% Mizar ND problem: t6_diff_4,diff_4,132,5 thf(dh_c1_6__diff_4, definition, ( ( ( (m1_subset_1 @ c1_6__diff_4) @ k1_numbers) => (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => ( ( ( (r2_hidden @ c1_6__diff_4) @ ( (k1_relset_1 @ k1_numbers) @ k30_sin_cos) ) & ( (r2_hidden @ A) @ ( (k1_relset_1 @ k1_numbers) @ k30_sin_cos) ) ) => ( (= @ ( ( (k9_diff_1 @ ( ( ( ( (k20_valued_1 @ k1_numbers) @ k1_numbers) @ k1_numbers) @ k30_sin_cos) @ k30_sin_cos) ) @ c1_6__diff_4) @ A) ) @ (k10_complex1 @ ( (k13_complex1 @ ( (k9_real_1 @ (k5_square_1 @ (k21_sin_cos @ A) ) ) @ (k5_square_1 @ (k21_sin_cos @ c1_6__diff_4) ) ) ) @ ( (k8_real_1 @ (k5_square_1 @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ A) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ A) ) ) ) ) ) ) ) ) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ k1_numbers) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ k1_numbers) => ( ( ( (r2_hidden @ B) @ ( (k1_relset_1 @ k1_numbers) @ k30_sin_cos) ) & ( (r2_hidden @ C) @ ( (k1_relset_1 @ k1_numbers) @ k30_sin_cos) ) ) => ( (= @ ( ( (k9_diff_1 @ ( ( ( ( (k20_valued_1 @ k1_numbers) @ k1_numbers) @ k1_numbers) @ k30_sin_cos) @ k30_sin_cos) ) @ B) @ C) ) @ (k10_complex1 @ ( (k13_complex1 @ ( (k9_real_1 @ (k5_square_1 @ (k21_sin_cos @ C) ) ) @ (k5_square_1 @ (k21_sin_cos @ B) ) ) ) @ ( (k8_real_1 @ (k5_square_1 @ ( (k8_real_1 @ (k18_sin_cos @ B) ) @ (k18_sin_cos @ C) ) ) ) @ ( (k9_real_1 @ B) @ C) ) ) ) ) ) ) ) ) ) ) , introduced(definition, [new_symbol(c1_6__diff_4), file(diff_4, c1_6__diff_4)]), [interesting(np__0.8), axiom, file(diff_4, c1_6__diff_4)]). thf(dh_c2_6__diff_4, definition, ( ( ( (m1_subset_1 @ c2_6__diff_4) @ k1_numbers) => ( ( ( (r2_hidden @ c1_6__diff_4) @ ( (k1_relset_1 @ k1_numbers) @ k30_sin_cos) ) & ( (r2_hidden @ c2_6__diff_4) @ ( (k1_relset_1 @ k1_numbers) @ k30_sin_cos) ) ) => ( (= @ ( ( (k9_diff_1 @ ( ( ( ( (k20_valued_1 @ k1_numbers) @ k1_numbers) @ k1_numbers) @ k30_sin_cos) @ k30_sin_cos) ) @ c1_6__diff_4) @ c2_6__diff_4) ) @ (k10_complex1 @ ( (k13_complex1 @ ( (k9_real_1 @ (k5_square_1 @ (k21_sin_cos @ c2_6__diff_4) ) ) @ (k5_square_1 @ (k21_sin_cos @ c1_6__diff_4) ) ) ) @ ( (k8_real_1 @ (k5_square_1 @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ c2_6__diff_4) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) ) ) ) ) => (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => ( ( ( (r2_hidden @ c1_6__diff_4) @ ( (k1_relset_1 @ k1_numbers) @ k30_sin_cos) ) & ( (r2_hidden @ A) @ ( (k1_relset_1 @ k1_numbers) @ k30_sin_cos) ) ) => ( (= @ ( ( (k9_diff_1 @ ( ( ( ( (k20_valued_1 @ k1_numbers) @ k1_numbers) @ k1_numbers) @ k30_sin_cos) @ k30_sin_cos) ) @ c1_6__diff_4) @ A) ) @ (k10_complex1 @ ( (k13_complex1 @ ( (k9_real_1 @ (k5_square_1 @ (k21_sin_cos @ A) ) ) @ (k5_square_1 @ (k21_sin_cos @ c1_6__diff_4) ) ) ) @ ( (k8_real_1 @ (k5_square_1 @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ A) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ A) ) ) ) ) ) ) ) ) , introduced(definition, [new_symbol(c2_6__diff_4), file(diff_4, c2_6__diff_4)]), [interesting(np__0.8), axiom, file(diff_4, c2_6__diff_4)]). thf(e1_6__diff_4, assumption, ( ( (r2_hidden @ c1_6__diff_4) @ ( (k1_relset_1 @ k1_numbers) @ k30_sin_cos) ) & ( (r2_hidden @ c2_6__diff_4) @ ( (k1_relset_1 @ k1_numbers) @ k30_sin_cos) ) ) , introduced(assumption, [file(diff_4, e1_6__diff_4)]), [interesting(np__0.8), axiom, file(diff_4, e1_6__diff_4)]). thf(cc10_valued_2, theorem, (! [A: $i] : ( (v2_valued_2 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v2_valued_2 @ B) ) ) ) ) , file(valued_2, cc10_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc10_valued_2)]). thf(cc15_valued_2, theorem, (! [A: $i] : ( (v1_valued_2 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => (v1_valued_0 @ B) ) ) ) ) , file(valued_2, cc15_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc15_valued_2)]). thf(cc16_valued_2, theorem, (! [A: $i] : ( (v2_valued_2 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => (v2_valued_0 @ B) ) ) ) ) , file(valued_2, cc16_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc16_valued_2)]). thf(cc21_valued_2, theorem, (! [A: $i] : ( (v1_valued_2 @ A) => (! [B: $i] : ( ( (v1_relat_1 @ B) & ( ( (v5_relat_1 @ B) @ A) & (v1_funct_1 @ B) ) ) => ( (v1_relat_1 @ B) & ( ( (v5_relat_1 @ B) @ A) & ( (v1_funct_1 @ B) & (v7_valued_2 @ B) ) ) ) ) ) ) ) , file(valued_2, cc21_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc21_valued_2)]). thf(cc28_valued_2, theorem, (! [A: $i, B: $i] : ( (v1_valued_2 @ B) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => ( (v1_funct_1 @ C) => ( (v1_funct_1 @ C) & (v7_valued_2 @ C) ) ) ) ) ) ) , file(valued_2, cc28_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc28_valued_2)]). thf(cc29_valued_2, theorem, (! [A: $i, B: $i] : ( (v2_valued_2 @ B) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => ( (v1_funct_1 @ C) => ( (v1_funct_1 @ C) & (v8_valued_2 @ C) ) ) ) ) ) ) , file(valued_2, cc29_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc29_valued_2)]). thf(cc7_valued_2, theorem, (! [A: $i] : ( (v1_valued_2 @ A) => (v4_funct_1 @ A) ) ) , file(valued_2, cc7_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc7_valued_2)]). thf(cc8_valued_2, theorem, (! [A: $i] : ( (v2_valued_2 @ A) => (v4_funct_1 @ A) ) ) , file(valued_2, cc8_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc8_valued_2)]). thf(cc9_valued_2, theorem, (! [A: $i] : ( (v1_valued_2 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v1_valued_2 @ B) ) ) ) ) , file(valued_2, cc9_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc9_valued_2)]). thf(fc14_valued_2, theorem, (! [A: $i, B: $i, C: $i, D: $i] : ( ( (v1_valued_2 @ C) & ( (v1_funct_1 @ D) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) => ( (v1_relat_1 @ ( (k1_funct_1 @ D) @ B) ) & (v1_funct_1 @ ( (k1_funct_1 @ D) @ B) ) ) ) ) , file(valued_2, fc14_valued_2), [interesting(np__0.9), axiom, file(valued_2, fc14_valued_2)]). thf(fc15_valued_2, theorem, (! [A: $i, B: $i, C: $i, D: $i] : ( ( (v2_valued_2 @ C) & ( (v1_funct_1 @ D) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) => ( (v1_relat_1 @ ( (k1_funct_1 @ D) @ B) ) & (v1_funct_1 @ ( (k1_funct_1 @ D) @ B) ) ) ) ) , file(valued_2, fc15_valued_2), [interesting(np__0.9), axiom, file(valued_2, fc15_valued_2)]). thf(fc16_valued_2, theorem, (! [A: $i, B: $i, C: $i, D: $i] : ( ( (v1_valued_2 @ C) & ( (v1_funct_1 @ D) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) => (v1_valued_0 @ ( (k1_funct_1 @ D) @ B) ) ) ) , file(valued_2, fc16_valued_2), [interesting(np__0.9), axiom, file(valued_2, fc16_valued_2)]). thf(fc17_valued_2, theorem, (! [A: $i, B: $i, C: $i, D: $i] : ( ( (v2_valued_2 @ C) & ( (v1_funct_1 @ D) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) => (v2_valued_0 @ ( (k1_funct_1 @ D) @ B) ) ) ) , file(valued_2, fc17_valued_2), [interesting(np__0.9), axiom, file(valued_2, fc17_valued_2)]). thf(fc40_valued_2, theorem, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v7_valued_2 @ A) ) ) => ( (v1_relat_1 @ ( (k1_funct_1 @ A) @ B) ) & (v1_funct_1 @ ( (k1_funct_1 @ A) @ B) ) ) ) ) , file(valued_2, fc40_valued_2), [interesting(np__0.9), axiom, file(valued_2, fc40_valued_2)]). thf(fc41_valued_2, theorem, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v8_valued_2 @ A) ) ) => ( (v1_relat_1 @ ( (k1_funct_1 @ A) @ B) ) & (v1_funct_1 @ ( (k1_funct_1 @ A) @ B) ) ) ) ) , file(valued_2, fc41_valued_2), [interesting(np__0.9), axiom, file(valued_2, fc41_valued_2)]). thf(fc42_valued_2, theorem, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v7_valued_2 @ A) ) ) => (v1_valued_0 @ ( (k1_funct_1 @ A) @ B) ) ) ) , file(valued_2, fc42_valued_2), [interesting(np__0.9), axiom, file(valued_2, fc42_valued_2)]). thf(fc43_valued_2, theorem, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v8_valued_2 @ A) ) ) => (v2_valued_0 @ ( (k1_funct_1 @ A) @ B) ) ) ) , file(valued_2, fc43_valued_2), [interesting(np__0.9), axiom, file(valued_2, fc43_valued_2)]). thf(cc11_valued_2, theorem, (! [A: $i] : ( (v3_valued_2 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v3_valued_2 @ B) ) ) ) ) , file(valued_2, cc11_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc11_valued_2)]). thf(cc17_valued_2, theorem, (! [A: $i] : ( (v3_valued_2 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => (v3_valued_0 @ B) ) ) ) ) , file(valued_2, cc17_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc17_valued_2)]). thf(cc25_valued_2, theorem, (! [A: $i] : ( ( (v1_relat_1 @ A) & (v9_valued_2 @ A) ) => ( (v1_relat_1 @ A) & (v8_valued_2 @ A) ) ) ) , file(valued_2, cc25_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc25_valued_2)]). thf(cc26_valued_2, theorem, (! [A: $i] : ( ( (v1_relat_1 @ A) & (v9_valued_2 @ A) ) => ( (v1_relat_1 @ A) & (v7_valued_2 @ A) ) ) ) , file(valued_2, cc26_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc26_valued_2)]). thf(cc30_valued_2, theorem, (! [A: $i, B: $i] : ( (v3_valued_2 @ B) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => ( (v1_funct_1 @ C) => ( (v1_funct_1 @ C) & (v9_valued_2 @ C) ) ) ) ) ) ) , file(valued_2, cc30_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc30_valued_2)]). thf(cc4_valued_2, theorem, (! [A: $i] : ( (v3_valued_2 @ A) => (v1_valued_2 @ A) ) ) , file(valued_2, cc4_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc4_valued_2)]). thf(cc5_valued_2, theorem, (! [A: $i] : ( (v3_valued_2 @ A) => (v2_valued_2 @ A) ) ) , file(valued_2, cc5_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc5_valued_2)]). thf(fc18_valued_2, theorem, (! [A: $i, B: $i, C: $i, D: $i] : ( ( (v3_valued_2 @ C) & ( (v1_funct_1 @ D) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) => (v3_valued_0 @ ( (k1_funct_1 @ D) @ B) ) ) ) , file(valued_2, fc18_valued_2), [interesting(np__0.9), axiom, file(valued_2, fc18_valued_2)]). thf(fc44_valued_2, theorem, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v9_valued_2 @ A) ) ) => (v3_valued_0 @ ( (k1_funct_1 @ A) @ B) ) ) ) , file(valued_2, fc44_valued_2), [interesting(np__0.9), axiom, file(valued_2, fc44_valued_2)]). thf(cc12_valued_2, theorem, (! [A: $i] : ( (v4_valued_2 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v4_valued_2 @ B) ) ) ) ) , file(valued_2, cc12_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc12_valued_2)]). thf(cc15_membered, theorem, (! [A: $i] : ( (v4_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => (v1_rat_1 @ B) ) ) ) ) , file(membered, cc15_membered), [interesting(np__0.9), axiom, file(membered, cc15_membered)]). thf(cc18_valued_2, theorem, (! [A: $i] : ( (v4_valued_2 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => ( (v5_relat_1 @ B) @ k3_numbers) ) ) ) ) , file(valued_2, cc18_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc18_valued_2)]). thf(cc19_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, cc19_valued_0)]). thf(cc22_membered, theorem, (! [A: $i] : ( (v4_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v4_membered @ B) ) ) ) ) , file(membered, cc22_membered), [interesting(np__0.9), axiom, file(membered, cc22_membered)]). thf(cc23_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, cc23_valued_0)]). thf(cc24_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, cc24_valued_0)]). thf(cc24_valued_2, theorem, (! [A: $i] : ( ( (v1_relat_1 @ A) & (v10_valued_2 @ A) ) => ( (v1_relat_1 @ A) & (v9_valued_2 @ A) ) ) ) , file(valued_2, cc24_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc24_valued_2)]). thf(cc2_seq_2, theorem, (! [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), [interesting(np__0.9), axiom, file(seq_2, cc2_seq_2)]). thf(cc31_valued_2, theorem, (! [A: $i, B: $i] : ( (v4_valued_2 @ B) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => ( (v1_funct_1 @ C) => ( (v1_funct_1 @ C) & (v10_valued_2 @ C) ) ) ) ) ) ) , file(valued_2, cc31_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc31_valued_2)]). thf(cc3_membered, theorem, (! [A: $i] : ( (v4_membered @ A) => (v3_membered @ A) ) ) , file(membered, cc3_membered), [interesting(np__0.9), axiom, file(membered, cc3_membered)]). thf(cc3_valued_2, theorem, (! [A: $i] : ( (v4_valued_2 @ A) => (v3_valued_2 @ A) ) ) , file(valued_2, cc3_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc3_valued_2)]). thf(fc19_valued_2, theorem, (! [A: $i, B: $i, C: $i, D: $i] : ( ( (v4_valued_2 @ C) & ( (v1_funct_1 @ D) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) => ( (v5_relat_1 @ ( (k1_funct_1 @ D) @ B) ) @ k3_numbers) ) ) , file(valued_2, fc19_valued_2), [interesting(np__0.9), axiom, file(valued_2, fc19_valued_2)]). thf(fc40_valued_1, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_1, fc40_valued_1)]). thf(fc45_valued_2, theorem, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v10_valued_2 @ A) ) ) => ( (v5_relat_1 @ ( (k1_funct_1 @ A) @ B) ) @ k3_numbers) ) ) , file(valued_2, fc45_valued_2), [interesting(np__0.9), axiom, file(valued_2, fc45_valued_2)]). thf(fc88_valued_0, theorem, (! [A: $i, B: $i] : ( (v4_membered @ B) => ( (v5_relat_1 @ ( (k2_zfmisc_1 @ A) @ B) ) @ k3_numbers) ) ) , file(valued_0, fc88_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc88_valued_0)]). thf(dt_k3_numbers, plain, $true, file(numbers, k3_numbers), [interesting(np__0.9), axiom, file(numbers, k3_numbers)]). thf(dt_k4_numbers, plain, $true, file(numbers, k4_numbers), [interesting(np__0.9), axiom, file(numbers, k4_numbers)]). thf(dt_o_0_0_xboole_0, axiom, (v1_xboole_0 @ o_0_0_xboole_0) , file(xboole_0, o_0_0_xboole_0), [interesting(np__0.9), axiom, file(xboole_0, o_0_0_xboole_0)]). thf(cc10_membered, theorem, (! [A: $i] : ( ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ k4_numbers) ) => (v5_membered @ A) ) ) , file(membered, cc10_membered), [interesting(np__0.9), axiom, file(membered, cc10_membered)]). thf(cc13_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, cc13_valued_0)]). thf(cc13_valued_2, theorem, (! [A: $i] : ( (v5_valued_2 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v5_valued_2 @ B) ) ) ) ) , file(valued_2, cc13_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc13_valued_2)]). thf(cc14_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, cc14_valued_0)]). thf(cc16_membered, theorem, (! [A: $i] : ( (v5_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => (v1_int_1 @ B) ) ) ) ) , file(membered, cc16_membered), [interesting(np__0.9), axiom, file(membered, cc16_membered)]). thf(cc19_valued_2, theorem, (! [A: $i] : ( (v5_valued_2 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => ( (v5_relat_1 @ B) @ k4_numbers) ) ) ) ) , file(valued_2, cc19_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc19_valued_2)]). thf(cc1_int_1, theorem, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k4_numbers) => (v1_int_1 @ A) ) ) , file(int_1, cc1_int_1), [interesting(np__0.9), axiom, file(int_1, cc1_int_1)]). thf(cc1_seq_2, theorem, (! [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), [interesting(np__0.9), axiom, file(seq_2, cc1_seq_2)]). thf(cc20_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, cc20_valued_0)]). thf(cc22_valued_0, theorem, (! [A: $i] : ( ( (v1_zfmisc_1 @ A) & ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v2_valued_0 @ A) ) ) ) => ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v2_valued_0 @ A) & ( (v5_valued_0 @ A) & (v6_valued_0 @ A) ) ) ) ) ) ) , file(valued_0, cc22_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc22_valued_0)]). thf(cc23_membered, theorem, (! [A: $i] : ( (v5_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v5_membered @ B) ) ) ) ) , file(membered, cc23_membered), [interesting(np__0.9), axiom, file(membered, cc23_membered)]). thf(cc23_valued_2, theorem, (! [A: $i] : ( ( (v1_relat_1 @ A) & (v11_valued_2 @ A) ) => ( (v1_relat_1 @ A) & (v10_valued_2 @ A) ) ) ) , file(valued_2, cc23_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc23_valued_2)]). thf(cc2_membered, theorem, (! [A: $i] : ( (v5_membered @ A) => (v4_membered @ A) ) ) , file(membered, cc2_membered), [interesting(np__0.9), axiom, file(membered, cc2_membered)]). thf(cc2_ordinal1, theorem, (! [A: $i] : ( ( (v1_ordinal1 @ A) & (v2_ordinal1 @ A) ) => (v3_ordinal1 @ A) ) ) , file(ordinal1, cc2_ordinal1), [interesting(np__0.9), axiom, file(ordinal1, cc2_ordinal1)]). thf(cc2_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, cc2_valued_0)]). thf(cc2_valued_2, theorem, (! [A: $i] : ( (v5_valued_2 @ A) => (v4_valued_2 @ A) ) ) , file(valued_2, cc2_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc2_valued_2)]). thf(cc32_valued_2, theorem, (! [A: $i, B: $i] : ( (v5_valued_2 @ B) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => ( (v1_funct_1 @ C) => ( (v1_funct_1 @ C) & (v11_valued_2 @ C) ) ) ) ) ) ) , file(valued_2, cc32_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc32_valued_2)]). thf(cc3_int_1, theorem, (! [A: $i] : ( (v1_int_1 @ A) => (v1_xreal_0 @ A) ) ) , file(int_1, cc3_int_1), [interesting(np__0.9), axiom, file(int_1, cc3_int_1)]). thf(cc3_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, cc3_valued_0)]). thf(cc3_xxreal_0, theorem, (! [A: $i] : ( ( (v1_xxreal_0 @ A) & (v2_xxreal_0 @ A) ) => ( ~ ( (v1_xboole_0 @ A) ) & ( (v1_xxreal_0 @ A) & ~ ( (v3_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc3_xxreal_0), [interesting(np__0.9), axiom, file(xxreal_0, cc3_xxreal_0)]). thf(cc4_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, cc4_valued_0)]). thf(cc4_xxreal_0, theorem, (! [A: $i] : ( ( ~ ( (v1_xboole_0 @ A) ) & ( (v1_xxreal_0 @ A) & ~ ( (v3_xxreal_0 @ A) ) ) ) => ( (v1_xxreal_0 @ A) & (v2_xxreal_0 @ A) ) ) ) , file(xxreal_0, cc4_xxreal_0), [interesting(np__0.9), axiom, file(xxreal_0, cc4_xxreal_0)]). thf(cc5_xxreal_0, theorem, (! [A: $i] : ( ( (v1_xxreal_0 @ A) & (v3_xxreal_0 @ A) ) => ( ~ ( (v1_xboole_0 @ A) ) & ( (v1_xxreal_0 @ A) & ~ ( (v2_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc5_xxreal_0), [interesting(np__0.9), axiom, file(xxreal_0, cc5_xxreal_0)]). thf(cc6_funct_1, theorem, (! [A: $i] : ( ( (v1_zfmisc_1 @ A) & ( (v1_relat_1 @ A) & (v1_funct_1 @ A) ) ) => ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v3_funct_1 @ A) ) ) ) ) , file(funct_1, cc6_funct_1), [interesting(np__0.9), axiom, file(funct_1, cc6_funct_1)]). thf(cc6_xxreal_0, theorem, (! [A: $i] : ( ( ~ ( (v1_xboole_0 @ A) ) & ( (v1_xxreal_0 @ A) & ~ ( (v2_xxreal_0 @ A) ) ) ) => ( (v1_xxreal_0 @ A) & (v3_xxreal_0 @ A) ) ) ) , file(xxreal_0, cc6_xxreal_0), [interesting(np__0.9), axiom, file(xxreal_0, cc6_xxreal_0)]). thf(cc8_xxreal_0, theorem, (! [A: $i] : ( ( (v1_xxreal_0 @ A) & ( ~ ( (v2_xxreal_0 @ A) ) & ~ ( (v3_xxreal_0 @ A) ) ) ) => ( (v1_xboole_0 @ A) & (v1_xxreal_0 @ A) ) ) ) , file(xxreal_0, cc8_xxreal_0), [interesting(np__0.9), axiom, file(xxreal_0, cc8_xxreal_0)]). thf(cc9_membered, theorem, (! [A: $i] : ( ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ k3_numbers) ) => (v4_membered @ A) ) ) , file(membered, cc9_membered), [interesting(np__0.9), axiom, file(membered, cc9_membered)]). thf(fc10_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc10_xreal_0)]). thf(fc11_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc11_xreal_0)]). thf(fc12_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc12_xreal_0)]). thf(fc13_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc13_xreal_0)]). thf(fc14_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc14_xreal_0)]). thf(fc15_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc15_xreal_0)]). thf(fc16_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc16_xreal_0)]). thf(fc17_rfunct_1, theorem, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v3_valued_0 @ A) & (v1_comseq_2 @ A) ) ) ) & ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & ( (v3_valued_0 @ B) & (v1_comseq_2 @ 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) ) & (v1_comseq_2 @ ( (k18_valued_1 @ A) @ B) ) ) ) ) ) ) , file(rfunct_1, fc17_rfunct_1), [interesting(np__0.9), axiom, file(rfunct_1, fc17_rfunct_1)]). thf(fc17_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc17_xreal_0)]). thf(fc18_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc18_xreal_0)]). thf(fc19_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc19_xreal_0)]). thf(fc1_int_1, theorem, (! [A: $i, B: $i] : ( ( (v1_int_1 @ A) & (v1_int_1 @ B) ) => (v1_int_1 @ ( (k2_xcmplx_0 @ A) @ B) ) ) ) , file(int_1, fc1_int_1), [interesting(np__0.9), axiom, file(int_1, fc1_int_1)]). thf(fc20_valued_2, theorem, (! [A: $i, B: $i, C: $i, D: $i] : ( ( (v5_valued_2 @ C) & ( (v1_funct_1 @ D) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) => ( (v5_relat_1 @ ( (k1_funct_1 @ D) @ B) ) @ k4_numbers) ) ) , file(valued_2, fc20_valued_2), [interesting(np__0.9), axiom, file(valued_2, fc20_valued_2)]). thf(fc20_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc20_xreal_0)]). thf(fc21_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc21_xreal_0)]). thf(fc22_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc22_xreal_0)]). thf(fc23_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc23_xreal_0)]). thf(fc24_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc24_xreal_0)]). thf(fc25_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc25_xreal_0)]). thf(fc26_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc26_xreal_0)]). thf(fc27_xreal_0, theorem, (! [A: $i] : ( ( (v2_xxreal_0 @ A) & (v1_xreal_0 @ A) ) => ( (v1_xcmplx_0 @ (k5_xcmplx_0 @ A) ) & (v2_xxreal_0 @ (k5_xcmplx_0 @ A) ) ) ) ) , file(xreal_0, fc27_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, fc27_xreal_0)]). thf(fc28_xreal_0, theorem, (! [A: $i] : ( ( ~ ( (v2_xxreal_0 @ A) ) & (v1_xreal_0 @ A) ) => ( (v1_xcmplx_0 @ (k5_xcmplx_0 @ A) ) & ~ ( (v2_xxreal_0 @ (k5_xcmplx_0 @ A) ) ) ) ) ) , file(xreal_0, fc28_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, fc28_xreal_0)]). thf(fc29_xreal_0, theorem, (! [A: $i] : ( ( (v3_xxreal_0 @ A) & (v1_xreal_0 @ A) ) => ( (v1_xcmplx_0 @ (k5_xcmplx_0 @ A) ) & (v3_xxreal_0 @ (k5_xcmplx_0 @ A) ) ) ) ) , file(xreal_0, fc29_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, fc29_xreal_0)]). thf(fc2_int_1, theorem, (! [A: $i, B: $i] : ( ( (v1_int_1 @ A) & (v1_int_1 @ B) ) => (v1_int_1 @ ( (k3_xcmplx_0 @ A) @ B) ) ) ) , file(int_1, fc2_int_1), [interesting(np__0.9), axiom, file(int_1, fc2_int_1)]). thf(fc30_xreal_0, theorem, (! [A: $i] : ( ( ~ ( (v3_xxreal_0 @ A) ) & (v1_xreal_0 @ A) ) => ( (v1_xcmplx_0 @ (k5_xcmplx_0 @ A) ) & ~ ( (v3_xxreal_0 @ (k5_xcmplx_0 @ A) ) ) ) ) ) , file(xreal_0, fc30_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, fc30_xreal_0)]). thf(fc31_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc31_xreal_0)]). thf(fc32_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc32_xreal_0)]). thf(fc33_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc33_xreal_0)]). thf(fc34_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc34_xreal_0)]). thf(fc35_valued_1, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_1, fc35_valued_1)]). thf(fc36_valued_1, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_1, fc36_valued_1)]). thf(fc3_int_1, theorem, (! [A: $i] : ( (v1_int_1 @ A) => ( (v1_xcmplx_0 @ (k4_xcmplx_0 @ A) ) & (v1_int_1 @ (k4_xcmplx_0 @ A) ) ) ) ) , file(int_1, fc3_int_1), [interesting(np__0.9), axiom, file(int_1, fc3_int_1)]). thf(fc3_numbers, theorem, ~ ( (v1_xboole_0 @ k3_numbers) ) , file(numbers, fc3_numbers), [interesting(np__0.9), axiom, file(numbers, fc3_numbers)]). thf(fc41_valued_1, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_1, fc41_valued_1)]). thf(fc46_valued_2, theorem, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v11_valued_2 @ A) ) ) => ( (v5_relat_1 @ ( (k1_funct_1 @ A) @ B) ) @ k4_numbers) ) ) , file(valued_2, fc46_valued_2), [interesting(np__0.9), axiom, file(valued_2, fc46_valued_2)]). thf(fc4_int_1, theorem, (! [A: $i, B: $i] : ( ( (v1_int_1 @ A) & (v1_int_1 @ B) ) => (v1_int_1 @ ( (k6_xcmplx_0 @ A) @ B) ) ) ) , file(int_1, fc4_int_1), [interesting(np__0.9), axiom, file(int_1, fc4_int_1)]). thf(fc4_membered, theorem, (v4_membered @ k3_numbers) , file(membered, fc4_membered), [interesting(np__0.9), axiom, file(membered, fc4_membered)]). thf(fc4_numbers, theorem, ~ ( (v1_xboole_0 @ k4_numbers) ) , file(numbers, fc4_numbers), [interesting(np__0.9), axiom, file(numbers, fc4_numbers)]). thf(fc57_membered, theorem, (v7_membered @ k3_numbers) , file(membered, fc57_membered), [interesting(np__0.9), axiom, file(membered, fc57_membered)]). thf(fc58_membered, theorem, (v7_membered @ k4_numbers) , file(membered, fc58_membered), [interesting(np__0.9), axiom, file(membered, fc58_membered)]). thf(fc5_membered, theorem, (v5_membered @ k4_numbers) , file(membered, fc5_membered), [interesting(np__0.9), axiom, file(membered, fc5_membered)]). thf(fc64_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, fc64_valued_0)]). thf(fc65_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, fc65_valued_0)]). thf(fc6_numbers, theorem, ~ ( (v1_finset_1 @ k4_numbers) ) , file(numbers, fc6_numbers), [interesting(np__0.9), axiom, file(numbers, fc6_numbers)]). thf(fc7_numbers, theorem, ~ ( (v1_finset_1 @ k3_numbers) ) , file(numbers, fc7_numbers), [interesting(np__0.9), axiom, file(numbers, fc7_numbers)]). thf(fc89_valued_0, theorem, (! [A: $i, B: $i] : ( (v5_membered @ B) => ( (v5_relat_1 @ ( (k2_zfmisc_1 @ A) @ B) ) @ k4_numbers) ) ) , file(valued_0, fc89_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc89_valued_0)]). thf(fc9_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc9_xreal_0)]). thf(rc1_int_1, theorem, (? [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) & ( (v1_xxreal_0 @ A) & ( (v1_xcmplx_0 @ A) & ( (v1_xreal_0 @ A) & (v1_int_1 @ A) ) ) ) ) ) , file(int_1, rc1_int_1), [interesting(np__0.9), axiom, file(int_1, rc1_int_1)]). thf(rc2_int_1, theorem, (? [A: $i] : (v1_int_1 @ A) ) , file(int_1, rc2_int_1), [interesting(np__0.9), axiom, file(int_1, rc2_int_1)]). thf(rc2_ordinal1, theorem, (? [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) & ( (v1_ordinal1 @ A) & ( (v2_ordinal1 @ A) & (v3_ordinal1 @ A) ) ) ) ) , file(ordinal1, rc2_ordinal1), [interesting(np__0.9), axiom, file(ordinal1, rc2_ordinal1)]). thf(rc2_valued_0, theorem, (? [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) & ( (v1_relat_1 @ A) & ( ( (v5_relat_1 @ A) @ k3_numbers) & ( ( (v5_relat_1 @ A) @ k4_numbers) & ( (v1_funct_1 @ A) & ( (v3_funct_1 @ A) & (v4_valued_0 @ A) ) ) ) ) ) ) ) , file(valued_0, rc2_valued_0), [interesting(np__0.9), axiom, file(valued_0, rc2_valued_0)]). thf(rc2_xreal_0, theorem, (? [A: $i] : ( (v1_xcmplx_0 @ A) & ( (v1_xxreal_0 @ A) & ( (v2_xxreal_0 @ A) & (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc2_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, rc2_xreal_0)]). thf(rc2_xxreal_0, theorem, (? [A: $i] : ( (v1_xxreal_0 @ A) & (v2_xxreal_0 @ A) ) ) , file(xxreal_0, rc2_xxreal_0), [interesting(np__0.9), axiom, file(xxreal_0, rc2_xxreal_0)]). thf(rc3_xreal_0, theorem, (? [A: $i] : ( (v1_xcmplx_0 @ A) & ( (v1_xxreal_0 @ A) & ( (v3_xxreal_0 @ A) & (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc3_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, rc3_xreal_0)]). thf(rc3_xxreal_0, theorem, (? [A: $i] : ( (v1_xxreal_0 @ A) & (v3_xxreal_0 @ A) ) ) , file(xxreal_0, rc3_xxreal_0), [interesting(np__0.9), axiom, file(xxreal_0, rc3_xxreal_0)]). thf(rc5_valued_1, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_1, rc5_valued_1)]). thf(commutativity_k2_xcmplx_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xcmplx_0, k2_xcmplx_0)]). thf(involutiveness_k5_xcmplx_0, theorem, (! [A: $i] : ( (v1_xcmplx_0 @ A) => ( (= @ (k5_xcmplx_0 @ (k5_xcmplx_0 @ A) ) ) @ A) ) ) , file(xcmplx_0, k5_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, k5_xcmplx_0)]). thf(reflexivity_r1_tarski, theorem, (! [A: $i, B: $i] : ( (r1_tarski @ A) @ A) ) , file(tarski, r1_tarski), [interesting(np__0.9), axiom, file(tarski, r1_tarski)]). thf(antisymmetry_r2_hidden, theorem, (! [A: $i, B: $i] : ( ( (r2_hidden @ A) @ B) => ~ ( ( (r2_hidden @ B) @ A) ) ) ) , file(hidden, r2_hidden), [interesting(np__0.9), axiom, file(hidden, r2_hidden)]). thf(dt_k1_funct_1, plain, $true, file(funct_1, k1_funct_1), [interesting(np__0.9), axiom, file(funct_1, k1_funct_1)]). thf(dt_k1_rfunct_1, plain, (! [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_rfunct_1 @ A) @ B) ) & (v1_funct_1 @ ( (k1_rfunct_1 @ A) @ B) ) ) ) ) , file(rfunct_1, k1_rfunct_1), [interesting(np__0.9), axiom, file(rfunct_1, k1_rfunct_1)]). thf(dt_k1_xboole_0, plain, $true, file(xboole_0, k1_xboole_0), [interesting(np__0.9), axiom, file(xboole_0, k1_xboole_0)]). thf(dt_k2_xcmplx_0, plain, $true, file(xcmplx_0, k2_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, k2_xcmplx_0)]). thf(dt_k5_xcmplx_0, plain, (! [A: $i] : ( (v1_xcmplx_0 @ A) => (v1_xcmplx_0 @ (k5_xcmplx_0 @ A) ) ) ) , file(xcmplx_0, k5_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, k5_xcmplx_0)]). thf(cc10_ordinal1, theorem, (! [A: $i] : ( (v6_ordinal1 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v6_ordinal1 @ B) ) ) ) ) , file(ordinal1, cc10_ordinal1), [interesting(np__0.9), axiom, file(ordinal1, cc10_ordinal1)]). thf(cc10_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, cc10_valued_0)]). thf(cc11_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, cc11_valued_0)]). thf(cc12_membered, theorem, (! [A: $i] : ( (v1_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => (v1_xcmplx_0 @ B) ) ) ) ) , file(membered, cc12_membered), [interesting(np__0.9), axiom, file(membered, cc12_membered)]). thf(cc13_membered, theorem, (! [A: $i] : ( (v2_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => (v1_xxreal_0 @ B) ) ) ) ) , file(membered, cc13_membered), [interesting(np__0.9), axiom, file(membered, cc13_membered)]). thf(cc14_valued_2, theorem, (! [A: $i] : ( (v6_valued_2 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v6_valued_2 @ B) ) ) ) ) , file(valued_2, cc14_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc14_valued_2)]). thf(cc15_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, cc15_valued_0)]). thf(cc16_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, cc16_valued_0)]). thf(cc17_membered, theorem, (! [A: $i] : ( (v6_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => (v7_ordinal1 @ B) ) ) ) ) , file(membered, cc17_membered), [interesting(np__0.9), axiom, file(membered, cc17_membered)]). thf(cc17_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, cc17_valued_0)]). thf(cc19_membered, theorem, (! [A: $i] : ( (v1_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v1_membered @ B) ) ) ) ) , file(membered, cc19_membered), [interesting(np__0.9), axiom, file(membered, cc19_membered)]). thf(cc1_funct_2, theorem, (! [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), [interesting(np__0.9), axiom, file(funct_2, cc1_funct_2)]). thf(cc1_membered, theorem, (! [A: $i] : ( (v6_membered @ A) => (v5_membered @ A) ) ) , file(membered, cc1_membered), [interesting(np__0.9), axiom, file(membered, cc1_membered)]). thf(cc1_ordinal1, theorem, (! [A: $i] : ( (v3_ordinal1 @ A) => ( (v1_ordinal1 @ A) & (v2_ordinal1 @ A) ) ) ) , file(ordinal1, cc1_ordinal1), [interesting(np__0.9), axiom, file(ordinal1, cc1_ordinal1)]). thf(cc1_rfunct_1, theorem, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v3_funct_1 @ A) & (v3_valued_0 @ A) ) ) ) => ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ( (v3_valued_0 @ A) & (v1_comseq_2 @ A) ) ) ) ) ) , file(rfunct_1, cc1_rfunct_1), [interesting(np__0.9), axiom, file(rfunct_1, cc1_rfunct_1)]). thf(cc1_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, cc1_valued_0)]). thf(cc1_valued_2, theorem, (! [A: $i] : ( (v6_valued_2 @ A) => (v5_valued_2 @ A) ) ) , file(valued_2, cc1_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc1_valued_2)]). thf(cc20_membered, theorem, (! [A: $i] : ( (v2_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v2_membered @ B) ) ) ) ) , file(membered, cc20_membered), [interesting(np__0.9), axiom, file(membered, cc20_membered)]). thf(cc20_valued_2, theorem, (! [A: $i] : ( (v6_valued_2 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => (v4_valued_0 @ B) ) ) ) ) , file(valued_2, cc20_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc20_valued_2)]). thf(cc21_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, cc21_valued_0)]). thf(cc22_valued_2, theorem, (! [A: $i] : ( ( (v1_relat_1 @ A) & (v12_valued_2 @ A) ) => ( (v1_relat_1 @ A) & (v11_valued_2 @ A) ) ) ) , file(valued_2, cc22_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc22_valued_2)]). thf(cc24_membered, theorem, (! [A: $i] : ( (v6_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v6_membered @ B) ) ) ) ) , file(membered, cc24_membered), [interesting(np__0.9), axiom, file(membered, cc24_membered)]). thf(cc28_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, cc28_valued_0)]). thf(cc2_funct_2, theorem, (! [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), [interesting(np__0.9), axiom, file(funct_2, cc2_funct_2)]). thf(cc2_int_1, theorem, (! [A: $i] : ( (v7_ordinal1 @ A) => (v1_int_1 @ A) ) ) , file(int_1, cc2_int_1), [interesting(np__0.9), axiom, file(int_1, cc2_int_1)]). thf(cc2_xcmplx_0, theorem, (! [A: $i] : ( (v7_ordinal1 @ A) => (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, cc2_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, cc2_xcmplx_0)]). thf(cc2_xreal_0, theorem, (! [A: $i] : ( (v7_ordinal1 @ A) => (v1_xreal_0 @ A) ) ) , file(xreal_0, cc2_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, cc2_xreal_0)]). thf(cc2_xxreal_0, theorem, (! [A: $i] : ( (v7_ordinal1 @ A) => (v1_xxreal_0 @ A) ) ) , file(xxreal_0, cc2_xxreal_0), [interesting(np__0.9), axiom, file(xxreal_0, cc2_xxreal_0)]). thf(cc30_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, cc30_valued_0)]). thf(cc33_valued_2, theorem, (! [A: $i, B: $i] : ( (v6_valued_2 @ B) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => ( (v1_funct_1 @ C) => ( (v1_funct_1 @ C) & (v12_valued_2 @ C) ) ) ) ) ) ) , file(valued_2, cc33_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc33_valued_2)]). thf(cc3_funct_2, theorem, (! [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), [interesting(np__0.9), axiom, file(funct_2, cc3_funct_2)]). thf(cc4_funct_2, theorem, (! [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), [interesting(np__0.9), axiom, file(funct_2, cc4_funct_2)]). thf(cc5_funct_1, theorem, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ~ ( (v3_funct_1 @ A) ) ) ) => ( ~ ( (v1_zfmisc_1 @ A) ) & ( (v1_relat_1 @ A) & (v1_funct_1 @ A) ) ) ) ) , file(funct_1, cc5_funct_1), [interesting(np__0.9), axiom, file(funct_1, cc5_funct_1)]). thf(cc5_ordinal1, theorem, (! [A: $i] : ( (v3_ordinal1 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => (v3_ordinal1 @ B) ) ) ) ) , file(ordinal1, cc5_ordinal1), [interesting(np__0.9), axiom, file(ordinal1, cc5_ordinal1)]). thf(cc5_relat_1, theorem, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ B) & ( (v4_relat_1 @ B) @ A) ) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ B) ) => ( (v4_relat_1 @ C) @ A) ) ) ) ) , file(relat_1, cc5_relat_1), [interesting(np__0.9), axiom, file(relat_1, cc5_relat_1)]). thf(cc6_ordinal1, theorem, (! [A: $i] : ( (v7_ordinal1 @ A) => (v3_ordinal1 @ A) ) ) , file(ordinal1, cc6_ordinal1), [interesting(np__0.9), axiom, file(ordinal1, cc6_ordinal1)]). thf(cc6_relat_1, theorem, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ B) & ( (v5_relat_1 @ B) @ A) ) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ B) ) => ( (v5_relat_1 @ C) @ A) ) ) ) ) , file(relat_1, cc6_relat_1), [interesting(np__0.9), axiom, file(relat_1, cc6_relat_1)]). thf(cc7_relat_1, theorem, (! [A: $i] : ( (v1_xboole_0 @ A) => (! [B: $i] : ( ( (v1_relat_1 @ B) & ( (v4_relat_1 @ B) @ A) ) => ( (v1_xboole_0 @ B) & ( (v1_relat_1 @ B) & ( (v4_relat_1 @ B) @ A) ) ) ) ) ) ) , file(relat_1, cc7_relat_1), [interesting(np__0.9), axiom, file(relat_1, cc7_relat_1)]). thf(cc7_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, cc7_valued_0)]). thf(cc7_xxreal_0, theorem, (! [A: $i] : ( ( (v1_xboole_0 @ A) & (v1_xxreal_0 @ A) ) => ( (v1_xxreal_0 @ A) & ( ~ ( (v2_xxreal_0 @ A) ) & ~ ( (v3_xxreal_0 @ A) ) ) ) ) ) , file(xxreal_0, cc7_xxreal_0), [interesting(np__0.9), axiom, file(xxreal_0, cc7_xxreal_0)]). thf(cc8_funct_1, theorem, (! [A: $i] : ( (v4_funct_1 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => ( (v1_relat_1 @ B) & (v1_funct_1 @ B) ) ) ) ) ) , file(funct_1, cc8_funct_1), [interesting(np__0.9), axiom, file(funct_1, cc8_funct_1)]). thf(cc8_funct_2, theorem, (! [A: $i, B: $i] : ( ( ~ ( (v1_xboole_0 @ A) ) & ~ ( (v1_xboole_0 @ B) ) ) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => ( ( (v1_funct_1 @ C) & ( ( (v1_funct_2 @ C) @ A) @ B) ) => ( (v1_funct_1 @ C) & ( ~ ( (v1_xboole_0 @ C) ) & ( ( (v1_funct_2 @ C) @ A) @ B) ) ) ) ) ) ) ) , file(funct_2, cc8_funct_2), [interesting(np__0.9), axiom, file(funct_2, cc8_funct_2)]). thf(cc8_relat_1, theorem, (! [A: $i] : ( (v1_xboole_0 @ A) => (! [B: $i] : ( ( (v1_relat_1 @ B) & ( (v5_relat_1 @ B) @ A) ) => ( (v1_xboole_0 @ B) & ( (v1_relat_1 @ B) & ( (v5_relat_1 @ B) @ A) ) ) ) ) ) ) , file(relat_1, cc8_relat_1), [interesting(np__0.9), axiom, file(relat_1, cc8_relat_1)]). thf(cc8_valued_0, theorem, (! [A: $i] : ( ( (v1_relat_1 @ A) & (v4_valued_0 @ A) ) => ( (v1_relat_1 @ A) & (v3_valued_0 @ A) ) ) ) , file(valued_0, cc8_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc8_valued_0)]). thf(cc9_funct_1, theorem, (! [A: $i] : ( (v4_funct_1 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v4_funct_1 @ B) ) ) ) ) , file(funct_1, cc9_funct_1), [interesting(np__0.9), axiom, file(funct_1, cc9_funct_1)]). thf(fc127_valued_1, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_1, fc127_valued_1)]). thf(fc131_valued_1, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_1, fc131_valued_1)]). thf(fc17_funct_1, theorem, (! [A: $i, B: $i, C: $i] : ( ( (v4_funct_1 @ A) & ( (v1_relat_1 @ C) & ( ( (v5_relat_1 @ C) @ A) & (v1_funct_1 @ C) ) ) ) => ( (v1_relat_1 @ ( (k1_funct_1 @ C) @ B) ) & (v1_funct_1 @ ( (k1_funct_1 @ C) @ B) ) ) ) ) , file(funct_1, fc17_funct_1), [interesting(np__0.9), axiom, file(funct_1, fc17_funct_1)]). thf(fc19_funct_1, theorem, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v3_relat_1 @ A) & (v1_funct_1 @ A) ) ) => (v1_xboole_0 @ ( (k1_funct_1 @ A) @ B) ) ) ) , file(funct_1, fc19_funct_1), [interesting(np__0.9), axiom, file(funct_1, fc19_funct_1)]). thf(fc1_rfunct_1, theorem, (! [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_rfunct_1 @ A) @ B) ) & ( (v1_funct_1 @ ( (k1_rfunct_1 @ A) @ B) ) & (v1_valued_0 @ ( (k1_rfunct_1 @ A) @ B) ) ) ) ) ) , file(rfunct_1, fc1_rfunct_1), [interesting(np__0.9), axiom, file(rfunct_1, fc1_rfunct_1)]). thf(fc1_xboole_0, theorem, (v1_xboole_0 @ k1_xboole_0) , file(xboole_0, fc1_xboole_0), [interesting(np__0.9), axiom, file(xboole_0, fc1_xboole_0)]). thf(fc20_rfunct_1, theorem, (! [A: $i, B: $i, C: $i] : ( ( ~ ( (v1_xboole_0 @ A) ) & ( ( (v1_funct_1 @ B) & ( (v3_funct_1 @ B) & ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ k1_numbers) ) ) ) ) & ( (v1_funct_1 @ C) & ( (v3_funct_1 @ C) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ k1_numbers) ) ) ) ) ) ) => ( (v1_relat_1 @ ( (k18_valued_1 @ B) @ C) ) & ( (v1_funct_1 @ ( (k18_valued_1 @ B) @ C) ) & (v3_funct_1 @ ( (k18_valued_1 @ B) @ C) ) ) ) ) ) , file(rfunct_1, fc20_rfunct_1), [interesting(np__0.9), axiom, file(rfunct_1, fc20_rfunct_1)]). thf(fc21_valued_2, theorem, (! [A: $i, B: $i, C: $i, D: $i] : ( ( (v6_valued_2 @ C) & ( (v1_funct_1 @ D) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) => (v4_valued_0 @ ( (k1_funct_1 @ D) @ B) ) ) ) , file(valued_2, fc21_valued_2), [interesting(np__0.9), axiom, file(valued_2, fc21_valued_2)]). thf(fc2_rfunct_1, theorem, (! [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_rfunct_1 @ A) @ B) ) & ( (v1_funct_1 @ ( (k1_rfunct_1 @ A) @ B) ) & (v3_valued_0 @ ( (k1_rfunct_1 @ A) @ B) ) ) ) ) ) , file(rfunct_1, fc2_rfunct_1), [interesting(np__0.9), axiom, file(rfunct_1, fc2_rfunct_1)]). thf(fc2_xcmplx_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xcmplx_0, fc2_xcmplx_0)]). thf(fc33_valued_1, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_1, fc33_valued_1)]). thf(fc37_valued_1, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_1, fc37_valued_1)]). thf(fc38_valued_1, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_1, fc38_valued_1)]). thf(fc39_valued_1, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_1, fc39_valued_1)]). thf(fc42_valued_1, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_1, fc42_valued_1)]). thf(fc47_valued_2, theorem, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v12_valued_2 @ A) ) ) => (v4_valued_0 @ ( (k1_funct_1 @ A) @ B) ) ) ) , file(valued_2, fc47_valued_2), [interesting(np__0.9), axiom, file(valued_2, fc47_valued_2)]). thf(fc4_xreal_0, theorem, (! [A: $i] : ( (v1_xreal_0 @ A) => ( (v1_xcmplx_0 @ (k5_xcmplx_0 @ A) ) & (v1_xreal_0 @ (k5_xcmplx_0 @ A) ) ) ) ) , file(xreal_0, fc4_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, fc4_xreal_0)]). thf(fc5_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc5_xreal_0)]). thf(fc61_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, fc61_valued_0)]). thf(fc62_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, fc62_valued_0)]). thf(fc63_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, fc63_valued_0)]). thf(fc66_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, fc66_valued_0)]). thf(fc7_xcmplx_0, theorem, (! [A: $i] : ( ( ~ ( (v1_xboole_0 @ A) ) & (v1_xcmplx_0 @ A) ) => ( ~ ( (v1_xboole_0 @ (k5_xcmplx_0 @ A) ) ) & (v1_xcmplx_0 @ (k5_xcmplx_0 @ A) ) ) ) ) , file(xcmplx_0, fc7_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, fc7_xcmplx_0)]). thf(fc85_valued_0, theorem, (! [A: $i, B: $i] : ( (v1_membered @ B) => (v1_valued_0 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) , file(valued_0, fc85_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc85_valued_0)]). thf(fc86_valued_0, theorem, (! [A: $i, B: $i] : ( (v2_membered @ B) => (v2_valued_0 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) , file(valued_0, fc86_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc86_valued_0)]). thf(fc90_valued_0, theorem, (! [A: $i, B: $i] : ( (v6_membered @ B) => (v4_valued_0 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) , file(valued_0, fc90_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc90_valued_0)]). thf(rc1_funct_2, theorem, (! [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), [interesting(np__0.9), axiom, file(funct_2, rc1_funct_2)]). thf(rc1_membered, theorem, (? [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) & (v6_membered @ A) ) ) , file(membered, rc1_membered), [interesting(np__0.9), axiom, file(membered, rc1_membered)]). thf(rc1_ordinal1, theorem, (? [A: $i] : (v3_ordinal1 @ A) ) , file(ordinal1, rc1_ordinal1), [interesting(np__0.9), axiom, file(ordinal1, rc1_ordinal1)]). thf(rc1_partfun1, theorem, (! [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) ) ) ) ) ) ) , file(partfun1, rc1_partfun1), [interesting(np__0.9), axiom, file(partfun1, rc1_partfun1)]). thf(rc1_relset_1, theorem, (! [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), [interesting(np__0.9), axiom, file(relset_1, rc1_relset_1)]). thf(rc1_valued_0, theorem, (? [A: $i] : ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v4_valued_0 @ A) ) ) ) , file(valued_0, rc1_valued_0), [interesting(np__0.9), axiom, file(valued_0, rc1_valued_0)]). thf(rc1_valued_2, theorem, (? [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) & (v6_valued_2 @ A) ) ) , file(valued_2, rc1_valued_2), [interesting(np__0.9), axiom, file(valued_2, rc1_valued_2)]). thf(rc1_xxreal_0, theorem, (? [A: $i] : (v1_xxreal_0 @ A) ) , file(xxreal_0, rc1_xxreal_0), [interesting(np__0.9), axiom, file(xxreal_0, rc1_xxreal_0)]). thf(rc2_funct_1, theorem, (? [A: $i] : ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v2_funct_1 @ A) ) ) ) , file(funct_1, rc2_funct_1), [interesting(np__0.9), axiom, file(funct_1, rc2_funct_1)]). thf(rc2_membered, theorem, (? [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) & (v6_membered @ A) ) ) , file(membered, rc2_membered), [interesting(np__0.9), axiom, file(membered, rc2_membered)]). thf(rc2_relat_1, theorem, (? [A: $i] : ( (v1_relat_1 @ A) & (v2_relat_1 @ A) ) ) , file(relat_1, rc2_relat_1), [interesting(np__0.9), axiom, file(relat_1, rc2_relat_1)]). thf(rc2_valued_2, theorem, (? [A: $i] : ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v12_valued_2 @ A) ) ) ) , file(valued_2, rc2_valued_2), [interesting(np__0.9), axiom, file(valued_2, rc2_valued_2)]). thf(rc3_funct_1, theorem, (? [A: $i] : ( (v1_relat_1 @ A) & ( (v2_relat_1 @ A) & (v1_funct_1 @ A) ) ) ) , file(funct_1, rc3_funct_1), [interesting(np__0.9), axiom, file(funct_1, rc3_funct_1)]). thf(rc3_membered, theorem, (? [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) & ( (v6_membered @ A) & (v7_membered @ A) ) ) ) , file(membered, rc3_membered), [interesting(np__0.9), axiom, file(membered, rc3_membered)]). thf(rc3_ordinal1, theorem, (! [A: $i] : (? [B: $i] : ( (v1_relat_1 @ B) & ( ( (v5_relat_1 @ B) @ A) & ( (v1_funct_1 @ B) & (v5_ordinal1 @ B) ) ) ) ) ) , file(ordinal1, rc3_ordinal1), [interesting(np__0.9), axiom, file(ordinal1, rc3_ordinal1)]). thf(rc3_partfun1, theorem, (! [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_relat_1 @ C) & ( ( (v4_relat_1 @ C) @ A) & ( ( (v5_relat_1 @ C) @ B) & ( (v1_funct_1 @ C) & ~ ( (v1_xboole_0 @ C) ) ) ) ) ) ) ) ) ) , file(partfun1, rc3_partfun1), [interesting(np__0.9), axiom, file(partfun1, rc3_partfun1)]). thf(rc3_relat_1, theorem, (! [A: $i, B: $i] : (? [C: $i] : ( (v1_relat_1 @ C) & ( ( (v4_relat_1 @ C) @ A) & ( (v5_relat_1 @ C) @ B) ) ) ) ) , file(relat_1, rc3_relat_1), [interesting(np__0.9), axiom, file(relat_1, rc3_relat_1)]). thf(rc4_funct_1, theorem, (? [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) & ( (v1_relat_1 @ A) & ( (v2_relat_1 @ A) & (v1_funct_1 @ A) ) ) ) ) , file(funct_1, rc4_funct_1), [interesting(np__0.9), axiom, file(funct_1, rc4_funct_1)]). thf(rc4_ordinal1, theorem, (? [A: $i] : (v7_ordinal1 @ A) ) , file(ordinal1, rc4_ordinal1), [interesting(np__0.9), axiom, file(ordinal1, rc4_ordinal1)]). thf(rc4_xreal_0, theorem, (? [A: $i] : ( (v1_xboole_0 @ A) & ( (v1_xcmplx_0 @ A) & ( (v1_xxreal_0 @ A) & (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc4_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, rc4_xreal_0)]). thf(rc4_xxreal_0, theorem, (? [A: $i] : ( (v1_xboole_0 @ A) & (v1_xxreal_0 @ A) ) ) , file(xxreal_0, rc4_xxreal_0), [interesting(np__0.9), axiom, file(xxreal_0, rc4_xxreal_0)]). thf(rc5_funct_1, theorem, (? [A: $i] : ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & ~ ( (v3_funct_1 @ A) ) ) ) ) , file(funct_1, rc5_funct_1), [interesting(np__0.9), axiom, file(funct_1, rc5_funct_1)]). thf(rc5_ordinal1, theorem, (? [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) & (v7_ordinal1 @ A) ) ) , file(ordinal1, rc5_ordinal1), [interesting(np__0.9), axiom, file(ordinal1, rc5_ordinal1)]). thf(rc6_funct_1, theorem, (! [A: $i, B: $i] : (? [C: $i] : ( (v1_relat_1 @ C) & ( ( (v4_relat_1 @ C) @ A) & ( ( (v5_relat_1 @ C) @ B) & (v1_funct_1 @ C) ) ) ) ) ) , file(funct_1, rc6_funct_1), [interesting(np__0.9), axiom, file(funct_1, rc6_funct_1)]). thf(rc6_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, rc6_valued_0)]). thf(rc7_funct_1, theorem, (? [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) & (v4_funct_1 @ A) ) ) , file(funct_1, rc7_funct_1), [interesting(np__0.9), axiom, file(funct_1, rc7_funct_1)]). thf(rc9_funct_1, theorem, (! [A: $i] : (? [B: $i] : ( (v1_relat_1 @ B) & ( (v2_relat_1 @ B) & ( ( (v4_relat_1 @ B) @ A) & (v1_funct_1 @ B) ) ) ) ) ) , file(funct_1, rc9_funct_1), [interesting(np__0.9), axiom, file(funct_1, rc9_funct_1)]). thf(spc10_arithm, theorem, (! [A: $i, B: $i] : ( ( (v1_xcmplx_0 @ A) & (v1_xcmplx_0 @ B) ) => ( (= @ ( (k3_xcmplx_0 @ (k5_xcmplx_0 @ A) ) @ (k5_xcmplx_0 @ B) ) ) @ (k5_xcmplx_0 @ ( (k3_xcmplx_0 @ A) @ B) ) ) ) ) , file(arithm, spc10_arithm), [interesting(np__0.9), axiom, file(arithm, spc10_arithm)]). thf(spc11_arithm, theorem, (! [A: $i, B: $i] : ( ( (v1_xcmplx_0 @ A) & (v1_xcmplx_0 @ B) ) => ( (= @ ( (k7_xcmplx_0 @ (k5_xcmplx_0 @ A) ) @ (k5_xcmplx_0 @ B) ) ) @ ( (k7_xcmplx_0 @ B) @ A) ) ) ) , file(arithm, spc11_arithm), [interesting(np__0.9), axiom, file(arithm, spc11_arithm)]). thf(spc12_arithm, theorem, (! [A: $i, B: $i] : ( ( (v1_xcmplx_0 @ A) & (v1_xcmplx_0 @ B) ) => ( (= @ ( (k3_xcmplx_0 @ A) @ (k5_xcmplx_0 @ B) ) ) @ ( (k7_xcmplx_0 @ A) @ B) ) ) ) , file(arithm, spc12_arithm), [interesting(np__0.9), axiom, file(arithm, spc12_arithm)]). thf(spc1_arithm, theorem, (! [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), [interesting(np__0.9), axiom, file(arithm, spc1_arithm)]). thf(spc5_arithm, theorem, (! [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), [interesting(np__0.9), axiom, file(arithm, spc5_arithm)]). thf(spc6_arithm, theorem, (! [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), [interesting(np__0.9), axiom, file(arithm, spc6_arithm)]). thf(spc8_arithm, theorem, (! [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), [interesting(np__0.9), axiom, file(arithm, spc8_arithm)]). thf(t1_subset, theorem, (! [A: $i] : (! [B: $i] : ( ( (r2_hidden @ A) @ B) => ( (m1_subset_1 @ A) @ B) ) ) ) , file(subset, t1_subset), [interesting(np__0.9), axiom, file(subset, t1_subset)]). thf(t4_subset, theorem, (! [A: $i] : (! [B: $i] : (! [C: $i] : ( ( ( (r2_hidden @ A) @ B) & ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ C) ) ) => ( (m1_subset_1 @ A) @ C) ) ) ) ) , file(subset, t4_subset), [interesting(np__0.9), axiom, file(subset, t4_subset)]). thf(t5_subset, theorem, (! [A: $i] : (! [B: $i] : (! [C: $i] : ~ ( ( ( (r2_hidden @ A) @ B) & ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ C) ) & (v1_xboole_0 @ C) ) ) ) ) ) ) , file(subset, t5_subset), [interesting(np__0.9), axiom, file(subset, t5_subset)]). thf(d2_xboole_0, definition, ( (= @ k1_xboole_0) @ o_0_0_xboole_0) , file(xboole_0, d2_xboole_0), [interesting(np__0.9), axiom, file(xboole_0, d2_xboole_0)]). thf(commutativity_k18_valued_1, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_1, k18_valued_1)]). thf(commutativity_k3_xcmplx_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xcmplx_0, k3_xcmplx_0)]). thf(involutiveness_k4_xcmplx_0, theorem, (! [A: $i] : ( (v1_xcmplx_0 @ A) => ( (= @ (k4_xcmplx_0 @ (k4_xcmplx_0 @ A) ) ) @ A) ) ) , file(xcmplx_0, k4_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, k4_xcmplx_0)]). thf(existence_m1_subset_1, plain, (! [A: $i] : (? [B: $i] : ( (m1_subset_1 @ B) @ A) ) ) , file(subset_1, m1_subset_1), [interesting(np__0.9), axiom, file(subset_1, m1_subset_1)]). thf(redefinition_k10_real_1, definition, (! [A: $i, B: $i] : ( ( ( (m1_subset_1 @ A) @ k1_numbers) & (v1_xreal_0 @ B) ) => ( (= @ ( (k10_real_1 @ A) @ B) ) @ ( (k7_xcmplx_0 @ A) @ B) ) ) ) , file(real_1, k10_real_1), [interesting(np__0.9), axiom, file(real_1, k10_real_1)]). thf(redefinition_k1_seq_1, definition, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v3_valued_0 @ A) ) ) => ( (= @ ( (k1_seq_1 @ A) @ B) ) @ ( (k1_funct_1 @ A) @ B) ) ) ) , file(seq_1, k1_seq_1), [interesting(np__0.9), axiom, file(seq_1, k1_seq_1)]). thf(redefinition_k3_rfunct_1, definition, (! [A: $i, B: $i, C: $i, D: $i] : ( ( (v3_membered @ B) & ( ( (v1_funct_1 @ C) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) & ( (v1_funct_1 @ D) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) ) => ( (= @ ( ( ( (k3_rfunct_1 @ A) @ B) @ C) @ D) ) @ ( (k1_rfunct_1 @ C) @ D) ) ) ) , file(rfunct_1, k3_rfunct_1), [interesting(np__0.9), axiom, file(rfunct_1, k3_rfunct_1)]). thf(dt_k10_real_1, plain, (! [A: $i, B: $i] : ( ( ( (m1_subset_1 @ A) @ k1_numbers) & (v1_xreal_0 @ B) ) => ( (m1_subset_1 @ ( (k10_real_1 @ A) @ B) ) @ k1_numbers) ) ) , file(real_1, k10_real_1), [interesting(np__0.9), axiom, file(real_1, k10_real_1)]). thf(dt_k16_sin_cos, plain, ( (v1_funct_1 @ k16_sin_cos) & ( ( ( (v1_funct_2 @ k16_sin_cos) @ k1_numbers) @ k1_numbers) & ( (m1_subset_1 @ k16_sin_cos) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k1_numbers) @ k1_numbers) ) ) ) ) , file(sin_cos, k16_sin_cos), [interesting(np__0.9), axiom, file(sin_cos, k16_sin_cos)]). thf(dt_k17_sin_cos, plain, $true, file(sin_cos, k17_sin_cos), [interesting(np__0.9), axiom, file(sin_cos, k17_sin_cos)]). thf(dt_k18_valued_1, plain, (! [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), [interesting(np__0.9), axiom, file(valued_1, k18_valued_1)]). thf(dt_k19_sin_cos, plain, ( (v1_funct_1 @ k19_sin_cos) & ( ( ( (v1_funct_2 @ k19_sin_cos) @ k1_numbers) @ k1_numbers) & ( (m1_subset_1 @ k19_sin_cos) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k1_numbers) @ k1_numbers) ) ) ) ) , file(sin_cos, k19_sin_cos), [interesting(np__0.9), axiom, file(sin_cos, k19_sin_cos)]). thf(dt_k1_seq_1, plain, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v3_valued_0 @ A) ) ) => ( (m1_subset_1 @ ( (k1_seq_1 @ A) @ B) ) @ k1_numbers) ) ) , file(seq_1, k1_seq_1), [interesting(np__0.9), axiom, file(seq_1, k1_seq_1)]). thf(dt_k1_zfmisc_1, plain, $true, file(zfmisc_1, k1_zfmisc_1), [interesting(np__0.9), axiom, file(zfmisc_1, k1_zfmisc_1)]). thf(dt_k20_sin_cos, plain, $true, file(sin_cos, k20_sin_cos), [interesting(np__0.9), axiom, file(sin_cos, k20_sin_cos)]). thf(dt_k2_numbers, plain, $true, file(numbers, k2_numbers), [interesting(np__0.9), axiom, file(numbers, k2_numbers)]). thf(dt_k2_zfmisc_1, plain, $true, file(zfmisc_1, k2_zfmisc_1), [interesting(np__0.9), axiom, file(zfmisc_1, k2_zfmisc_1)]). thf(dt_k3_rfunct_1, plain, (! [A: $i, B: $i, C: $i, D: $i] : ( ( (v3_membered @ B) & ( ( (v1_funct_1 @ C) & ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) & ( (v1_funct_1 @ D) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) ) ) => ( (v1_funct_1 @ ( ( ( (k3_rfunct_1 @ A) @ B) @ C) @ D) ) & ( (m1_subset_1 @ ( ( ( (k3_rfunct_1 @ A) @ B) @ C) @ D) ) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ k1_numbers) ) ) ) ) ) , file(rfunct_1, k3_rfunct_1), [interesting(np__0.9), axiom, file(rfunct_1, k3_rfunct_1)]). thf(dt_k3_square_1, plain, $true, file(square_1, k3_square_1), [interesting(np__0.9), axiom, file(square_1, k3_square_1)]). thf(dt_k3_xcmplx_0, plain, $true, file(xcmplx_0, k3_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, k3_xcmplx_0)]). thf(dt_k4_xcmplx_0, plain, (! [A: $i] : ( (v1_xcmplx_0 @ A) => (v1_xcmplx_0 @ (k4_xcmplx_0 @ A) ) ) ) , file(xcmplx_0, k4_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, k4_xcmplx_0)]). thf(dt_k6_xcmplx_0, plain, $true, file(xcmplx_0, k6_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, k6_xcmplx_0)]). thf(dt_k7_xcmplx_0, plain, $true, file(xcmplx_0, k7_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, k7_xcmplx_0)]). thf(dt_m1_subset_1, plain, $true, file(subset_1, m1_subset_1), [interesting(np__0.9), axiom, file(subset_1, m1_subset_1)]). thf(cc12_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, cc12_valued_0)]). thf(cc14_membered, theorem, (! [A: $i] : ( (v3_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ A) => (v1_xreal_0 @ B) ) ) ) ) , file(membered, cc14_membered), [interesting(np__0.9), axiom, file(membered, cc14_membered)]). thf(cc18_membered, theorem, (! [A: $i] : ( (v1_xboole_0 @ A) => (v6_membered @ A) ) ) , file(membered, cc18_membered), [interesting(np__0.9), axiom, file(membered, cc18_membered)]). thf(cc18_valued_0, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_0, cc18_valued_0)]). thf(cc1_funct_1, theorem, (! [A: $i] : ( (v1_xboole_0 @ A) => (v1_funct_1 @ A) ) ) , file(funct_1, cc1_funct_1), [interesting(np__0.9), axiom, file(funct_1, cc1_funct_1)]). thf(cc1_partfun1, theorem, (! [A: $i, B: $i] : ( (v1_xboole_0 @ A) => (! [C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) => ( (v1_partfun1 @ C) @ A) ) ) ) ) , file(partfun1, cc1_partfun1), [interesting(np__0.9), axiom, file(partfun1, cc1_partfun1)]). thf(cc1_relat_1, theorem, (! [A: $i] : ( (v1_xboole_0 @ A) => (v1_relat_1 @ A) ) ) , file(relat_1, cc1_relat_1), [interesting(np__0.9), axiom, file(relat_1, cc1_relat_1)]). thf(cc1_relset_1, theorem, (! [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), [interesting(np__0.9), axiom, file(relset_1, cc1_relset_1)]). thf(cc1_xcmplx_0, theorem, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, cc1_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, cc1_xcmplx_0)]). thf(cc1_xreal_0, theorem, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => (v1_xreal_0 @ A) ) ) , file(xreal_0, cc1_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, cc1_xreal_0)]). thf(cc21_membered, theorem, (! [A: $i] : ( (v3_membered @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v3_membered @ B) ) ) ) ) , file(membered, cc21_membered), [interesting(np__0.9), axiom, file(membered, cc21_membered)]). thf(cc26_membered, theorem, (! [A: $i] : ( (v1_xboole_0 @ A) => (v7_membered @ A) ) ) , file(membered, cc26_membered), [interesting(np__0.9), axiom, file(membered, cc26_membered)]). thf(cc27_valued_2, theorem, (! [A: $i] : ( ( (v1_relat_1 @ A) & (v1_xboole_0 @ A) ) => ( (v1_relat_1 @ A) & (v12_valued_2 @ A) ) ) ) , file(valued_2, cc27_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc27_valued_2)]). thf(cc2_funct_1, theorem, (! [A: $i] : ( ( (v1_xboole_0 @ A) & ( (v1_relat_1 @ A) & (v1_funct_1 @ A) ) ) => ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v2_funct_1 @ A) ) ) ) ) , file(funct_1, cc2_funct_1), [interesting(np__0.9), axiom, file(funct_1, cc2_funct_1)]). thf(cc2_partfun1, theorem, (! [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_partfun1 @ C) @ A) ) ) ) ) ) , file(partfun1, cc2_partfun1), [interesting(np__0.9), axiom, file(partfun1, cc2_partfun1)]). thf(cc2_relat_1, theorem, (! [A: $i] : ( (v1_relat_1 @ A) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v1_relat_1 @ B) ) ) ) ) , file(relat_1, cc2_relat_1), [interesting(np__0.9), axiom, file(relat_1, cc2_relat_1)]). thf(cc2_relset_1, theorem, (! [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), [interesting(np__0.9), axiom, file(relset_1, cc2_relset_1)]). thf(cc3_funct_1, theorem, (! [A: $i] : ( ( (v1_relat_1 @ A) & (v1_funct_1 @ A) ) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) => (v1_funct_1 @ B) ) ) ) ) , file(funct_1, cc3_funct_1), [interesting(np__0.9), axiom, file(funct_1, cc3_funct_1)]). thf(cc3_ordinal1, theorem, (! [A: $i] : ( (v1_xboole_0 @ A) => (v3_ordinal1 @ A) ) ) , file(ordinal1, cc3_ordinal1), [interesting(np__0.9), axiom, file(ordinal1, cc3_ordinal1)]). thf(cc3_relat_1, theorem, (! [A: $i] : ( ( (v1_xboole_0 @ A) & (v1_relat_1 @ A) ) => ( (v1_relat_1 @ A) & (v3_relat_1 @ A) ) ) ) , file(relat_1, cc3_relat_1), [interesting(np__0.9), axiom, file(relat_1, cc3_relat_1)]). thf(cc3_relset_1, theorem, (! [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), [interesting(np__0.9), axiom, file(relset_1, cc3_relset_1)]). thf(cc3_xcmplx_0, theorem, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k2_numbers) => (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, cc3_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, cc3_xcmplx_0)]). thf(cc3_xreal_0, theorem, (! [A: $i] : ( (v1_xreal_0 @ A) => (v1_xcmplx_0 @ A) ) ) , file(xreal_0, cc3_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, cc3_xreal_0)]). thf(cc4_funct_1, theorem, (! [A: $i] : ( ( (v1_xboole_0 @ A) & ( (v1_relat_1 @ A) & (v1_funct_1 @ A) ) ) => ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v3_funct_1 @ A) ) ) ) ) , file(funct_1, cc4_funct_1), [interesting(np__0.9), axiom, file(funct_1, cc4_funct_1)]). thf(cc4_membered, theorem, (! [A: $i] : ( (v3_membered @ A) => (v2_membered @ A) ) ) , file(membered, cc4_membered), [interesting(np__0.9), axiom, file(membered, cc4_membered)]). thf(cc4_ordinal1, theorem, (! [A: $i] : ( (v1_xboole_0 @ A) => (v5_ordinal1 @ A) ) ) , file(ordinal1, cc4_ordinal1), [interesting(np__0.9), axiom, file(ordinal1, cc4_ordinal1)]). thf(cc4_relat_1, theorem, (! [A: $i] : ( ( (v1_xboole_0 @ A) & (v1_relat_1 @ A) ) => ( (v1_relat_1 @ A) & (v2_relat_1 @ A) ) ) ) , file(relat_1, cc4_relat_1), [interesting(np__0.9), axiom, file(relat_1, cc4_relat_1)]). thf(cc4_relset_1, theorem, (! [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), [interesting(np__0.9), axiom, file(relset_1, cc4_relset_1)]). thf(cc4_xreal_0, theorem, (! [A: $i] : ( (v1_xreal_0 @ A) => (v1_xxreal_0 @ A) ) ) , file(xreal_0, cc4_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, cc4_xreal_0)]). thf(cc5_membered, theorem, (! [A: $i] : ( (v3_membered @ A) => (v1_membered @ A) ) ) , file(membered, cc5_membered), [interesting(np__0.9), axiom, file(membered, cc5_membered)]). thf(cc5_valued_0, theorem, (! [A: $i] : ( ( (v1_relat_1 @ A) & (v3_valued_0 @ A) ) => ( (v1_relat_1 @ A) & (v2_valued_0 @ A) ) ) ) , file(valued_0, cc5_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc5_valued_0)]). thf(cc6_membered, theorem, (! [A: $i] : ( ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ k2_numbers) ) => (v1_membered @ A) ) ) , file(membered, cc6_membered), [interesting(np__0.9), axiom, file(membered, cc6_membered)]). thf(cc6_valued_0, theorem, (! [A: $i] : ( ( (v1_relat_1 @ A) & (v3_valued_0 @ A) ) => ( (v1_relat_1 @ A) & (v1_valued_0 @ A) ) ) ) , file(valued_0, cc6_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc6_valued_0)]). thf(cc6_valued_2, theorem, (! [A: $i] : ( (v1_xboole_0 @ A) => (v6_valued_2 @ A) ) ) , file(valued_2, cc6_valued_2), [interesting(np__0.9), axiom, file(valued_2, cc6_valued_2)]). thf(cc7_funct_1, theorem, (! [A: $i] : ( (v1_xboole_0 @ A) => (v4_funct_1 @ A) ) ) , file(funct_1, cc7_funct_1), [interesting(np__0.9), axiom, file(funct_1, cc7_funct_1)]). thf(cc7_ordinal1, theorem, (! [A: $i] : ( (v1_xboole_0 @ A) => (v7_ordinal1 @ A) ) ) , file(ordinal1, cc7_ordinal1), [interesting(np__0.9), axiom, file(ordinal1, cc7_ordinal1)]). thf(cc8_membered, theorem, (! [A: $i] : ( ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ k1_numbers) ) => (v3_membered @ A) ) ) , file(membered, cc8_membered), [interesting(np__0.9), axiom, file(membered, cc8_membered)]). thf(cc9_ordinal1, theorem, (! [A: $i] : ( (v1_xboole_0 @ A) => (v6_ordinal1 @ A) ) ) , file(ordinal1, cc9_ordinal1), [interesting(np__0.9), axiom, file(ordinal1, cc9_ordinal1)]). thf(cc9_valued_0, theorem, (! [A: $i] : ( ( (v1_xboole_0 @ A) & (v1_relat_1 @ A) ) => ( (v1_relat_1 @ A) & (v4_valued_0 @ A) ) ) ) , file(valued_0, cc9_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc9_valued_0)]). thf(fc1_membered, theorem, (v1_membered @ k2_numbers) , file(membered, fc1_membered), [interesting(np__0.9), axiom, file(membered, fc1_membered)]). thf(fc1_square_1, theorem, (! [A: $i] : ( (v1_xcmplx_0 @ A) => (v1_xcmplx_0 @ (k3_square_1 @ A) ) ) ) , file(square_1, fc1_square_1), [interesting(np__0.9), axiom, file(square_1, fc1_square_1)]). thf(fc2_numbers, theorem, ~ ( (v1_xboole_0 @ k2_numbers) ) , file(numbers, fc2_numbers), [interesting(np__0.9), axiom, file(numbers, fc2_numbers)]). thf(fc2_square_1, theorem, (! [A: $i] : ( (v1_xreal_0 @ A) => (v1_xreal_0 @ (k3_square_1 @ A) ) ) ) , file(square_1, fc2_square_1), [interesting(np__0.9), axiom, file(square_1, fc2_square_1)]). thf(fc34_valued_1, theorem, (! [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), [interesting(np__0.9), axiom, file(valued_1, fc34_valued_1)]). thf(fc3_sin_cos, theorem, (! [A: $i] : ( (v1_xreal_0 @ A) => (v1_xreal_0 @ (k17_sin_cos @ A) ) ) ) , file(sin_cos, fc3_sin_cos), [interesting(np__0.9), axiom, file(sin_cos, fc3_sin_cos)]). thf(fc3_xcmplx_0, theorem, (! [A: $i, B: $i] : ( ( (v1_xcmplx_0 @ A) & (v1_xcmplx_0 @ B) ) => (v1_xcmplx_0 @ ( (k3_xcmplx_0 @ A) @ B) ) ) ) , file(xcmplx_0, fc3_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, fc3_xcmplx_0)]). thf(fc3_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc3_xreal_0)]). thf(fc4_sin_cos, theorem, (! [A: $i] : ( (v1_xreal_0 @ A) => (v1_xreal_0 @ (k20_sin_cos @ A) ) ) ) , file(sin_cos, fc4_sin_cos), [interesting(np__0.9), axiom, file(sin_cos, fc4_sin_cos)]). thf(fc4_xcmplx_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xcmplx_0, fc4_xcmplx_0)]). thf(fc55_membered, theorem, (v7_membered @ k2_numbers) , file(membered, fc55_membered), [interesting(np__0.9), axiom, file(membered, fc55_membered)]). thf(fc5_xcmplx_0, theorem, (! [A: $i, B: $i] : ( ( (v1_xcmplx_0 @ A) & (v1_xcmplx_0 @ B) ) => (v1_xcmplx_0 @ ( (k7_xcmplx_0 @ A) @ B) ) ) ) , file(xcmplx_0, fc5_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, fc5_xcmplx_0)]). thf(fc6_relat_1, theorem, (! [A: $i, B: $i] : (v1_relat_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) , file(relat_1, fc6_relat_1), [interesting(np__0.9), axiom, file(relat_1, fc6_relat_1)]). thf(fc6_sin_cos, theorem, ( (v1_funct_1 @ k16_sin_cos) & ( ( ( (v1_funct_2 @ k16_sin_cos) @ k1_numbers) @ k1_numbers) & (v1_fcont_1 @ k16_sin_cos) ) ) , file(sin_cos, fc6_sin_cos), [interesting(np__0.9), axiom, file(sin_cos, fc6_sin_cos)]). thf(fc6_xcmplx_0, theorem, (! [A: $i] : ( ( ~ ( (v1_xboole_0 @ A) ) & (v1_xcmplx_0 @ A) ) => ( ~ ( (v1_xboole_0 @ (k4_xcmplx_0 @ A) ) ) & (v1_xcmplx_0 @ (k4_xcmplx_0 @ A) ) ) ) ) , file(xcmplx_0, fc6_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, fc6_xcmplx_0)]). thf(fc6_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc6_xreal_0)]). thf(fc7_sin_cos, theorem, ( (v1_funct_1 @ k19_sin_cos) & ( ( ( (v1_funct_2 @ k19_sin_cos) @ k1_numbers) @ k1_numbers) & (v1_fcont_1 @ k19_sin_cos) ) ) , file(sin_cos, fc7_sin_cos), [interesting(np__0.9), axiom, file(sin_cos, fc7_sin_cos)]). thf(fc7_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc7_xreal_0)]). thf(fc87_valued_0, theorem, (! [A: $i, B: $i] : ( (v3_membered @ B) => (v3_valued_0 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) , file(valued_0, fc87_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc87_valued_0)]). thf(fc8_xcmplx_0, theorem, (! [A: $i, B: $i] : ( ( ( ~ ( (v1_xboole_0 @ A) ) & (v1_xcmplx_0 @ A) ) & ( ~ ( (v1_xboole_0 @ B) ) & (v1_xcmplx_0 @ B) ) ) => ~ ( (v1_xboole_0 @ ( (k3_xcmplx_0 @ A) @ B) ) ) ) ) , file(xcmplx_0, fc8_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, fc8_xcmplx_0)]). thf(fc8_xreal_0, theorem, (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc8_xreal_0)]). thf(fc9_numbers, theorem, ~ ( (v1_finset_1 @ k2_numbers) ) , file(numbers, fc9_numbers), [interesting(np__0.9), axiom, file(numbers, fc9_numbers)]). thf(fc9_xcmplx_0, theorem, (! [A: $i, B: $i] : ( ( ( ~ ( (v1_xboole_0 @ A) ) & (v1_xcmplx_0 @ A) ) & ( ~ ( (v1_xboole_0 @ B) ) & (v1_xcmplx_0 @ B) ) ) => ~ ( (v1_xboole_0 @ ( (k7_xcmplx_0 @ A) @ B) ) ) ) ) , file(xcmplx_0, fc9_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, fc9_xcmplx_0)]). thf(rc1_funct_1, theorem, (? [A: $i] : ( (v1_relat_1 @ A) & (v1_funct_1 @ A) ) ) , file(funct_1, rc1_funct_1), [interesting(np__0.9), axiom, file(funct_1, rc1_funct_1)]). thf(rc1_relat_1, theorem, (? [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) & (v1_relat_1 @ A) ) ) , file(relat_1, rc1_relat_1), [interesting(np__0.9), axiom, file(relat_1, rc1_relat_1)]). thf(rc1_xboole_0, theorem, (? [A: $i] : (v1_xboole_0 @ A) ) , file(xboole_0, rc1_xboole_0), [interesting(np__0.9), axiom, file(xboole_0, rc1_xboole_0)]). thf(rc1_xcmplx_0, theorem, (? [A: $i] : (v1_xcmplx_0 @ A) ) , file(xcmplx_0, rc1_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, rc1_xcmplx_0)]). thf(rc1_xreal_0, theorem, (? [A: $i] : (v1_xreal_0 @ A) ) , file(xreal_0, rc1_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, rc1_xreal_0)]). thf(rc2_xboole_0, theorem, (? [A: $i] : ~ ( (v1_xboole_0 @ A) ) ) , file(xboole_0, rc2_xboole_0), [interesting(np__0.9), axiom, file(xboole_0, rc2_xboole_0)]). thf(rc2_xcmplx_0, theorem, (? [A: $i] : ( ~ ( (v1_xboole_0 @ A) ) & (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, rc2_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, rc2_xcmplx_0)]). thf(spc4_arithm, theorem, (! [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), [interesting(np__0.9), axiom, file(arithm, spc4_arithm)]). thf(spc7_arithm, theorem, (! [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), [interesting(np__0.9), axiom, file(arithm, spc6_arithm)]). thf(spc9_arithm, theorem, (! [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), [interesting(np__0.9), axiom, file(arithm, spc9_arithm)]). thf(t2_subset, theorem, (! [A: $i] : (! [B: $i] : ( ( (m1_subset_1 @ A) @ B) => ( (v1_xboole_0 @ B) | ( (r2_hidden @ A) @ B) ) ) ) ) , file(subset, t2_subset), [interesting(np__0.9), axiom, file(subset, t2_subset)]). thf(t3_subset, theorem, (! [A: $i] : (! [B: $i] : ( ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ B) ) <=> ( (r1_tarski @ A) @ B) ) ) ) , file(subset, t3_subset), [interesting(np__0.9), axiom, file(subset, t3_subset)]). thf(t6_boole, theorem, (! [A: $i] : ( (v1_xboole_0 @ A) => ( (= @ A) @ k1_xboole_0) ) ) , file(boole, t6_boole), [interesting(np__0.9), axiom, file(boole, t6_boole)]). thf(t7_boole, theorem, (! [A: $i] : (! [B: $i] : ~ ( ( ( (r2_hidden @ A) @ B) & (v1_xboole_0 @ B) ) ) ) ) , file(boole, t7_boole), [interesting(np__0.9), axiom, file(boole, t7_boole)]). thf(t8_boole, theorem, (! [A: $i] : (! [B: $i] : ~ ( ( (v1_xboole_0 @ A) & ( ~ ( ( (= @ A) @ B) ) & (v1_xboole_0 @ B) ) ) ) ) ) , file(boole, t8_boole), [interesting(np__0.9), axiom, file(boole, t8_boole)]). thf(d17_sin_cos, definition, (! [A: $i] : ( (v1_xreal_0 @ A) => ( (= @ (k17_sin_cos @ A) ) @ ( (k1_seq_1 @ k16_sin_cos) @ A) ) ) ) , file(sin_cos, d17_sin_cos), [interesting(np__0.9), axiom, file(sin_cos, d17_sin_cos)]). thf(d19_sin_cos, definition, (! [A: $i] : ( (v1_xreal_0 @ A) => ( (= @ (k20_sin_cos @ A) ) @ ( (k1_seq_1 @ k19_sin_cos) @ A) ) ) ) , file(sin_cos, d19_sin_cos), [interesting(np__0.9), axiom, file(sin_cos, d19_sin_cos)]). thf(d1_square_1, definition, (! [A: $i] : ( (v1_xcmplx_0 @ A) => ( (= @ (k3_square_1 @ A) ) @ ( (k3_xcmplx_0 @ A) @ A) ) ) ) , file(square_1, d1_square_1), [interesting(np__0.9), axiom, file(square_1, d1_square_1)]). thf(d8_xcmplx_0, definition, (! [A: $i] : ( (v1_xcmplx_0 @ A) => (! [B: $i] : ( (v1_xcmplx_0 @ B) => ( (= @ ( (k6_xcmplx_0 @ A) @ B) ) @ ( (k2_xcmplx_0 @ A) @ (k4_xcmplx_0 @ B) ) ) ) ) ) ) , file(xcmplx_0, d8_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, d8_xcmplx_0)]). thf(d9_xcmplx_0, definition, (! [A: $i] : ( (v1_xcmplx_0 @ A) => (! [B: $i] : ( (v1_xcmplx_0 @ B) => ( (= @ ( (k7_xcmplx_0 @ A) @ B) ) @ ( (k3_xcmplx_0 @ A) @ (k5_xcmplx_0 @ B) ) ) ) ) ) ) , file(xcmplx_0, d9_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, d9_xcmplx_0)]). thf(involutiveness_k10_complex1, theorem, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k2_numbers) => ( (= @ (k10_complex1 @ (k10_complex1 @ A) ) ) @ A) ) ) , file(complex1, k10_complex1), [interesting(np__0.9), axiom, file(complex1, k10_complex1)]). thf(commutativity_k20_valued_1, theorem, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( (v3_membered @ B) & ( (v3_membered @ C) & ( ( (v1_funct_1 @ D) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) & ( (v1_funct_1 @ E) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) => ( (= @ ( ( ( ( (k20_valued_1 @ A) @ B) @ C) @ D) @ E) ) @ ( ( ( ( (k20_valued_1 @ A) @ B) @ C) @ E) @ D) ) ) ) , file(valued_1, k20_valued_1), [interesting(np__0.9), axiom, file(valued_1, k20_valued_1)]). thf(commutativity_k8_real_1, theorem, (! [A: $i, B: $i] : ( ( ( (m1_subset_1 @ A) @ k1_numbers) & (v1_xreal_0 @ B) ) => ( (= @ ( (k8_real_1 @ A) @ B) ) @ ( (k8_real_1 @ B) @ A) ) ) ) , file(real_1, k8_real_1), [interesting(np__0.9), axiom, file(real_1, k8_real_1)]). thf(redefinition_k10_complex1, definition, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k2_numbers) => ( (= @ (k10_complex1 @ A) ) @ (k4_xcmplx_0 @ A) ) ) ) , file(complex1, k10_complex1), [interesting(np__0.9), axiom, file(complex1, k10_complex1)]). thf(redefinition_k13_complex1, definition, (! [A: $i, B: $i] : ( ( (v1_xcmplx_0 @ A) & (v1_xcmplx_0 @ B) ) => ( (= @ ( (k13_complex1 @ A) @ B) ) @ ( (k7_xcmplx_0 @ A) @ B) ) ) ) , file(complex1, k13_complex1), [interesting(np__0.9), axiom, file(complex1, k13_complex1)]). thf(redefinition_k18_sin_cos, definition, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => ( (= @ (k18_sin_cos @ A) ) @ (k17_sin_cos @ A) ) ) ) , file(sin_cos, k18_sin_cos), [interesting(np__0.9), axiom, file(sin_cos, k18_sin_cos)]). thf(redefinition_k20_valued_1, definition, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( (v3_membered @ B) & ( (v3_membered @ C) & ( ( (v1_funct_1 @ D) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) & ( (v1_funct_1 @ E) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) => ( (= @ ( ( ( ( (k20_valued_1 @ A) @ B) @ C) @ D) @ E) ) @ ( (k18_valued_1 @ D) @ E) ) ) ) , file(valued_1, k20_valued_1), [interesting(np__0.9), axiom, file(valued_1, k20_valued_1)]). thf(redefinition_k21_sin_cos, definition, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => ( (= @ (k21_sin_cos @ A) ) @ (k20_sin_cos @ A) ) ) ) , file(sin_cos, k21_sin_cos), [interesting(np__0.9), axiom, file(sin_cos, k21_sin_cos)]). thf(redefinition_k5_square_1, definition, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => ( (= @ (k5_square_1 @ A) ) @ (k3_square_1 @ A) ) ) ) , file(square_1, k5_square_1), [interesting(np__0.9), axiom, file(square_1, k5_square_1)]). thf(redefinition_k8_real_1, definition, (! [A: $i, B: $i] : ( ( ( (m1_subset_1 @ A) @ k1_numbers) & (v1_xreal_0 @ B) ) => ( (= @ ( (k8_real_1 @ A) @ B) ) @ ( (k3_xcmplx_0 @ A) @ B) ) ) ) , file(real_1, k8_real_1), [interesting(np__0.9), axiom, file(real_1, k8_real_1)]). thf(redefinition_k9_real_1, definition, (! [A: $i, B: $i] : ( ( ( (m1_subset_1 @ A) @ k1_numbers) & (v1_xreal_0 @ B) ) => ( (= @ ( (k9_real_1 @ A) @ B) ) @ ( (k6_xcmplx_0 @ A) @ B) ) ) ) , file(real_1, k9_real_1), [interesting(np__0.9), axiom, file(real_1, k9_real_1)]). thf(dt_k10_complex1, plain, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k2_numbers) => ( (m1_subset_1 @ (k10_complex1 @ A) ) @ k2_numbers) ) ) , file(complex1, k10_complex1), [interesting(np__0.9), axiom, file(complex1, k10_complex1)]). thf(dt_k13_complex1, plain, (! [A: $i, B: $i] : ( ( (v1_xcmplx_0 @ A) & (v1_xcmplx_0 @ B) ) => ( (m1_subset_1 @ ( (k13_complex1 @ A) @ B) ) @ k2_numbers) ) ) , file(complex1, k13_complex1), [interesting(np__0.9), axiom, file(complex1, k13_complex1)]). thf(dt_k18_sin_cos, plain, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => ( (m1_subset_1 @ (k18_sin_cos @ A) ) @ k1_numbers) ) ) , file(sin_cos, k18_sin_cos), [interesting(np__0.9), axiom, file(sin_cos, k18_sin_cos)]). thf(dt_k1_numbers, plain, $true, file(numbers, k1_numbers), [interesting(np__0.9), axiom, file(numbers, k1_numbers)]). thf(dt_k20_valued_1, plain, (! [A: $i, B: $i, C: $i, D: $i, E: $i] : ( ( (v3_membered @ B) & ( (v3_membered @ C) & ( ( (v1_funct_1 @ D) & ( (m1_subset_1 @ D) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ B) ) ) ) & ( (v1_funct_1 @ E) & ( (m1_subset_1 @ E) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ C) ) ) ) ) ) ) => ( (v1_funct_1 @ ( ( ( ( (k20_valued_1 @ A) @ B) @ C) @ D) @ E) ) & ( (m1_subset_1 @ ( ( ( ( (k20_valued_1 @ A) @ B) @ C) @ D) @ E) ) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ A) @ k1_numbers) ) ) ) ) ) , file(valued_1, k20_valued_1), [interesting(np__0.9), axiom, file(valued_1, k20_valued_1)]). thf(dt_k21_sin_cos, plain, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => ( (m1_subset_1 @ (k21_sin_cos @ A) ) @ k1_numbers) ) ) , file(sin_cos, k21_sin_cos), [interesting(np__0.9), axiom, file(sin_cos, k21_sin_cos)]). thf(dt_k30_sin_cos, plain, ( (v1_funct_1 @ k30_sin_cos) & ( (m1_subset_1 @ k30_sin_cos) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k1_numbers) @ k1_numbers) ) ) ) , file(sin_cos, k30_sin_cos), [interesting(np__0.9), axiom, file(sin_cos, k30_sin_cos)]). thf(dt_k5_square_1, plain, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => ( (m1_subset_1 @ (k5_square_1 @ A) ) @ k1_numbers) ) ) , file(square_1, k5_square_1), [interesting(np__0.9), axiom, file(square_1, k5_square_1)]). thf(dt_k8_real_1, plain, (! [A: $i, B: $i] : ( ( ( (m1_subset_1 @ A) @ k1_numbers) & (v1_xreal_0 @ B) ) => ( (m1_subset_1 @ ( (k8_real_1 @ A) @ B) ) @ k1_numbers) ) ) , file(real_1, k8_real_1), [interesting(np__0.9), axiom, file(real_1, k8_real_1)]). thf(dt_k9_diff_1, plain, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v3_valued_0 @ A) ) ) & ( (v1_xreal_0 @ B) & (v1_xreal_0 @ C) ) ) => ( (m1_subset_1 @ ( ( (k9_diff_1 @ A) @ B) @ C) ) @ k1_numbers) ) ) , file(diff_1, k9_diff_1), [interesting(np__0.9), axiom, file(diff_1, k9_diff_1)]). thf(dt_k9_real_1, plain, (! [A: $i, B: $i] : ( ( ( (m1_subset_1 @ A) @ k1_numbers) & (v1_xreal_0 @ B) ) => ( (m1_subset_1 @ ( (k9_real_1 @ A) @ B) ) @ k1_numbers) ) ) , file(real_1, k9_real_1), [interesting(np__0.9), axiom, file(real_1, k9_real_1)]). thf(dt_c1_6__diff_4, assumption, ( (m1_subset_1 @ c1_6__diff_4) @ k1_numbers) , introduced(assumption, [file(diff_4, c1_6__diff_4)]), [interesting(np__0.8), axiom, file(diff_4, c1_6__diff_4)]). thf(dt_c2_6__diff_4, assumption, ( (m1_subset_1 @ c2_6__diff_4) @ k1_numbers) , introduced(assumption, [file(diff_4, c2_6__diff_4)]), [interesting(np__0.8), axiom, file(diff_4, c2_6__diff_4)]). thf(fc1_numbers, theorem, ~ ( (v1_xboole_0 @ k1_numbers) ) , file(numbers, fc1_numbers), [interesting(np__0.9), axiom, file(numbers, fc1_numbers)]). thf(fc3_membered, theorem, (v3_membered @ k1_numbers) , file(membered, fc3_membered), [interesting(np__0.9), axiom, file(membered, fc3_membered)]). thf(fc56_membered, theorem, (v7_membered @ k1_numbers) , file(membered, fc56_membered), [interesting(np__0.9), axiom, file(membered, fc56_membered)]). thf(fc8_numbers, theorem, ~ ( (v1_finset_1 @ k1_numbers) ) , file(numbers, fc8_numbers), [interesting(np__0.9), axiom, file(numbers, fc8_numbers)]). thf(d27_sin_cos, definition, ( (= @ k30_sin_cos) @ ( ( ( (k3_rfunct_1 @ k1_numbers) @ k1_numbers) @ k19_sin_cos) @ k16_sin_cos) ) , file(sin_cos, d27_sin_cos), [interesting(np__0.9), axiom, file(sin_cos, d27_sin_cos)]). thf(d9_diff_1, definition, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v3_valued_0 @ A) ) ) => (! [B: $i] : ( (v1_xreal_0 @ B) => (! [C: $i] : ( (v1_xreal_0 @ C) => ( (= @ ( ( (k9_diff_1 @ A) @ B) @ C) ) @ ( (k10_real_1 @ ( (k9_real_1 @ ( (k1_seq_1 @ A) @ B) ) @ ( (k1_seq_1 @ A) @ C) ) ) @ ( (k6_xcmplx_0 @ B) @ C) ) ) ) ) ) ) ) ) , file(diff_1, d9_diff_1), [interesting(np__0.9), axiom, file(diff_1, d9_diff_1)]). thf(involutiveness_k1_real_1, theorem, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => ( (= @ (k1_real_1 @ (k1_real_1 @ A) ) ) @ A) ) ) , file(real_1, k1_real_1), [interesting(np__0.9), axiom, file(real_1, k1_real_1)]). thf(involutiveness_k2_real_1, theorem, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => ( (= @ (k2_real_1 @ (k2_real_1 @ A) ) ) @ A) ) ) , file(real_1, k2_real_1), [interesting(np__0.9), axiom, file(real_1, k2_real_1)]). thf(commutativity_k4_real_1, theorem, (! [A: $i, B: $i] : ( ( (v1_xreal_0 @ A) & ( (m1_subset_1 @ B) @ k1_numbers) ) => ( (= @ ( (k4_real_1 @ A) @ B) ) @ ( (k4_real_1 @ B) @ A) ) ) ) , file(real_1, k4_real_1), [interesting(np__0.9), axiom, file(real_1, k4_real_1)]). thf(commutativity_k7_real_1, theorem, (! [A: $i, B: $i] : ( ( ( (m1_subset_1 @ A) @ k1_numbers) & (v1_xreal_0 @ B) ) => ( (= @ ( (k7_real_1 @ A) @ B) ) @ ( (k7_real_1 @ B) @ A) ) ) ) , file(real_1, k7_real_1), [interesting(np__0.9), axiom, file(real_1, k7_real_1)]). thf(commutativity_k9_complex1, theorem, (! [A: $i, B: $i] : ( ( ( (m1_subset_1 @ A) @ k2_numbers) & ( (m1_subset_1 @ B) @ k2_numbers) ) => ( (= @ ( (k9_complex1 @ A) @ B) ) @ ( (k9_complex1 @ B) @ A) ) ) ) , file(complex1, k9_complex1), [interesting(np__0.9), axiom, file(complex1, k9_complex1)]). thf(redefinition_k1_real_1, definition, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => ( (= @ (k1_real_1 @ A) ) @ (k4_xcmplx_0 @ A) ) ) ) , file(real_1, k1_real_1), [interesting(np__0.9), axiom, file(real_1, k1_real_1)]). thf(redefinition_k2_real_1, definition, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => ( (= @ (k2_real_1 @ A) ) @ (k5_xcmplx_0 @ A) ) ) ) , file(real_1, k2_real_1), [interesting(np__0.9), axiom, file(real_1, k2_real_1)]). thf(redefinition_k3_funct_2, definition, (! [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), [interesting(np__0.9), axiom, file(funct_2, k3_funct_2)]). thf(redefinition_k4_real_1, definition, (! [A: $i, B: $i] : ( ( (v1_xreal_0 @ A) & ( (m1_subset_1 @ B) @ k1_numbers) ) => ( (= @ ( (k4_real_1 @ A) @ B) ) @ ( (k3_xcmplx_0 @ A) @ B) ) ) ) , file(real_1, k4_real_1), [interesting(np__0.9), axiom, file(real_1, k4_real_1)]). thf(redefinition_k7_real_1, definition, (! [A: $i, B: $i] : ( ( ( (m1_subset_1 @ A) @ k1_numbers) & (v1_xreal_0 @ B) ) => ( (= @ ( (k7_real_1 @ A) @ B) ) @ ( (k2_xcmplx_0 @ A) @ B) ) ) ) , file(real_1, k7_real_1), [interesting(np__0.9), axiom, file(real_1, k7_real_1)]). thf(redefinition_k9_complex1, definition, (! [A: $i, B: $i] : ( ( ( (m1_subset_1 @ A) @ k2_numbers) & ( (m1_subset_1 @ B) @ k2_numbers) ) => ( (= @ ( (k9_complex1 @ A) @ B) ) @ ( (k3_xcmplx_0 @ A) @ B) ) ) ) , file(complex1, k9_complex1), [interesting(np__0.9), axiom, file(complex1, k9_complex1)]). thf(dt_k1_real_1, plain, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => ( (m1_subset_1 @ (k1_real_1 @ A) ) @ k1_numbers) ) ) , file(real_1, k1_real_1), [interesting(np__0.9), axiom, file(real_1, k1_real_1)]). thf(dt_k2_real_1, plain, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => ( (m1_subset_1 @ (k2_real_1 @ A) ) @ k1_numbers) ) ) , file(real_1, k2_real_1), [interesting(np__0.9), axiom, file(real_1, k2_real_1)]). thf(dt_k2_sin_cos4, plain, (! [A: $i] : ( (v1_xreal_0 @ A) => ( (m1_subset_1 @ (k2_sin_cos4 @ A) ) @ k1_numbers) ) ) , file(sin_cos4, k2_sin_cos4), [interesting(np__0.9), axiom, file(sin_cos4, k2_sin_cos4)]). thf(dt_k3_funct_2, plain, (! [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), [interesting(np__0.9), axiom, file(funct_2, k3_funct_2)]). thf(dt_k4_real_1, plain, (! [A: $i, B: $i] : ( ( (v1_xreal_0 @ A) & ( (m1_subset_1 @ B) @ k1_numbers) ) => ( (m1_subset_1 @ ( (k4_real_1 @ A) @ B) ) @ k1_numbers) ) ) , file(real_1, k4_real_1), [interesting(np__0.9), axiom, file(real_1, k4_real_1)]). thf(dt_k7_real_1, plain, (! [A: $i, B: $i] : ( ( ( (m1_subset_1 @ A) @ k1_numbers) & (v1_xreal_0 @ B) ) => ( (m1_subset_1 @ ( (k7_real_1 @ A) @ B) ) @ k1_numbers) ) ) , file(real_1, k7_real_1), [interesting(np__0.9), axiom, file(real_1, k7_real_1)]). thf(dt_k9_complex1, plain, (! [A: $i, B: $i] : ( ( ( (m1_subset_1 @ A) @ k2_numbers) & ( (m1_subset_1 @ B) @ k2_numbers) ) => ( (m1_subset_1 @ ( (k9_complex1 @ A) @ B) ) @ k2_numbers) ) ) , file(complex1, k9_complex1), [interesting(np__0.9), axiom, file(complex1, k9_complex1)]). thf(rc3_valued_0, theorem, (? [A: $i] : ( ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k5_numbers) @ k5_numbers) ) ) & ( ~ ( (v1_xboole_0 @ A) ) & ( (v1_relat_1 @ A) & ( ( (v4_relat_1 @ A) @ k5_numbers) & ( ( (v5_relat_1 @ A) @ k5_numbers) & ( (v1_funct_1 @ A) & ( ( (v1_partfun1 @ A) @ k5_numbers) & ( ( ( (v1_funct_2 @ A) @ k5_numbers) @ k5_numbers) & ( (v1_valued_0 @ A) & ( (v2_valued_0 @ A) & ( (v3_valued_0 @ A) & ( (v4_valued_0 @ A) & (v5_valued_0 @ A) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(valued_0, rc3_valued_0), [interesting(np__0.9), axiom, file(valued_0, rc3_valued_0)]). thf(cc4_seq_2, theorem, (! [A: $i] : ( ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k5_numbers) @ k1_numbers) ) ) => ( ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k5_numbers) @ k1_numbers) & (v2_comseq_2 @ A) ) ) => ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k5_numbers) @ k1_numbers) & (v1_comseq_2 @ A) ) ) ) ) ) , file(seq_2, cc4_seq_2), [interesting(np__0.9), axiom, file(seq_2, cc4_seq_2)]). thf(fc5_seq_2, theorem, (! [A: $i, B: $i] : ( ( ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k5_numbers) @ k1_numbers) & ( (v2_comseq_2 @ A) & ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k5_numbers) @ k1_numbers) ) ) ) ) ) & ( (v1_funct_1 @ B) & ( ( ( (v1_funct_2 @ B) @ k5_numbers) @ k1_numbers) & ( (v2_comseq_2 @ B) & ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k5_numbers) @ k1_numbers) ) ) ) ) ) ) => ( (v1_funct_1 @ ( (k18_valued_1 @ A) @ B) ) & ( ( ( (v1_funct_2 @ ( (k18_valued_1 @ A) @ B) ) @ k5_numbers) @ k1_numbers) & (v2_comseq_2 @ ( (k18_valued_1 @ A) @ B) ) ) ) ) ) , file(seq_2, fc5_seq_2), [interesting(np__0.9), axiom, file(seq_2, fc5_seq_2)]). thf(dt_k4_ordinal1, plain, $true, file(ordinal1, k4_ordinal1), [interesting(np__0.9), axiom, file(ordinal1, k4_ordinal1)]). thf(cc31_valued_0, theorem, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v5_relat_1 @ A) @ k5_numbers) ) => ( (v1_relat_1 @ A) & (v4_valued_0 @ A) ) ) ) , file(valued_0, cc31_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc31_valued_0)]). thf(cc3_seq_2, theorem, (! [A: $i] : ( ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k5_numbers) @ k1_numbers) ) ) => ( ( (v1_funct_1 @ A) & ( (v3_funct_1 @ A) & ( ( (v1_funct_2 @ A) @ k5_numbers) @ k1_numbers) ) ) => ( (v1_funct_1 @ A) & ( ( ( (v1_funct_2 @ A) @ k5_numbers) @ k1_numbers) & (v2_comseq_2 @ A) ) ) ) ) ) , file(seq_2, cc3_seq_2), [interesting(np__0.9), axiom, file(seq_2, cc3_seq_2)]). thf(cc8_ordinal1, theorem, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k4_ordinal1) => (v7_ordinal1 @ A) ) ) , file(ordinal1, cc8_ordinal1), [interesting(np__0.9), axiom, file(ordinal1, cc8_ordinal1)]). thf(fc59_membered, theorem, (v7_membered @ k4_ordinal1) , file(membered, fc59_membered), [interesting(np__0.9), axiom, file(membered, fc59_membered)]). thf(fc6_membered, theorem, (v6_membered @ k4_ordinal1) , file(membered, fc6_membered), [interesting(np__0.9), axiom, file(membered, fc6_membered)]). thf(fc6_ordinal1, theorem, ( ~ ( (v1_xboole_0 @ k4_ordinal1) ) & (v3_ordinal1 @ k4_ordinal1) ) , file(ordinal1, fc6_ordinal1), [interesting(np__0.9), axiom, file(ordinal1, fc6_ordinal1)]). thf(rc1_seq_2, theorem, (? [A: $i] : ( ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k5_numbers) @ k1_numbers) ) ) & ( ~ ( (v1_xboole_0 @ A) ) & ( (v1_relat_1 @ A) & ( ( (v4_relat_1 @ A) @ k5_numbers) & ( ( (v5_relat_1 @ A) @ k1_numbers) & ( (v1_funct_1 @ A) & ( (v3_funct_1 @ A) & ( ( (v1_partfun1 @ A) @ k5_numbers) & ( ( ( (v1_funct_2 @ A) @ k5_numbers) @ k1_numbers) & ( (v1_valued_0 @ A) & ( (v2_valued_0 @ A) & (v3_valued_0 @ A) ) ) ) ) ) ) ) ) ) ) ) ) , file(seq_2, rc1_seq_2), [interesting(np__0.9), axiom, file(seq_2, rc1_seq_2)]). thf(rc2_valued_1, theorem, (? [A: $i] : ( (v1_relat_1 @ A) & ( ( (v4_relat_1 @ A) @ k5_numbers) & ( (v1_funct_1 @ A) & ~ ( (v1_xboole_0 @ A) ) ) ) ) ) , file(valued_1, rc2_valued_1), [interesting(np__0.9), axiom, file(valued_1, rc2_valued_1)]). thf(rc3_valued_1, theorem, (? [A: $i] : ( (v1_relat_1 @ A) & ( ( (v4_relat_1 @ A) @ k5_numbers) & ( (v1_funct_1 @ A) & ( ~ ( (v1_xboole_0 @ A) ) & (v1_finset_1 @ A) ) ) ) ) ) , file(valued_1, rc3_valued_1), [interesting(np__0.9), axiom, file(valued_1, rc3_valued_1)]). thf(rc4_valued_0, theorem, (! [A: $i] : (? [B: $i] : ( ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ ( (k2_zfmisc_1 @ k5_numbers) @ A) ) ) & ( (v1_relat_1 @ B) & ( ( (v4_relat_1 @ B) @ k5_numbers) & ( ( (v5_relat_1 @ B) @ A) & ( (v1_funct_1 @ B) & ( (v3_funct_1 @ B) & ( ( (v1_funct_2 @ B) @ k5_numbers) @ A) ) ) ) ) ) ) ) ) , file(valued_0, rc4_valued_0), [interesting(np__0.9), axiom, file(valued_0, rc4_valued_0)]). thf(spc3_arithm, theorem, (! [A: $i] : ( (v1_xcmplx_0 @ A) => ( (= @ ( (k7_xcmplx_0 @ np__1) @ A) ) @ (k5_xcmplx_0 @ A) ) ) ) , file(arithm, spc3_arithm), [interesting(np__0.9), axiom, file(arithm, spc3_arithm)]). thf(t1_numerals, theorem, ( (m1_subset_1 @ k1_xboole_0) @ k4_ordinal1) , file(numerals, t1_numerals), [interesting(np__0.9), axiom, file(numerals, t1_numerals)]). thf(existence_m2_subset_1, plain, (! [A: $i, B: $i] : ( ( ~ ( (v1_xboole_0 @ A) ) & ( ~ ( (v1_xboole_0 @ B) ) & ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) ) ) => (? [C: $i] : ( ( (m2_subset_1 @ C) @ A) @ B) ) ) ) , file(subset_1, m2_subset_1), [interesting(np__0.9), axiom, file(subset_1, m2_subset_1)]). thf(redefinition_k5_numbers, definition, ( (= @ k5_numbers) @ k4_ordinal1) , file(numbers, k5_numbers), [interesting(np__0.9), axiom, file(numbers, k5_numbers)]). thf(redefinition_m2_subset_1, definition, (! [A: $i, B: $i] : ( ( ~ ( (v1_xboole_0 @ A) ) & ( ~ ( (v1_xboole_0 @ B) ) & ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) ) ) => (! [C: $i] : ( ( ( (m2_subset_1 @ C) @ A) @ B) <=> ( (m1_subset_1 @ C) @ B) ) ) ) ) , file(subset_1, m2_subset_1), [interesting(np__0.9), axiom, file(subset_1, m2_subset_1)]). thf(dt_k5_numbers, plain, ( (m1_subset_1 @ k5_numbers) @ (k1_zfmisc_1 @ k1_numbers) ) , file(numbers, k5_numbers), [interesting(np__0.9), axiom, file(numbers, k5_numbers)]). thf(dt_m2_subset_1, plain, (! [A: $i, B: $i] : ( ( ~ ( (v1_xboole_0 @ A) ) & ( ~ ( (v1_xboole_0 @ B) ) & ( (m1_subset_1 @ B) @ (k1_zfmisc_1 @ A) ) ) ) => (! [C: $i] : ( ( ( (m2_subset_1 @ C) @ A) @ B) => ( (m1_subset_1 @ C) @ A) ) ) ) ) , file(subset_1, m2_subset_1), [interesting(np__0.9), axiom, file(subset_1, m2_subset_1)]). thf(cc11_membered, theorem, (! [A: $i] : ( ( (m1_subset_1 @ A) @ (k1_zfmisc_1 @ k5_numbers) ) => (v6_membered @ A) ) ) , file(membered, cc11_membered), [interesting(np__0.9), axiom, file(membered, cc11_membered)]). thf(cc25_membered, theorem, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k5_numbers) => (v6_membered @ A) ) ) , file(membered, cc25_membered), [interesting(np__0.9), axiom, file(membered, cc25_membered)]). thf(rqRealAdd__k2_xcmplx_0__r0_r0_r0, theorem, ( (= @ ( (k2_xcmplx_0 @ np__0) @ np__0) ) @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r0_r0), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r0_r0_r0)]). thf(rqRealAdd__k2_xcmplx_0__r0_r1_r1, theorem, ( (= @ ( (k2_xcmplx_0 @ np__0) @ np__1) ) @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r1_r1), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r0_r1_r1)]). thf(rqRealAdd__k2_xcmplx_0__r0_r2_r2, theorem, ( (= @ ( (k2_xcmplx_0 @ np__0) @ np__2) ) @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r2_r2), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r0_r2_r2)]). thf(rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, theorem, ( (= @ ( (k2_xcmplx_0 @ np__0) @ (k4_xcmplx_0 @ np__1) ) ) @ (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1)]). thf(rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, theorem, ( (= @ ( (k2_xcmplx_0 @ np__0) @ (k4_xcmplx_0 @ np__2) ) ) @ (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2)]). thf(rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2)]). thf(rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2)]). thf(rqRealAdd__k2_xcmplx_0__r1_r0_r1, theorem, ( (= @ ( (k2_xcmplx_0 @ np__1) @ np__0) ) @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r0_r1), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r1_r0_r1)]). thf(rqRealAdd__k2_xcmplx_0__r1_r1_r2, theorem, ( (= @ ( (k2_xcmplx_0 @ np__1) @ np__1) ) @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r1_r2), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r1_r1_r2)]). thf(rqRealAdd__k2_xcmplx_0__r1_rm1_r0, theorem, ( (= @ ( (k2_xcmplx_0 @ np__1) @ (k4_xcmplx_0 @ np__1) ) ) @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm1_r0), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm1_r0)]). thf(rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, theorem, ( (= @ ( (k2_xcmplx_0 @ np__1) @ (k4_xcmplx_0 @ np__2) ) ) @ (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1)]). thf(rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2)]). thf(rqRealAdd__k2_xcmplx_0__r2_r0_r2, theorem, ( (= @ ( (k2_xcmplx_0 @ np__2) @ np__0) ) @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_r0_r2), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r2_r0_r2)]). thf(rqRealAdd__k2_xcmplx_0__r2_rm1_r1, theorem, ( (= @ ( (k2_xcmplx_0 @ np__2) @ (k4_xcmplx_0 @ np__1) ) ) @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm1_r1), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm1_r1)]). thf(rqRealAdd__k2_xcmplx_0__r2_rm2_r0, theorem, ( (= @ ( (k2_xcmplx_0 @ np__2) @ (k4_xcmplx_0 @ np__2) ) ) @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm2_r0), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm2_r0)]). thf(rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, theorem, ( (= @ ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__0) ) @ (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1)]). thf(rqRealAdd__k2_xcmplx_0__rm1_r1_r0, theorem, ( (= @ ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__1) ) @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r1_r0), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r1_r0)]). thf(rqRealAdd__k2_xcmplx_0__rm1_r2_r1, theorem, ( (= @ ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__2) ) @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r2_r1), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r2_r1)]). thf(rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2)]). thf(rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2)]). thf(rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, theorem, ( (= @ ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__1) ) @ (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1)]). thf(rqRealAdd__k2_xcmplx_0__rm2_r2_r0, theorem, ( (= @ ( (k2_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__2) ) @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r2_r0), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r2_r0)]). thf(rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2)]). thf(rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2)]). thf(rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1)]). thf(rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0)]). thf(rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2)]). thf(rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0)]). thf(rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1)]). thf(rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2)]). thf(rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2)]). thf(rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2)]). thf(rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2)]). thf(rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2)]). thf(rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2)]). thf(rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0)]). thf(rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1)]). thf(rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2)]). thf(rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2)]). thf(rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1)]). thf(rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0)]). thf(rqRealDiv__k7_xcmplx_0__r1_r1_r1, theorem, ( (= @ ( (k7_xcmplx_0 @ np__1) @ np__1) ) @ np__1) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_r1_r1), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__r1_r1_r1)]). thf(rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, theorem, ( (= @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2)]). thf(rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, theorem, ( (= @ ( (k7_xcmplx_0 @ np__1) @ (k4_xcmplx_0 @ np__1) ) ) @ (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1)]). thf(rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2)]). thf(rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, theorem, ( (= @ ( (k7_xcmplx_0 @ np__1) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) ) @ np__2) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2)]). thf(rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2)]). thf(rqRealDiv__k7_xcmplx_0__r2_r1_r2, theorem, ( (= @ ( (k7_xcmplx_0 @ np__2) @ np__1) ) @ np__2) , file(arithm, rqRealDiv__k7_xcmplx_0__r2_r1_r2), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__r2_r1_r2)]). thf(rqRealDiv__k7_xcmplx_0__r2_r2_r1, theorem, ( (= @ ( (k7_xcmplx_0 @ np__2) @ np__2) ) @ np__1) , file(arithm, rqRealDiv__k7_xcmplx_0__r2_r2_r1), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__r2_r2_r1)]). thf(rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, theorem, ( (= @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__1) ) @ (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1)]). thf(rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2)]). thf(rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, theorem, ( (= @ ( (k7_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__2) ) @ (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1)]). thf(rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1, theorem, ( (= @ ( (k7_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, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1)]). thf(rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, theorem, ( (= @ ( (k3_xcmplx_0 @ np__0) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) ) @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0)]). thf(rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2)]). thf(rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2)]). thf(rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, theorem, ( (= @ ( (k3_xcmplx_0 @ np__2) @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) ) @ np__1) , file(arithm, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1)]). thf(rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1)]). thf(rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1)]). thf(rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1)]). thf(rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, theorem, ( (= @ ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ np__0) ) @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0)]). thf(rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2)]). thf(rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, theorem, ( (= @ ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ np__1) @ np__2) ) @ np__2) ) @ np__1) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1)]). thf(rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1)]). thf(rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2)]). thf(rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1)]). thf(rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1)]). thf(rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, theorem, ( (= @ (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), [interesting(np__0.9), axiom, file(arithm, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2)]). thf(rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, theorem, ( (= @ (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), [interesting(np__0.9), axiom, file(arithm, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2)]). thf(spc2_arithm, theorem, (! [A: $i] : ( (v1_xcmplx_0 @ A) => ( (= @ ( (k3_xcmplx_0 @ A) @ (k4_xcmplx_0 @ np__1) ) ) @ (k4_xcmplx_0 @ A) ) ) ) , file(arithm, spc2_arithm), [interesting(np__0.9), axiom, file(arithm, spc2_arithm)]). thf(t3_arithm, theorem, (! [A: $i] : ( (v1_xcmplx_0 @ A) => ( (= @ ( (k3_xcmplx_0 @ np__1) @ A) ) @ A) ) ) , file(arithm, t3_arithm), [interesting(np__0.9), axiom, file(arithm, t3_arithm)]). thf(t6_arithm, theorem, (! [A: $i] : ( (v1_xcmplx_0 @ A) => ( (= @ ( (k7_xcmplx_0 @ A) @ np__1) ) @ A) ) ) , file(arithm, t6_arithm), [interesting(np__0.9), axiom, file(arithm, t6_arithm)]). thf(rqRealDiff__k6_xcmplx_0__r0_r0_r0, theorem, ( (= @ ( (k6_xcmplx_0 @ np__0) @ np__0) ) @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r0_r0), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r0_r0_r0)]). thf(rqRealDiff__k6_xcmplx_0__r0_r1_rm1, theorem, ( (= @ ( (k6_xcmplx_0 @ np__0) @ np__1) ) @ (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r1_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r0_r1_rm1)]). thf(rqRealDiff__k6_xcmplx_0__r0_r2_rm2, theorem, ( (= @ ( (k6_xcmplx_0 @ np__0) @ np__2) ) @ (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r2_rm2), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r0_r2_rm2)]). thf(rqRealDiff__k6_xcmplx_0__r0_rm1_r1, theorem, ( (= @ ( (k6_xcmplx_0 @ np__0) @ (k4_xcmplx_0 @ np__1) ) ) @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm1_r1), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm1_r1)]). thf(rqRealDiff__k6_xcmplx_0__r0_rm2_r2, theorem, ( (= @ ( (k6_xcmplx_0 @ np__0) @ (k4_xcmplx_0 @ np__2) ) ) @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm2_r2), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm2_r2)]). thf(rqRealDiff__k6_xcmplx_0__r1_r0_r1, theorem, ( (= @ ( (k6_xcmplx_0 @ np__1) @ np__0) ) @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r0_r1), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r1_r0_r1)]). thf(rqRealDiff__k6_xcmplx_0__r1_r2_rm1, theorem, ( (= @ ( (k6_xcmplx_0 @ np__1) @ np__2) ) @ (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r2_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r1_r2_rm1)]). thf(rqRealDiff__k6_xcmplx_0__r2_r0_r2, theorem, ( (= @ ( (k6_xcmplx_0 @ np__2) @ np__0) ) @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r0_r2), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r2_r0_r2)]). thf(rqRealDiff__k6_xcmplx_0__r2_r1_r1, theorem, ( (= @ ( (k6_xcmplx_0 @ np__2) @ np__1) ) @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r1_r1), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r2_r1_r1)]). thf(rqRealDiff__k6_xcmplx_0__r2_r2_r0, theorem, ( (= @ ( (k6_xcmplx_0 @ np__2) @ np__2) ) @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r2_r0), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r2_r2_r0)]). thf(rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, theorem, ( (= @ ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__0) ) @ (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1)]). thf(rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, theorem, ( (= @ ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ (k4_xcmplx_0 @ np__2) ) ) @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1)]). thf(rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, theorem, ( (= @ ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__0) ) @ (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2)]). thf(rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, theorem, ( (= @ ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1)]). thf(rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, theorem, ( (= @ ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ (k4_xcmplx_0 @ np__2) ) ) @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0)]). thf(rqRealMult__k3_xcmplx_0__r0_r0_r0, theorem, ( (= @ ( (k3_xcmplx_0 @ np__0) @ np__0) ) @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_r0_r0), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r0_r0_r0)]). thf(rqRealMult__k3_xcmplx_0__r0_r1_r0, theorem, ( (= @ ( (k3_xcmplx_0 @ np__0) @ np__1) ) @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_r1_r0), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r0_r1_r0)]). thf(rqRealMult__k3_xcmplx_0__r0_r2_r0, theorem, ( (= @ ( (k3_xcmplx_0 @ np__0) @ np__2) ) @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_r2_r0), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r0_r2_r0)]). thf(rqRealMult__k3_xcmplx_0__r0_rm2_r0, theorem, ( (= @ ( (k3_xcmplx_0 @ np__0) @ (k4_xcmplx_0 @ np__2) ) ) @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_rm2_r0), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r0_rm2_r0)]). thf(rqRealMult__k3_xcmplx_0__r1_r0_r0, theorem, ( (= @ ( (k3_xcmplx_0 @ np__1) @ np__0) ) @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r1_r0_r0), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r1_r0_r0)]). thf(rqRealMult__k3_xcmplx_0__r1_r2_r2, theorem, ( (= @ ( (k3_xcmplx_0 @ np__1) @ np__2) ) @ np__2) , file(arithm, rqRealMult__k3_xcmplx_0__r1_r2_r2), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r1_r2_r2)]). thf(rqRealMult__k3_xcmplx_0__r1_rm2_rm2, theorem, ( (= @ ( (k3_xcmplx_0 @ np__1) @ (k4_xcmplx_0 @ np__2) ) ) @ (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__r1_rm2_rm2), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r1_rm2_rm2)]). thf(rqRealMult__k3_xcmplx_0__r2_r0_r0, theorem, ( (= @ ( (k3_xcmplx_0 @ np__2) @ np__0) ) @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r2_r0_r0), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r2_r0_r0)]). thf(rqRealMult__k3_xcmplx_0__r2_r1_r2, theorem, ( (= @ ( (k3_xcmplx_0 @ np__2) @ np__1) ) @ np__2) , file(arithm, rqRealMult__k3_xcmplx_0__r2_r1_r2), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r2_r1_r2)]). thf(rqRealMult__k3_xcmplx_0__rm2_r0_r0, theorem, ( (= @ ( (k3_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__0) ) @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__rm2_r0_r0), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rm2_r0_r0)]). thf(rqRealMult__k3_xcmplx_0__rm2_r1_rm2, theorem, ( (= @ ( (k3_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) @ np__1) ) @ (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rm2_r1_rm2), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rm2_r1_rm2)]). thf(rqRealNeg__k4_xcmplx_0__r0_r0, theorem, ( (= @ (k4_xcmplx_0 @ np__0) ) @ np__0) , file(arithm, rqRealNeg__k4_xcmplx_0__r0_r0), [interesting(np__0.9), axiom, file(arithm, rqRealNeg__k4_xcmplx_0__r0_r0)]). thf(rqRealNeg__k4_xcmplx_0__r2_rm2, theorem, ( (= @ (k4_xcmplx_0 @ np__2) ) @ (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r2_rm2), [interesting(np__0.9), axiom, file(arithm, rqRealNeg__k4_xcmplx_0__r2_rm2)]). thf(rqRealNeg__k4_xcmplx_0__rm2_r2, theorem, ( (= @ (k4_xcmplx_0 @ (k4_xcmplx_0 @ np__2) ) ) @ np__2) , file(arithm, rqRealNeg__k4_xcmplx_0__rm2_r2), [interesting(np__0.9), axiom, file(arithm, rqRealNeg__k4_xcmplx_0__rm2_r2)]). thf(spc0_numerals, theorem, ( ( ( (m2_subset_1 @ np__0) @ k1_numbers) @ k5_numbers) & ( ( (m1_subset_1 @ np__0) @ k5_numbers) & ( (m1_subset_1 @ np__0) @ k1_numbers) ) ) , file(numerals, spc0_numerals), [interesting(np__0.9), axiom, file(numerals, spc0_numerals)]). thf(spc1_numerals, theorem, ( ( (v2_xxreal_0 @ np__1) & ( ( (m2_subset_1 @ np__1) @ k1_numbers) @ k5_numbers) ) & ( ( (m1_subset_1 @ np__1) @ k5_numbers) & ( (m1_subset_1 @ np__1) @ k1_numbers) ) ) , file(numerals, spc1_numerals), [interesting(np__0.9), axiom, file(numerals, spc1_numerals)]). thf(spc2_numerals, theorem, ( ( (v2_xxreal_0 @ np__2) & ( ( (m2_subset_1 @ np__2) @ k1_numbers) @ k5_numbers) ) & ( ( (m1_subset_1 @ np__2) @ k5_numbers) & ( (m1_subset_1 @ np__2) @ k1_numbers) ) ) , file(numerals, spc2_numerals), [interesting(np__0.9), axiom, file(numerals, spc2_numerals)]). thf(spc0_boole, theorem, (v1_xboole_0 @ np__0) , file(boole, spc0_boole), [interesting(np__0.9), axiom, file(boole, spc0_boole)]). thf(spc1_boole, theorem, ~ ( (v1_xboole_0 @ np__1) ) , file(boole, spc1_boole), [interesting(np__0.9), axiom, file(boole, spc1_boole)]). thf(spc2_boole, theorem, ~ ( (v1_xboole_0 @ np__2) ) , file(boole, spc2_boole), [interesting(np__0.9), axiom, file(boole, spc2_boole)]). thf(t5_valued_1, theorem, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) => (! [B: $i] : ( ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v1_valued_0 @ B) ) ) => (! [C: $i] : ( (= @ ( (k1_funct_1 @ ( (k18_valued_1 @ A) @ B) ) @ C) ) @ ( (k3_xcmplx_0 @ ( (k1_funct_1 @ A) @ C) ) @ ( (k1_funct_1 @ B) @ C) ) ) ) ) ) ) ) , file(valued_1, t5_valued_1), [interesting(np__0.9), axiom, file(valued_1, t5_valued_1)]). thf(rqRealMult__k3_xcmplx_0__r1_r1_r1, theorem, ( (= @ ( (k3_xcmplx_0 @ np__1) @ np__1) ) @ np__1) , file(arithm, rqRealMult__k3_xcmplx_0__r1_r1_r1), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r1_r1_r1)]). thf(rqRealNeg__k4_xcmplx_0__r1_rm1, theorem, ( (= @ (k4_xcmplx_0 @ np__1) ) @ (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r1_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealNeg__k4_xcmplx_0__r1_rm1)]). thf(rqRealNeg__k4_xcmplx_0__rm1_r1, theorem, ( (= @ (k4_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) ) @ np__1) , file(arithm, rqRealNeg__k4_xcmplx_0__rm1_r1), [interesting(np__0.9), axiom, file(arithm, rqRealNeg__k4_xcmplx_0__rm1_r1)]). thf(rqRealDiff__k6_xcmplx_0__r1_r1_r0, theorem, ( (= @ ( (k6_xcmplx_0 @ np__1) @ np__1) ) @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r1_r0), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r1_r1_r0)]). thf(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, theorem, ( (= @ ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ (k4_xcmplx_0 @ np__1) ) ) @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0)]). thf(rqRealDiff__k6_xcmplx_0__r1_rm1_r2, theorem, ( (= @ ( (k6_xcmplx_0 @ np__1) @ (k4_xcmplx_0 @ np__1) ) ) @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_rm1_r2), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r1_rm1_r2)]). thf(rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, theorem, ( (= @ ( (k6_xcmplx_0 @ (k4_xcmplx_0 @ np__1) ) @ np__1) ) @ (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2)]). thf(e1_6_1__diff_4, plain, ( (= @ ( ( (k9_diff_1 @ ( ( ( ( (k20_valued_1 @ k1_numbers) @ k1_numbers) @ k1_numbers) @ k30_sin_cos) @ k30_sin_cos) ) @ c1_6__diff_4) @ c2_6__diff_4) ) @ ( (k13_complex1 @ ( (k9_real_1 @ ( (k8_real_1 @ ( (k1_seq_1 @ k30_sin_cos) @ c1_6__diff_4) ) @ ( (k1_seq_1 @ k30_sin_cos) @ c1_6__diff_4) ) ) @ ( (k1_seq_1 @ ( ( ( ( (k20_valued_1 @ k1_numbers) @ k1_numbers) @ k1_numbers) @ k30_sin_cos) @ k30_sin_cos) ) @ c2_6__diff_4) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) , inference(mizar_by, [status(thm), assumptions([dt_c1_6__diff_4, dt_c2_6__diff_4])], [cc10_valued_2, cc15_valued_2, cc16_valued_2, cc21_valued_2, cc28_valued_2, cc29_valued_2, cc7_valued_2, cc8_valued_2, cc9_valued_2, fc14_valued_2, fc15_valued_2, fc16_valued_2, fc17_valued_2, fc40_valued_2, fc41_valued_2, fc42_valued_2, fc43_valued_2, cc11_valued_2, cc17_valued_2, cc25_valued_2, cc26_valued_2, cc30_valued_2, cc4_valued_2, cc5_valued_2, fc18_valued_2, fc44_valued_2, cc12_valued_2, cc15_membered, cc18_valued_2, cc19_valued_0, cc22_membered, cc23_valued_0, cc24_valued_0, cc24_valued_2, cc2_seq_2, cc31_valued_2, cc3_membered, cc3_valued_2, fc19_valued_2, fc40_valued_1, fc45_valued_2, fc88_valued_0, rc3_valued_0, dt_k3_numbers, dt_k4_numbers, dt_o_0_0_xboole_0, cc10_membered, cc13_valued_0, cc13_valued_2, cc14_valued_0, cc16_membered, cc19_valued_2, cc1_int_1, cc1_seq_2, cc20_valued_0, cc22_valued_0, cc23_membered, cc23_valued_2, cc2_membered, cc2_ordinal1, cc2_valued_0, cc2_valued_2, cc32_valued_2, cc3_int_1, cc3_valued_0, cc4_seq_2, cc4_valued_0, cc6_funct_1, cc9_membered, fc17_rfunct_1, fc1_int_1, fc20_valued_2, fc2_int_1, fc35_valued_1, fc36_valued_1, fc3_int_1, fc3_numbers, fc41_valued_1, fc46_valued_2, fc4_int_1, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc5_seq_2, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc89_valued_0, rc1_int_1, rc2_int_1, rc2_ordinal1, rc2_valued_0, rc5_valued_1, involutiveness_k5_xcmplx_0, reflexivity_r1_tarski, antisymmetry_r2_hidden, dt_k1_rfunct_1, dt_k1_xboole_0, dt_k4_ordinal1, dt_k5_xcmplx_0, cc10_ordinal1, cc11_valued_0, cc12_membered, cc13_membered, cc14_valued_2, cc15_valued_0, cc16_valued_0, cc17_membered, cc17_valued_0, cc19_membered, cc1_funct_2, cc1_membered, cc1_ordinal1, cc1_rfunct_1, cc1_valued_0, cc1_valued_2, cc20_membered, cc20_valued_2, cc21_valued_0, cc22_valued_2, cc24_membered, cc28_valued_0, cc2_funct_2, cc2_int_1, cc2_xcmplx_0, cc2_xreal_0, cc2_xxreal_0, cc30_valued_0, cc31_valued_0, cc33_valued_2, cc3_funct_2, cc3_seq_2, cc3_xxreal_0, cc4_funct_2, cc4_xxreal_0, cc5_funct_1, cc5_ordinal1, cc5_relat_1, cc5_xxreal_0, cc6_ordinal1, cc6_relat_1, cc6_xxreal_0, cc7_relat_1, cc7_valued_0, cc7_xxreal_0, cc8_funct_1, cc8_funct_2, cc8_ordinal1, cc8_relat_1, cc8_valued_0, cc8_xxreal_0, cc9_funct_1, fc11_xreal_0, fc127_valued_1, fc12_xreal_0, fc131_valued_1, fc13_xreal_0, fc14_xreal_0, fc16_xreal_0, fc17_funct_1, fc17_xreal_0, fc18_xreal_0, fc19_funct_1, fc1_rfunct_1, fc1_xboole_0, fc20_rfunct_1, fc21_valued_2, fc21_xreal_0, fc22_xreal_0, fc23_xreal_0, fc24_xreal_0, fc26_xreal_0, fc27_xreal_0, fc28_xreal_0, fc29_xreal_0, fc2_rfunct_1, fc30_xreal_0, fc31_xreal_0, fc32_xreal_0, fc33_xreal_0, fc37_valued_1, fc38_valued_1, fc39_valued_1, fc42_valued_1, fc47_valued_2, fc4_xreal_0, fc59_membered, fc62_valued_0, fc66_valued_0, fc6_membered, fc6_ordinal1, fc7_xcmplx_0, fc85_valued_0, fc86_valued_0, fc90_valued_0, fc9_xreal_0, rc1_funct_2, rc1_membered, rc1_ordinal1, rc1_partfun1, rc1_relset_1, rc1_seq_2, rc1_valued_0, rc1_valued_2, rc1_xxreal_0, rc2_funct_1, rc2_membered, rc2_relat_1, rc2_valued_1, rc2_valued_2, rc2_xreal_0, rc2_xxreal_0, rc3_funct_1, rc3_membered, rc3_ordinal1, rc3_partfun1, rc3_relat_1, rc3_valued_1, rc3_xreal_0, rc3_xxreal_0, rc4_funct_1, rc4_ordinal1, rc4_valued_0, rc4_xreal_0, rc4_xxreal_0, rc5_funct_1, rc5_ordinal1, rc6_funct_1, rc6_valued_0, rc7_funct_1, rc9_funct_1, spc10_arithm, spc11_arithm, spc12_arithm, spc3_arithm, t1_numerals, t1_subset, t4_subset, t5_subset, d2_xboole_0, commutativity_k2_xcmplx_0, existence_m1_subset_1, existence_m2_subset_1, redefinition_k10_real_1, redefinition_k3_rfunct_1, redefinition_k5_numbers, redefinition_m2_subset_1, dt_k10_real_1, dt_k16_sin_cos, dt_k19_sin_cos, dt_k1_zfmisc_1, dt_k2_numbers, dt_k2_xcmplx_0, dt_k2_zfmisc_1, dt_k3_rfunct_1, dt_k5_numbers, dt_k7_xcmplx_0, dt_m1_subset_1, dt_m2_subset_1, cc10_valued_0, cc11_membered, cc12_valued_0, cc14_membered, cc18_membered, cc18_valued_0, cc1_funct_1, cc1_partfun1, cc1_relat_1, cc1_relset_1, cc1_xcmplx_0, cc1_xreal_0, cc21_membered, cc25_membered, cc26_membered, cc27_valued_2, cc2_funct_1, cc2_partfun1, cc2_relat_1, cc2_relset_1, cc3_funct_1, cc3_ordinal1, cc3_relat_1, cc3_relset_1, cc3_xcmplx_0, cc3_xreal_0, cc4_funct_1, cc4_membered, cc4_ordinal1, cc4_relat_1, cc4_relset_1, cc4_xreal_0, cc5_membered, cc5_valued_0, cc6_membered, cc6_valued_0, cc6_valued_2, cc7_funct_1, cc7_ordinal1, cc8_membered, cc9_ordinal1, cc9_valued_0, fc10_xreal_0, fc15_xreal_0, fc19_xreal_0, fc1_membered, fc20_xreal_0, fc25_xreal_0, fc2_numbers, fc2_xcmplx_0, fc34_valued_1, fc34_xreal_0, fc3_xcmplx_0, fc3_xreal_0, fc4_xcmplx_0, fc55_membered, fc5_xcmplx_0, fc5_xreal_0, fc63_valued_0, fc6_relat_1, fc6_sin_cos, fc6_xcmplx_0, fc6_xreal_0, fc7_sin_cos, fc7_xreal_0, fc87_valued_0, fc8_xcmplx_0, fc8_xreal_0, fc9_numbers, fc9_xcmplx_0, rc1_relat_1, rc1_xboole_0, rc1_xcmplx_0, rc1_xreal_0, rc2_xboole_0, rc2_xcmplx_0, rqRealAdd__k2_xcmplx_0__r0_r0_r0, rqRealAdd__k2_xcmplx_0__r0_r1_r1, rqRealAdd__k2_xcmplx_0__r0_r2_r2, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__r1_r0_r1, rqRealAdd__k2_xcmplx_0__r1_r1_r2, rqRealAdd__k2_xcmplx_0__r1_rm1_r0, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r2_r0_r2, rqRealAdd__k2_xcmplx_0__r2_rm1_r1, rqRealAdd__k2_xcmplx_0__r2_rm2_r0, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, rqRealAdd__k2_xcmplx_0__rm1_r1_r0, rqRealAdd__k2_xcmplx_0__rm1_r2_r1, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, rqRealAdd__k2_xcmplx_0__rm2_r2_r0, rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, rqRealDiv__k7_xcmplx_0__r1_r1_r1, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, rqRealDiv__k7_xcmplx_0__r2_r1_r2, rqRealDiv__k7_xcmplx_0__r2_r2_r1, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, spc1_arithm, spc2_arithm, spc4_arithm, spc5_arithm, spc6_arithm, spc7_arithm, spc8_arithm, spc9_arithm, t2_subset, t3_arithm, t3_subset, t6_arithm, t6_boole, t7_boole, t8_boole, d9_xcmplx_0, commutativity_k18_valued_1, commutativity_k20_valued_1, commutativity_k3_xcmplx_0, involutiveness_k4_xcmplx_0, commutativity_k8_real_1, redefinition_k13_complex1, redefinition_k1_seq_1, redefinition_k20_valued_1, redefinition_k8_real_1, redefinition_k9_real_1, dt_k13_complex1, dt_k18_valued_1, dt_k1_funct_1, dt_k1_numbers, dt_k1_seq_1, dt_k20_valued_1, dt_k30_sin_cos, dt_k3_xcmplx_0, dt_k4_xcmplx_0, dt_k6_xcmplx_0, dt_k8_real_1, dt_k9_diff_1, dt_k9_real_1, dt_c1_6__diff_4, dt_c2_6__diff_4, fc1_numbers, fc33_valued_1, fc3_membered, fc56_membered, fc61_valued_0, fc8_numbers, rc1_funct_1, rqRealDiff__k6_xcmplx_0__r0_r0_r0, rqRealDiff__k6_xcmplx_0__r0_r1_rm1, rqRealDiff__k6_xcmplx_0__r0_r2_rm2, rqRealDiff__k6_xcmplx_0__r0_rm1_r1, rqRealDiff__k6_xcmplx_0__r0_rm2_r2, rqRealDiff__k6_xcmplx_0__r1_r0_r1, rqRealDiff__k6_xcmplx_0__r1_r2_rm1, rqRealDiff__k6_xcmplx_0__r2_r0_r2, rqRealDiff__k6_xcmplx_0__r2_r1_r1, rqRealDiff__k6_xcmplx_0__r2_r2_r0, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, rqRealMult__k3_xcmplx_0__r0_r0_r0, rqRealMult__k3_xcmplx_0__r0_r1_r0, rqRealMult__k3_xcmplx_0__r0_r2_r0, rqRealMult__k3_xcmplx_0__r0_rm2_r0, rqRealMult__k3_xcmplx_0__r1_r0_r0, rqRealMult__k3_xcmplx_0__r1_r2_r2, rqRealMult__k3_xcmplx_0__r1_rm2_rm2, rqRealMult__k3_xcmplx_0__r2_r0_r0, rqRealMult__k3_xcmplx_0__r2_r1_r2, rqRealMult__k3_xcmplx_0__rm2_r0_r0, rqRealMult__k3_xcmplx_0__rm2_r1_rm2, rqRealNeg__k4_xcmplx_0__r0_r0, rqRealNeg__k4_xcmplx_0__r2_rm2, rqRealNeg__k4_xcmplx_0__rm2_r2, d27_sin_cos, d8_xcmplx_0, d9_diff_1, spc0_numerals, spc1_numerals, spc2_numerals, spc0_boole, spc1_boole, spc2_boole, t5_valued_1, rqRealMult__k3_xcmplx_0__r1_r1_r1, rqRealNeg__k4_xcmplx_0__r1_rm1, rqRealNeg__k4_xcmplx_0__rm1_r1, rqRealDiff__k6_xcmplx_0__r1_r1_r0, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, rqRealDiff__k6_xcmplx_0__r1_rm1_r2, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2]), [interesting(np__0.65), file(diff_4, e1_6_1__diff_4), [file(diff_4, e1_6_1__diff_4)]]). thf(e2_6_1__diff_4, plain, ( (= @ ( (k13_complex1 @ ( (k9_real_1 @ ( (k8_real_1 @ ( (k1_seq_1 @ k30_sin_cos) @ c1_6__diff_4) ) @ ( (k1_seq_1 @ k30_sin_cos) @ c1_6__diff_4) ) ) @ ( (k1_seq_1 @ ( ( ( ( (k20_valued_1 @ k1_numbers) @ k1_numbers) @ k1_numbers) @ k30_sin_cos) @ k30_sin_cos) ) @ c2_6__diff_4) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ ( (k13_complex1 @ ( (k9_real_1 @ ( (k8_real_1 @ ( (k1_seq_1 @ k30_sin_cos) @ c1_6__diff_4) ) @ ( (k1_seq_1 @ k30_sin_cos) @ c1_6__diff_4) ) ) @ ( (k8_real_1 @ ( (k1_seq_1 @ k30_sin_cos) @ c2_6__diff_4) ) @ ( (k1_seq_1 @ k30_sin_cos) @ c2_6__diff_4) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) , inference(mizar_by, [status(thm), assumptions([dt_c1_6__diff_4, dt_c2_6__diff_4])], [cc10_valued_2, cc15_valued_2, cc16_valued_2, cc21_valued_2, cc28_valued_2, cc29_valued_2, cc7_valued_2, cc8_valued_2, cc9_valued_2, fc14_valued_2, fc15_valued_2, fc16_valued_2, fc17_valued_2, fc40_valued_2, fc41_valued_2, fc42_valued_2, fc43_valued_2, cc11_valued_2, cc17_valued_2, cc25_valued_2, cc26_valued_2, cc30_valued_2, cc4_valued_2, cc5_valued_2, fc18_valued_2, fc44_valued_2, cc12_valued_2, cc15_membered, cc18_valued_2, cc19_valued_0, cc22_membered, cc23_valued_0, cc24_valued_0, cc24_valued_2, cc2_seq_2, cc31_valued_2, cc3_membered, cc3_valued_2, fc19_valued_2, fc40_valued_1, fc45_valued_2, fc88_valued_0, rc3_valued_0, dt_k3_numbers, dt_k4_numbers, dt_o_0_0_xboole_0, cc10_membered, cc13_valued_0, cc13_valued_2, cc14_valued_0, cc16_membered, cc19_valued_2, cc1_int_1, cc1_seq_2, cc20_valued_0, cc22_valued_0, cc23_membered, cc23_valued_2, cc2_membered, cc2_ordinal1, cc2_valued_0, cc2_valued_2, cc32_valued_2, cc3_int_1, cc3_valued_0, cc4_seq_2, cc4_valued_0, cc6_funct_1, cc9_membered, fc17_rfunct_1, fc1_int_1, fc20_valued_2, fc2_int_1, fc35_valued_1, fc36_valued_1, fc3_int_1, fc3_numbers, fc41_valued_1, fc46_valued_2, fc4_int_1, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc5_seq_2, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc89_valued_0, rc1_int_1, rc2_int_1, rc2_ordinal1, rc2_valued_0, rc5_valued_1, reflexivity_r1_tarski, antisymmetry_r2_hidden, dt_k1_rfunct_1, dt_k1_xboole_0, dt_k4_ordinal1, cc10_ordinal1, cc11_valued_0, cc12_membered, cc13_membered, cc14_valued_2, cc15_valued_0, cc16_valued_0, cc17_membered, cc17_valued_0, cc19_membered, cc1_funct_2, cc1_membered, cc1_ordinal1, cc1_rfunct_1, cc1_valued_0, cc1_valued_2, cc20_membered, cc20_valued_2, cc21_valued_0, cc22_valued_2, cc24_membered, cc28_valued_0, cc2_funct_2, cc2_int_1, cc2_xcmplx_0, cc2_xreal_0, cc2_xxreal_0, cc30_valued_0, cc31_valued_0, cc33_valued_2, cc3_funct_2, cc3_seq_2, cc3_xxreal_0, cc4_funct_2, cc4_xxreal_0, cc5_funct_1, cc5_ordinal1, cc5_relat_1, cc5_xxreal_0, cc6_ordinal1, cc6_relat_1, cc6_xxreal_0, cc7_relat_1, cc7_valued_0, cc7_xxreal_0, cc8_funct_1, cc8_funct_2, cc8_ordinal1, cc8_relat_1, cc8_valued_0, cc8_xxreal_0, cc9_funct_1, fc11_xreal_0, fc127_valued_1, fc12_xreal_0, fc131_valued_1, fc13_xreal_0, fc14_xreal_0, fc16_xreal_0, fc17_funct_1, fc17_xreal_0, fc18_xreal_0, fc19_funct_1, fc1_rfunct_1, fc1_xboole_0, fc20_rfunct_1, fc21_valued_2, fc21_xreal_0, fc22_xreal_0, fc23_xreal_0, fc24_xreal_0, fc26_xreal_0, fc29_xreal_0, fc2_rfunct_1, fc30_xreal_0, fc31_xreal_0, fc32_xreal_0, fc33_xreal_0, fc37_valued_1, fc38_valued_1, fc39_valued_1, fc42_valued_1, fc47_valued_2, fc59_membered, fc62_valued_0, fc66_valued_0, fc6_membered, fc6_ordinal1, fc85_valued_0, fc86_valued_0, fc90_valued_0, fc9_xreal_0, rc1_funct_2, rc1_membered, rc1_ordinal1, rc1_partfun1, rc1_relset_1, rc1_seq_2, rc1_valued_0, rc1_valued_2, rc1_xxreal_0, rc2_funct_1, rc2_membered, rc2_relat_1, rc2_valued_1, rc2_valued_2, rc2_xreal_0, rc2_xxreal_0, rc3_funct_1, rc3_membered, rc3_ordinal1, rc3_partfun1, rc3_relat_1, rc3_valued_1, rc3_xreal_0, rc3_xxreal_0, rc4_funct_1, rc4_ordinal1, rc4_valued_0, rc4_xreal_0, rc4_xxreal_0, rc5_funct_1, rc5_ordinal1, rc6_funct_1, rc6_valued_0, rc7_funct_1, rc9_funct_1, t1_numerals, t1_subset, t4_subset, t5_subset, d2_xboole_0, commutativity_k2_xcmplx_0, involutiveness_k5_xcmplx_0, existence_m1_subset_1, existence_m2_subset_1, redefinition_k3_rfunct_1, redefinition_k5_numbers, redefinition_m2_subset_1, dt_k16_sin_cos, dt_k19_sin_cos, dt_k1_zfmisc_1, dt_k2_numbers, dt_k2_xcmplx_0, dt_k2_zfmisc_1, dt_k3_rfunct_1, dt_k5_numbers, dt_k5_xcmplx_0, dt_m1_subset_1, dt_m2_subset_1, cc10_valued_0, cc11_membered, cc12_valued_0, cc14_membered, cc18_membered, cc18_valued_0, cc1_funct_1, cc1_partfun1, cc1_relat_1, cc1_relset_1, cc1_xcmplx_0, cc1_xreal_0, cc21_membered, cc25_membered, cc26_membered, cc27_valued_2, cc2_funct_1, cc2_partfun1, cc2_relat_1, cc2_relset_1, cc3_funct_1, cc3_ordinal1, cc3_relat_1, cc3_relset_1, cc3_xcmplx_0, cc3_xreal_0, cc4_funct_1, cc4_membered, cc4_ordinal1, cc4_relat_1, cc4_relset_1, cc4_xreal_0, cc5_membered, cc5_valued_0, cc6_membered, cc6_valued_0, cc6_valued_2, cc7_funct_1, cc7_ordinal1, cc8_membered, cc9_ordinal1, cc9_valued_0, fc10_xreal_0, fc15_xreal_0, fc19_xreal_0, fc1_membered, fc20_xreal_0, fc25_xreal_0, fc27_xreal_0, fc28_xreal_0, fc2_numbers, fc2_xcmplx_0, fc34_valued_1, fc34_xreal_0, fc3_xcmplx_0, fc3_xreal_0, fc4_xcmplx_0, fc4_xreal_0, fc55_membered, fc5_xcmplx_0, fc5_xreal_0, fc63_valued_0, fc6_relat_1, fc6_sin_cos, fc6_xcmplx_0, fc6_xreal_0, fc7_sin_cos, fc7_xcmplx_0, fc7_xreal_0, fc87_valued_0, fc8_xcmplx_0, fc8_xreal_0, fc9_numbers, fc9_xcmplx_0, rc1_relat_1, rc1_xboole_0, rc1_xcmplx_0, rc1_xreal_0, rc2_xboole_0, rc2_xcmplx_0, rqRealAdd__k2_xcmplx_0__r0_r0_r0, rqRealAdd__k2_xcmplx_0__r0_r1_r1, rqRealAdd__k2_xcmplx_0__r0_r2_r2, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__r1_r0_r1, rqRealAdd__k2_xcmplx_0__r1_r1_r2, rqRealAdd__k2_xcmplx_0__r1_rm1_r0, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r2_r0_r2, rqRealAdd__k2_xcmplx_0__r2_rm1_r1, rqRealAdd__k2_xcmplx_0__r2_rm2_r0, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, rqRealAdd__k2_xcmplx_0__rm1_r1_r0, rqRealAdd__k2_xcmplx_0__rm1_r2_r1, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, rqRealAdd__k2_xcmplx_0__rm2_r2_r0, rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, spc10_arithm, spc11_arithm, spc12_arithm, spc1_arithm, spc2_arithm, spc3_arithm, spc4_arithm, spc5_arithm, spc6_arithm, spc7_arithm, spc8_arithm, spc9_arithm, t2_subset, t3_arithm, t3_subset, t6_arithm, t6_boole, t7_boole, t8_boole, commutativity_k18_valued_1, commutativity_k20_valued_1, commutativity_k3_xcmplx_0, involutiveness_k4_xcmplx_0, commutativity_k8_real_1, redefinition_k13_complex1, redefinition_k1_seq_1, redefinition_k20_valued_1, redefinition_k8_real_1, redefinition_k9_real_1, dt_k13_complex1, dt_k18_valued_1, dt_k1_funct_1, dt_k1_numbers, dt_k1_seq_1, dt_k20_valued_1, dt_k30_sin_cos, dt_k3_xcmplx_0, dt_k4_xcmplx_0, dt_k6_xcmplx_0, dt_k7_xcmplx_0, dt_k8_real_1, dt_k9_real_1, dt_c1_6__diff_4, dt_c2_6__diff_4, fc1_numbers, fc33_valued_1, fc3_membered, fc56_membered, fc61_valued_0, fc8_numbers, rc1_funct_1, rqRealDiff__k6_xcmplx_0__r0_r0_r0, rqRealDiff__k6_xcmplx_0__r0_r1_rm1, rqRealDiff__k6_xcmplx_0__r0_r2_rm2, rqRealDiff__k6_xcmplx_0__r0_rm1_r1, rqRealDiff__k6_xcmplx_0__r0_rm2_r2, rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r1_r0_r1, rqRealDiff__k6_xcmplx_0__r1_r2_rm1, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r2_r0_r2, rqRealDiff__k6_xcmplx_0__r2_r1_r1, rqRealDiff__k6_xcmplx_0__r2_r2_r0, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, rqRealDiv__k7_xcmplx_0__r1_r1_r1, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, rqRealDiv__k7_xcmplx_0__r2_r1_r2, rqRealDiv__k7_xcmplx_0__r2_r2_r1, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__r0_r0_r0, rqRealMult__k3_xcmplx_0__r0_r1_r0, rqRealMult__k3_xcmplx_0__r0_r2_r0, rqRealMult__k3_xcmplx_0__r0_rm2_r0, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, rqRealMult__k3_xcmplx_0__r1_r0_r0, rqRealMult__k3_xcmplx_0__r1_r2_r2, rqRealMult__k3_xcmplx_0__r1_rm2_rm2, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r2_r0_r0, rqRealMult__k3_xcmplx_0__r2_r1_r2, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_r0_r0, rqRealMult__k3_xcmplx_0__rm2_r1_rm2, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, rqRealNeg__k4_xcmplx_0__r0_r0, rqRealNeg__k4_xcmplx_0__r2_rm2, rqRealNeg__k4_xcmplx_0__rm2_r2, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, d27_sin_cos, d8_xcmplx_0, d9_xcmplx_0, spc0_numerals, spc1_numerals, spc2_numerals, spc0_boole, spc1_boole, spc2_boole, t5_valued_1, rqRealMult__k3_xcmplx_0__r1_r1_r1, rqRealNeg__k4_xcmplx_0__r1_rm1, rqRealNeg__k4_xcmplx_0__rm1_r1, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, rqRealDiff__k6_xcmplx_0__r1_r1_r0, rqRealDiff__k6_xcmplx_0__r1_rm1_r2, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2]), [interesting(np__0.65), file(diff_4, e2_6_1__diff_4), [file(diff_4, e2_6_1__diff_4)]]). thf(fc10_membered, theorem, (! [A: $i] : ( (v1_rat_1 @ A) => (v4_membered @ (k1_tarski @ A) ) ) ) , file(membered, fc10_membered), [interesting(np__0.9), axiom, file(membered, fc10_membered)]). thf(fc37_membered, theorem, (! [A: $i, B: $i] : ( (v4_membered @ A) => (v4_membered @ ( (k3_xboole_0 @ A) @ B) ) ) ) , file(membered, fc37_membered), [interesting(np__0.9), axiom, file(membered, fc37_membered)]). thf(fc38_membered, theorem, (! [A: $i, B: $i] : ( (v4_membered @ A) => (v4_membered @ ( (k3_xboole_0 @ B) @ A) ) ) ) , file(membered, fc38_membered), [interesting(np__0.9), axiom, file(membered, fc38_membered)]). thf(fc46_membered, theorem, (! [A: $i, B: $i] : ( (v4_membered @ A) => (v4_membered @ ( (k4_xboole_0 @ A) @ B) ) ) ) , file(membered, fc46_membered), [interesting(np__0.9), axiom, file(membered, fc46_membered)]). thf(fc11_membered, theorem, (! [A: $i] : ( (v1_int_1 @ A) => (v5_membered @ (k1_tarski @ A) ) ) ) , file(membered, fc11_membered), [interesting(np__0.9), axiom, file(membered, fc11_membered)]). thf(fc18_funct_1, theorem, (! [A: $i] : ( ( ~ ( (v1_zfmisc_1 @ A) ) & ( (v1_relat_1 @ A) & (v1_funct_1 @ A) ) ) => ~ ( (v1_zfmisc_1 @ (k9_xtuple_0 @ A) ) ) ) ) , file(funct_1, fc18_funct_1), [interesting(np__0.9), axiom, file(funct_1, fc18_funct_1)]). thf(fc19_valued_0, theorem, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v5_relat_1 @ A) @ k3_numbers) ) & (v1_relat_1 @ B) ) => ( (v5_relat_1 @ ( (k3_xboole_0 @ A) @ B) ) @ k3_numbers) ) ) , file(valued_0, fc19_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc19_valued_0)]). thf(fc20_valued_0, theorem, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v5_relat_1 @ A) @ k3_numbers) ) & (v1_relat_1 @ B) ) => ( (v5_relat_1 @ ( (k4_xboole_0 @ A) @ B) ) @ k3_numbers) ) ) , file(valued_0, fc20_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc20_valued_0)]). thf(fc21_valued_0, theorem, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v5_relat_1 @ A) @ k4_numbers) ) & (v1_relat_1 @ B) ) => ( (v5_relat_1 @ ( (k3_xboole_0 @ A) @ B) ) @ k4_numbers) ) ) , file(valued_0, fc21_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc21_valued_0)]). thf(fc22_valued_0, theorem, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & ( (v5_relat_1 @ A) @ k4_numbers) ) & (v1_relat_1 @ B) ) => ( (v5_relat_1 @ ( (k4_xboole_0 @ A) @ B) ) @ k4_numbers) ) ) , file(valued_0, fc22_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc22_valued_0)]). thf(fc24_relat_1, theorem, (! [A: $i] : ( ( (v1_zfmisc_1 @ A) & (v1_relat_1 @ A) ) => (v1_zfmisc_1 @ (k9_xtuple_0 @ A) ) ) ) , file(relat_1, fc24_relat_1), [interesting(np__0.9), axiom, file(relat_1, fc24_relat_1)]). thf(fc39_membered, theorem, (! [A: $i, B: $i] : ( (v5_membered @ A) => (v5_membered @ ( (k3_xboole_0 @ A) @ B) ) ) ) , file(membered, fc39_membered), [interesting(np__0.9), axiom, file(membered, fc39_membered)]). thf(fc40_membered, theorem, (! [A: $i, B: $i] : ( (v5_membered @ A) => (v5_membered @ ( (k3_xboole_0 @ B) @ A) ) ) ) , file(membered, fc40_membered), [interesting(np__0.9), axiom, file(membered, fc40_membered)]). thf(fc47_membered, theorem, (! [A: $i, B: $i] : ( (v5_membered @ A) => (v5_membered @ ( (k4_xboole_0 @ A) @ B) ) ) ) , file(membered, fc47_membered), [interesting(np__0.9), axiom, file(membered, fc47_membered)]). thf(fc11_funct_1, theorem, (! [A: $i, B: $i] : ( ( ( ~ ( (v1_xboole_0 @ A) ) & ( (v1_relat_1 @ A) & ( (v2_relat_1 @ A) & (v1_funct_1 @ A) ) ) ) & ( (m1_subset_1 @ B) @ (k9_xtuple_0 @ A) ) ) => ~ ( (v1_xboole_0 @ ( (k1_funct_1 @ A) @ B) ) ) ) ) , file(funct_1, fc11_funct_1), [interesting(np__0.9), axiom, file(funct_1, fc11_funct_1)]). thf(fc12_membered, theorem, (! [A: $i] : ( (v7_ordinal1 @ A) => (v6_membered @ (k1_tarski @ A) ) ) ) , file(membered, fc12_membered), [interesting(np__0.9), axiom, file(membered, fc12_membered)]). thf(fc15_valued_0, theorem, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & (v2_valued_0 @ A) ) & (v1_relat_1 @ B) ) => (v2_valued_0 @ ( (k3_xboole_0 @ A) @ B) ) ) ) , file(valued_0, fc15_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc15_valued_0)]). thf(fc16_valued_0, theorem, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & (v2_valued_0 @ A) ) & (v1_relat_1 @ B) ) => (v2_valued_0 @ ( (k4_xboole_0 @ A) @ B) ) ) ) , file(valued_0, fc16_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc16_valued_0)]). thf(fc23_valued_0, theorem, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & (v4_valued_0 @ A) ) & (v1_relat_1 @ B) ) => (v4_valued_0 @ ( (k3_xboole_0 @ A) @ B) ) ) ) , file(valued_0, fc23_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc23_valued_0)]). thf(fc24_valued_0, theorem, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & (v4_valued_0 @ A) ) & (v1_relat_1 @ B) ) => (v4_valued_0 @ ( (k4_xboole_0 @ A) @ B) ) ) ) , file(valued_0, fc24_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc24_valued_0)]). thf(fc31_membered, theorem, (! [A: $i, B: $i] : ( (v1_membered @ A) => (v1_membered @ ( (k3_xboole_0 @ A) @ B) ) ) ) , file(membered, fc31_membered), [interesting(np__0.9), axiom, file(membered, fc31_membered)]). thf(fc32_membered, theorem, (! [A: $i, B: $i] : ( (v1_membered @ A) => (v1_membered @ ( (k3_xboole_0 @ B) @ A) ) ) ) , file(membered, fc32_membered), [interesting(np__0.9), axiom, file(membered, fc32_membered)]). thf(fc33_membered, theorem, (! [A: $i, B: $i] : ( (v2_membered @ A) => (v2_membered @ ( (k3_xboole_0 @ A) @ B) ) ) ) , file(membered, fc33_membered), [interesting(np__0.9), axiom, file(membered, fc33_membered)]). thf(fc34_membered, theorem, (! [A: $i, B: $i] : ( (v2_membered @ A) => (v2_membered @ ( (k3_xboole_0 @ B) @ A) ) ) ) , file(membered, fc34_membered), [interesting(np__0.9), axiom, file(membered, fc34_membered)]). thf(fc41_membered, theorem, (! [A: $i, B: $i] : ( (v6_membered @ A) => (v6_membered @ ( (k3_xboole_0 @ A) @ B) ) ) ) , file(membered, fc41_membered), [interesting(np__0.9), axiom, file(membered, fc41_membered)]). thf(fc42_membered, theorem, (! [A: $i, B: $i] : ( (v6_membered @ A) => (v6_membered @ ( (k3_xboole_0 @ B) @ A) ) ) ) , file(membered, fc42_membered), [interesting(np__0.9), axiom, file(membered, fc42_membered)]). thf(fc43_membered, theorem, (! [A: $i, B: $i] : ( (v1_membered @ A) => (v1_membered @ ( (k4_xboole_0 @ A) @ B) ) ) ) , file(membered, fc43_membered), [interesting(np__0.9), axiom, file(membered, fc43_membered)]). thf(fc44_membered, theorem, (! [A: $i, B: $i] : ( (v2_membered @ A) => (v2_membered @ ( (k4_xboole_0 @ A) @ B) ) ) ) , file(membered, fc44_membered), [interesting(np__0.9), axiom, file(membered, fc44_membered)]). thf(fc48_membered, theorem, (! [A: $i, B: $i] : ( (v6_membered @ A) => (v6_membered @ ( (k4_xboole_0 @ A) @ B) ) ) ) , file(membered, fc48_membered), [interesting(np__0.9), axiom, file(membered, fc48_membered)]). thf(fc4_ordinal1, theorem, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v5_ordinal1 @ A) ) ) => (v3_ordinal1 @ (k9_xtuple_0 @ A) ) ) ) , file(ordinal1, fc4_ordinal1), [interesting(np__0.9), axiom, file(ordinal1, fc4_ordinal1)]). thf(fc5_relset_1, theorem, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_relat_1 @ B) & ( (v5_relat_1 @ B) @ A) ) & (v1_relat_1 @ C) ) => ( (v5_relat_1 @ ( (k3_xboole_0 @ B) @ C) ) @ A) ) ) , file(relset_1, fc5_relset_1), [interesting(np__0.9), axiom, file(relset_1, fc5_relset_1)]). thf(fc6_relset_1, theorem, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_relat_1 @ B) & ( (v5_relat_1 @ B) @ A) ) & (v1_relat_1 @ C) ) => ( (v5_relat_1 @ ( (k4_xboole_0 @ B) @ C) ) @ A) ) ) , file(relset_1, fc6_relset_1), [interesting(np__0.9), axiom, file(relset_1, fc6_relset_1)]). thf(fc8_membered, theorem, (! [A: $i] : ( (v1_xxreal_0 @ A) => (v2_membered @ (k1_tarski @ A) ) ) ) , file(membered, fc8_membered), [interesting(np__0.9), axiom, file(membered, fc8_membered)]). thf(commutativity_k3_xboole_0, theorem, (! [A: $i, B: $i] : ( (= @ ( (k3_xboole_0 @ A) @ B) ) @ ( (k3_xboole_0 @ B) @ A) ) ) , file(xboole_0, k3_xboole_0), [interesting(np__0.9), axiom, file(xboole_0, k3_xboole_0)]). thf(idempotence_k3_xboole_0, theorem, (! [A: $i, B: $i] : ( (= @ ( (k3_xboole_0 @ A) @ A) ) @ A) ) , file(xboole_0, k3_xboole_0), [interesting(np__0.9), axiom, file(xboole_0, k3_xboole_0)]). thf(dt_k3_xboole_0, plain, $true, file(xboole_0, k3_xboole_0), [interesting(np__0.9), axiom, file(xboole_0, k3_xboole_0)]). thf(dt_k4_xboole_0, plain, $true, file(xboole_0, k4_xboole_0), [interesting(np__0.9), axiom, file(xboole_0, k4_xboole_0)]). thf(fc108_valued_1, theorem, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v4_relat_1 @ A) @ k5_numbers) ) => (v6_membered @ (k9_xtuple_0 @ A) ) ) ) , file(valued_1, fc108_valued_1), [interesting(np__0.9), axiom, file(valued_1, fc108_valued_1)]). thf(fc10_relat_1, theorem, (! [A: $i] : ( (v1_xboole_0 @ A) => (v1_xboole_0 @ (k9_xtuple_0 @ A) ) ) ) , file(relat_1, fc10_relat_1), [interesting(np__0.9), axiom, file(relat_1, fc10_relat_1)]). thf(fc13_valued_0, theorem, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & (v1_valued_0 @ A) ) & (v1_relat_1 @ B) ) => (v1_valued_0 @ ( (k3_xboole_0 @ A) @ B) ) ) ) , file(valued_0, fc13_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc13_valued_0)]). thf(fc14_valued_0, theorem, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & (v1_valued_0 @ A) ) & (v1_relat_1 @ B) ) => (v1_valued_0 @ ( (k4_xboole_0 @ A) @ B) ) ) ) , file(valued_0, fc14_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc14_valued_0)]). thf(fc17_valued_0, theorem, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & (v3_valued_0 @ A) ) & (v1_relat_1 @ B) ) => (v3_valued_0 @ ( (k3_xboole_0 @ A) @ B) ) ) ) , file(valued_0, fc17_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc17_valued_0)]). thf(fc18_valued_0, theorem, (! [A: $i, B: $i] : ( ( ( (v1_relat_1 @ A) & (v3_valued_0 @ A) ) & (v1_relat_1 @ B) ) => (v3_valued_0 @ ( (k4_xboole_0 @ A) @ B) ) ) ) , file(valued_0, fc18_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc18_valued_0)]). thf(fc1_relat_1, theorem, (! [A: $i, B: $i] : ( (v1_relat_1 @ A) => (v1_relat_1 @ ( (k3_xboole_0 @ A) @ B) ) ) ) , file(relat_1, fc1_relat_1), [interesting(np__0.9), axiom, file(relat_1, fc1_relat_1)]). thf(fc21_relat_1, theorem, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ A) & (v1_xboole_0 @ B) ) => (v1_xboole_0 @ ( (k8_relat_1 @ A) @ B) ) ) ) , file(relat_1, fc21_relat_1), [interesting(np__0.9), axiom, file(relat_1, fc21_relat_1)]). thf(fc22_relat_1, theorem, (! [A: $i, B: $i] : ( ( (v1_xboole_0 @ A) & (v1_relat_1 @ A) ) => (v1_xboole_0 @ ( (k8_relat_1 @ A) @ B) ) ) ) , file(relat_1, fc22_relat_1), [interesting(np__0.9), axiom, file(relat_1, fc22_relat_1)]). thf(fc2_relat_1, theorem, (! [A: $i, B: $i] : ( (v1_relat_1 @ A) => (v1_relat_1 @ ( (k4_xboole_0 @ A) @ B) ) ) ) , file(relat_1, fc2_relat_1), [interesting(np__0.9), axiom, file(relat_1, fc2_relat_1)]). thf(fc2_relset_1, theorem, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_relat_1 @ B) & ( (v4_relat_1 @ B) @ A) ) & (v1_relat_1 @ C) ) => ( (v4_relat_1 @ ( (k3_xboole_0 @ B) @ C) ) @ A) ) ) , file(relset_1, fc2_relset_1), [interesting(np__0.9), axiom, file(relset_1, fc2_relset_1)]). thf(fc35_membered, theorem, (! [A: $i, B: $i] : ( (v3_membered @ A) => (v3_membered @ ( (k3_xboole_0 @ A) @ B) ) ) ) , file(membered, fc35_membered), [interesting(np__0.9), axiom, file(membered, fc35_membered)]). thf(fc36_membered, theorem, (! [A: $i, B: $i] : ( (v3_membered @ A) => (v3_membered @ ( (k3_xboole_0 @ B) @ A) ) ) ) , file(membered, fc36_membered), [interesting(np__0.9), axiom, file(membered, fc36_membered)]). thf(fc3_relset_1, theorem, (! [A: $i, B: $i, C: $i] : ( ( ( (v1_relat_1 @ B) & ( (v4_relat_1 @ B) @ A) ) & (v1_relat_1 @ C) ) => ( (v4_relat_1 @ ( (k4_xboole_0 @ B) @ C) ) @ A) ) ) , file(relset_1, fc3_relset_1), [interesting(np__0.9), axiom, file(relset_1, fc3_relset_1)]). thf(fc45_membered, theorem, (! [A: $i, B: $i] : ( (v3_membered @ A) => (v3_membered @ ( (k4_xboole_0 @ A) @ B) ) ) ) , file(membered, fc45_membered), [interesting(np__0.9), axiom, file(membered, fc45_membered)]). thf(fc7_membered, theorem, (! [A: $i] : ( (v1_xcmplx_0 @ A) => (v1_membered @ (k1_tarski @ A) ) ) ) , file(membered, fc7_membered), [interesting(np__0.9), axiom, file(membered, fc7_membered)]). thf(fc8_relat_1, theorem, (! [A: $i] : ( ( ~ ( (v1_xboole_0 @ A) ) & (v1_relat_1 @ A) ) => ~ ( (v1_xboole_0 @ (k9_xtuple_0 @ A) ) ) ) ) , file(relat_1, fc8_relat_1), [interesting(np__0.9), axiom, file(relat_1, fc8_relat_1)]). thf(fc8_relset_1, theorem, (! [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), [interesting(np__0.9), axiom, file(relset_1, fc8_relset_1)]). thf(fc9_membered, theorem, (! [A: $i] : ( (v1_xreal_0 @ A) => (v3_membered @ (k1_tarski @ A) ) ) ) , file(membered, fc9_membered), [interesting(np__0.9), axiom, file(membered, fc9_membered)]). thf(t1_arithm, theorem, (! [A: $i] : ( (v1_xcmplx_0 @ A) => ( (= @ ( (k2_xcmplx_0 @ A) @ k6_numbers) ) @ A) ) ) , file(arithm, t1_arithm), [interesting(np__0.9), axiom, file(arithm, t1_arithm)]). thf(t2_arithm, theorem, (! [A: $i] : ( (v1_xcmplx_0 @ A) => ( (= @ ( (k3_xcmplx_0 @ A) @ k6_numbers) ) @ k6_numbers) ) ) , file(arithm, t2_arithm), [interesting(np__0.9), axiom, file(arithm, t2_arithm)]). thf(t2_boole, theorem, (! [A: $i] : ( (= @ ( (k3_xboole_0 @ A) @ k1_xboole_0) ) @ k1_xboole_0) ) , file(boole, t2_boole), [interesting(np__0.9), axiom, file(boole, t2_boole)]). thf(t3_boole, theorem, (! [A: $i] : ( (= @ ( (k4_xboole_0 @ A) @ k1_xboole_0) ) @ A) ) , file(boole, t3_boole), [interesting(np__0.9), axiom, file(boole, t3_boole)]). thf(t4_arithm, theorem, (! [A: $i] : ( (v1_xcmplx_0 @ A) => ( (= @ ( (k6_xcmplx_0 @ A) @ k6_numbers) ) @ A) ) ) , file(arithm, t4_arithm), [interesting(np__0.9), axiom, file(arithm, t4_arithm)]). thf(t4_boole, theorem, (! [A: $i] : ( (= @ ( (k4_xboole_0 @ k1_xboole_0) @ A) ) @ k1_xboole_0) ) , file(boole, t4_boole), [interesting(np__0.9), axiom, file(boole, t4_boole)]). thf(t5_arithm, theorem, (! [A: $i] : ( (v1_xcmplx_0 @ A) => ( (= @ ( (k7_xcmplx_0 @ k6_numbers) @ A) ) @ k6_numbers) ) ) , file(arithm, t5_arithm), [interesting(np__0.9), axiom, file(arithm, t5_arithm)]). thf(commutativity_k9_subset_1, theorem, (! [A: $i, B: $i, C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ A) ) => ( (= @ ( ( (k9_subset_1 @ A) @ B) @ C) ) @ ( ( (k9_subset_1 @ A) @ C) @ B) ) ) ) , file(subset_1, k9_subset_1), [interesting(np__0.9), axiom, file(subset_1, k9_subset_1)]). thf(idempotence_k9_subset_1, theorem, (! [A: $i, B: $i, C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ A) ) => ( (= @ ( ( (k9_subset_1 @ A) @ B) @ B) ) @ B) ) ) , file(subset_1, k9_subset_1), [interesting(np__0.9), axiom, file(subset_1, k9_subset_1)]). thf(redefinition_k1_relset_1, definition, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ B) & ( (v4_relat_1 @ B) @ A) ) => ( (= @ ( (k1_relset_1 @ A) @ B) ) @ (k9_xtuple_0 @ B) ) ) ) , file(relset_1, k1_relset_1), [interesting(np__0.9), axiom, file(relset_1, k1_relset_1)]). thf(redefinition_k6_numbers, definition, ( (= @ k6_numbers) @ k1_xboole_0) , file(numbers, k6_numbers), [interesting(np__0.9), axiom, file(numbers, k6_numbers)]). thf(redefinition_k6_subset_1, definition, (! [A: $i, B: $i] : ( (= @ ( (k6_subset_1 @ A) @ B) ) @ ( (k4_xboole_0 @ A) @ B) ) ) , file(subset_1, k6_subset_1), [interesting(np__0.9), axiom, file(subset_1, k6_subset_1)]). thf(redefinition_k9_subset_1, definition, (! [A: $i, B: $i, C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ A) ) => ( (= @ ( ( (k9_subset_1 @ A) @ B) @ C) ) @ ( (k3_xboole_0 @ B) @ C) ) ) ) , file(subset_1, k9_subset_1), [interesting(np__0.9), axiom, file(subset_1, k9_subset_1)]). thf(dt_k1_relset_1, plain, (! [A: $i, B: $i] : ( ( (v1_relat_1 @ B) & ( (v4_relat_1 @ B) @ A) ) => ( (m1_subset_1 @ ( (k1_relset_1 @ A) @ B) ) @ (k1_zfmisc_1 @ A) ) ) ) , file(relset_1, k1_relset_1), [interesting(np__0.9), axiom, file(relset_1, k1_relset_1)]). thf(dt_k1_tarski, plain, $true, file(tarski, k1_tarski), [interesting(np__0.9), axiom, file(tarski, k1_tarski)]). thf(dt_k6_numbers, plain, ( ( (m2_subset_1 @ k6_numbers) @ k1_numbers) @ k5_numbers) , file(numbers, k6_numbers), [interesting(np__0.9), axiom, file(numbers, k6_numbers)]). thf(dt_k6_subset_1, plain, (! [A: $i, B: $i] : ( (m1_subset_1 @ ( (k6_subset_1 @ A) @ B) ) @ (k1_zfmisc_1 @ A) ) ) , file(subset_1, k6_subset_1), [interesting(np__0.9), axiom, file(subset_1, k6_subset_1)]). thf(dt_k8_relat_1, plain, $true, file(relat_1, k8_relat_1), [interesting(np__0.9), axiom, file(relat_1, k8_relat_1)]). thf(dt_k9_subset_1, plain, (! [A: $i, B: $i, C: $i] : ( ( (m1_subset_1 @ C) @ (k1_zfmisc_1 @ A) ) => ( (m1_subset_1 @ ( ( (k9_subset_1 @ A) @ B) @ C) ) @ (k1_zfmisc_1 @ A) ) ) ) , file(subset_1, k9_subset_1), [interesting(np__0.9), axiom, file(subset_1, k9_subset_1)]). thf(dt_k9_xtuple_0, plain, $true, file(xtuple_0, k9_xtuple_0), [interesting(np__0.9), axiom, file(xtuple_0, k9_xtuple_0)]). thf(fc14_funct_1, theorem, (! [A: $i] : ( ( (v1_relat_1 @ A) & (v1_funct_1 @ A) ) => (v4_funct_1 @ (k1_tarski @ A) ) ) ) , file(funct_1, fc14_funct_1), [interesting(np__0.9), axiom, file(funct_1, fc14_funct_1)]). thf(fc1_valued_2, theorem, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) => (v1_valued_2 @ (k1_tarski @ A) ) ) ) , file(valued_2, fc1_valued_2), [interesting(np__0.9), axiom, file(valued_2, fc1_valued_2)]). thf(fc2_xboole_0, theorem, (! [A: $i] : ~ ( (v1_xboole_0 @ (k1_tarski @ A) ) ) ) , file(xboole_0, fc2_xboole_0), [interesting(np__0.9), axiom, file(xboole_0, fc2_xboole_0)]). thf(d1_rfunct_1, definition, (! [A: $i] : ( ( (v1_relat_1 @ A) & ( (v1_funct_1 @ A) & (v1_valued_0 @ A) ) ) => (! [B: $i] : ( ( (v1_relat_1 @ B) & ( (v1_funct_1 @ B) & (v1_valued_0 @ B) ) ) => (! [C: $i] : ( ( (v1_relat_1 @ C) & (v1_funct_1 @ C) ) => ( ( (= @ C) @ ( (k1_rfunct_1 @ A) @ B) ) <=> ( ( (= @ (k9_xtuple_0 @ C) ) @ ( ( (k9_subset_1 @ (k9_xtuple_0 @ B) ) @ (k9_xtuple_0 @ A) ) @ ( (k6_subset_1 @ (k9_xtuple_0 @ B) ) @ ( (k8_relat_1 @ B) @ (k1_tarski @ k6_numbers) ) ) ) ) & (! [D: $i] : ( ( (r2_hidden @ D) @ (k9_xtuple_0 @ C) ) => ( (= @ ( (k1_funct_1 @ C) @ D) ) @ ( (k3_xcmplx_0 @ ( (k1_funct_1 @ A) @ D) ) @ (k5_xcmplx_0 @ ( (k1_funct_1 @ B) @ D) ) ) ) ) ) ) ) ) ) ) ) ) ) , file(rfunct_1, d1_rfunct_1), [interesting(np__0.9), axiom, file(rfunct_1, d1_rfunct_1)]). thf(e3_6_1__diff_4, plain, ( (= @ ( (k13_complex1 @ ( (k9_real_1 @ ( (k8_real_1 @ ( (k1_seq_1 @ k30_sin_cos) @ c1_6__diff_4) ) @ ( (k1_seq_1 @ k30_sin_cos) @ c1_6__diff_4) ) ) @ ( (k8_real_1 @ ( (k1_seq_1 @ k30_sin_cos) @ c2_6__diff_4) ) @ ( (k1_seq_1 @ k30_sin_cos) @ c2_6__diff_4) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ ( (k13_complex1 @ ( (k9_real_1 @ ( (k8_real_1 @ ( (k8_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k19_sin_cos) @ c1_6__diff_4) ) @ (k2_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k16_sin_cos) @ c1_6__diff_4) ) ) ) @ ( (k1_seq_1 @ k30_sin_cos) @ c1_6__diff_4) ) ) @ ( (k8_real_1 @ ( (k1_seq_1 @ k30_sin_cos) @ c2_6__diff_4) ) @ ( (k1_seq_1 @ k30_sin_cos) @ c2_6__diff_4) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) , inference(mizar_by, [status(thm), assumptions([dt_c1_6__diff_4, dt_c2_6__diff_4, e1_6__diff_4])], [cc10_valued_2, cc16_valued_2, cc29_valued_2, cc8_valued_2, fc15_valued_2, fc17_valued_2, fc41_valued_2, fc43_valued_2, cc11_valued_2, cc17_valued_2, cc25_valued_2, cc26_valued_2, cc30_valued_2, cc4_valued_2, cc5_valued_2, fc18_valued_2, fc44_valued_2, cc12_valued_2, cc15_membered, cc18_valued_2, cc19_valued_0, cc22_membered, cc23_valued_0, cc24_valued_0, cc24_valued_2, cc2_seq_2, cc31_valued_2, cc3_membered, cc3_valued_2, fc10_membered, fc19_valued_2, fc37_membered, fc38_membered, fc45_valued_2, fc46_membered, fc88_valued_0, rc3_valued_0, dt_k3_numbers, dt_k4_numbers, cc10_membered, cc13_valued_0, cc13_valued_2, cc14_valued_0, cc16_membered, cc19_valued_2, cc1_int_1, cc1_seq_2, cc20_valued_0, cc22_valued_0, cc23_membered, cc23_valued_2, cc2_membered, cc2_ordinal1, cc2_valued_0, cc2_valued_2, cc32_valued_2, cc3_int_1, cc3_valued_0, cc4_seq_2, cc4_valued_0, cc6_funct_1, cc9_membered, fc11_membered, fc18_funct_1, fc19_valued_0, fc1_int_1, fc20_valued_0, fc20_valued_2, fc21_valued_0, fc22_valued_0, fc24_relat_1, fc2_int_1, fc39_membered, fc3_int_1, fc3_numbers, fc40_membered, fc46_valued_2, fc47_membered, fc4_int_1, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc89_valued_0, rc1_int_1, rc2_int_1, rc2_ordinal1, rc2_valued_0, rc5_valued_1, reflexivity_r1_tarski, dt_k4_ordinal1, dt_o_0_0_xboole_0, cc10_ordinal1, cc11_valued_0, cc12_membered, cc13_membered, cc14_valued_2, cc15_valued_0, cc16_valued_0, cc17_membered, cc17_valued_0, cc19_membered, cc1_funct_2, cc1_membered, cc1_ordinal1, cc1_rfunct_1, cc1_valued_0, cc1_valued_2, cc20_membered, cc20_valued_2, cc21_valued_0, cc21_valued_2, cc22_valued_2, cc24_membered, cc28_valued_0, cc2_int_1, cc2_xcmplx_0, cc2_xreal_0, cc2_xxreal_0, cc30_valued_0, cc31_valued_0, cc33_valued_2, cc3_seq_2, cc3_xxreal_0, cc4_xxreal_0, cc5_funct_1, cc5_ordinal1, cc5_xxreal_0, cc6_ordinal1, cc6_relat_1, cc6_xxreal_0, cc7_valued_0, cc7_xxreal_0, cc8_ordinal1, cc8_relat_1, cc8_valued_0, cc8_xxreal_0, fc11_funct_1, fc11_xreal_0, fc12_membered, fc12_xreal_0, fc13_xreal_0, fc14_xreal_0, fc15_valued_0, fc16_valued_0, fc16_xreal_0, fc17_funct_1, fc17_xreal_0, fc18_xreal_0, fc19_funct_1, fc21_valued_2, fc21_xreal_0, fc22_xreal_0, fc23_valued_0, fc23_xreal_0, fc24_valued_0, fc24_xreal_0, fc26_xreal_0, fc29_xreal_0, fc30_xreal_0, fc31_membered, fc31_xreal_0, fc32_membered, fc32_xreal_0, fc33_membered, fc33_xreal_0, fc34_membered, fc40_valued_2, fc41_membered, fc42_membered, fc42_valued_2, fc43_membered, fc44_membered, fc47_valued_2, fc48_membered, fc4_ordinal1, fc59_membered, fc5_relset_1, fc62_valued_0, fc66_valued_0, fc6_membered, fc6_ordinal1, fc6_relset_1, fc85_valued_0, fc86_valued_0, fc8_membered, fc90_valued_0, fc9_xreal_0, rc1_funct_2, rc1_membered, rc1_ordinal1, rc1_partfun1, rc1_relset_1, rc1_seq_2, rc1_valued_0, rc1_valued_2, rc1_xxreal_0, rc2_funct_1, rc2_membered, rc2_relat_1, rc2_valued_2, rc2_xreal_0, rc2_xxreal_0, rc3_funct_1, rc3_membered, rc3_ordinal1, rc3_partfun1, rc3_relat_1, rc3_xreal_0, rc3_xxreal_0, rc4_funct_1, rc4_ordinal1, rc4_valued_0, rc4_xreal_0, rc4_xxreal_0, rc5_funct_1, rc5_ordinal1, rc6_funct_1, rc6_valued_0, rc9_funct_1, t1_numerals, commutativity_k2_xcmplx_0, commutativity_k3_xboole_0, idempotence_k3_xboole_0, existence_m1_subset_1, existence_m2_subset_1, redefinition_k3_rfunct_1, redefinition_k5_numbers, redefinition_m2_subset_1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_numbers, dt_k2_xcmplx_0, dt_k2_zfmisc_1, dt_k3_rfunct_1, dt_k3_xboole_0, dt_k4_xboole_0, dt_k5_numbers, dt_k7_xcmplx_0, dt_m1_subset_1, dt_m2_subset_1, cc10_valued_0, cc11_membered, cc12_valued_0, cc14_membered, cc15_valued_2, cc18_membered, cc18_valued_0, cc1_funct_1, cc1_partfun1, cc1_relat_1, cc1_relset_1, cc1_xcmplx_0, cc1_xreal_0, cc21_membered, cc25_membered, cc26_membered, cc27_valued_2, cc28_valued_2, cc2_funct_1, cc2_funct_2, cc2_partfun1, cc2_relat_1, cc2_relset_1, cc3_funct_1, cc3_funct_2, cc3_ordinal1, cc3_relat_1, cc3_relset_1, cc3_xcmplx_0, cc3_xreal_0, cc4_funct_1, cc4_funct_2, cc4_membered, cc4_ordinal1, cc4_relat_1, cc4_relset_1, cc4_xreal_0, cc5_membered, cc5_relat_1, cc5_valued_0, cc6_membered, cc6_valued_0, cc6_valued_2, cc7_funct_1, cc7_ordinal1, cc7_relat_1, cc7_valued_2, cc8_funct_1, cc8_funct_2, cc8_membered, cc9_funct_1, cc9_ordinal1, cc9_valued_0, cc9_valued_2, fc108_valued_1, fc10_relat_1, fc10_xreal_0, fc13_valued_0, fc14_valued_0, fc14_valued_2, fc15_xreal_0, fc16_valued_2, fc17_valued_0, fc18_valued_0, fc19_xreal_0, fc1_membered, fc1_relat_1, fc1_xboole_0, fc20_xreal_0, fc21_relat_1, fc22_relat_1, fc25_xreal_0, fc27_xreal_0, fc28_xreal_0, fc2_numbers, fc2_relat_1, fc2_relset_1, fc2_rfunct_1, fc2_xcmplx_0, fc34_xreal_0, fc35_membered, fc36_membered, fc3_relset_1, fc3_xcmplx_0, fc3_xreal_0, fc45_membered, fc4_xcmplx_0, fc4_xreal_0, fc55_membered, fc5_xcmplx_0, fc5_xreal_0, fc63_valued_0, fc6_relat_1, fc6_xcmplx_0, fc6_xreal_0, fc7_membered, fc7_xcmplx_0, fc7_xreal_0, fc87_valued_0, fc8_relat_1, fc8_relset_1, fc8_xcmplx_0, fc8_xreal_0, fc9_membered, fc9_numbers, fc9_xcmplx_0, rc1_relat_1, rc1_xboole_0, rc1_xcmplx_0, rc1_xreal_0, rc2_valued_1, rc2_xboole_0, rc2_xcmplx_0, rc3_valued_1, rc7_funct_1, rqRealAdd__k2_xcmplx_0__r0_r0_r0, rqRealAdd__k2_xcmplx_0__r0_r1_r1, rqRealAdd__k2_xcmplx_0__r0_r2_r2, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__r1_r0_r1, rqRealAdd__k2_xcmplx_0__r1_r1_r2, rqRealAdd__k2_xcmplx_0__r1_rm1_r0, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r2_r0_r2, rqRealAdd__k2_xcmplx_0__r2_rm1_r1, rqRealAdd__k2_xcmplx_0__r2_rm2_r0, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, rqRealAdd__k2_xcmplx_0__rm1_r1_r0, rqRealAdd__k2_xcmplx_0__rm1_r2_r1, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, rqRealAdd__k2_xcmplx_0__rm2_r2_r0, rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, rqRealDiv__k7_xcmplx_0__r1_r1_r1, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, rqRealDiv__k7_xcmplx_0__r2_r1_r2, rqRealDiv__k7_xcmplx_0__r2_r2_r1, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, spc10_arithm, spc11_arithm, spc12_arithm, spc1_arithm, spc2_arithm, spc3_arithm, spc4_arithm, spc5_arithm, spc6_arithm, spc7_arithm, spc8_arithm, spc9_arithm, t1_arithm, t2_arithm, t2_boole, t2_subset, t3_arithm, t3_boole, t3_subset, t4_arithm, t4_boole, t4_subset, t5_arithm, t5_subset, t6_arithm, t6_boole, t8_boole, d2_xboole_0, d9_xcmplx_0, involutiveness_k2_real_1, commutativity_k3_xcmplx_0, involutiveness_k4_xcmplx_0, involutiveness_k5_xcmplx_0, commutativity_k8_real_1, commutativity_k9_subset_1, idempotence_k9_subset_1, antisymmetry_r2_hidden, redefinition_k13_complex1, redefinition_k1_relset_1, redefinition_k1_seq_1, redefinition_k2_real_1, redefinition_k3_funct_2, redefinition_k6_numbers, redefinition_k6_subset_1, redefinition_k8_real_1, redefinition_k9_real_1, redefinition_k9_subset_1, dt_k13_complex1, dt_k16_sin_cos, dt_k19_sin_cos, dt_k1_funct_1, dt_k1_numbers, dt_k1_relset_1, dt_k1_rfunct_1, dt_k1_seq_1, dt_k1_tarski, dt_k2_real_1, dt_k30_sin_cos, dt_k3_funct_2, dt_k3_xcmplx_0, dt_k4_xcmplx_0, dt_k5_xcmplx_0, dt_k6_numbers, dt_k6_subset_1, dt_k6_xcmplx_0, dt_k8_real_1, dt_k8_relat_1, dt_k9_real_1, dt_k9_subset_1, dt_k9_xtuple_0, dt_c1_6__diff_4, dt_c2_6__diff_4, fc14_funct_1, fc1_numbers, fc1_rfunct_1, fc1_valued_2, fc2_xboole_0, fc3_membered, fc56_membered, fc61_valued_0, fc6_sin_cos, fc7_sin_cos, fc8_numbers, rc1_funct_1, rqRealDiff__k6_xcmplx_0__r0_r0_r0, rqRealDiff__k6_xcmplx_0__r0_r1_rm1, rqRealDiff__k6_xcmplx_0__r0_r2_rm2, rqRealDiff__k6_xcmplx_0__r0_rm1_r1, rqRealDiff__k6_xcmplx_0__r0_rm2_r2, rqRealDiff__k6_xcmplx_0__r1_r0_r1, rqRealDiff__k6_xcmplx_0__r1_r2_rm1, rqRealDiff__k6_xcmplx_0__r2_r0_r2, rqRealDiff__k6_xcmplx_0__r2_r1_r1, rqRealDiff__k6_xcmplx_0__r2_r2_r0, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, rqRealMult__k3_xcmplx_0__r0_r0_r0, rqRealMult__k3_xcmplx_0__r0_r1_r0, rqRealMult__k3_xcmplx_0__r0_r2_r0, rqRealMult__k3_xcmplx_0__r0_rm2_r0, rqRealMult__k3_xcmplx_0__r1_r0_r0, rqRealMult__k3_xcmplx_0__r1_r2_r2, rqRealMult__k3_xcmplx_0__r1_rm2_rm2, rqRealMult__k3_xcmplx_0__r2_r0_r0, rqRealMult__k3_xcmplx_0__r2_r1_r2, rqRealMult__k3_xcmplx_0__rm2_r0_r0, rqRealMult__k3_xcmplx_0__rm2_r1_rm2, rqRealNeg__k4_xcmplx_0__r2_rm2, rqRealNeg__k4_xcmplx_0__rm2_r2, t1_subset, t7_boole, d27_sin_cos, d8_xcmplx_0, spc0_numerals, spc1_numerals, spc2_numerals, spc0_boole, spc1_boole, spc2_boole, e1_6__diff_4, d1_rfunct_1, rqRealMult__k3_xcmplx_0__r1_r1_r1, rqRealNeg__k4_xcmplx_0__r1_rm1, rqRealNeg__k4_xcmplx_0__rm1_r1, rqRealDiff__k6_xcmplx_0__r1_r1_r0, rqRealNeg__k4_xcmplx_0__r0_r0, rqRealDiff__k6_xcmplx_0__r1_rm1_r2, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2]), [interesting(np__0.65), file(diff_4, e3_6_1__diff_4), [file(diff_4, e3_6_1__diff_4)]]). thf(e4_6_1__diff_4, plain, ( (= @ ( (k13_complex1 @ ( (k9_real_1 @ ( (k8_real_1 @ ( (k8_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k19_sin_cos) @ c1_6__diff_4) ) @ (k2_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k16_sin_cos) @ c1_6__diff_4) ) ) ) @ ( (k1_seq_1 @ k30_sin_cos) @ c1_6__diff_4) ) ) @ ( (k8_real_1 @ ( (k1_seq_1 @ k30_sin_cos) @ c2_6__diff_4) ) @ ( (k1_seq_1 @ k30_sin_cos) @ c2_6__diff_4) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ ( (k13_complex1 @ ( (k9_real_1 @ ( (k8_real_1 @ ( (k8_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k19_sin_cos) @ c1_6__diff_4) ) @ (k2_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k16_sin_cos) @ c1_6__diff_4) ) ) ) @ ( (k8_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k19_sin_cos) @ c1_6__diff_4) ) @ (k2_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k16_sin_cos) @ c1_6__diff_4) ) ) ) ) @ ( (k8_real_1 @ ( (k1_seq_1 @ k30_sin_cos) @ c2_6__diff_4) ) @ ( (k1_seq_1 @ k30_sin_cos) @ c2_6__diff_4) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) , inference(mizar_by, [status(thm), assumptions([dt_c1_6__diff_4, dt_c2_6__diff_4, e1_6__diff_4])], [cc10_valued_2, cc16_valued_2, cc29_valued_2, cc8_valued_2, fc15_valued_2, fc17_valued_2, fc41_valued_2, fc43_valued_2, cc11_valued_2, cc17_valued_2, cc25_valued_2, cc26_valued_2, cc30_valued_2, cc4_valued_2, cc5_valued_2, fc18_valued_2, fc44_valued_2, cc12_valued_2, cc15_membered, cc18_valued_2, cc19_valued_0, cc22_membered, cc23_valued_0, cc24_valued_0, cc24_valued_2, cc2_seq_2, cc31_valued_2, cc3_membered, cc3_valued_2, fc10_membered, fc19_valued_2, fc37_membered, fc38_membered, fc45_valued_2, fc46_membered, fc88_valued_0, rc3_valued_0, dt_k3_numbers, dt_k4_numbers, cc10_membered, cc13_valued_0, cc13_valued_2, cc14_valued_0, cc16_membered, cc19_valued_2, cc1_int_1, cc1_seq_2, cc20_valued_0, cc22_valued_0, cc23_membered, cc23_valued_2, cc2_membered, cc2_ordinal1, cc2_valued_0, cc2_valued_2, cc32_valued_2, cc3_int_1, cc3_valued_0, cc4_seq_2, cc4_valued_0, cc6_funct_1, cc9_membered, fc11_membered, fc18_funct_1, fc19_valued_0, fc1_int_1, fc20_valued_0, fc20_valued_2, fc21_valued_0, fc22_valued_0, fc24_relat_1, fc2_int_1, fc39_membered, fc3_int_1, fc3_numbers, fc40_membered, fc46_valued_2, fc47_membered, fc4_int_1, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc89_valued_0, rc1_int_1, rc2_int_1, rc2_ordinal1, rc2_valued_0, rc5_valued_1, reflexivity_r1_tarski, dt_k4_ordinal1, dt_o_0_0_xboole_0, cc10_ordinal1, cc11_valued_0, cc12_membered, cc13_membered, cc14_valued_2, cc15_valued_0, cc16_valued_0, cc17_membered, cc17_valued_0, cc19_membered, cc1_funct_2, cc1_membered, cc1_ordinal1, cc1_rfunct_1, cc1_valued_0, cc1_valued_2, cc20_membered, cc20_valued_2, cc21_valued_0, cc21_valued_2, cc22_valued_2, cc24_membered, cc28_valued_0, cc2_int_1, cc2_xcmplx_0, cc2_xreal_0, cc2_xxreal_0, cc30_valued_0, cc31_valued_0, cc33_valued_2, cc3_seq_2, cc3_xxreal_0, cc4_xxreal_0, cc5_funct_1, cc5_ordinal1, cc5_xxreal_0, cc6_ordinal1, cc6_relat_1, cc6_xxreal_0, cc7_valued_0, cc7_xxreal_0, cc8_ordinal1, cc8_relat_1, cc8_valued_0, cc8_xxreal_0, fc11_funct_1, fc11_xreal_0, fc12_membered, fc12_xreal_0, fc13_xreal_0, fc14_xreal_0, fc15_valued_0, fc16_valued_0, fc16_xreal_0, fc17_funct_1, fc17_xreal_0, fc18_xreal_0, fc19_funct_1, fc21_valued_2, fc21_xreal_0, fc22_xreal_0, fc23_valued_0, fc23_xreal_0, fc24_valued_0, fc24_xreal_0, fc26_xreal_0, fc29_xreal_0, fc30_xreal_0, fc31_membered, fc31_xreal_0, fc32_membered, fc32_xreal_0, fc33_membered, fc33_xreal_0, fc34_membered, fc40_valued_2, fc41_membered, fc42_membered, fc42_valued_2, fc43_membered, fc44_membered, fc47_valued_2, fc48_membered, fc4_ordinal1, fc59_membered, fc5_relset_1, fc62_valued_0, fc66_valued_0, fc6_membered, fc6_ordinal1, fc6_relset_1, fc85_valued_0, fc86_valued_0, fc8_membered, fc90_valued_0, fc9_xreal_0, rc1_funct_2, rc1_membered, rc1_ordinal1, rc1_partfun1, rc1_relset_1, rc1_seq_2, rc1_valued_0, rc1_valued_2, rc1_xxreal_0, rc2_funct_1, rc2_membered, rc2_relat_1, rc2_valued_2, rc2_xreal_0, rc2_xxreal_0, rc3_funct_1, rc3_membered, rc3_ordinal1, rc3_partfun1, rc3_relat_1, rc3_xreal_0, rc3_xxreal_0, rc4_funct_1, rc4_ordinal1, rc4_valued_0, rc4_xreal_0, rc4_xxreal_0, rc5_funct_1, rc5_ordinal1, rc6_funct_1, rc6_valued_0, rc9_funct_1, t1_numerals, commutativity_k2_xcmplx_0, commutativity_k3_xboole_0, idempotence_k3_xboole_0, existence_m1_subset_1, existence_m2_subset_1, redefinition_k3_rfunct_1, redefinition_k5_numbers, redefinition_m2_subset_1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_numbers, dt_k2_xcmplx_0, dt_k2_zfmisc_1, dt_k3_rfunct_1, dt_k3_xboole_0, dt_k4_xboole_0, dt_k5_numbers, dt_k7_xcmplx_0, dt_m1_subset_1, dt_m2_subset_1, cc10_valued_0, cc11_membered, cc12_valued_0, cc14_membered, cc15_valued_2, cc18_membered, cc18_valued_0, cc1_funct_1, cc1_partfun1, cc1_relat_1, cc1_relset_1, cc1_xcmplx_0, cc1_xreal_0, cc21_membered, cc25_membered, cc26_membered, cc27_valued_2, cc28_valued_2, cc2_funct_1, cc2_funct_2, cc2_partfun1, cc2_relat_1, cc2_relset_1, cc3_funct_1, cc3_funct_2, cc3_ordinal1, cc3_relat_1, cc3_relset_1, cc3_xcmplx_0, cc3_xreal_0, cc4_funct_1, cc4_funct_2, cc4_membered, cc4_ordinal1, cc4_relat_1, cc4_relset_1, cc4_xreal_0, cc5_membered, cc5_relat_1, cc5_valued_0, cc6_membered, cc6_valued_0, cc6_valued_2, cc7_funct_1, cc7_ordinal1, cc7_relat_1, cc7_valued_2, cc8_funct_1, cc8_funct_2, cc8_membered, cc9_funct_1, cc9_ordinal1, cc9_valued_0, cc9_valued_2, fc108_valued_1, fc10_relat_1, fc10_xreal_0, fc13_valued_0, fc14_valued_0, fc14_valued_2, fc15_xreal_0, fc16_valued_2, fc17_valued_0, fc18_valued_0, fc19_xreal_0, fc1_membered, fc1_relat_1, fc1_xboole_0, fc20_xreal_0, fc21_relat_1, fc22_relat_1, fc25_xreal_0, fc27_xreal_0, fc28_xreal_0, fc2_numbers, fc2_relat_1, fc2_relset_1, fc2_rfunct_1, fc2_xcmplx_0, fc34_xreal_0, fc35_membered, fc36_membered, fc3_relset_1, fc3_xcmplx_0, fc3_xreal_0, fc45_membered, fc4_xcmplx_0, fc4_xreal_0, fc55_membered, fc5_xcmplx_0, fc5_xreal_0, fc63_valued_0, fc6_relat_1, fc6_xcmplx_0, fc6_xreal_0, fc7_membered, fc7_xcmplx_0, fc7_xreal_0, fc87_valued_0, fc8_relat_1, fc8_relset_1, fc8_xcmplx_0, fc8_xreal_0, fc9_membered, fc9_numbers, fc9_xcmplx_0, rc1_relat_1, rc1_xboole_0, rc1_xcmplx_0, rc1_xreal_0, rc2_valued_1, rc2_xboole_0, rc2_xcmplx_0, rc3_valued_1, rc7_funct_1, rqRealAdd__k2_xcmplx_0__r0_r0_r0, rqRealAdd__k2_xcmplx_0__r0_r1_r1, rqRealAdd__k2_xcmplx_0__r0_r2_r2, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__r1_r0_r1, rqRealAdd__k2_xcmplx_0__r1_r1_r2, rqRealAdd__k2_xcmplx_0__r1_rm1_r0, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r2_r0_r2, rqRealAdd__k2_xcmplx_0__r2_rm1_r1, rqRealAdd__k2_xcmplx_0__r2_rm2_r0, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, rqRealAdd__k2_xcmplx_0__rm1_r1_r0, rqRealAdd__k2_xcmplx_0__rm1_r2_r1, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, rqRealAdd__k2_xcmplx_0__rm2_r2_r0, rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, rqRealDiv__k7_xcmplx_0__r1_r1_r1, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, rqRealDiv__k7_xcmplx_0__r2_r1_r2, rqRealDiv__k7_xcmplx_0__r2_r2_r1, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, spc10_arithm, spc11_arithm, spc12_arithm, spc1_arithm, spc2_arithm, spc3_arithm, spc4_arithm, spc5_arithm, spc6_arithm, spc7_arithm, spc8_arithm, spc9_arithm, t1_arithm, t2_arithm, t2_boole, t2_subset, t3_arithm, t3_boole, t3_subset, t4_arithm, t4_boole, t4_subset, t5_arithm, t5_subset, t6_arithm, t6_boole, t8_boole, d2_xboole_0, d9_xcmplx_0, involutiveness_k2_real_1, commutativity_k3_xcmplx_0, involutiveness_k4_xcmplx_0, involutiveness_k5_xcmplx_0, commutativity_k8_real_1, commutativity_k9_subset_1, idempotence_k9_subset_1, antisymmetry_r2_hidden, redefinition_k13_complex1, redefinition_k1_relset_1, redefinition_k1_seq_1, redefinition_k2_real_1, redefinition_k3_funct_2, redefinition_k6_numbers, redefinition_k6_subset_1, redefinition_k8_real_1, redefinition_k9_real_1, redefinition_k9_subset_1, dt_k13_complex1, dt_k16_sin_cos, dt_k19_sin_cos, dt_k1_funct_1, dt_k1_numbers, dt_k1_relset_1, dt_k1_rfunct_1, dt_k1_seq_1, dt_k1_tarski, dt_k2_real_1, dt_k30_sin_cos, dt_k3_funct_2, dt_k3_xcmplx_0, dt_k4_xcmplx_0, dt_k5_xcmplx_0, dt_k6_numbers, dt_k6_subset_1, dt_k6_xcmplx_0, dt_k8_real_1, dt_k8_relat_1, dt_k9_real_1, dt_k9_subset_1, dt_k9_xtuple_0, dt_c1_6__diff_4, dt_c2_6__diff_4, fc14_funct_1, fc1_numbers, fc1_rfunct_1, fc1_valued_2, fc2_xboole_0, fc3_membered, fc56_membered, fc61_valued_0, fc6_sin_cos, fc7_sin_cos, fc8_numbers, rc1_funct_1, rqRealDiff__k6_xcmplx_0__r0_r0_r0, rqRealDiff__k6_xcmplx_0__r0_r1_rm1, rqRealDiff__k6_xcmplx_0__r0_r2_rm2, rqRealDiff__k6_xcmplx_0__r0_rm1_r1, rqRealDiff__k6_xcmplx_0__r0_rm2_r2, rqRealDiff__k6_xcmplx_0__r1_r0_r1, rqRealDiff__k6_xcmplx_0__r1_r2_rm1, rqRealDiff__k6_xcmplx_0__r2_r0_r2, rqRealDiff__k6_xcmplx_0__r2_r1_r1, rqRealDiff__k6_xcmplx_0__r2_r2_r0, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, rqRealMult__k3_xcmplx_0__r0_r0_r0, rqRealMult__k3_xcmplx_0__r0_r1_r0, rqRealMult__k3_xcmplx_0__r0_r2_r0, rqRealMult__k3_xcmplx_0__r0_rm2_r0, rqRealMult__k3_xcmplx_0__r1_r0_r0, rqRealMult__k3_xcmplx_0__r1_r2_r2, rqRealMult__k3_xcmplx_0__r1_rm2_rm2, rqRealMult__k3_xcmplx_0__r2_r0_r0, rqRealMult__k3_xcmplx_0__r2_r1_r2, rqRealMult__k3_xcmplx_0__rm2_r0_r0, rqRealMult__k3_xcmplx_0__rm2_r1_rm2, rqRealNeg__k4_xcmplx_0__r2_rm2, rqRealNeg__k4_xcmplx_0__rm2_r2, t1_subset, t7_boole, d27_sin_cos, d8_xcmplx_0, spc0_numerals, spc1_numerals, spc2_numerals, spc0_boole, spc1_boole, spc2_boole, e1_6__diff_4, d1_rfunct_1, rqRealMult__k3_xcmplx_0__r1_r1_r1, rqRealNeg__k4_xcmplx_0__r1_rm1, rqRealNeg__k4_xcmplx_0__rm1_r1, rqRealDiff__k6_xcmplx_0__r1_r1_r0, rqRealNeg__k4_xcmplx_0__r0_r0, rqRealDiff__k6_xcmplx_0__r1_rm1_r2, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2]), [interesting(np__0.65), file(diff_4, e4_6_1__diff_4), [file(diff_4, e4_6_1__diff_4)]]). thf(e5_6_1__diff_4, plain, ( (= @ ( (k13_complex1 @ ( (k9_real_1 @ ( (k8_real_1 @ ( (k8_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k19_sin_cos) @ c1_6__diff_4) ) @ (k2_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k16_sin_cos) @ c1_6__diff_4) ) ) ) @ ( (k8_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k19_sin_cos) @ c1_6__diff_4) ) @ (k2_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k16_sin_cos) @ c1_6__diff_4) ) ) ) ) @ ( (k8_real_1 @ ( (k1_seq_1 @ k30_sin_cos) @ c2_6__diff_4) ) @ ( (k1_seq_1 @ k30_sin_cos) @ c2_6__diff_4) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ ( (k13_complex1 @ ( (k9_real_1 @ ( (k8_real_1 @ ( (k8_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k19_sin_cos) @ c1_6__diff_4) ) @ (k2_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k16_sin_cos) @ c1_6__diff_4) ) ) ) @ ( (k8_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k19_sin_cos) @ c1_6__diff_4) ) @ (k2_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k16_sin_cos) @ c1_6__diff_4) ) ) ) ) @ ( (k8_real_1 @ ( (k8_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k19_sin_cos) @ c2_6__diff_4) ) @ (k2_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k16_sin_cos) @ c2_6__diff_4) ) ) ) @ ( (k1_seq_1 @ k30_sin_cos) @ c2_6__diff_4) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) , inference(mizar_by, [status(thm), assumptions([dt_c1_6__diff_4, dt_c2_6__diff_4, e1_6__diff_4])], [cc10_valued_2, cc16_valued_2, cc29_valued_2, cc8_valued_2, fc15_valued_2, fc17_valued_2, fc41_valued_2, fc43_valued_2, cc11_valued_2, cc17_valued_2, cc25_valued_2, cc26_valued_2, cc30_valued_2, cc4_valued_2, cc5_valued_2, fc18_valued_2, fc44_valued_2, cc12_valued_2, cc15_membered, cc18_valued_2, cc19_valued_0, cc22_membered, cc23_valued_0, cc24_valued_0, cc24_valued_2, cc2_seq_2, cc31_valued_2, cc3_membered, cc3_valued_2, fc10_membered, fc19_valued_2, fc37_membered, fc38_membered, fc45_valued_2, fc46_membered, fc88_valued_0, rc3_valued_0, dt_k3_numbers, dt_k4_numbers, cc10_membered, cc13_valued_0, cc13_valued_2, cc14_valued_0, cc16_membered, cc19_valued_2, cc1_int_1, cc1_seq_2, cc20_valued_0, cc22_valued_0, cc23_membered, cc23_valued_2, cc2_membered, cc2_ordinal1, cc2_valued_0, cc2_valued_2, cc32_valued_2, cc3_int_1, cc3_valued_0, cc4_seq_2, cc4_valued_0, cc6_funct_1, cc9_membered, fc11_membered, fc18_funct_1, fc19_valued_0, fc1_int_1, fc20_valued_0, fc20_valued_2, fc21_valued_0, fc22_valued_0, fc24_relat_1, fc2_int_1, fc39_membered, fc3_int_1, fc3_numbers, fc40_membered, fc46_valued_2, fc47_membered, fc4_int_1, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc89_valued_0, rc1_int_1, rc2_int_1, rc2_ordinal1, rc2_valued_0, rc5_valued_1, reflexivity_r1_tarski, dt_k4_ordinal1, dt_o_0_0_xboole_0, cc10_ordinal1, cc11_valued_0, cc12_membered, cc13_membered, cc14_valued_2, cc15_valued_0, cc16_valued_0, cc17_membered, cc17_valued_0, cc19_membered, cc1_funct_2, cc1_membered, cc1_ordinal1, cc1_rfunct_1, cc1_valued_0, cc1_valued_2, cc20_membered, cc20_valued_2, cc21_valued_0, cc21_valued_2, cc22_valued_2, cc24_membered, cc28_valued_0, cc2_int_1, cc2_xcmplx_0, cc2_xreal_0, cc2_xxreal_0, cc30_valued_0, cc31_valued_0, cc33_valued_2, cc3_seq_2, cc3_xxreal_0, cc4_xxreal_0, cc5_funct_1, cc5_ordinal1, cc5_xxreal_0, cc6_ordinal1, cc6_relat_1, cc6_xxreal_0, cc7_valued_0, cc7_xxreal_0, cc8_ordinal1, cc8_relat_1, cc8_valued_0, cc8_xxreal_0, fc11_funct_1, fc11_xreal_0, fc12_membered, fc12_xreal_0, fc13_xreal_0, fc14_xreal_0, fc15_valued_0, fc16_valued_0, fc16_xreal_0, fc17_funct_1, fc17_xreal_0, fc18_xreal_0, fc19_funct_1, fc21_valued_2, fc21_xreal_0, fc22_xreal_0, fc23_valued_0, fc23_xreal_0, fc24_valued_0, fc24_xreal_0, fc26_xreal_0, fc29_xreal_0, fc30_xreal_0, fc31_membered, fc31_xreal_0, fc32_membered, fc32_xreal_0, fc33_membered, fc33_xreal_0, fc34_membered, fc40_valued_2, fc41_membered, fc42_membered, fc42_valued_2, fc43_membered, fc44_membered, fc47_valued_2, fc48_membered, fc4_ordinal1, fc59_membered, fc5_relset_1, fc62_valued_0, fc66_valued_0, fc6_membered, fc6_ordinal1, fc6_relset_1, fc85_valued_0, fc86_valued_0, fc8_membered, fc90_valued_0, fc9_xreal_0, rc1_funct_2, rc1_membered, rc1_ordinal1, rc1_partfun1, rc1_relset_1, rc1_seq_2, rc1_valued_0, rc1_valued_2, rc1_xxreal_0, rc2_funct_1, rc2_membered, rc2_relat_1, rc2_valued_2, rc2_xreal_0, rc2_xxreal_0, rc3_funct_1, rc3_membered, rc3_ordinal1, rc3_partfun1, rc3_relat_1, rc3_xreal_0, rc3_xxreal_0, rc4_funct_1, rc4_ordinal1, rc4_valued_0, rc4_xreal_0, rc4_xxreal_0, rc5_funct_1, rc5_ordinal1, rc6_funct_1, rc6_valued_0, rc9_funct_1, t1_numerals, commutativity_k2_xcmplx_0, commutativity_k3_xboole_0, idempotence_k3_xboole_0, existence_m1_subset_1, existence_m2_subset_1, redefinition_k3_rfunct_1, redefinition_k5_numbers, redefinition_m2_subset_1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_numbers, dt_k2_xcmplx_0, dt_k2_zfmisc_1, dt_k3_rfunct_1, dt_k3_xboole_0, dt_k4_xboole_0, dt_k5_numbers, dt_m1_subset_1, dt_m2_subset_1, cc10_valued_0, cc11_membered, cc12_valued_0, cc14_membered, cc15_valued_2, cc18_membered, cc18_valued_0, cc1_funct_1, cc1_partfun1, cc1_relat_1, cc1_relset_1, cc1_xcmplx_0, cc1_xreal_0, cc21_membered, cc25_membered, cc26_membered, cc27_valued_2, cc28_valued_2, cc2_funct_1, cc2_funct_2, cc2_partfun1, cc2_relat_1, cc2_relset_1, cc3_funct_1, cc3_funct_2, cc3_ordinal1, cc3_relat_1, cc3_relset_1, cc3_xcmplx_0, cc3_xreal_0, cc4_funct_1, cc4_funct_2, cc4_membered, cc4_ordinal1, cc4_relat_1, cc4_relset_1, cc4_xreal_0, cc5_membered, cc5_relat_1, cc5_valued_0, cc6_membered, cc6_valued_0, cc6_valued_2, cc7_funct_1, cc7_ordinal1, cc7_relat_1, cc7_valued_2, cc8_funct_1, cc8_funct_2, cc8_membered, cc9_funct_1, cc9_ordinal1, cc9_valued_0, cc9_valued_2, fc108_valued_1, fc10_relat_1, fc10_xreal_0, fc13_valued_0, fc14_valued_0, fc14_valued_2, fc15_xreal_0, fc16_valued_2, fc17_valued_0, fc18_valued_0, fc19_xreal_0, fc1_membered, fc1_relat_1, fc1_xboole_0, fc20_xreal_0, fc21_relat_1, fc22_relat_1, fc25_xreal_0, fc27_xreal_0, fc28_xreal_0, fc2_numbers, fc2_relat_1, fc2_relset_1, fc2_rfunct_1, fc2_xcmplx_0, fc34_xreal_0, fc35_membered, fc36_membered, fc3_relset_1, fc3_xcmplx_0, fc3_xreal_0, fc45_membered, fc4_xcmplx_0, fc4_xreal_0, fc55_membered, fc5_xcmplx_0, fc5_xreal_0, fc63_valued_0, fc6_relat_1, fc6_xcmplx_0, fc6_xreal_0, fc7_membered, fc7_xcmplx_0, fc7_xreal_0, fc87_valued_0, fc8_relat_1, fc8_relset_1, fc8_xcmplx_0, fc8_xreal_0, fc9_membered, fc9_numbers, fc9_xcmplx_0, rc1_relat_1, rc1_xboole_0, rc1_xcmplx_0, rc1_xreal_0, rc2_valued_1, rc2_xboole_0, rc2_xcmplx_0, rc3_valued_1, rc7_funct_1, rqRealAdd__k2_xcmplx_0__r0_r0_r0, rqRealAdd__k2_xcmplx_0__r0_r1_r1, rqRealAdd__k2_xcmplx_0__r0_r2_r2, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__r1_r0_r1, rqRealAdd__k2_xcmplx_0__r1_r1_r2, rqRealAdd__k2_xcmplx_0__r1_rm1_r0, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r2_r0_r2, rqRealAdd__k2_xcmplx_0__r2_rm1_r1, rqRealAdd__k2_xcmplx_0__r2_rm2_r0, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, rqRealAdd__k2_xcmplx_0__rm1_r1_r0, rqRealAdd__k2_xcmplx_0__rm1_r2_r1, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, rqRealAdd__k2_xcmplx_0__rm2_r2_r0, rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, spc10_arithm, spc11_arithm, spc12_arithm, spc1_arithm, spc2_arithm, spc3_arithm, spc4_arithm, spc5_arithm, spc6_arithm, spc7_arithm, spc8_arithm, spc9_arithm, t1_arithm, t2_arithm, t2_boole, t2_subset, t3_arithm, t3_boole, t3_subset, t4_arithm, t4_boole, t4_subset, t5_arithm, t5_subset, t6_arithm, t6_boole, t8_boole, d2_xboole_0, involutiveness_k2_real_1, commutativity_k3_xcmplx_0, involutiveness_k4_xcmplx_0, involutiveness_k5_xcmplx_0, commutativity_k8_real_1, commutativity_k9_subset_1, idempotence_k9_subset_1, antisymmetry_r2_hidden, redefinition_k13_complex1, redefinition_k1_relset_1, redefinition_k1_seq_1, redefinition_k2_real_1, redefinition_k3_funct_2, redefinition_k6_numbers, redefinition_k6_subset_1, redefinition_k8_real_1, redefinition_k9_real_1, redefinition_k9_subset_1, dt_k13_complex1, dt_k16_sin_cos, dt_k19_sin_cos, dt_k1_funct_1, dt_k1_numbers, dt_k1_relset_1, dt_k1_rfunct_1, dt_k1_seq_1, dt_k1_tarski, dt_k2_real_1, dt_k30_sin_cos, dt_k3_funct_2, dt_k3_xcmplx_0, dt_k4_xcmplx_0, dt_k5_xcmplx_0, dt_k6_numbers, dt_k6_subset_1, dt_k6_xcmplx_0, dt_k7_xcmplx_0, dt_k8_real_1, dt_k8_relat_1, dt_k9_real_1, dt_k9_subset_1, dt_k9_xtuple_0, dt_c1_6__diff_4, dt_c2_6__diff_4, fc14_funct_1, fc1_numbers, fc1_rfunct_1, fc1_valued_2, fc2_xboole_0, fc3_membered, fc56_membered, fc61_valued_0, fc6_sin_cos, fc7_sin_cos, fc8_numbers, rc1_funct_1, rqRealDiff__k6_xcmplx_0__r0_r0_r0, rqRealDiff__k6_xcmplx_0__r0_r1_rm1, rqRealDiff__k6_xcmplx_0__r0_r2_rm2, rqRealDiff__k6_xcmplx_0__r0_rm1_r1, rqRealDiff__k6_xcmplx_0__r0_rm2_r2, rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r1_r0_r1, rqRealDiff__k6_xcmplx_0__r1_r2_rm1, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r2_r0_r2, rqRealDiff__k6_xcmplx_0__r2_r1_r1, rqRealDiff__k6_xcmplx_0__r2_r2_r0, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, rqRealDiv__k7_xcmplx_0__r1_r1_r1, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, rqRealDiv__k7_xcmplx_0__r2_r1_r2, rqRealDiv__k7_xcmplx_0__r2_r2_r1, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__r0_r0_r0, rqRealMult__k3_xcmplx_0__r0_r1_r0, rqRealMult__k3_xcmplx_0__r0_r2_r0, rqRealMult__k3_xcmplx_0__r0_rm2_r0, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, rqRealMult__k3_xcmplx_0__r1_r0_r0, rqRealMult__k3_xcmplx_0__r1_r2_r2, rqRealMult__k3_xcmplx_0__r1_rm2_rm2, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r2_r0_r0, rqRealMult__k3_xcmplx_0__r2_r1_r2, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_r0_r0, rqRealMult__k3_xcmplx_0__rm2_r1_rm2, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, rqRealNeg__k4_xcmplx_0__r2_rm2, rqRealNeg__k4_xcmplx_0__rm2_r2, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, t1_subset, t7_boole, d27_sin_cos, d8_xcmplx_0, d9_xcmplx_0, spc0_numerals, spc1_numerals, spc2_numerals, spc0_boole, spc1_boole, spc2_boole, e1_6__diff_4, d1_rfunct_1, rqRealMult__k3_xcmplx_0__r1_r1_r1, rqRealNeg__k4_xcmplx_0__r1_rm1, rqRealNeg__k4_xcmplx_0__rm1_r1, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, rqRealNeg__k4_xcmplx_0__r0_r0, rqRealDiff__k6_xcmplx_0__r1_r1_r0, rqRealDiff__k6_xcmplx_0__r1_rm1_r2, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2]), [interesting(np__0.65), file(diff_4, e5_6_1__diff_4), [file(diff_4, e5_6_1__diff_4)]]). thf(d2_sin_cos4, definition, (! [A: $i] : ( (v1_xreal_0 @ A) => ( (= @ (k2_sin_cos4 @ A) ) @ ( (k7_xcmplx_0 @ (k20_sin_cos @ A) ) @ (k17_sin_cos @ A) ) ) ) ) , file(sin_cos4, d2_sin_cos4), [interesting(np__0.9), axiom, file(sin_cos4, d2_sin_cos4)]). thf(e6_6_1__diff_4, plain, ( (= @ ( (k13_complex1 @ ( (k9_real_1 @ ( (k8_real_1 @ ( (k8_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k19_sin_cos) @ c1_6__diff_4) ) @ (k2_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k16_sin_cos) @ c1_6__diff_4) ) ) ) @ ( (k8_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k19_sin_cos) @ c1_6__diff_4) ) @ (k2_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k16_sin_cos) @ c1_6__diff_4) ) ) ) ) @ ( (k8_real_1 @ ( (k8_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k19_sin_cos) @ c2_6__diff_4) ) @ (k2_real_1 @ ( ( ( (k3_funct_2 @ k1_numbers) @ k1_numbers) @ k16_sin_cos) @ c2_6__diff_4) ) ) ) @ ( (k1_seq_1 @ k30_sin_cos) @ c2_6__diff_4) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ ( (k13_complex1 @ ( (k9_real_1 @ (k5_square_1 @ (k2_sin_cos4 @ c1_6__diff_4) ) ) @ (k5_square_1 @ (k2_sin_cos4 @ c2_6__diff_4) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) , inference(mizar_by, [status(thm), assumptions([dt_c1_6__diff_4, dt_c2_6__diff_4, e1_6__diff_4])], [cc10_valued_2, cc16_valued_2, cc29_valued_2, cc8_valued_2, fc15_valued_2, fc17_valued_2, fc41_valued_2, fc43_valued_2, cc11_valued_2, cc17_valued_2, cc25_valued_2, cc26_valued_2, cc30_valued_2, cc4_valued_2, cc5_valued_2, fc18_valued_2, fc44_valued_2, cc12_valued_2, cc15_membered, cc18_valued_2, cc19_valued_0, cc22_membered, cc23_valued_0, cc24_valued_0, cc24_valued_2, cc2_seq_2, cc31_valued_2, cc3_membered, cc3_valued_2, fc10_membered, fc19_valued_2, fc37_membered, fc38_membered, fc45_valued_2, fc46_membered, fc88_valued_0, rc3_valued_0, dt_k3_numbers, dt_k4_numbers, cc10_membered, cc13_valued_0, cc13_valued_2, cc14_valued_0, cc16_membered, cc19_valued_2, cc1_int_1, cc1_seq_2, cc20_valued_0, cc22_valued_0, cc23_membered, cc23_valued_2, cc2_membered, cc2_ordinal1, cc2_valued_0, cc2_valued_2, cc32_valued_2, cc3_int_1, cc3_valued_0, cc4_seq_2, cc4_valued_0, cc6_funct_1, cc9_membered, fc11_membered, fc18_funct_1, fc19_valued_0, fc1_int_1, fc20_valued_0, fc20_valued_2, fc21_valued_0, fc22_valued_0, fc24_relat_1, fc2_int_1, fc39_membered, fc3_int_1, fc3_numbers, fc40_membered, fc46_valued_2, fc47_membered, fc4_int_1, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc89_valued_0, rc1_int_1, rc2_int_1, rc2_ordinal1, rc2_valued_0, rc5_valued_1, reflexivity_r1_tarski, dt_k4_ordinal1, dt_o_0_0_xboole_0, cc10_ordinal1, cc11_valued_0, cc12_membered, cc13_membered, cc14_valued_2, cc15_valued_0, cc16_valued_0, cc17_membered, cc17_valued_0, cc19_membered, cc1_funct_2, cc1_membered, cc1_ordinal1, cc1_rfunct_1, cc1_valued_0, cc1_valued_2, cc20_membered, cc20_valued_2, cc21_valued_0, cc21_valued_2, cc22_valued_2, cc24_membered, cc28_valued_0, cc2_int_1, cc2_xcmplx_0, cc2_xreal_0, cc2_xxreal_0, cc30_valued_0, cc31_valued_0, cc33_valued_2, cc3_seq_2, cc3_xxreal_0, cc4_xxreal_0, cc5_funct_1, cc5_ordinal1, cc5_xxreal_0, cc6_ordinal1, cc6_relat_1, cc6_xxreal_0, cc7_valued_0, cc7_xxreal_0, cc8_ordinal1, cc8_relat_1, cc8_valued_0, cc8_xxreal_0, fc11_funct_1, fc11_xreal_0, fc12_membered, fc12_xreal_0, fc13_xreal_0, fc14_xreal_0, fc15_valued_0, fc16_valued_0, fc16_xreal_0, fc17_funct_1, fc17_xreal_0, fc18_xreal_0, fc19_funct_1, fc21_valued_2, fc21_xreal_0, fc22_xreal_0, fc23_valued_0, fc23_xreal_0, fc24_valued_0, fc24_xreal_0, fc26_xreal_0, fc29_xreal_0, fc30_xreal_0, fc31_membered, fc31_xreal_0, fc32_membered, fc32_xreal_0, fc33_membered, fc33_xreal_0, fc34_membered, fc40_valued_2, fc41_membered, fc42_membered, fc42_valued_2, fc43_membered, fc44_membered, fc47_valued_2, fc48_membered, fc4_ordinal1, fc59_membered, fc5_relset_1, fc62_valued_0, fc66_valued_0, fc6_membered, fc6_ordinal1, fc6_relset_1, fc85_valued_0, fc86_valued_0, fc8_membered, fc90_valued_0, fc9_xreal_0, rc1_funct_2, rc1_membered, rc1_ordinal1, rc1_partfun1, rc1_relset_1, rc1_seq_2, rc1_valued_0, rc1_valued_2, rc1_xxreal_0, rc2_funct_1, rc2_membered, rc2_relat_1, rc2_valued_2, rc2_xreal_0, rc2_xxreal_0, rc3_funct_1, rc3_membered, rc3_ordinal1, rc3_partfun1, rc3_relat_1, rc3_xreal_0, rc3_xxreal_0, rc4_funct_1, rc4_ordinal1, rc4_valued_0, rc4_xreal_0, rc4_xxreal_0, rc5_funct_1, rc5_ordinal1, rc6_funct_1, rc6_valued_0, rc9_funct_1, t1_numerals, commutativity_k2_xcmplx_0, commutativity_k3_xboole_0, idempotence_k3_xboole_0, existence_m1_subset_1, existence_m2_subset_1, redefinition_k3_rfunct_1, redefinition_k5_numbers, redefinition_m2_subset_1, dt_k17_sin_cos, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k20_sin_cos, dt_k2_numbers, dt_k2_xcmplx_0, dt_k2_zfmisc_1, dt_k3_rfunct_1, dt_k3_square_1, dt_k3_xboole_0, dt_k4_xboole_0, dt_k5_numbers, dt_k7_xcmplx_0, dt_m1_subset_1, dt_m2_subset_1, cc10_valued_0, cc11_membered, cc12_valued_0, cc14_membered, cc15_valued_2, cc18_membered, cc18_valued_0, cc1_funct_1, cc1_partfun1, cc1_relat_1, cc1_relset_1, cc1_xcmplx_0, cc1_xreal_0, cc21_membered, cc25_membered, cc26_membered, cc27_valued_2, cc28_valued_2, cc2_funct_1, cc2_funct_2, cc2_partfun1, cc2_relat_1, cc2_relset_1, cc3_funct_1, cc3_funct_2, cc3_ordinal1, cc3_relat_1, cc3_relset_1, cc3_xcmplx_0, cc3_xreal_0, cc4_funct_1, cc4_funct_2, cc4_membered, cc4_ordinal1, cc4_relat_1, cc4_relset_1, cc4_xreal_0, cc5_membered, cc5_relat_1, cc5_valued_0, cc6_membered, cc6_valued_0, cc6_valued_2, cc7_funct_1, cc7_ordinal1, cc7_relat_1, cc7_valued_2, cc8_funct_1, cc8_funct_2, cc8_membered, cc9_funct_1, cc9_ordinal1, cc9_valued_0, cc9_valued_2, fc108_valued_1, fc10_relat_1, fc10_xreal_0, fc13_valued_0, fc14_valued_0, fc14_valued_2, fc15_xreal_0, fc16_valued_2, fc17_valued_0, fc18_valued_0, fc19_xreal_0, fc1_membered, fc1_relat_1, fc1_square_1, fc1_xboole_0, fc20_xreal_0, fc21_relat_1, fc22_relat_1, fc25_xreal_0, fc27_xreal_0, fc28_xreal_0, fc2_numbers, fc2_relat_1, fc2_relset_1, fc2_rfunct_1, fc2_square_1, fc2_xcmplx_0, fc34_xreal_0, fc35_membered, fc36_membered, fc3_relset_1, fc3_sin_cos, fc3_xcmplx_0, fc3_xreal_0, fc45_membered, fc4_sin_cos, fc4_xcmplx_0, fc4_xreal_0, fc55_membered, fc5_xcmplx_0, fc5_xreal_0, fc63_valued_0, fc6_relat_1, fc6_xcmplx_0, fc6_xreal_0, fc7_membered, fc7_xcmplx_0, fc7_xreal_0, fc87_valued_0, fc8_relat_1, fc8_relset_1, fc8_xcmplx_0, fc8_xreal_0, fc9_membered, fc9_numbers, fc9_xcmplx_0, rc1_relat_1, rc1_xboole_0, rc1_xcmplx_0, rc1_xreal_0, rc2_valued_1, rc2_xboole_0, rc2_xcmplx_0, rc3_valued_1, rc7_funct_1, rqRealAdd__k2_xcmplx_0__r0_r0_r0, rqRealAdd__k2_xcmplx_0__r0_r1_r1, rqRealAdd__k2_xcmplx_0__r0_r2_r2, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__r1_r0_r1, rqRealAdd__k2_xcmplx_0__r1_r1_r2, rqRealAdd__k2_xcmplx_0__r1_rm1_r0, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r2_r0_r2, rqRealAdd__k2_xcmplx_0__r2_rm1_r1, rqRealAdd__k2_xcmplx_0__r2_rm2_r0, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, rqRealAdd__k2_xcmplx_0__rm1_r1_r0, rqRealAdd__k2_xcmplx_0__rm1_r2_r1, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, rqRealAdd__k2_xcmplx_0__rm2_r2_r0, rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, rqRealDiv__k7_xcmplx_0__r1_r1_r1, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, rqRealDiv__k7_xcmplx_0__r2_r1_r2, rqRealDiv__k7_xcmplx_0__r2_r2_r1, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, spc10_arithm, spc11_arithm, spc12_arithm, spc1_arithm, spc2_arithm, spc3_arithm, spc4_arithm, spc5_arithm, spc6_arithm, spc7_arithm, spc8_arithm, spc9_arithm, t1_arithm, t2_arithm, t2_boole, t2_subset, t3_arithm, t3_boole, t3_subset, t4_arithm, t4_boole, t4_subset, t5_arithm, t5_subset, t6_arithm, t6_boole, t8_boole, d17_sin_cos, d2_xboole_0, d19_sin_cos, d1_square_1, d9_xcmplx_0, involutiveness_k2_real_1, commutativity_k3_xcmplx_0, involutiveness_k4_xcmplx_0, involutiveness_k5_xcmplx_0, commutativity_k8_real_1, commutativity_k9_subset_1, idempotence_k9_subset_1, antisymmetry_r2_hidden, redefinition_k13_complex1, redefinition_k1_relset_1, redefinition_k1_seq_1, redefinition_k2_real_1, redefinition_k3_funct_2, redefinition_k5_square_1, redefinition_k6_numbers, redefinition_k6_subset_1, redefinition_k8_real_1, redefinition_k9_real_1, redefinition_k9_subset_1, dt_k13_complex1, dt_k16_sin_cos, dt_k19_sin_cos, dt_k1_funct_1, dt_k1_numbers, dt_k1_relset_1, dt_k1_rfunct_1, dt_k1_seq_1, dt_k1_tarski, dt_k2_real_1, dt_k2_sin_cos4, dt_k30_sin_cos, dt_k3_funct_2, dt_k3_xcmplx_0, dt_k4_xcmplx_0, dt_k5_square_1, dt_k5_xcmplx_0, dt_k6_numbers, dt_k6_subset_1, dt_k6_xcmplx_0, dt_k8_real_1, dt_k8_relat_1, dt_k9_real_1, dt_k9_subset_1, dt_k9_xtuple_0, dt_c1_6__diff_4, dt_c2_6__diff_4, fc14_funct_1, fc1_numbers, fc1_rfunct_1, fc1_valued_2, fc2_xboole_0, fc3_membered, fc56_membered, fc61_valued_0, fc6_sin_cos, fc7_sin_cos, fc8_numbers, rc1_funct_1, rqRealDiff__k6_xcmplx_0__r0_r0_r0, rqRealDiff__k6_xcmplx_0__r0_r1_rm1, rqRealDiff__k6_xcmplx_0__r0_r2_rm2, rqRealDiff__k6_xcmplx_0__r0_rm1_r1, rqRealDiff__k6_xcmplx_0__r0_rm2_r2, rqRealDiff__k6_xcmplx_0__r1_r0_r1, rqRealDiff__k6_xcmplx_0__r1_r2_rm1, rqRealDiff__k6_xcmplx_0__r2_r0_r2, rqRealDiff__k6_xcmplx_0__r2_r1_r1, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, rqRealMult__k3_xcmplx_0__r0_r0_r0, rqRealMult__k3_xcmplx_0__r0_r1_r0, rqRealMult__k3_xcmplx_0__r0_r2_r0, rqRealMult__k3_xcmplx_0__r0_rm2_r0, rqRealMult__k3_xcmplx_0__r1_r0_r0, rqRealMult__k3_xcmplx_0__r1_r2_r2, rqRealMult__k3_xcmplx_0__r1_rm2_rm2, rqRealMult__k3_xcmplx_0__r2_r0_r0, rqRealMult__k3_xcmplx_0__rm2_r0_r0, rqRealMult__k3_xcmplx_0__rm2_r1_rm2, t1_subset, t7_boole, d2_sin_cos4, d27_sin_cos, d8_xcmplx_0, spc0_numerals, spc1_numerals, spc2_numerals, spc0_boole, spc1_boole, spc2_boole, e1_6__diff_4, d1_rfunct_1, rqRealMult__k3_xcmplx_0__r1_r1_r1, rqRealNeg__k4_xcmplx_0__r1_rm1, rqRealNeg__k4_xcmplx_0__rm1_r1, rqRealNeg__k4_xcmplx_0__r0_r0, rqRealDiff__k6_xcmplx_0__r1_r1_r0, rqRealDiff__k6_xcmplx_0__r1_rm1_r2, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, rqRealMult__k3_xcmplx_0__r2_r1_r2, rqRealNeg__k4_xcmplx_0__r2_rm2, rqRealDiff__k6_xcmplx_0__r2_r2_r0, rqRealNeg__k4_xcmplx_0__rm2_r2]), [interesting(np__0.65), file(diff_4, e6_6_1__diff_4), [file(diff_4, e6_6_1__diff_4)]]). thf(e7_6_1__diff_4, plain, ( (= @ ( (k13_complex1 @ ( (k9_real_1 @ (k5_square_1 @ (k2_sin_cos4 @ c1_6__diff_4) ) ) @ (k5_square_1 @ (k2_sin_cos4 @ c2_6__diff_4) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ ( (k13_complex1 @ ( (k8_real_1 @ ( (k9_real_1 @ (k2_sin_cos4 @ c1_6__diff_4) ) @ (k2_sin_cos4 @ c2_6__diff_4) ) ) @ ( (k7_real_1 @ (k2_sin_cos4 @ c1_6__diff_4) ) @ (k2_sin_cos4 @ c2_6__diff_4) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) , inference(mizar_by, [status(thm), assumptions([dt_c1_6__diff_4, dt_c2_6__diff_4])], [fc40_valued_2, fc41_valued_2, fc42_valued_2, fc43_valued_2, cc10_valued_2, cc15_valued_2, cc16_valued_2, cc21_valued_2, cc25_valued_2, cc26_valued_2, cc28_valued_2, cc29_valued_2, cc7_valued_2, cc8_valued_2, cc9_valued_2, fc14_valued_2, fc15_valued_2, fc16_valued_2, fc17_valued_2, fc44_valued_2, cc11_valued_2, cc17_valued_2, cc23_valued_0, cc24_valued_0, cc24_valued_2, cc2_seq_2, cc30_valued_2, cc4_valued_2, cc5_valued_2, fc18_valued_2, fc45_valued_2, rc3_valued_0, dt_k3_numbers, dt_k4_numbers, cc10_membered, cc10_valued_0, cc11_valued_0, cc12_valued_2, cc13_valued_0, cc14_valued_0, cc15_membered, cc18_valued_2, cc19_valued_0, cc1_funct_2, cc1_int_1, cc1_seq_2, cc22_membered, cc22_valued_0, cc23_valued_2, cc28_valued_0, cc2_valued_0, cc30_valued_0, cc31_valued_0, cc31_valued_2, cc3_membered, cc3_valued_0, cc3_valued_2, cc4_seq_2, cc4_valued_0, cc5_relat_1, cc6_funct_1, cc6_relat_1, cc7_relat_1, cc8_relat_1, cc9_membered, fc17_funct_1, fc19_valued_2, fc3_numbers, fc46_valued_2, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc61_valued_0, fc62_valued_0, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc88_valued_0, rc1_funct_2, rc1_partfun1, rc1_relset_1, rc1_seq_2, rc2_valued_0, rc2_valued_1, rc3_ordinal1, rc3_partfun1, rc3_relat_1, rc3_valued_1, rc4_valued_0, rc5_valued_1, rc6_funct_1, rc6_valued_0, rc9_funct_1, reflexivity_r1_tarski, dt_k1_funct_1, dt_k2_zfmisc_1, dt_o_0_0_xboole_0, cc12_valued_0, cc13_membered, cc13_valued_2, cc15_valued_0, cc16_membered, cc16_valued_0, cc17_valued_0, cc18_valued_0, cc19_valued_2, cc1_partfun1, cc1_relset_1, cc1_rfunct_1, cc1_valued_0, cc20_membered, cc20_valued_0, cc21_valued_0, cc22_valued_2, cc23_membered, cc2_funct_2, cc2_membered, cc2_ordinal1, cc2_partfun1, cc2_relset_1, cc2_valued_2, cc32_valued_2, cc33_valued_2, cc3_funct_2, cc3_int_1, cc3_relset_1, cc3_seq_2, cc4_funct_2, cc4_relset_1, cc5_funct_1, cc5_valued_0, cc6_valued_0, cc7_valued_0, cc8_funct_2, cc8_valued_0, fc19_funct_1, fc1_int_1, fc20_valued_2, fc21_valued_2, fc2_int_1, fc3_int_1, fc47_valued_2, fc4_int_1, fc63_valued_0, fc66_valued_0, fc6_relat_1, fc85_valued_0, fc86_valued_0, fc87_valued_0, fc89_valued_0, fc90_valued_0, rc1_int_1, rc1_valued_0, rc2_funct_1, rc2_int_1, rc2_ordinal1, rc2_relat_1, rc2_valued_2, rc3_funct_1, rc4_funct_1, rc5_funct_1, involutiveness_k5_xcmplx_0, antisymmetry_r2_hidden, redefinition_k1_seq_1, dt_k16_sin_cos, dt_k19_sin_cos, dt_k1_seq_1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k4_ordinal1, dt_k5_xcmplx_0, cc10_ordinal1, cc11_membered, cc12_membered, cc14_membered, cc14_valued_2, cc17_membered, cc19_membered, cc1_membered, cc1_ordinal1, cc1_valued_2, cc20_valued_2, cc21_membered, cc24_membered, cc27_valued_2, cc2_funct_1, cc2_int_1, cc2_relat_1, cc2_xcmplx_0, cc2_xreal_0, cc2_xxreal_0, cc3_funct_1, cc3_relat_1, cc3_xxreal_0, cc4_funct_1, cc4_membered, cc4_relat_1, cc4_xxreal_0, cc5_membered, cc5_ordinal1, cc5_xxreal_0, cc6_membered, cc6_ordinal1, cc6_xxreal_0, cc7_xxreal_0, cc8_funct_1, cc8_membered, cc8_ordinal1, cc8_xxreal_0, cc9_funct_1, cc9_valued_0, fc11_xreal_0, fc12_xreal_0, fc13_xreal_0, fc14_xreal_0, fc16_xreal_0, fc17_xreal_0, fc18_xreal_0, fc1_xboole_0, fc21_xreal_0, fc22_xreal_0, fc23_xreal_0, fc24_xreal_0, fc26_xreal_0, fc27_xreal_0, fc28_xreal_0, fc29_xreal_0, fc30_xreal_0, fc31_xreal_0, fc32_xreal_0, fc33_xreal_0, fc4_xreal_0, fc59_membered, fc6_membered, fc6_ordinal1, fc6_sin_cos, fc7_sin_cos, fc7_xcmplx_0, fc9_xreal_0, rc1_funct_1, rc1_membered, rc1_ordinal1, rc1_relat_1, rc1_valued_2, rc1_xxreal_0, rc2_membered, rc2_xreal_0, rc2_xxreal_0, rc3_membered, rc3_xreal_0, rc3_xxreal_0, rc4_ordinal1, rc4_xreal_0, rc4_xxreal_0, rc5_ordinal1, rc7_funct_1, spc10_arithm, spc11_arithm, spc12_arithm, spc3_arithm, t1_numerals, t1_subset, t3_subset, t4_subset, t5_subset, d2_xboole_0, existence_m1_subset_1, existence_m2_subset_1, redefinition_k5_numbers, redefinition_m2_subset_1, dt_k17_sin_cos, dt_k1_numbers, dt_k20_sin_cos, dt_k2_numbers, dt_k3_square_1, dt_k5_numbers, dt_k7_xcmplx_0, dt_m1_subset_1, dt_m2_subset_1, cc18_membered, cc1_funct_1, cc1_relat_1, cc1_xcmplx_0, cc1_xreal_0, cc25_membered, cc26_membered, cc3_ordinal1, cc3_xcmplx_0, cc3_xreal_0, cc4_ordinal1, cc4_xreal_0, cc6_valued_2, cc7_funct_1, cc7_ordinal1, cc9_ordinal1, fc10_xreal_0, fc15_xreal_0, fc19_xreal_0, fc1_membered, fc1_numbers, fc1_square_1, fc20_xreal_0, fc25_xreal_0, fc2_numbers, fc2_square_1, fc2_xcmplx_0, fc34_xreal_0, fc3_membered, fc3_sin_cos, fc3_xcmplx_0, fc3_xreal_0, fc4_sin_cos, fc4_xcmplx_0, fc55_membered, fc56_membered, fc5_xcmplx_0, fc5_xreal_0, fc6_xcmplx_0, fc6_xreal_0, fc7_xreal_0, fc8_numbers, fc8_xcmplx_0, fc8_xreal_0, fc9_numbers, fc9_xcmplx_0, rc1_xboole_0, rc1_xcmplx_0, rc1_xreal_0, rc2_xboole_0, rc2_xcmplx_0, rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, rqRealDiv__k7_xcmplx_0__r1_r1_r1, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, rqRealDiv__k7_xcmplx_0__r2_r1_r2, rqRealDiv__k7_xcmplx_0__r2_r2_r1, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, spc1_arithm, spc2_arithm, spc4_arithm, spc5_arithm, spc6_arithm, spc7_arithm, spc8_arithm, spc9_arithm, t2_subset, t3_arithm, t6_arithm, t6_boole, t7_boole, t8_boole, d17_sin_cos, d19_sin_cos, d1_square_1, d9_xcmplx_0, commutativity_k2_xcmplx_0, commutativity_k3_xcmplx_0, involutiveness_k4_xcmplx_0, commutativity_k7_real_1, commutativity_k8_real_1, redefinition_k13_complex1, redefinition_k5_square_1, redefinition_k7_real_1, redefinition_k8_real_1, redefinition_k9_real_1, dt_k13_complex1, dt_k2_sin_cos4, dt_k2_xcmplx_0, dt_k3_xcmplx_0, dt_k4_xcmplx_0, dt_k5_square_1, dt_k6_xcmplx_0, dt_k7_real_1, dt_k8_real_1, dt_k9_real_1, dt_c1_6__diff_4, dt_c2_6__diff_4, rqRealAdd__k2_xcmplx_0__r0_r0_r0, rqRealAdd__k2_xcmplx_0__r0_r1_r1, rqRealAdd__k2_xcmplx_0__r0_r2_r2, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, rqRealAdd__k2_xcmplx_0__r1_r0_r1, rqRealAdd__k2_xcmplx_0__r1_r1_r2, rqRealAdd__k2_xcmplx_0__r1_rm1_r0, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, rqRealAdd__k2_xcmplx_0__r2_r0_r2, rqRealAdd__k2_xcmplx_0__r2_rm1_r1, rqRealAdd__k2_xcmplx_0__r2_rm2_r0, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, rqRealAdd__k2_xcmplx_0__rm1_r2_r1, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, rqRealAdd__k2_xcmplx_0__rm2_r2_r0, rqRealDiff__k6_xcmplx_0__r0_r0_r0, rqRealDiff__k6_xcmplx_0__r0_r1_rm1, rqRealDiff__k6_xcmplx_0__r0_r2_rm2, rqRealDiff__k6_xcmplx_0__r0_rm1_r1, rqRealDiff__k6_xcmplx_0__r0_rm2_r2, rqRealDiff__k6_xcmplx_0__r1_r0_r1, rqRealDiff__k6_xcmplx_0__r1_r2_rm1, rqRealDiff__k6_xcmplx_0__r2_r0_r2, rqRealDiff__k6_xcmplx_0__r2_r1_r1, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, rqRealMult__k3_xcmplx_0__r0_r0_r0, rqRealMult__k3_xcmplx_0__r0_r1_r0, rqRealMult__k3_xcmplx_0__r0_r2_r0, rqRealMult__k3_xcmplx_0__r0_rm2_r0, rqRealMult__k3_xcmplx_0__r1_r0_r0, rqRealMult__k3_xcmplx_0__r1_r2_r2, rqRealMult__k3_xcmplx_0__r1_rm2_rm2, rqRealMult__k3_xcmplx_0__r2_r0_r0, rqRealMult__k3_xcmplx_0__rm2_r0_r0, rqRealNeg__k4_xcmplx_0__r0_r0, d2_sin_cos4, d8_xcmplx_0, spc0_numerals, spc1_numerals, spc2_numerals, spc0_boole, spc1_boole, spc2_boole, rqRealMult__k3_xcmplx_0__r1_r1_r1, rqRealNeg__k4_xcmplx_0__r1_rm1, rqRealAdd__k2_xcmplx_0__rm1_r1_r0, rqRealNeg__k4_xcmplx_0__rm1_r1, rqRealDiff__k6_xcmplx_0__r1_r1_r0, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, rqRealDiff__k6_xcmplx_0__r1_rm1_r2, rqRealMult__k3_xcmplx_0__r2_r1_r2, rqRealNeg__k4_xcmplx_0__r2_rm2, rqRealDiff__k6_xcmplx_0__r2_r2_r0, rqRealNeg__k4_xcmplx_0__rm2_r2, rqRealMult__k3_xcmplx_0__rm2_r1_rm2, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0]), [interesting(np__0.65), file(diff_4, e7_6_1__diff_4), [file(diff_4, e7_6_1__diff_4)]]). thf(t2_fdiff_8, theorem, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => ~ ( ( ( (r2_hidden @ A) @ ( (k1_relset_1 @ k1_numbers) @ k30_sin_cos) ) & ( (= @ ( (k1_seq_1 @ k16_sin_cos) @ A) ) @ k6_numbers) ) ) ) ) , file(fdiff_8, t2_fdiff_8), [interesting(np__0.9), axiom, file(fdiff_8, t2_fdiff_8)]). thf(e2_6__diff_4, plain, ( ~ ( ( (= @ (k18_sin_cos @ c1_6__diff_4) ) @ k6_numbers) ) & ~ ( ( (= @ (k18_sin_cos @ c2_6__diff_4) ) @ k6_numbers) ) ) , inference(mizar_by, [status(thm), assumptions([dt_c1_6__diff_4, dt_c2_6__diff_4, e1_6__diff_4])], [cc10_valued_2, cc15_valued_2, cc16_valued_2, cc21_valued_2, cc28_valued_2, cc29_valued_2, cc7_valued_2, cc8_valued_2, cc9_valued_2, fc14_valued_2, fc15_valued_2, fc16_valued_2, fc17_valued_2, fc40_valued_2, fc41_valued_2, fc42_valued_2, fc43_valued_2, cc11_valued_2, cc17_valued_2, cc25_valued_2, cc26_valued_2, cc30_valued_2, cc4_valued_2, cc5_valued_2, fc18_valued_2, fc44_valued_2, cc12_valued_2, cc15_membered, cc18_valued_2, cc19_valued_0, cc22_membered, cc23_valued_0, cc24_valued_0, cc24_valued_2, cc2_seq_2, cc31_valued_2, cc3_membered, cc3_valued_2, fc19_valued_2, fc45_valued_2, fc88_valued_0, rc3_valued_0, dt_k3_numbers, dt_k4_numbers, cc10_membered, cc13_valued_0, cc13_valued_2, cc14_valued_0, cc16_membered, cc19_valued_2, cc1_int_1, cc1_seq_2, cc20_valued_0, cc22_valued_0, cc23_membered, cc23_valued_2, cc2_membered, cc2_ordinal1, cc2_valued_0, cc2_valued_2, cc32_valued_2, cc3_int_1, cc3_valued_0, cc3_xxreal_0, cc4_seq_2, cc4_valued_0, cc4_xxreal_0, cc5_xxreal_0, cc6_funct_1, cc6_xxreal_0, cc8_xxreal_0, cc9_membered, fc18_funct_1, fc20_valued_2, fc24_relat_1, fc3_numbers, fc46_valued_2, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc89_valued_0, rc1_int_1, rc2_int_1, rc2_ordinal1, rc2_valued_0, rc2_xreal_0, rc2_xxreal_0, rc3_xreal_0, rc3_xxreal_0, rc5_valued_1, reflexivity_r1_tarski, dt_k1_rfunct_1, dt_k4_ordinal1, dt_o_0_0_xboole_0, cc10_ordinal1, cc10_valued_0, cc11_valued_0, cc12_membered, cc13_membered, cc14_valued_2, cc15_valued_0, cc16_valued_0, cc17_membered, cc17_valued_0, cc19_membered, cc1_funct_2, cc1_membered, cc1_ordinal1, cc1_rfunct_1, cc1_valued_0, cc1_valued_2, cc20_membered, cc20_valued_2, cc21_valued_0, cc22_valued_2, cc24_membered, cc2_int_1, cc2_xcmplx_0, cc2_xreal_0, cc2_xxreal_0, cc30_valued_0, cc31_valued_0, cc33_valued_2, cc3_seq_2, cc5_funct_1, cc5_ordinal1, cc6_ordinal1, cc6_relat_1, cc7_valued_0, cc7_xxreal_0, cc8_funct_1, cc8_ordinal1, cc8_relat_1, cc8_valued_0, cc9_funct_1, fc11_funct_1, fc17_funct_1, fc19_funct_1, fc1_rfunct_1, fc21_valued_2, fc2_rfunct_1, fc47_valued_2, fc4_ordinal1, fc59_membered, fc61_valued_0, fc62_valued_0, fc66_valued_0, fc6_membered, fc6_ordinal1, fc85_valued_0, fc86_valued_0, fc90_valued_0, rc1_funct_2, rc1_membered, rc1_ordinal1, rc1_partfun1, rc1_relset_1, rc1_seq_2, rc1_valued_0, rc1_valued_2, rc1_xxreal_0, rc2_funct_1, rc2_membered, rc2_relat_1, rc2_valued_2, rc3_funct_1, rc3_membered, rc3_ordinal1, rc3_partfun1, rc3_relat_1, rc4_funct_1, rc4_ordinal1, rc4_valued_0, rc4_xreal_0, rc4_xxreal_0, rc5_funct_1, rc5_ordinal1, rc6_funct_1, rc6_valued_0, rc7_funct_1, rc9_funct_1, t1_numerals, existence_m2_subset_1, redefinition_k3_rfunct_1, redefinition_k5_numbers, redefinition_m2_subset_1, dt_k17_sin_cos, dt_k19_sin_cos, dt_k1_funct_1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_k3_rfunct_1, dt_k5_numbers, dt_k9_xtuple_0, dt_m2_subset_1, cc11_membered, cc12_valued_0, cc14_membered, cc18_membered, cc18_valued_0, cc1_funct_1, cc1_partfun1, cc1_relat_1, cc1_relset_1, cc21_membered, cc25_membered, cc26_membered, cc27_valued_2, cc2_funct_1, cc2_funct_2, cc2_partfun1, cc2_relat_1, cc2_relset_1, cc3_funct_1, cc3_funct_2, cc3_ordinal1, cc3_relat_1, cc3_relset_1, cc3_xreal_0, cc4_funct_1, cc4_funct_2, cc4_membered, cc4_ordinal1, cc4_relat_1, cc4_relset_1, cc4_xreal_0, cc5_membered, cc5_relat_1, cc5_valued_0, cc6_valued_0, cc6_valued_2, cc7_funct_1, cc7_ordinal1, cc7_relat_1, cc8_funct_2, cc8_membered, cc9_ordinal1, cc9_valued_0, fc108_valued_1, fc10_relat_1, fc1_xboole_0, fc3_sin_cos, fc63_valued_0, fc6_relat_1, fc7_sin_cos, fc87_valued_0, fc8_relat_1, fc8_relset_1, rc1_funct_1, rc1_relat_1, rc1_xboole_0, rc1_xcmplx_0, rc1_xreal_0, rc2_valued_1, rc2_xboole_0, rc2_xcmplx_0, rc3_valued_1, t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t8_boole, d17_sin_cos, d2_xboole_0, antisymmetry_r2_hidden, existence_m1_subset_1, redefinition_k18_sin_cos, redefinition_k1_relset_1, redefinition_k1_seq_1, redefinition_k6_numbers, dt_k16_sin_cos, dt_k18_sin_cos, dt_k1_numbers, dt_k1_relset_1, dt_k1_seq_1, dt_k30_sin_cos, dt_k6_numbers, dt_m1_subset_1, dt_c1_6__diff_4, dt_c2_6__diff_4, cc1_xcmplx_0, cc1_xreal_0, fc1_numbers, fc3_membered, fc56_membered, fc6_sin_cos, fc8_numbers, t1_subset, t7_boole, d27_sin_cos, e1_6__diff_4, t2_fdiff_8]), [interesting(np__0.8), file(diff_4, e2_6__diff_4), [file(diff_4, e2_6__diff_4)]]). thf(t24_sin_cos4, theorem, (! [A: $i] : ( (v1_xreal_0 @ A) => (! [B: $i] : ( (v1_xreal_0 @ B) => ~ ( ( ~ ( ( (= @ (k17_sin_cos @ A) ) @ k6_numbers) ) & ( ~ ( ( (= @ (k17_sin_cos @ B) ) @ k6_numbers) ) & ~ ( ( (= @ ( (k6_xcmplx_0 @ (k2_sin_cos4 @ A) ) @ (k2_sin_cos4 @ B) ) ) @ (k4_xcmplx_0 @ ( (k7_xcmplx_0 @ (k17_sin_cos @ ( (k6_xcmplx_0 @ A) @ B) ) ) @ ( (k3_xcmplx_0 @ (k17_sin_cos @ A) ) @ (k17_sin_cos @ B) ) ) ) ) ) ) ) ) ) ) ) ) , file(sin_cos4, t24_sin_cos4), [interesting(np__0.9), axiom, file(sin_cos4, t24_sin_cos4)]). thf(e8_6_1__diff_4, plain, ( (= @ ( (k13_complex1 @ ( (k8_real_1 @ ( (k9_real_1 @ (k2_sin_cos4 @ c1_6__diff_4) ) @ (k2_sin_cos4 @ c2_6__diff_4) ) ) @ ( (k7_real_1 @ (k2_sin_cos4 @ c1_6__diff_4) ) @ (k2_sin_cos4 @ c2_6__diff_4) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ ( (k13_complex1 @ ( (k4_real_1 @ (k10_complex1 @ ( (k13_complex1 @ (k18_sin_cos @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ c2_6__diff_4) ) ) ) ) @ ( (k7_real_1 @ (k2_sin_cos4 @ c1_6__diff_4) ) @ (k2_sin_cos4 @ c2_6__diff_4) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) , inference(mizar_by, [status(thm), assumptions([dt_c1_6__diff_4, dt_c2_6__diff_4, e1_6__diff_4])], [fc40_valued_2, fc41_valued_2, fc42_valued_2, fc43_valued_2, cc10_valued_2, cc15_valued_2, cc16_valued_2, cc21_valued_2, cc25_valued_2, cc26_valued_2, cc28_valued_2, cc29_valued_2, cc7_valued_2, cc8_valued_2, cc9_valued_2, fc14_valued_2, fc15_valued_2, fc16_valued_2, fc17_valued_2, fc44_valued_2, cc11_valued_2, cc17_valued_2, cc23_valued_0, cc24_valued_0, cc24_valued_2, cc2_seq_2, cc30_valued_2, cc4_valued_2, cc5_valued_2, fc18_valued_2, fc45_valued_2, rc3_valued_0, dt_k3_numbers, dt_k4_numbers, cc10_membered, cc12_valued_2, cc13_valued_0, cc14_valued_0, cc15_membered, cc18_valued_2, cc19_valued_0, cc1_int_1, cc1_seq_2, cc22_membered, cc22_valued_0, cc23_valued_2, cc2_valued_0, cc31_valued_2, cc3_membered, cc3_valued_0, cc3_valued_2, cc4_seq_2, cc4_valued_0, cc6_funct_1, cc9_membered, fc19_valued_2, fc3_numbers, fc46_valued_2, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc88_valued_0, rc2_valued_0, rc5_valued_1, reflexivity_r1_tarski, cc10_valued_0, cc11_valued_0, cc13_membered, cc13_valued_2, cc15_valued_0, cc16_membered, cc17_valued_0, cc19_valued_2, cc1_funct_2, cc1_rfunct_1, cc1_valued_0, cc20_membered, cc20_valued_0, cc22_valued_2, cc23_membered, cc28_valued_0, cc2_membered, cc2_ordinal1, cc2_valued_2, cc30_valued_0, cc31_valued_0, cc32_valued_2, cc3_int_1, cc3_seq_2, cc5_funct_1, cc5_relat_1, cc6_relat_1, cc7_relat_1, cc7_valued_0, cc8_relat_1, cc8_valued_0, fc17_funct_1, fc19_funct_1, fc1_int_1, fc20_valued_2, fc2_int_1, fc3_int_1, fc47_valued_2, fc4_int_1, fc61_valued_0, fc62_valued_0, fc66_valued_0, fc86_valued_0, fc89_valued_0, rc1_funct_2, rc1_int_1, rc1_partfun1, rc1_relset_1, rc1_seq_2, rc1_valued_0, rc2_funct_1, rc2_int_1, rc2_ordinal1, rc2_relat_1, rc2_valued_1, rc2_valued_2, rc3_funct_1, rc3_ordinal1, rc3_partfun1, rc3_relat_1, rc3_valued_1, rc4_funct_1, rc4_valued_0, rc5_funct_1, rc6_funct_1, rc6_valued_0, rc9_funct_1, antisymmetry_r2_hidden, dt_k19_sin_cos, dt_k1_funct_1, dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_k4_ordinal1, dt_o_0_0_xboole_0, cc10_ordinal1, cc11_membered, cc12_membered, cc12_valued_0, cc14_membered, cc14_valued_2, cc16_valued_0, cc17_membered, cc18_valued_0, cc19_membered, cc1_membered, cc1_ordinal1, cc1_partfun1, cc1_relset_1, cc1_valued_2, cc20_valued_2, cc21_membered, cc21_valued_0, cc24_membered, cc27_valued_2, cc2_funct_1, cc2_funct_2, cc2_int_1, cc2_partfun1, cc2_relat_1, cc2_relset_1, cc2_xcmplx_0, cc2_xreal_0, cc2_xxreal_0, cc33_valued_2, cc3_funct_1, cc3_funct_2, cc3_relat_1, cc3_relset_1, cc4_funct_1, cc4_funct_2, cc4_membered, cc4_relat_1, cc4_relset_1, cc4_xxreal_0, cc5_membered, cc5_ordinal1, cc5_valued_0, cc5_xxreal_0, cc6_membered, cc6_ordinal1, cc6_valued_0, cc8_funct_1, cc8_funct_2, cc8_membered, cc8_ordinal1, cc8_xxreal_0, cc9_funct_1, cc9_valued_0, fc11_xreal_0, fc12_xreal_0, fc13_xreal_0, fc14_xreal_0, fc16_xreal_0, fc17_xreal_0, fc18_xreal_0, fc21_valued_2, fc21_xreal_0, fc22_xreal_0, fc23_xreal_0, fc24_xreal_0, fc26_xreal_0, fc29_xreal_0, fc30_xreal_0, fc31_xreal_0, fc32_xreal_0, fc33_xreal_0, fc59_membered, fc63_valued_0, fc6_membered, fc6_ordinal1, fc6_relat_1, fc7_sin_cos, fc85_valued_0, fc87_valued_0, fc90_valued_0, fc9_xreal_0, rc1_funct_1, rc1_membered, rc1_ordinal1, rc1_relat_1, rc1_valued_2, rc2_membered, rc3_membered, rc3_xreal_0, rc3_xxreal_0, rc4_ordinal1, rc5_ordinal1, rc7_funct_1, t1_numerals, t1_subset, t3_subset, t4_subset, t5_subset, involutiveness_k5_xcmplx_0, existence_m1_subset_1, existence_m2_subset_1, redefinition_k1_seq_1, redefinition_k5_numbers, redefinition_m2_subset_1, dt_k16_sin_cos, dt_k1_numbers, dt_k1_seq_1, dt_k1_xboole_0, dt_k20_sin_cos, dt_k2_numbers, dt_k5_numbers, dt_k5_xcmplx_0, dt_m1_subset_1, dt_m2_subset_1, cc18_membered, cc1_funct_1, cc1_relat_1, cc1_xcmplx_0, cc1_xreal_0, cc25_membered, cc26_membered, cc3_ordinal1, cc3_xcmplx_0, cc3_xxreal_0, cc4_ordinal1, cc6_valued_2, cc6_xxreal_0, cc7_funct_1, cc7_ordinal1, cc7_xxreal_0, cc9_ordinal1, fc10_xreal_0, fc15_xreal_0, fc19_xreal_0, fc1_membered, fc1_numbers, fc1_xboole_0, fc20_xreal_0, fc25_xreal_0, fc27_xreal_0, fc28_xreal_0, fc2_numbers, fc2_xcmplx_0, fc34_xreal_0, fc3_membered, fc3_xcmplx_0, fc4_sin_cos, fc4_xcmplx_0, fc4_xreal_0, fc55_membered, fc56_membered, fc5_xcmplx_0, fc6_sin_cos, fc6_xcmplx_0, fc7_xcmplx_0, fc8_numbers, fc8_xcmplx_0, fc9_numbers, fc9_xcmplx_0, rc1_xboole_0, rc1_xcmplx_0, rc1_xxreal_0, rc2_xboole_0, rc2_xcmplx_0, rc2_xreal_0, rc2_xxreal_0, rc4_xreal_0, rc4_xxreal_0, spc10_arithm, spc11_arithm, spc12_arithm, spc1_arithm, spc2_arithm, spc3_arithm, spc4_arithm, spc5_arithm, spc6_arithm, spc7_arithm, spc8_arithm, spc9_arithm, t1_arithm, t2_arithm, t2_subset, t3_arithm, t4_arithm, t5_arithm, t6_arithm, t6_boole, t7_boole, t8_boole, d2_xboole_0, d19_sin_cos, involutiveness_k10_complex1, commutativity_k2_xcmplx_0, commutativity_k3_xcmplx_0, commutativity_k4_real_1, involutiveness_k4_xcmplx_0, commutativity_k7_real_1, commutativity_k8_real_1, redefinition_k10_complex1, redefinition_k13_complex1, redefinition_k18_sin_cos, redefinition_k4_real_1, redefinition_k6_numbers, redefinition_k7_real_1, redefinition_k8_real_1, redefinition_k9_real_1, dt_k10_complex1, dt_k13_complex1, dt_k17_sin_cos, dt_k18_sin_cos, dt_k2_sin_cos4, dt_k2_xcmplx_0, dt_k3_xcmplx_0, dt_k4_real_1, dt_k4_xcmplx_0, dt_k6_numbers, dt_k6_xcmplx_0, dt_k7_real_1, dt_k7_xcmplx_0, dt_k8_real_1, dt_k9_real_1, dt_c1_6__diff_4, dt_c2_6__diff_4, cc3_xreal_0, cc4_xreal_0, fc3_sin_cos, fc3_xreal_0, fc5_xreal_0, fc6_xreal_0, fc7_xreal_0, fc8_xreal_0, rc1_xreal_0, rqRealAdd__k2_xcmplx_0__r0_r0_r0, rqRealAdd__k2_xcmplx_0__r0_r1_r1, rqRealAdd__k2_xcmplx_0__r0_r2_r2, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__r1_r0_r1, rqRealAdd__k2_xcmplx_0__r1_r1_r2, rqRealAdd__k2_xcmplx_0__r1_rm1_r0, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r2_r0_r2, rqRealAdd__k2_xcmplx_0__r2_rm1_r1, rqRealAdd__k2_xcmplx_0__r2_rm2_r0, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, rqRealAdd__k2_xcmplx_0__rm1_r2_r1, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, rqRealAdd__k2_xcmplx_0__rm2_r2_r0, rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, rqRealDiff__k6_xcmplx_0__r0_r0_r0, rqRealDiff__k6_xcmplx_0__r0_r1_rm1, rqRealDiff__k6_xcmplx_0__r0_r2_rm2, rqRealDiff__k6_xcmplx_0__r0_rm1_r1, rqRealDiff__k6_xcmplx_0__r0_rm2_r2, rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r1_r0_r1, rqRealDiff__k6_xcmplx_0__r1_r2_rm1, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r2_r0_r2, rqRealDiff__k6_xcmplx_0__r2_r1_r1, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, rqRealDiv__k7_xcmplx_0__r1_r1_r1, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, rqRealDiv__k7_xcmplx_0__r2_r1_r2, rqRealDiv__k7_xcmplx_0__r2_r2_r1, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__r0_r0_r0, rqRealMult__k3_xcmplx_0__r0_r1_r0, rqRealMult__k3_xcmplx_0__r0_r2_r0, rqRealMult__k3_xcmplx_0__r0_rm2_r0, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, rqRealMult__k3_xcmplx_0__r1_r0_r0, rqRealMult__k3_xcmplx_0__r1_r2_r2, rqRealMult__k3_xcmplx_0__r1_rm2_rm2, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r2_r0_r0, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_r0_r0, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, rqRealNeg__k4_xcmplx_0__r0_r0, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, d17_sin_cos, d2_sin_cos4, d8_xcmplx_0, d9_xcmplx_0, spc0_numerals, spc1_numerals, spc2_numerals, spc0_boole, spc1_boole, spc2_boole, e2_6__diff_4, t24_sin_cos4, rqRealMult__k3_xcmplx_0__r1_r1_r1, rqRealNeg__k4_xcmplx_0__r1_rm1, rqRealAdd__k2_xcmplx_0__rm1_r1_r0, rqRealNeg__k4_xcmplx_0__rm1_r1, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, rqRealDiff__k6_xcmplx_0__r1_r1_r0, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, rqRealDiff__k6_xcmplx_0__r1_rm1_r2, rqRealMult__k3_xcmplx_0__rm2_r1_rm2, rqRealNeg__k4_xcmplx_0__rm2_r2, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, rqRealNeg__k4_xcmplx_0__r2_rm2, rqRealMult__k3_xcmplx_0__r2_r1_r2, rqRealDiff__k6_xcmplx_0__r2_r2_r0]), [interesting(np__0.65), file(diff_4, e8_6_1__diff_4), [file(diff_4, e8_6_1__diff_4)]]). thf(e9_6_1__diff_4, plain, ( (= @ ( (k13_complex1 @ ( (k4_real_1 @ (k10_complex1 @ ( (k13_complex1 @ (k18_sin_cos @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ c2_6__diff_4) ) ) ) ) @ ( (k7_real_1 @ (k2_sin_cos4 @ c1_6__diff_4) ) @ (k2_sin_cos4 @ c2_6__diff_4) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ ( (k13_complex1 @ (k1_real_1 @ ( (k4_real_1 @ ( (k13_complex1 @ (k18_sin_cos @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ c2_6__diff_4) ) ) ) @ ( (k7_real_1 @ (k2_sin_cos4 @ c1_6__diff_4) ) @ (k2_sin_cos4 @ c2_6__diff_4) ) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) , inference(mizar_by, [status(thm), assumptions([dt_c1_6__diff_4, dt_c2_6__diff_4])], [fc40_valued_2, fc41_valued_2, fc42_valued_2, fc43_valued_2, cc10_valued_2, cc15_valued_2, cc16_valued_2, cc21_valued_2, cc25_valued_2, cc26_valued_2, cc28_valued_2, cc29_valued_2, cc7_valued_2, cc8_valued_2, cc9_valued_2, fc14_valued_2, fc15_valued_2, fc16_valued_2, fc17_valued_2, fc44_valued_2, cc11_valued_2, cc17_valued_2, cc23_valued_0, cc24_valued_0, cc24_valued_2, cc2_seq_2, cc30_valued_2, cc4_valued_2, cc5_valued_2, fc18_valued_2, fc45_valued_2, rc3_valued_0, dt_k3_numbers, dt_k4_numbers, cc10_membered, cc10_valued_0, cc11_valued_0, cc12_valued_2, cc13_valued_0, cc14_valued_0, cc15_membered, cc18_valued_2, cc19_valued_0, cc1_funct_2, cc1_int_1, cc1_seq_2, cc22_membered, cc22_valued_0, cc23_valued_2, cc28_valued_0, cc2_valued_0, cc30_valued_0, cc31_valued_0, cc31_valued_2, cc3_membered, cc3_valued_0, cc3_valued_2, cc4_seq_2, cc4_valued_0, cc5_relat_1, cc6_funct_1, cc6_relat_1, cc7_relat_1, cc8_relat_1, cc9_membered, fc17_funct_1, fc19_valued_2, fc3_numbers, fc46_valued_2, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc61_valued_0, fc62_valued_0, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc88_valued_0, rc1_funct_2, rc1_partfun1, rc1_relset_1, rc1_seq_2, rc2_valued_0, rc2_valued_1, rc3_ordinal1, rc3_partfun1, rc3_relat_1, rc3_valued_1, rc4_valued_0, rc5_valued_1, rc6_funct_1, rc6_valued_0, rc9_funct_1, reflexivity_r1_tarski, dt_k1_funct_1, dt_k2_zfmisc_1, dt_o_0_0_xboole_0, cc12_valued_0, cc13_membered, cc13_valued_2, cc15_valued_0, cc16_membered, cc16_valued_0, cc17_valued_0, cc18_valued_0, cc19_valued_2, cc1_partfun1, cc1_relset_1, cc1_rfunct_1, cc1_valued_0, cc20_membered, cc20_valued_0, cc21_valued_0, cc22_valued_2, cc23_membered, cc2_funct_2, cc2_membered, cc2_ordinal1, cc2_partfun1, cc2_relset_1, cc2_valued_2, cc32_valued_2, cc33_valued_2, cc3_funct_2, cc3_int_1, cc3_relset_1, cc3_seq_2, cc4_funct_2, cc4_relset_1, cc5_funct_1, cc5_valued_0, cc6_valued_0, cc7_valued_0, cc8_funct_2, cc8_valued_0, fc19_funct_1, fc1_int_1, fc20_valued_2, fc21_valued_2, fc2_int_1, fc3_int_1, fc47_valued_2, fc4_int_1, fc63_valued_0, fc66_valued_0, fc6_relat_1, fc85_valued_0, fc86_valued_0, fc87_valued_0, fc89_valued_0, fc90_valued_0, rc1_int_1, rc1_valued_0, rc2_funct_1, rc2_int_1, rc2_ordinal1, rc2_relat_1, rc2_valued_2, rc3_funct_1, rc4_funct_1, rc5_funct_1, involutiveness_k5_xcmplx_0, antisymmetry_r2_hidden, redefinition_k1_seq_1, dt_k16_sin_cos, dt_k19_sin_cos, dt_k1_seq_1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k4_ordinal1, dt_k5_xcmplx_0, cc10_ordinal1, cc11_membered, cc12_membered, cc14_membered, cc14_valued_2, cc17_membered, cc19_membered, cc1_membered, cc1_ordinal1, cc1_valued_2, cc20_valued_2, cc21_membered, cc24_membered, cc27_valued_2, cc2_funct_1, cc2_int_1, cc2_relat_1, cc2_xcmplx_0, cc2_xreal_0, cc2_xxreal_0, cc3_funct_1, cc3_relat_1, cc3_xxreal_0, cc4_funct_1, cc4_membered, cc4_relat_1, cc4_xxreal_0, cc5_membered, cc5_ordinal1, cc5_xxreal_0, cc6_membered, cc6_ordinal1, cc6_xxreal_0, cc7_xxreal_0, cc8_funct_1, cc8_membered, cc8_ordinal1, cc8_xxreal_0, cc9_funct_1, cc9_valued_0, fc11_xreal_0, fc12_xreal_0, fc13_xreal_0, fc14_xreal_0, fc16_xreal_0, fc17_xreal_0, fc18_xreal_0, fc1_xboole_0, fc21_xreal_0, fc22_xreal_0, fc23_xreal_0, fc24_xreal_0, fc26_xreal_0, fc27_xreal_0, fc28_xreal_0, fc29_xreal_0, fc30_xreal_0, fc31_xreal_0, fc32_xreal_0, fc33_xreal_0, fc4_xreal_0, fc59_membered, fc6_membered, fc6_ordinal1, fc6_sin_cos, fc7_sin_cos, fc7_xcmplx_0, fc9_xreal_0, rc1_funct_1, rc1_membered, rc1_ordinal1, rc1_relat_1, rc1_valued_2, rc1_xxreal_0, rc2_membered, rc2_xreal_0, rc2_xxreal_0, rc3_membered, rc3_xreal_0, rc3_xxreal_0, rc4_ordinal1, rc4_xreal_0, rc4_xxreal_0, rc5_ordinal1, rc7_funct_1, spc10_arithm, spc11_arithm, spc12_arithm, spc3_arithm, t1_numerals, t1_subset, t3_subset, t4_subset, t5_subset, d2_xboole_0, commutativity_k2_xcmplx_0, existence_m1_subset_1, existence_m2_subset_1, redefinition_k5_numbers, redefinition_m2_subset_1, dt_k17_sin_cos, dt_k1_numbers, dt_k20_sin_cos, dt_k2_numbers, dt_k2_xcmplx_0, dt_k5_numbers, dt_k7_xcmplx_0, dt_m1_subset_1, dt_m2_subset_1, cc18_membered, cc1_funct_1, cc1_relat_1, cc1_xcmplx_0, cc1_xreal_0, cc25_membered, cc26_membered, cc3_ordinal1, cc3_xcmplx_0, cc3_xreal_0, cc4_ordinal1, cc4_xreal_0, cc6_valued_2, cc7_funct_1, cc7_ordinal1, cc9_ordinal1, fc10_xreal_0, fc15_xreal_0, fc19_xreal_0, fc1_membered, fc1_numbers, fc20_xreal_0, fc25_xreal_0, fc2_numbers, fc2_xcmplx_0, fc34_xreal_0, fc3_membered, fc3_sin_cos, fc3_xcmplx_0, fc3_xreal_0, fc4_sin_cos, fc4_xcmplx_0, fc55_membered, fc56_membered, fc5_xcmplx_0, fc5_xreal_0, fc6_xcmplx_0, fc6_xreal_0, fc7_xreal_0, fc8_numbers, fc8_xcmplx_0, fc8_xreal_0, fc9_numbers, fc9_xcmplx_0, rc1_xboole_0, rc1_xcmplx_0, rc1_xreal_0, rc2_xboole_0, rc2_xcmplx_0, rqRealAdd__k2_xcmplx_0__r0_r0_r0, rqRealAdd__k2_xcmplx_0__r0_r1_r1, rqRealAdd__k2_xcmplx_0__r0_r2_r2, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__r1_r0_r1, rqRealAdd__k2_xcmplx_0__r1_r1_r2, rqRealAdd__k2_xcmplx_0__r1_rm1_r0, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r2_r0_r2, rqRealAdd__k2_xcmplx_0__r2_rm1_r1, rqRealAdd__k2_xcmplx_0__r2_rm2_r0, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, rqRealAdd__k2_xcmplx_0__rm1_r1_r0, rqRealAdd__k2_xcmplx_0__rm1_r2_r1, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, rqRealAdd__k2_xcmplx_0__rm2_r2_r0, rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, rqRealDiv__k7_xcmplx_0__r1_r1_r1, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, rqRealDiv__k7_xcmplx_0__r2_r1_r2, rqRealDiv__k7_xcmplx_0__r2_r2_r1, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, spc1_arithm, spc2_arithm, spc4_arithm, spc5_arithm, spc6_arithm, spc7_arithm, spc8_arithm, spc9_arithm, t2_subset, t3_arithm, t6_arithm, t6_boole, t7_boole, t8_boole, d17_sin_cos, d19_sin_cos, d9_xcmplx_0, involutiveness_k10_complex1, involutiveness_k1_real_1, commutativity_k3_xcmplx_0, commutativity_k4_real_1, involutiveness_k4_xcmplx_0, commutativity_k7_real_1, commutativity_k8_real_1, redefinition_k10_complex1, redefinition_k13_complex1, redefinition_k18_sin_cos, redefinition_k1_real_1, redefinition_k4_real_1, redefinition_k7_real_1, redefinition_k8_real_1, redefinition_k9_real_1, dt_k10_complex1, dt_k13_complex1, dt_k18_sin_cos, dt_k1_real_1, dt_k2_sin_cos4, dt_k3_xcmplx_0, dt_k4_real_1, dt_k4_xcmplx_0, dt_k6_xcmplx_0, dt_k7_real_1, dt_k8_real_1, dt_k9_real_1, dt_c1_6__diff_4, dt_c2_6__diff_4, rqRealDiff__k6_xcmplx_0__r0_r0_r0, rqRealDiff__k6_xcmplx_0__r0_r1_rm1, rqRealDiff__k6_xcmplx_0__r0_r2_rm2, rqRealDiff__k6_xcmplx_0__r0_rm1_r1, rqRealDiff__k6_xcmplx_0__r0_rm2_r2, rqRealDiff__k6_xcmplx_0__r1_r0_r1, rqRealDiff__k6_xcmplx_0__r1_r2_rm1, rqRealDiff__k6_xcmplx_0__r2_r0_r2, rqRealDiff__k6_xcmplx_0__r2_r1_r1, rqRealDiff__k6_xcmplx_0__r2_r2_r0, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, rqRealMult__k3_xcmplx_0__r0_r0_r0, rqRealMult__k3_xcmplx_0__r0_r1_r0, rqRealMult__k3_xcmplx_0__r0_r2_r0, rqRealMult__k3_xcmplx_0__r0_rm2_r0, rqRealMult__k3_xcmplx_0__r1_r0_r0, rqRealMult__k3_xcmplx_0__r1_r2_r2, rqRealMult__k3_xcmplx_0__r1_rm2_rm2, rqRealMult__k3_xcmplx_0__r2_r0_r0, rqRealMult__k3_xcmplx_0__r2_r1_r2, rqRealMult__k3_xcmplx_0__rm2_r0_r0, rqRealNeg__k4_xcmplx_0__r0_r0, d2_sin_cos4, d8_xcmplx_0, spc0_numerals, spc1_numerals, spc2_numerals, spc0_boole, spc1_boole, spc2_boole, rqRealMult__k3_xcmplx_0__r1_r1_r1, rqRealNeg__k4_xcmplx_0__r1_rm1, rqRealNeg__k4_xcmplx_0__rm1_r1, rqRealDiff__k6_xcmplx_0__r1_r1_r0, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, rqRealMult__k3_xcmplx_0__rm2_r1_rm2, rqRealNeg__k4_xcmplx_0__rm2_r2, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, rqRealNeg__k4_xcmplx_0__r2_rm2, rqRealDiff__k6_xcmplx_0__r1_rm1_r2]), [interesting(np__0.65), file(diff_4, e9_6_1__diff_4), [file(diff_4, e9_6_1__diff_4)]]). thf(t23_sin_cos4, theorem, (! [A: $i] : ( (v1_xreal_0 @ A) => (! [B: $i] : ( (v1_xreal_0 @ B) => ~ ( ( ~ ( ( (= @ (k17_sin_cos @ A) ) @ k6_numbers) ) & ( ~ ( ( (= @ (k17_sin_cos @ B) ) @ k6_numbers) ) & ~ ( ( (= @ ( (k2_xcmplx_0 @ (k2_sin_cos4 @ A) ) @ (k2_sin_cos4 @ B) ) ) @ ( (k7_xcmplx_0 @ (k17_sin_cos @ ( (k2_xcmplx_0 @ A) @ B) ) ) @ ( (k3_xcmplx_0 @ (k17_sin_cos @ A) ) @ (k17_sin_cos @ B) ) ) ) ) ) ) ) ) ) ) ) , file(sin_cos4, t23_sin_cos4), [interesting(np__0.9), axiom, file(sin_cos4, t23_sin_cos4)]). thf(e10_6_1__diff_4, plain, ( (= @ ( (k13_complex1 @ (k1_real_1 @ ( (k4_real_1 @ ( (k13_complex1 @ (k18_sin_cos @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ c2_6__diff_4) ) ) ) @ ( (k7_real_1 @ (k2_sin_cos4 @ c1_6__diff_4) ) @ (k2_sin_cos4 @ c2_6__diff_4) ) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ ( (k13_complex1 @ (k10_complex1 @ ( (k9_complex1 @ ( (k13_complex1 @ (k18_sin_cos @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ c2_6__diff_4) ) ) ) @ ( (k13_complex1 @ (k18_sin_cos @ ( (k7_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ c2_6__diff_4) ) ) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) , inference(mizar_by, [status(thm), assumptions([dt_c1_6__diff_4, dt_c2_6__diff_4, e1_6__diff_4])], [fc40_valued_2, fc41_valued_2, fc42_valued_2, fc43_valued_2, cc10_valued_2, cc15_valued_2, cc16_valued_2, cc21_valued_2, cc25_valued_2, cc26_valued_2, cc28_valued_2, cc29_valued_2, cc7_valued_2, cc8_valued_2, cc9_valued_2, fc14_valued_2, fc15_valued_2, fc16_valued_2, fc17_valued_2, fc44_valued_2, cc11_valued_2, cc17_valued_2, cc23_valued_0, cc24_valued_0, cc24_valued_2, cc2_seq_2, cc30_valued_2, cc4_valued_2, cc5_valued_2, fc18_valued_2, fc45_valued_2, rc3_valued_0, dt_k3_numbers, dt_k4_numbers, cc10_membered, cc12_valued_2, cc13_valued_0, cc14_valued_0, cc15_membered, cc18_valued_2, cc19_valued_0, cc1_int_1, cc1_seq_2, cc22_membered, cc22_valued_0, cc23_valued_2, cc2_valued_0, cc31_valued_2, cc3_membered, cc3_valued_0, cc3_valued_2, cc4_seq_2, cc4_valued_0, cc6_funct_1, cc9_membered, fc19_valued_2, fc3_numbers, fc46_valued_2, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc88_valued_0, rc2_valued_0, rc5_valued_1, reflexivity_r1_tarski, cc10_valued_0, cc11_valued_0, cc13_membered, cc13_valued_2, cc15_valued_0, cc16_membered, cc17_valued_0, cc19_valued_2, cc1_funct_2, cc1_rfunct_1, cc1_valued_0, cc20_membered, cc20_valued_0, cc22_valued_2, cc23_membered, cc28_valued_0, cc2_membered, cc2_ordinal1, cc2_valued_2, cc30_valued_0, cc31_valued_0, cc32_valued_2, cc3_int_1, cc3_seq_2, cc5_funct_1, cc5_relat_1, cc6_relat_1, cc7_relat_1, cc7_valued_0, cc8_relat_1, cc8_valued_0, fc17_funct_1, fc19_funct_1, fc1_int_1, fc20_valued_2, fc2_int_1, fc3_int_1, fc47_valued_2, fc4_int_1, fc61_valued_0, fc62_valued_0, fc66_valued_0, fc86_valued_0, fc89_valued_0, rc1_funct_2, rc1_int_1, rc1_partfun1, rc1_relset_1, rc1_seq_2, rc1_valued_0, rc2_funct_1, rc2_int_1, rc2_ordinal1, rc2_relat_1, rc2_valued_1, rc2_valued_2, rc3_funct_1, rc3_ordinal1, rc3_partfun1, rc3_relat_1, rc3_valued_1, rc4_funct_1, rc4_valued_0, rc5_funct_1, rc6_funct_1, rc6_valued_0, rc9_funct_1, antisymmetry_r2_hidden, dt_k19_sin_cos, dt_k1_funct_1, dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_k4_ordinal1, dt_o_0_0_xboole_0, cc10_ordinal1, cc11_membered, cc12_membered, cc12_valued_0, cc14_membered, cc14_valued_2, cc16_valued_0, cc17_membered, cc18_valued_0, cc19_membered, cc1_membered, cc1_ordinal1, cc1_partfun1, cc1_relset_1, cc1_valued_2, cc20_valued_2, cc21_membered, cc21_valued_0, cc24_membered, cc27_valued_2, cc2_funct_1, cc2_funct_2, cc2_int_1, cc2_partfun1, cc2_relat_1, cc2_relset_1, cc2_xcmplx_0, cc2_xreal_0, cc2_xxreal_0, cc33_valued_2, cc3_funct_1, cc3_funct_2, cc3_relat_1, cc3_relset_1, cc4_funct_1, cc4_funct_2, cc4_membered, cc4_relat_1, cc4_relset_1, cc4_xxreal_0, cc5_membered, cc5_ordinal1, cc5_valued_0, cc5_xxreal_0, cc6_membered, cc6_ordinal1, cc6_valued_0, cc8_funct_1, cc8_funct_2, cc8_membered, cc8_ordinal1, cc8_xxreal_0, cc9_funct_1, cc9_valued_0, fc11_xreal_0, fc12_xreal_0, fc13_xreal_0, fc14_xreal_0, fc16_xreal_0, fc17_xreal_0, fc18_xreal_0, fc21_valued_2, fc21_xreal_0, fc22_xreal_0, fc23_xreal_0, fc24_xreal_0, fc26_xreal_0, fc29_xreal_0, fc30_xreal_0, fc31_xreal_0, fc32_xreal_0, fc33_xreal_0, fc59_membered, fc63_valued_0, fc6_membered, fc6_ordinal1, fc6_relat_1, fc7_sin_cos, fc85_valued_0, fc87_valued_0, fc90_valued_0, fc9_xreal_0, rc1_funct_1, rc1_membered, rc1_ordinal1, rc1_relat_1, rc1_valued_2, rc2_membered, rc3_membered, rc3_xreal_0, rc3_xxreal_0, rc4_ordinal1, rc5_ordinal1, rc7_funct_1, t1_numerals, t1_subset, t3_subset, t4_subset, t5_subset, involutiveness_k5_xcmplx_0, existence_m1_subset_1, existence_m2_subset_1, redefinition_k1_seq_1, redefinition_k5_numbers, redefinition_m2_subset_1, dt_k16_sin_cos, dt_k1_numbers, dt_k1_seq_1, dt_k1_xboole_0, dt_k20_sin_cos, dt_k2_numbers, dt_k5_numbers, dt_k5_xcmplx_0, dt_m1_subset_1, dt_m2_subset_1, cc18_membered, cc1_funct_1, cc1_relat_1, cc1_xcmplx_0, cc1_xreal_0, cc25_membered, cc26_membered, cc3_ordinal1, cc3_xcmplx_0, cc3_xxreal_0, cc4_ordinal1, cc6_valued_2, cc6_xxreal_0, cc7_funct_1, cc7_ordinal1, cc7_xxreal_0, cc9_ordinal1, fc10_xreal_0, fc15_xreal_0, fc19_xreal_0, fc1_membered, fc1_numbers, fc1_xboole_0, fc20_xreal_0, fc25_xreal_0, fc27_xreal_0, fc28_xreal_0, fc2_numbers, fc2_xcmplx_0, fc34_xreal_0, fc3_membered, fc3_xcmplx_0, fc4_sin_cos, fc4_xcmplx_0, fc4_xreal_0, fc55_membered, fc56_membered, fc5_xcmplx_0, fc6_sin_cos, fc6_xcmplx_0, fc7_xcmplx_0, fc8_numbers, fc8_xcmplx_0, fc9_numbers, fc9_xcmplx_0, rc1_xboole_0, rc1_xcmplx_0, rc1_xxreal_0, rc2_xboole_0, rc2_xcmplx_0, rc2_xreal_0, rc2_xxreal_0, rc4_xreal_0, rc4_xxreal_0, spc10_arithm, spc11_arithm, spc12_arithm, spc1_arithm, spc2_arithm, spc3_arithm, spc4_arithm, spc5_arithm, spc6_arithm, spc7_arithm, spc8_arithm, spc9_arithm, t1_arithm, t2_arithm, t2_subset, t3_arithm, t4_arithm, t5_arithm, t6_arithm, t6_boole, t7_boole, t8_boole, d2_xboole_0, d19_sin_cos, involutiveness_k10_complex1, involutiveness_k1_real_1, commutativity_k2_xcmplx_0, commutativity_k3_xcmplx_0, commutativity_k4_real_1, involutiveness_k4_xcmplx_0, commutativity_k7_real_1, commutativity_k8_real_1, commutativity_k9_complex1, redefinition_k10_complex1, redefinition_k13_complex1, redefinition_k18_sin_cos, redefinition_k1_real_1, redefinition_k4_real_1, redefinition_k6_numbers, redefinition_k7_real_1, redefinition_k8_real_1, redefinition_k9_complex1, redefinition_k9_real_1, dt_k10_complex1, dt_k13_complex1, dt_k17_sin_cos, dt_k18_sin_cos, dt_k1_real_1, dt_k2_sin_cos4, dt_k2_xcmplx_0, dt_k3_xcmplx_0, dt_k4_real_1, dt_k4_xcmplx_0, dt_k6_numbers, dt_k6_xcmplx_0, dt_k7_real_1, dt_k7_xcmplx_0, dt_k8_real_1, dt_k9_complex1, dt_k9_real_1, dt_c1_6__diff_4, dt_c2_6__diff_4, cc3_xreal_0, cc4_xreal_0, fc3_sin_cos, fc3_xreal_0, fc5_xreal_0, fc6_xreal_0, fc7_xreal_0, fc8_xreal_0, rc1_xreal_0, rqRealAdd__k2_xcmplx_0__r0_r0_r0, rqRealAdd__k2_xcmplx_0__r0_r1_r1, rqRealAdd__k2_xcmplx_0__r0_r2_r2, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__r1_r0_r1, rqRealAdd__k2_xcmplx_0__r1_r1_r2, rqRealAdd__k2_xcmplx_0__r1_rm1_r0, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r2_r0_r2, rqRealAdd__k2_xcmplx_0__r2_rm1_r1, rqRealAdd__k2_xcmplx_0__r2_rm2_r0, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, rqRealAdd__k2_xcmplx_0__rm1_r1_r0, rqRealAdd__k2_xcmplx_0__rm1_r2_r1, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, rqRealAdd__k2_xcmplx_0__rm2_r2_r0, rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, rqRealDiff__k6_xcmplx_0__r0_r0_r0, rqRealDiff__k6_xcmplx_0__r0_r1_rm1, rqRealDiff__k6_xcmplx_0__r0_r2_rm2, rqRealDiff__k6_xcmplx_0__r0_rm1_r1, rqRealDiff__k6_xcmplx_0__r0_rm2_r2, rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r1_r0_r1, rqRealDiff__k6_xcmplx_0__r1_r2_rm1, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r2_r0_r2, rqRealDiff__k6_xcmplx_0__r2_r1_r1, rqRealDiff__k6_xcmplx_0__r2_r2_r0, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, rqRealDiv__k7_xcmplx_0__r1_r1_r1, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, rqRealDiv__k7_xcmplx_0__r2_r1_r2, rqRealDiv__k7_xcmplx_0__r2_r2_r1, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__r0_r0_r0, rqRealMult__k3_xcmplx_0__r0_r1_r0, rqRealMult__k3_xcmplx_0__r0_r2_r0, rqRealMult__k3_xcmplx_0__r0_rm2_r0, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, rqRealMult__k3_xcmplx_0__r1_r0_r0, rqRealMult__k3_xcmplx_0__r1_r2_r2, rqRealMult__k3_xcmplx_0__r1_rm2_rm2, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r2_r0_r0, rqRealMult__k3_xcmplx_0__r2_r1_r2, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_r0_r0, rqRealMult__k3_xcmplx_0__rm2_r1_rm2, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, rqRealNeg__k4_xcmplx_0__r0_r0, rqRealNeg__k4_xcmplx_0__r2_rm2, rqRealNeg__k4_xcmplx_0__rm2_r2, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, d17_sin_cos, d2_sin_cos4, d8_xcmplx_0, d9_xcmplx_0, spc0_numerals, spc1_numerals, spc2_numerals, spc0_boole, spc1_boole, spc2_boole, e2_6__diff_4, t23_sin_cos4, rqRealMult__k3_xcmplx_0__r1_r1_r1, rqRealNeg__k4_xcmplx_0__r1_rm1, rqRealNeg__k4_xcmplx_0__rm1_r1, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, rqRealDiff__k6_xcmplx_0__r1_r1_r0, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, rqRealDiff__k6_xcmplx_0__r1_rm1_r2]), [interesting(np__0.65), file(diff_4, e10_6_1__diff_4), [file(diff_4, e10_6_1__diff_4)]]). thf(t76_xcmplx_1, theorem, (! [A: $i] : ( (v1_xcmplx_0 @ A) => (! [B: $i] : ( (v1_xcmplx_0 @ B) => (! [C: $i] : ( (v1_xcmplx_0 @ C) => (! [D: $i] : ( (v1_xcmplx_0 @ D) => ( (= @ ( (k3_xcmplx_0 @ ( (k7_xcmplx_0 @ A) @ B) ) @ ( (k7_xcmplx_0 @ C) @ D) ) ) @ ( (k7_xcmplx_0 @ ( (k3_xcmplx_0 @ A) @ C) ) @ ( (k3_xcmplx_0 @ B) @ D) ) ) ) ) ) ) ) ) ) ) , file(xcmplx_1, t76_xcmplx_1), [interesting(np__0.9), axiom, file(xcmplx_1, t76_xcmplx_1)]). thf(e11_6_1__diff_4, plain, ( (= @ ( (k13_complex1 @ (k10_complex1 @ ( (k9_complex1 @ ( (k13_complex1 @ (k18_sin_cos @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ c2_6__diff_4) ) ) ) @ ( (k13_complex1 @ (k18_sin_cos @ ( (k7_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ c2_6__diff_4) ) ) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ ( (k13_complex1 @ (k10_complex1 @ ( (k13_complex1 @ ( (k8_real_1 @ (k18_sin_cos @ ( (k7_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ (k18_sin_cos @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) ) @ (k5_square_1 @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ c2_6__diff_4) ) ) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) , inference(mizar_by, [status(thm), assumptions([dt_c1_6__diff_4, dt_c2_6__diff_4])], [fc40_valued_2, fc41_valued_2, fc42_valued_2, fc43_valued_2, cc10_valued_2, cc15_valued_2, cc16_valued_2, cc21_valued_2, cc25_valued_2, cc26_valued_2, cc28_valued_2, cc29_valued_2, cc7_valued_2, cc8_valued_2, cc9_valued_2, fc14_valued_2, fc15_valued_2, fc16_valued_2, fc17_valued_2, fc44_valued_2, cc11_valued_2, cc17_valued_2, cc23_valued_0, cc24_valued_0, cc24_valued_2, cc2_seq_2, cc30_valued_2, cc4_valued_2, cc5_valued_2, fc18_valued_2, fc45_valued_2, rc3_valued_0, dt_k3_numbers, dt_k4_numbers, cc10_membered, cc10_valued_0, cc11_valued_0, cc12_valued_2, cc13_valued_0, cc14_valued_0, cc15_membered, cc18_valued_2, cc19_valued_0, cc1_funct_2, cc1_int_1, cc1_seq_2, cc22_membered, cc22_valued_0, cc23_valued_2, cc28_valued_0, cc2_valued_0, cc30_valued_0, cc31_valued_0, cc31_valued_2, cc3_membered, cc3_valued_0, cc3_valued_2, cc4_seq_2, cc4_valued_0, cc5_relat_1, cc6_funct_1, cc6_relat_1, cc7_relat_1, cc8_relat_1, cc9_membered, fc17_funct_1, fc19_valued_2, fc3_numbers, fc46_valued_2, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc61_valued_0, fc62_valued_0, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc88_valued_0, rc1_funct_2, rc1_partfun1, rc1_relset_1, rc1_seq_2, rc2_valued_0, rc2_valued_1, rc3_ordinal1, rc3_partfun1, rc3_relat_1, rc3_valued_1, rc4_valued_0, rc5_valued_1, rc6_funct_1, rc6_valued_0, rc9_funct_1, reflexivity_r1_tarski, dt_k1_funct_1, dt_k2_zfmisc_1, dt_o_0_0_xboole_0, cc12_valued_0, cc13_membered, cc13_valued_2, cc15_valued_0, cc16_membered, cc16_valued_0, cc17_valued_0, cc18_valued_0, cc19_valued_2, cc1_partfun1, cc1_relset_1, cc1_rfunct_1, cc1_valued_0, cc20_membered, cc20_valued_0, cc21_valued_0, cc22_valued_2, cc23_membered, cc2_funct_2, cc2_membered, cc2_ordinal1, cc2_partfun1, cc2_relset_1, cc2_valued_2, cc32_valued_2, cc33_valued_2, cc3_funct_2, cc3_int_1, cc3_relset_1, cc3_seq_2, cc4_funct_2, cc4_relset_1, cc5_funct_1, cc5_valued_0, cc6_valued_0, cc7_valued_0, cc8_funct_2, cc8_valued_0, fc19_funct_1, fc1_int_1, fc20_valued_2, fc21_valued_2, fc2_int_1, fc3_int_1, fc47_valued_2, fc4_int_1, fc63_valued_0, fc66_valued_0, fc6_relat_1, fc85_valued_0, fc86_valued_0, fc87_valued_0, fc89_valued_0, fc90_valued_0, rc1_int_1, rc1_valued_0, rc2_funct_1, rc2_int_1, rc2_ordinal1, rc2_relat_1, rc2_valued_2, rc3_funct_1, rc4_funct_1, rc5_funct_1, antisymmetry_r2_hidden, redefinition_k1_seq_1, dt_k16_sin_cos, dt_k1_seq_1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k4_ordinal1, cc10_ordinal1, cc11_membered, cc12_membered, cc14_membered, cc14_valued_2, cc17_membered, cc19_membered, cc1_membered, cc1_ordinal1, cc1_valued_2, cc20_valued_2, cc21_membered, cc24_membered, cc27_valued_2, cc2_funct_1, cc2_int_1, cc2_relat_1, cc2_xcmplx_0, cc2_xreal_0, cc2_xxreal_0, cc3_funct_1, cc3_relat_1, cc3_xxreal_0, cc4_funct_1, cc4_membered, cc4_relat_1, cc4_xxreal_0, cc5_membered, cc5_ordinal1, cc5_xxreal_0, cc6_membered, cc6_ordinal1, cc6_xxreal_0, cc7_xxreal_0, cc8_funct_1, cc8_membered, cc8_ordinal1, cc8_xxreal_0, cc9_funct_1, cc9_valued_0, fc11_xreal_0, fc12_xreal_0, fc13_xreal_0, fc14_xreal_0, fc16_xreal_0, fc17_xreal_0, fc18_xreal_0, fc1_xboole_0, fc21_xreal_0, fc22_xreal_0, fc23_xreal_0, fc24_xreal_0, fc26_xreal_0, fc29_xreal_0, fc30_xreal_0, fc31_xreal_0, fc32_xreal_0, fc33_xreal_0, fc59_membered, fc6_membered, fc6_ordinal1, fc6_sin_cos, fc9_xreal_0, rc1_funct_1, rc1_membered, rc1_ordinal1, rc1_relat_1, rc1_valued_2, rc1_xxreal_0, rc2_membered, rc2_xreal_0, rc2_xxreal_0, rc3_membered, rc3_xreal_0, rc3_xxreal_0, rc4_ordinal1, rc4_xreal_0, rc4_xxreal_0, rc5_ordinal1, rc7_funct_1, t1_numerals, t1_subset, t3_subset, t4_subset, t5_subset, d2_xboole_0, commutativity_k2_xcmplx_0, involutiveness_k5_xcmplx_0, existence_m1_subset_1, existence_m2_subset_1, redefinition_k5_numbers, redefinition_m2_subset_1, dt_k17_sin_cos, dt_k1_numbers, dt_k2_numbers, dt_k2_xcmplx_0, dt_k3_square_1, dt_k5_numbers, dt_k5_xcmplx_0, dt_m1_subset_1, dt_m2_subset_1, cc18_membered, cc1_funct_1, cc1_relat_1, cc1_xcmplx_0, cc1_xreal_0, cc25_membered, cc26_membered, cc3_ordinal1, cc3_xcmplx_0, cc3_xreal_0, cc4_ordinal1, cc4_xreal_0, cc6_valued_2, cc7_funct_1, cc7_ordinal1, cc9_ordinal1, fc10_xreal_0, fc15_xreal_0, fc19_xreal_0, fc1_membered, fc1_numbers, fc1_square_1, fc20_xreal_0, fc25_xreal_0, fc27_xreal_0, fc28_xreal_0, fc2_numbers, fc2_square_1, fc2_xcmplx_0, fc34_xreal_0, fc3_membered, fc3_sin_cos, fc3_xreal_0, fc4_xreal_0, fc55_membered, fc56_membered, fc5_xreal_0, fc6_xcmplx_0, fc6_xreal_0, fc7_xcmplx_0, fc7_xreal_0, fc8_numbers, fc8_xcmplx_0, fc8_xreal_0, fc9_numbers, fc9_xcmplx_0, rc1_xboole_0, rc1_xreal_0, rc2_xboole_0, rc2_xcmplx_0, rqRealAdd__k2_xcmplx_0__r0_r0_r0, rqRealAdd__k2_xcmplx_0__r0_r1_r1, rqRealAdd__k2_xcmplx_0__r0_r2_r2, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__r1_r0_r1, rqRealAdd__k2_xcmplx_0__r1_r1_r2, rqRealAdd__k2_xcmplx_0__r1_rm1_r0, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r2_r0_r2, rqRealAdd__k2_xcmplx_0__r2_rm1_r1, rqRealAdd__k2_xcmplx_0__r2_rm2_r0, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, rqRealAdd__k2_xcmplx_0__rm1_r1_r0, rqRealAdd__k2_xcmplx_0__rm1_r2_r1, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, rqRealAdd__k2_xcmplx_0__rm2_r2_r0, rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, spc10_arithm, spc11_arithm, spc12_arithm, spc1_arithm, spc3_arithm, spc5_arithm, spc6_arithm, spc8_arithm, t2_subset, t6_boole, t7_boole, t8_boole, d17_sin_cos, d1_square_1, involutiveness_k10_complex1, commutativity_k3_xcmplx_0, involutiveness_k4_xcmplx_0, commutativity_k7_real_1, commutativity_k8_real_1, commutativity_k9_complex1, redefinition_k10_complex1, redefinition_k13_complex1, redefinition_k18_sin_cos, redefinition_k5_square_1, redefinition_k7_real_1, redefinition_k8_real_1, redefinition_k9_complex1, redefinition_k9_real_1, dt_k10_complex1, dt_k13_complex1, dt_k18_sin_cos, dt_k3_xcmplx_0, dt_k4_xcmplx_0, dt_k5_square_1, dt_k6_xcmplx_0, dt_k7_real_1, dt_k7_xcmplx_0, dt_k8_real_1, dt_k9_complex1, dt_k9_real_1, dt_c1_6__diff_4, dt_c2_6__diff_4, fc3_xcmplx_0, fc4_xcmplx_0, fc5_xcmplx_0, rc1_xcmplx_0, rqRealDiff__k6_xcmplx_0__r0_r0_r0, rqRealDiff__k6_xcmplx_0__r0_r1_rm1, rqRealDiff__k6_xcmplx_0__r0_r2_rm2, rqRealDiff__k6_xcmplx_0__r0_rm1_r1, rqRealDiff__k6_xcmplx_0__r0_rm2_r2, rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r1_r0_r1, rqRealDiff__k6_xcmplx_0__r1_r2_rm1, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r2_r0_r2, rqRealDiff__k6_xcmplx_0__r2_r1_r1, rqRealDiff__k6_xcmplx_0__r2_r2_r0, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, rqRealDiv__k7_xcmplx_0__r1_r1_r1, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, rqRealDiv__k7_xcmplx_0__r2_r1_r2, rqRealDiv__k7_xcmplx_0__r2_r2_r1, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__r0_r0_r0, rqRealMult__k3_xcmplx_0__r0_r1_r0, rqRealMult__k3_xcmplx_0__r0_r2_r0, rqRealMult__k3_xcmplx_0__r0_rm2_r0, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, rqRealMult__k3_xcmplx_0__r1_r0_r0, rqRealMult__k3_xcmplx_0__r1_r2_r2, rqRealMult__k3_xcmplx_0__r1_rm2_rm2, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r2_r0_r0, rqRealMult__k3_xcmplx_0__r2_r1_r2, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_r0_r0, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, rqRealNeg__k4_xcmplx_0__r0_r0, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, spc2_arithm, spc4_arithm, spc7_arithm, spc9_arithm, t3_arithm, t6_arithm, d8_xcmplx_0, d9_xcmplx_0, spc0_numerals, spc1_numerals, spc2_numerals, spc0_boole, spc1_boole, spc2_boole, t76_xcmplx_1, rqRealMult__k3_xcmplx_0__r1_r1_r1, rqRealNeg__k4_xcmplx_0__r1_rm1, rqRealNeg__k4_xcmplx_0__rm1_r1, rqRealDiff__k6_xcmplx_0__r1_r1_r0, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, rqRealMult__k3_xcmplx_0__rm2_r1_rm2, rqRealNeg__k4_xcmplx_0__rm2_r2, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, rqRealNeg__k4_xcmplx_0__r2_rm2, rqRealDiff__k6_xcmplx_0__r1_rm1_r2]), [interesting(np__0.65), file(diff_4, e11_6_1__diff_4), [file(diff_4, e11_6_1__diff_4)]]). thf(t38_sin_cos4, theorem, (! [A: $i] : ( (v1_xreal_0 @ A) => (! [B: $i] : ( (v1_xreal_0 @ B) => ( (= @ ( (k3_xcmplx_0 @ (k17_sin_cos @ ( (k2_xcmplx_0 @ A) @ B) ) ) @ (k17_sin_cos @ ( (k6_xcmplx_0 @ A) @ B) ) ) ) @ ( (k6_xcmplx_0 @ ( (k3_xcmplx_0 @ (k20_sin_cos @ B) ) @ (k20_sin_cos @ B) ) ) @ ( (k3_xcmplx_0 @ (k20_sin_cos @ A) ) @ (k20_sin_cos @ A) ) ) ) ) ) ) ) , file(sin_cos4, t38_sin_cos4), [interesting(np__0.9), axiom, file(sin_cos4, t38_sin_cos4)]). thf(e12_6_1__diff_4, plain, ( (= @ ( (k13_complex1 @ (k10_complex1 @ ( (k13_complex1 @ ( (k8_real_1 @ (k18_sin_cos @ ( (k7_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ (k18_sin_cos @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) ) @ (k5_square_1 @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ c2_6__diff_4) ) ) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ ( (k13_complex1 @ (k10_complex1 @ ( (k13_complex1 @ ( (k9_real_1 @ (k5_square_1 @ (k21_sin_cos @ c2_6__diff_4) ) ) @ (k5_square_1 @ (k21_sin_cos @ c1_6__diff_4) ) ) ) @ (k5_square_1 @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ c2_6__diff_4) ) ) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) , inference(mizar_by, [status(thm), assumptions([dt_c1_6__diff_4, dt_c2_6__diff_4])], [fc40_valued_2, fc41_valued_2, fc42_valued_2, fc43_valued_2, cc10_valued_2, cc15_valued_2, cc16_valued_2, cc21_valued_2, cc25_valued_2, cc26_valued_2, cc28_valued_2, cc29_valued_2, cc7_valued_2, cc8_valued_2, cc9_valued_2, fc14_valued_2, fc15_valued_2, fc16_valued_2, fc17_valued_2, fc44_valued_2, cc11_valued_2, cc17_valued_2, cc23_valued_0, cc24_valued_0, cc24_valued_2, cc2_seq_2, cc30_valued_2, cc4_valued_2, cc5_valued_2, fc18_valued_2, fc45_valued_2, rc3_valued_0, dt_k3_numbers, dt_k4_numbers, cc10_membered, cc12_valued_2, cc13_valued_0, cc14_valued_0, cc15_membered, cc18_valued_2, cc19_valued_0, cc1_int_1, cc1_seq_2, cc22_membered, cc22_valued_0, cc23_valued_2, cc2_valued_0, cc31_valued_2, cc3_membered, cc3_valued_0, cc3_valued_2, cc4_seq_2, cc4_valued_0, cc6_funct_1, cc9_membered, fc19_valued_2, fc3_numbers, fc46_valued_2, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc88_valued_0, rc2_valued_0, rc5_valued_1, reflexivity_r1_tarski, dt_o_0_0_xboole_0, cc10_valued_0, cc11_valued_0, cc13_membered, cc13_valued_2, cc15_valued_0, cc16_membered, cc17_valued_0, cc19_valued_2, cc1_funct_2, cc1_rfunct_1, cc1_valued_0, cc20_membered, cc20_valued_0, cc22_valued_2, cc23_membered, cc28_valued_0, cc2_membered, cc2_ordinal1, cc2_valued_2, cc30_valued_0, cc31_valued_0, cc32_valued_2, cc3_int_1, cc3_seq_2, cc5_funct_1, cc5_relat_1, cc6_relat_1, cc7_relat_1, cc7_valued_0, cc8_relat_1, cc8_valued_0, fc17_funct_1, fc19_funct_1, fc1_int_1, fc20_valued_2, fc2_int_1, fc3_int_1, fc47_valued_2, fc4_int_1, fc61_valued_0, fc62_valued_0, fc66_valued_0, fc86_valued_0, fc89_valued_0, rc1_funct_2, rc1_int_1, rc1_partfun1, rc1_relset_1, rc1_seq_2, rc1_valued_0, rc2_funct_1, rc2_int_1, rc2_ordinal1, rc2_relat_1, rc2_valued_1, rc2_valued_2, rc3_funct_1, rc3_ordinal1, rc3_partfun1, rc3_relat_1, rc3_valued_1, rc4_funct_1, rc4_valued_0, rc5_funct_1, rc6_funct_1, rc6_valued_0, rc9_funct_1, involutiveness_k5_xcmplx_0, antisymmetry_r2_hidden, dt_k1_funct_1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_k4_ordinal1, dt_k5_xcmplx_0, cc10_ordinal1, cc11_membered, cc12_membered, cc12_valued_0, cc14_membered, cc14_valued_2, cc16_valued_0, cc17_membered, cc18_valued_0, cc19_membered, cc1_membered, cc1_ordinal1, cc1_partfun1, cc1_relset_1, cc1_valued_2, cc20_valued_2, cc21_membered, cc21_valued_0, cc24_membered, cc27_valued_2, cc2_funct_1, cc2_funct_2, cc2_int_1, cc2_partfun1, cc2_relat_1, cc2_relset_1, cc2_xcmplx_0, cc2_xreal_0, cc2_xxreal_0, cc33_valued_2, cc3_funct_1, cc3_funct_2, cc3_relat_1, cc3_relset_1, cc4_funct_1, cc4_funct_2, cc4_membered, cc4_relat_1, cc4_relset_1, cc4_xxreal_0, cc5_membered, cc5_ordinal1, cc5_valued_0, cc5_xxreal_0, cc6_membered, cc6_ordinal1, cc6_valued_0, cc8_funct_1, cc8_funct_2, cc8_membered, cc8_ordinal1, cc8_xxreal_0, cc9_funct_1, cc9_valued_0, fc11_xreal_0, fc12_xreal_0, fc13_xreal_0, fc14_xreal_0, fc16_xreal_0, fc17_xreal_0, fc18_xreal_0, fc1_xboole_0, fc21_valued_2, fc21_xreal_0, fc22_xreal_0, fc23_xreal_0, fc24_xreal_0, fc26_xreal_0, fc27_xreal_0, fc28_xreal_0, fc29_xreal_0, fc30_xreal_0, fc31_xreal_0, fc32_xreal_0, fc33_xreal_0, fc4_xreal_0, fc59_membered, fc63_valued_0, fc6_membered, fc6_ordinal1, fc6_relat_1, fc7_xcmplx_0, fc85_valued_0, fc87_valued_0, fc90_valued_0, fc9_xreal_0, rc1_funct_1, rc1_membered, rc1_ordinal1, rc1_relat_1, rc1_valued_2, rc2_membered, rc3_membered, rc3_xreal_0, rc3_xxreal_0, rc4_ordinal1, rc5_ordinal1, rc7_funct_1, spc10_arithm, spc11_arithm, spc12_arithm, spc3_arithm, t1_numerals, t1_subset, t3_subset, t4_subset, t5_subset, d2_xboole_0, existence_m1_subset_1, existence_m2_subset_1, redefinition_k1_seq_1, redefinition_k5_numbers, redefinition_m2_subset_1, dt_k16_sin_cos, dt_k19_sin_cos, dt_k1_numbers, dt_k1_seq_1, dt_k2_numbers, dt_k3_square_1, dt_k5_numbers, dt_k7_xcmplx_0, dt_m1_subset_1, dt_m2_subset_1, cc18_membered, cc1_funct_1, cc1_relat_1, cc1_xcmplx_0, cc1_xreal_0, cc25_membered, cc26_membered, cc3_ordinal1, cc3_xcmplx_0, cc3_xxreal_0, cc4_ordinal1, cc6_valued_2, cc6_xxreal_0, cc7_funct_1, cc7_ordinal1, cc7_xxreal_0, cc9_ordinal1, fc10_xreal_0, fc15_xreal_0, fc19_xreal_0, fc1_membered, fc1_numbers, fc1_square_1, fc20_xreal_0, fc25_xreal_0, fc2_numbers, fc2_square_1, fc2_xcmplx_0, fc34_xreal_0, fc3_membered, fc3_xcmplx_0, fc4_xcmplx_0, fc55_membered, fc56_membered, fc5_xcmplx_0, fc6_sin_cos, fc6_xcmplx_0, fc7_sin_cos, fc8_numbers, fc8_xcmplx_0, fc8_xreal_0, fc9_numbers, fc9_xcmplx_0, rc1_xboole_0, rc1_xcmplx_0, rc1_xxreal_0, rc2_xboole_0, rc2_xcmplx_0, rc2_xreal_0, rc2_xxreal_0, rc4_xreal_0, rc4_xxreal_0, rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, rqRealDiv__k7_xcmplx_0__r1_r1_r1, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, rqRealDiv__k7_xcmplx_0__r2_r1_r2, rqRealDiv__k7_xcmplx_0__r2_r2_r1, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, spc1_arithm, spc2_arithm, spc4_arithm, spc5_arithm, spc6_arithm, spc7_arithm, spc8_arithm, spc9_arithm, t2_subset, t3_arithm, t6_arithm, t6_boole, t7_boole, t8_boole, d1_square_1, d9_xcmplx_0, involutiveness_k10_complex1, commutativity_k2_xcmplx_0, commutativity_k3_xcmplx_0, involutiveness_k4_xcmplx_0, commutativity_k7_real_1, commutativity_k8_real_1, redefinition_k10_complex1, redefinition_k13_complex1, redefinition_k18_sin_cos, redefinition_k21_sin_cos, redefinition_k5_square_1, redefinition_k7_real_1, redefinition_k8_real_1, redefinition_k9_real_1, dt_k10_complex1, dt_k13_complex1, dt_k17_sin_cos, dt_k18_sin_cos, dt_k20_sin_cos, dt_k21_sin_cos, dt_k2_xcmplx_0, dt_k3_xcmplx_0, dt_k4_xcmplx_0, dt_k5_square_1, dt_k6_xcmplx_0, dt_k7_real_1, dt_k8_real_1, dt_k9_real_1, dt_c1_6__diff_4, dt_c2_6__diff_4, cc3_xreal_0, cc4_xreal_0, fc3_sin_cos, fc3_xreal_0, fc4_sin_cos, fc5_xreal_0, fc6_xreal_0, fc7_xreal_0, rc1_xreal_0, rqRealAdd__k2_xcmplx_0__r0_r0_r0, rqRealAdd__k2_xcmplx_0__r0_r1_r1, rqRealAdd__k2_xcmplx_0__r0_r2_r2, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, rqRealAdd__k2_xcmplx_0__r1_r0_r1, rqRealAdd__k2_xcmplx_0__r1_r1_r2, rqRealAdd__k2_xcmplx_0__r1_rm1_r0, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, rqRealAdd__k2_xcmplx_0__r2_r0_r2, rqRealAdd__k2_xcmplx_0__r2_rm1_r1, rqRealAdd__k2_xcmplx_0__r2_rm2_r0, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, rqRealAdd__k2_xcmplx_0__rm1_r1_r0, rqRealAdd__k2_xcmplx_0__rm1_r2_r1, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, rqRealAdd__k2_xcmplx_0__rm2_r2_r0, rqRealDiff__k6_xcmplx_0__r0_r0_r0, rqRealDiff__k6_xcmplx_0__r0_r1_rm1, rqRealDiff__k6_xcmplx_0__r0_r2_rm2, rqRealDiff__k6_xcmplx_0__r0_rm1_r1, rqRealDiff__k6_xcmplx_0__r0_rm2_r2, rqRealDiff__k6_xcmplx_0__r1_r0_r1, rqRealDiff__k6_xcmplx_0__r1_r2_rm1, rqRealDiff__k6_xcmplx_0__r2_r0_r2, rqRealDiff__k6_xcmplx_0__r2_r1_r1, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, rqRealMult__k3_xcmplx_0__r0_r0_r0, rqRealMult__k3_xcmplx_0__r0_r1_r0, rqRealMult__k3_xcmplx_0__r0_r2_r0, rqRealMult__k3_xcmplx_0__r0_rm2_r0, rqRealMult__k3_xcmplx_0__r1_r0_r0, rqRealMult__k3_xcmplx_0__r1_r2_r2, rqRealMult__k3_xcmplx_0__r1_rm2_rm2, rqRealMult__k3_xcmplx_0__r2_r0_r0, rqRealMult__k3_xcmplx_0__rm2_r0_r0, rqRealNeg__k4_xcmplx_0__r0_r0, d17_sin_cos, d19_sin_cos, d8_xcmplx_0, spc0_numerals, spc1_numerals, spc2_numerals, spc0_boole, spc1_boole, spc2_boole, t38_sin_cos4, rqRealMult__k3_xcmplx_0__r1_r1_r1, rqRealNeg__k4_xcmplx_0__r1_rm1, rqRealNeg__k4_xcmplx_0__rm1_r1, rqRealDiff__k6_xcmplx_0__r1_r1_r0, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, rqRealMult__k3_xcmplx_0__rm2_r1_rm2, rqRealNeg__k4_xcmplx_0__rm2_r2, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, rqRealNeg__k4_xcmplx_0__r2_rm2, rqRealDiff__k6_xcmplx_0__r1_rm1_r2, rqRealMult__k3_xcmplx_0__r2_r1_r2, rqRealDiff__k6_xcmplx_0__r2_r2_r0]), [interesting(np__0.65), file(diff_4, e12_6_1__diff_4), [file(diff_4, e12_6_1__diff_4)]]). thf(e13_6_1__diff_4, plain, ( (= @ ( (k13_complex1 @ (k10_complex1 @ ( (k13_complex1 @ ( (k9_real_1 @ (k5_square_1 @ (k21_sin_cos @ c2_6__diff_4) ) ) @ (k5_square_1 @ (k21_sin_cos @ c1_6__diff_4) ) ) ) @ (k5_square_1 @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ c2_6__diff_4) ) ) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) @ (k10_complex1 @ ( (k13_complex1 @ ( (k13_complex1 @ ( (k9_real_1 @ (k5_square_1 @ (k21_sin_cos @ c2_6__diff_4) ) ) @ (k5_square_1 @ (k21_sin_cos @ c1_6__diff_4) ) ) ) @ (k5_square_1 @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ c2_6__diff_4) ) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) ) , inference(mizar_by, [status(thm), assumptions([dt_c1_6__diff_4, dt_c2_6__diff_4])], [fc40_valued_2, fc41_valued_2, fc42_valued_2, fc43_valued_2, cc10_valued_2, cc15_valued_2, cc16_valued_2, cc21_valued_2, cc25_valued_2, cc26_valued_2, cc28_valued_2, cc29_valued_2, cc7_valued_2, cc8_valued_2, cc9_valued_2, fc14_valued_2, fc15_valued_2, fc16_valued_2, fc17_valued_2, fc44_valued_2, cc11_valued_2, cc17_valued_2, cc23_valued_0, cc24_valued_0, cc24_valued_2, cc2_seq_2, cc30_valued_2, cc4_valued_2, cc5_valued_2, fc18_valued_2, fc45_valued_2, rc3_valued_0, dt_k3_numbers, dt_k4_numbers, cc10_membered, cc10_valued_0, cc11_valued_0, cc12_valued_2, cc13_valued_0, cc14_valued_0, cc15_membered, cc18_valued_2, cc19_valued_0, cc1_funct_2, cc1_int_1, cc1_seq_2, cc22_membered, cc22_valued_0, cc23_valued_2, cc28_valued_0, cc2_valued_0, cc30_valued_0, cc31_valued_0, cc31_valued_2, cc3_membered, cc3_valued_0, cc3_valued_2, cc4_seq_2, cc4_valued_0, cc5_relat_1, cc6_funct_1, cc6_relat_1, cc7_relat_1, cc8_relat_1, cc9_membered, fc17_funct_1, fc19_valued_2, fc3_numbers, fc46_valued_2, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc61_valued_0, fc62_valued_0, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc88_valued_0, rc1_funct_2, rc1_partfun1, rc1_relset_1, rc1_seq_2, rc2_valued_0, rc2_valued_1, rc3_ordinal1, rc3_partfun1, rc3_relat_1, rc3_valued_1, rc4_valued_0, rc5_valued_1, rc6_funct_1, rc6_valued_0, rc9_funct_1, reflexivity_r1_tarski, dt_k1_funct_1, dt_k2_zfmisc_1, dt_o_0_0_xboole_0, cc12_valued_0, cc13_membered, cc13_valued_2, cc15_valued_0, cc16_membered, cc16_valued_0, cc17_valued_0, cc18_valued_0, cc19_valued_2, cc1_partfun1, cc1_relset_1, cc1_rfunct_1, cc1_valued_0, cc20_membered, cc20_valued_0, cc21_valued_0, cc22_valued_2, cc23_membered, cc2_funct_2, cc2_membered, cc2_ordinal1, cc2_partfun1, cc2_relset_1, cc2_valued_2, cc32_valued_2, cc33_valued_2, cc3_funct_2, cc3_int_1, cc3_relset_1, cc3_seq_2, cc4_funct_2, cc4_relset_1, cc5_funct_1, cc5_valued_0, cc6_valued_0, cc7_valued_0, cc8_funct_2, cc8_valued_0, fc19_funct_1, fc1_int_1, fc20_valued_2, fc21_valued_2, fc2_int_1, fc3_int_1, fc47_valued_2, fc4_int_1, fc63_valued_0, fc66_valued_0, fc6_relat_1, fc85_valued_0, fc86_valued_0, fc87_valued_0, fc89_valued_0, fc90_valued_0, rc1_int_1, rc1_valued_0, rc2_funct_1, rc2_int_1, rc2_ordinal1, rc2_relat_1, rc2_valued_2, rc3_funct_1, rc4_funct_1, rc5_funct_1, antisymmetry_r2_hidden, redefinition_k1_seq_1, dt_k16_sin_cos, dt_k19_sin_cos, dt_k1_seq_1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k4_ordinal1, cc10_ordinal1, cc11_membered, cc12_membered, cc14_membered, cc14_valued_2, cc17_membered, cc19_membered, cc1_membered, cc1_ordinal1, cc1_valued_2, cc20_valued_2, cc21_membered, cc24_membered, cc27_valued_2, cc2_funct_1, cc2_int_1, cc2_relat_1, cc2_xcmplx_0, cc2_xreal_0, cc2_xxreal_0, cc3_funct_1, cc3_relat_1, cc3_xxreal_0, cc4_funct_1, cc4_membered, cc4_relat_1, cc4_xxreal_0, cc5_membered, cc5_ordinal1, cc5_xxreal_0, cc6_membered, cc6_ordinal1, cc6_xxreal_0, cc7_xxreal_0, cc8_funct_1, cc8_membered, cc8_ordinal1, cc8_xxreal_0, cc9_funct_1, cc9_valued_0, fc11_xreal_0, fc12_xreal_0, fc13_xreal_0, fc14_xreal_0, fc16_xreal_0, fc17_xreal_0, fc18_xreal_0, fc1_xboole_0, fc21_xreal_0, fc22_xreal_0, fc23_xreal_0, fc24_xreal_0, fc26_xreal_0, fc29_xreal_0, fc30_xreal_0, fc31_xreal_0, fc32_xreal_0, fc33_xreal_0, fc59_membered, fc6_membered, fc6_ordinal1, fc6_sin_cos, fc7_sin_cos, fc9_xreal_0, rc1_funct_1, rc1_membered, rc1_ordinal1, rc1_relat_1, rc1_valued_2, rc1_xxreal_0, rc2_membered, rc2_xreal_0, rc2_xxreal_0, rc3_membered, rc3_xreal_0, rc3_xxreal_0, rc4_ordinal1, rc4_xreal_0, rc4_xxreal_0, rc5_ordinal1, rc7_funct_1, t1_numerals, t1_subset, t3_subset, t4_subset, t5_subset, d2_xboole_0, commutativity_k2_xcmplx_0, involutiveness_k5_xcmplx_0, existence_m1_subset_1, existence_m2_subset_1, redefinition_k5_numbers, redefinition_m2_subset_1, dt_k17_sin_cos, dt_k1_numbers, dt_k20_sin_cos, dt_k2_numbers, dt_k2_xcmplx_0, dt_k3_square_1, dt_k5_numbers, dt_k5_xcmplx_0, dt_m1_subset_1, dt_m2_subset_1, cc18_membered, cc1_funct_1, cc1_relat_1, cc1_xcmplx_0, cc1_xreal_0, cc25_membered, cc26_membered, cc3_ordinal1, cc3_xcmplx_0, cc3_xreal_0, cc4_ordinal1, cc4_xreal_0, cc6_valued_2, cc7_funct_1, cc7_ordinal1, cc9_ordinal1, fc10_xreal_0, fc15_xreal_0, fc19_xreal_0, fc1_membered, fc1_numbers, fc1_square_1, fc20_xreal_0, fc25_xreal_0, fc27_xreal_0, fc28_xreal_0, fc2_numbers, fc2_square_1, fc2_xcmplx_0, fc34_xreal_0, fc3_membered, fc3_sin_cos, fc3_xcmplx_0, fc3_xreal_0, fc4_sin_cos, fc4_xcmplx_0, fc4_xreal_0, fc55_membered, fc56_membered, fc5_xcmplx_0, fc5_xreal_0, fc6_xcmplx_0, fc6_xreal_0, fc7_xcmplx_0, fc7_xreal_0, fc8_numbers, fc8_xcmplx_0, fc8_xreal_0, fc9_numbers, fc9_xcmplx_0, rc1_xboole_0, rc1_xcmplx_0, rc1_xreal_0, rc2_xboole_0, rc2_xcmplx_0, rqRealAdd__k2_xcmplx_0__r0_r0_r0, rqRealAdd__k2_xcmplx_0__r0_r1_r1, rqRealAdd__k2_xcmplx_0__r0_r2_r2, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__r1_r0_r1, rqRealAdd__k2_xcmplx_0__r1_r1_r2, rqRealAdd__k2_xcmplx_0__r1_rm1_r0, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r2_r0_r2, rqRealAdd__k2_xcmplx_0__r2_rm1_r1, rqRealAdd__k2_xcmplx_0__r2_rm2_r0, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, rqRealAdd__k2_xcmplx_0__rm1_r1_r0, rqRealAdd__k2_xcmplx_0__rm1_r2_r1, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, rqRealAdd__k2_xcmplx_0__rm2_r2_r0, rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, spc10_arithm, spc11_arithm, spc12_arithm, spc1_arithm, spc2_arithm, spc3_arithm, spc4_arithm, spc5_arithm, spc6_arithm, spc7_arithm, spc8_arithm, spc9_arithm, t2_subset, t3_arithm, t6_arithm, t6_boole, t7_boole, t8_boole, d17_sin_cos, d19_sin_cos, d1_square_1, involutiveness_k10_complex1, commutativity_k3_xcmplx_0, involutiveness_k4_xcmplx_0, commutativity_k8_real_1, redefinition_k10_complex1, redefinition_k13_complex1, redefinition_k18_sin_cos, redefinition_k21_sin_cos, redefinition_k5_square_1, redefinition_k8_real_1, redefinition_k9_real_1, dt_k10_complex1, dt_k13_complex1, dt_k18_sin_cos, dt_k21_sin_cos, dt_k3_xcmplx_0, dt_k4_xcmplx_0, dt_k5_square_1, dt_k6_xcmplx_0, dt_k7_xcmplx_0, dt_k8_real_1, dt_k9_real_1, dt_c1_6__diff_4, dt_c2_6__diff_4, rqRealDiff__k6_xcmplx_0__r0_r0_r0, rqRealDiff__k6_xcmplx_0__r0_r1_rm1, rqRealDiff__k6_xcmplx_0__r0_r2_rm2, rqRealDiff__k6_xcmplx_0__r0_rm1_r1, rqRealDiff__k6_xcmplx_0__r0_rm2_r2, rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r1_r0_r1, rqRealDiff__k6_xcmplx_0__r1_r2_rm1, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r2_r0_r2, rqRealDiff__k6_xcmplx_0__r2_r1_r1, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, rqRealDiv__k7_xcmplx_0__r1_r1_r1, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, rqRealDiv__k7_xcmplx_0__r2_r1_r2, rqRealDiv__k7_xcmplx_0__r2_r2_r1, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__r0_r0_r0, rqRealMult__k3_xcmplx_0__r0_r1_r0, rqRealMult__k3_xcmplx_0__r0_r2_r0, rqRealMult__k3_xcmplx_0__r0_rm2_r0, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, rqRealMult__k3_xcmplx_0__r1_r0_r0, rqRealMult__k3_xcmplx_0__r1_r2_r2, rqRealMult__k3_xcmplx_0__r1_rm2_rm2, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r2_r0_r0, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_r0_r0, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, rqRealNeg__k4_xcmplx_0__r0_r0, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, d8_xcmplx_0, d9_xcmplx_0, spc0_numerals, spc1_numerals, spc2_numerals, spc0_boole, spc1_boole, spc2_boole, rqRealNeg__k4_xcmplx_0__r1_rm1, rqRealMult__k3_xcmplx_0__r1_r1_r1, rqRealNeg__k4_xcmplx_0__rm1_r1, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, rqRealDiff__k6_xcmplx_0__r1_r1_r0, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, rqRealMult__k3_xcmplx_0__rm2_r1_rm2, rqRealNeg__k4_xcmplx_0__rm2_r2, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, rqRealNeg__k4_xