A) ) , file(ordinal1, rc9_ordinal1)). thf(redefinition_k2_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( (v1_membered @ B) & ( (v1_membered @ C) & ( ( (v1_funct_1 @ D) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) & ( (v1_funct_1 @ E) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) => ( (= @ ( ( ( ( (k2_valued_1 @ A) @ B) @ C) @ D) @ E) ) @ ( (k1_valued_1 @ D) @ E) ) ) ) , file(valued_1, k2_valued_1)). thf(redefinition_k31_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v1_membered @ B) & ( (v1_funct_1 @ C) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) => ( (= @ ( ( (k31_valued_1 @ A) @ B) @ C) ) @ (k30_valued_1 @ C) ) ) ) , file(valued_1, k31_valued_1)). thf(redefinition_k46_valued_1, axiom, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( (v1_membered @ B) & ( (v1_membered @ C) & ( ( (v1_funct_1 @ D) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) & ( (v1_funct_1 @ E) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) => ( (= @ ( ( ( ( (k46_valued_1 @ A) @ B) @ C) @ D) @ E) ) @ ( (k45_valued_1 @ D) @ E) ) ) ) , file(valued_1, k46_valued_1)). thf(redefinition_k55_valued_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v1_membered @ B) & ( (v1_funct_1 @ C) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) => ( (= @ ( ( (k55_valued_1 @ A) @ B) @ C) ) @ (k54_valued_1 @ C) ) ) ) , file(valued_1, k55_valued_1)). thf(redefinition_k8_funcop_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ~ ( (v1_xboole_0 @ A) ) & ( (m1_subset_1 @ C) @ A) ) => ( (= @ ( ( (k8_funcop_1 @ A) @ B) @ C) ) @ ( (k2_funcop_1 @ B) @ C) ) ) ) , file(funcop_1, k8_funcop_1)). thf(redefinition_k8_nat_1, axiom, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_funct_1 @ B) & ( ( ( (v1_funct_2 @ B) @ k4_ordinal1) @ A) & ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ A) ) ) ) ) & (v7_ordinal1 @ C) ) => ( (= @ ( ( (k8_nat_1 @ A) @ B) @ C) ) @ ( (k1_funct_1 @ B) @ C) ) ) ) , file(nat_1, k8_nat_1)). thf(redefinition_r2_relset_1, axiom, (! [A: $i, B: $i, C: $i, D: $i] : ( ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) => ( ( ( ( (r2_relset_1 @ A) @ B) @ C) @ D) <=> ( (= @ C) @ D) ) ) ) , file(relset_1, r2_relset_1)). thf(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(reflexivity_r2_relset_1, axiom, (! [A: $i, B: $i, C: $i, D: $i] : ( ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) => ( ( ( (r2_relset_1 @ A) @ B) @ C) @ C) ) ) , file(relset_1, r2_relset_1)). thf(rqRealNeg__k4_xcmplx_0__r1_rm1, axiom, ( (= @ (k4_xcmplx_0 @ 1) ) @ (k4_xcmplx_0 @ 1) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r1_rm1)). thf(rqRealNeg__k4_xcmplx_0__rm1_r1, axiom, ( (= @ (k4_xcmplx_0 @ (k4_xcmplx_0 @ 1) ) ) @ 1) , file(arithm, rqRealNeg__k4_xcmplx_0__rm1_r1)). 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 @ 1) ) , file(boole, spc1_boole)). thf(spc1_numerals, axiom, ( (v2_xxreal_0 @ 1) & ( (m1_subset_1 @ 1) @ k4_ordinal1) ) , file(numerals, spc1_numerals)). thf(spc6_arithm, axiom, (! [A: $i, B: $i, C: $i] : ( ( (v1_xcmplx_0 @ A) & ( (v1_xcmplx_0 @ B) & (v1_xcmplx_0 @ C) ) ) => ( (= @ ( (k2_xcmplx_0 @ ( (k2_xcmplx_0 @ A) @ B) ) @ C) ) @ ( (k2_xcmplx_0 @ A) @ ( (k2_xcmplx_0 @ B) @ C) ) ) ) ) , file(arithm, spc6_arithm)). thf(spc8_arithm, axiom, (! [A: $i, B: $i] : ( ( (v1_xcmplx_0 @ A) & (v1_xcmplx_0 @ B) ) => ( (= @ ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ A) ) @ (k4_xcmplx_0 @ B) ) ) @ (k4_xcmplx_0 @ ( (k2_xcmplx_0 @ A) @ B) ) ) ) ) , file(arithm, spc8_arithm)). thf(spc9_arithm, axiom, (! [A: $i, B: $i] : ( ( (v1_xcmplx_0 @ A) & (v1_xcmplx_0 @ B) ) => ( (= @ ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ A) ) @ (k4_xcmplx_0 @ B) ) ) @ ( (k6_xcmplx_0 @ B) @ A) ) ) ) , file(arithm, spc9_arithm)). thf(symmetry_r2_relset_1, axiom, (! [A: $i, B: $i, C: $i, D: $i] : ( ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) => ( ( ( ( (r2_relset_1 @ A) @ B) @ C) @ D) => ( ( ( (r2_relset_1 @ A) @ B) @ D) @ C) ) ) ) , file(relset_1, r2_relset_1)). thf(t10_comseq_2, axiom, (! [A: $i] : ( ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k2_numbers) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k2_numbers) ) ) ) ) => (! [B: $i] : ( (v1_xcmplx_0 @ B) => ( (! [C: $i] : ( (v7_ordinal1 @ C) => ( (= @ ( ( (k8_nat_1 @ k2_numbers) @ A) @ C) ) @ B) ) ) => ( (= @ (k3_comseq_2 @ A) ) @ B) ) ) ) ) ) , file(comseq_2, t10_comseq_2)). thf(t12_funct_2, axiom, (! [A: $i] : (! [B: $i] : (! [C: $i] : ( ( (v1_funct_1 @ C) & ( ( ( (v1_funct_2 @ C) @ A) @ B) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) => (! [D: $i] : ( ( (v1_funct_1 @ D) & ( ( ( (v1_funct_2 @ D) @ A) @ B) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) => ( (! [E: $i] : ( ( (r2_hidden @ E) @ A) => ( (= @ ( (k1_funct_1 @ C) @ E) ) @ ( (k1_funct_1 @ D) @ E) ) ) ) => ( ( ( (r2_relset_1 @ A) @ B) @ C) @ D) ) ) ) ) ) ) ) , file(funct_2, t12_funct_2)). thf(t18_valued_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) => (! [B: $i] : ( (= @ ( (k1_funct_1 @ (k54_valued_1 @ A) ) @ B) ) @ (k9_complex1 @ ( (k1_funct_1 @ A) @ B) ) ) ) ) ) , file(valued_1, t18_valued_1)). 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(t1_valued_1, axiom, (! [A: $i] : (! [B: $i] : ( ( ~ ( (v1_xboole_0 @ B) ) & (v1_membered @ B) ) => (! [C: $i] : ( ( ~ ( (v1_xboole_0 @ C) ) & (v1_membered @ C) ) => (! [D: $i] : ( ( (v1_funct_1 @ D) & ( ( ( (v1_funct_2 @ D) @ A) @ B) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) => (! [E: $i] : ( ( (v1_funct_1 @ E) & ( ( ( (v1_funct_2 @ E) @ A) @ C) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) => (! [F: $i] : ( ( (m1_subset_1 @ F) @ A) => ( (= @ ( (k1_funct_1 @ ( ( ( ( (k2_valued_1 @ A) @ B) @ C) @ D) @ E) ) @ F) ) @ ( (k2_xcmplx_0 @ ( (k1_funct_1 @ D) @ F) ) @ ( (k1_funct_1 @ E) @ F) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(valued_1, t1_valued_1)). thf(t26_comseq_2, axiom, (! [A: $i] : ( ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k2_numbers) & ( (v2_comseq_2 @ A) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k2_numbers) ) ) ) ) ) => (! [B: $i] : ( ( (v1_funct_1 @ B) & ( ( ( (v1_funct_2 @ B) @ k4_ordinal1) @ k2_numbers) & ( (v2_comseq_2 @ B) & ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k2_numbers) ) ) ) ) ) => ( (= @ (k3_comseq_2 @ ( ( ( ( (k46_valued_1 @ k4_ordinal1) @ k2_numbers) @ k2_numbers) @ A) @ B) ) ) @ ( (k6_xcmplx_0 @ (k3_comseq_2 @ A) ) @ (k3_comseq_2 @ B) ) ) ) ) ) ) , file(comseq_2, t26_comseq_2)). thf(t27_seq_2, axiom, (! [A: $i] : ( ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k2_numbers) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k2_numbers) ) ) ) ) => ( (v2_comseq_2 @ A) => ( (= @ (k1_seq_2 @ ( ( (k55_valued_1 @ k4_ordinal1) @ k2_numbers) @ A) ) ) @ (k9_complex1 @ (k3_comseq_2 @ A) ) ) ) ) ) , file(seq_2, t27_seq_2)). thf(t2_subset, axiom, (! [A: $i] : (! [B: $i] : ( ( (m1_subset_1 @ A) @ B) => ( (v1_xboole_0 @ B) | ( (r2_tarski @ A) @ B) ) ) ) ) , file(subset, t2_subset)). thf(t3_subset, axiom, (! [A: $i] : (! [B: $i] : ( ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ B) ) <=> ( (r1_tarski @ A) @ B) ) ) ) , file(subset, t3_subset)). thf(t4_subset, axiom, (! [A: $i] : (! [B: $i] : (! [C: $i] : ( ( ( (r2_tarski @ A) @ B) & ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ C) ) ) => ( (m1_subset_1 @ A) @ C) ) ) ) ) , file(subset, t4_subset)). thf(t5_subset, axiom, (! [A: $i] : (! [B: $i] : (! [C: $i] : ~ ( ( ( (r2_tarski @ A) @ B) & ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ C) ) & (v1_xboole_0 @ C) ) ) ) ) ) ) , file(subset, t5_subset)). thf(t6_boole, axiom, (! [A: $i] : ( (v1_xboole_0 @ A) => ( (= @ A) @ k1_xboole_0) ) ) , file(boole, t6_boole)). thf(t7_boole, axiom, (! [A: $i] : (! [B: $i] : ~ ( ( ( (r2_tarski @ A) @ B) & (v1_xboole_0 @ B) ) ) ) ) , file(boole, t7_boole)). thf(t7_funcop_1, axiom, (! [A: $i] : (! [B: $i] : (! [C: $i] : ( ( (r2_hidden @ B) @ A) => ( (= @ ( (k1_funct_1 @ ( (k2_funcop_1 @ A) @ C) ) @ B) ) @ C) ) ) ) ) , file(funcop_1, t7_funcop_1)). thf(t8_boole, axiom, (! [A: $i] : (! [B: $i] : ~ ( ( (v1_xboole_0 @ A) & ( ~ ( ( (= @ A) @ B) ) & (v1_xboole_0 @ B) ) ) ) ) ) , file(boole, t8_boole)). thf(t8_valued_1, axiom, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) => ( ( (= @ (k9_xtuple_0 @ (k30_valued_1 @ A) ) ) @ (k9_xtuple_0 @ A) ) & (! [B: $i] : ( (= @ ( (k1_funct_1 @ (k30_valued_1 @ A) ) @ B) ) @ (k4_xcmplx_0 @ ( (k1_funct_1 @ A) @ B) ) ) ) ) ) ) , file(valued_1, t8_valued_1)). thf(t9_comseq_2, axiom, (! [A: $i] : ( ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k4_ordinal1) @ k2_numbers) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k2_numbers) ) ) ) ) => ( (? [B: $i] : ( (v1_xcmplx_0 @ B) & (! [C: $i] : ( (v7_ordinal1 @ C) => ( (= @ ( ( (k8_nat_1 @ k2_numbers) @ A) @ C) ) @ B) ) ) ) ) => (v2_comseq_2 @ A) ) ) ) , file(comseq_2, t9_comseq_2)). thf(t1_csspace3, conjecture, (! [A: $i] : ( (v1_xcmplx_0 @ A) => (! [B: $i] : ( ( (v1_funct_1 @ B) & ( ( ( (v1_funct_2 @ B) @ k4_ordinal1) @ k2_numbers) & ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k2_numbers) ) ) ) ) => (! [C: $i] : ( ( (v1_funct_1 @ C) & ( ( ( (v1_funct_2 @ C) @ k4_ordinal1) @ k1_numbers) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k4_ordinal1) @ k1_numbers) ) ) ) ) => ( ( (v2_comseq_2 @ B) & (! [D: $i] : ( (v7_ordinal1 @ D) => ( (= @ ( (k1_funct_1 @ C) @ D) ) @ (k9_complex1 @ ( (k6_xcmplx_0 @ ( (k1_funct_1 @ B) @ D) ) @ A) ) ) ) ) ) => ( (v2_comseq_2 @ C) & ( (= @ (k1_seq_2 @ C) ) @ (k9_complex1 @ ( (k6_xcmplx_0 @ (k3_comseq_2 @ B) ) @ A) ) ) ) ) ) ) ) ) ) ) , file(csspace3, t1_csspace3)).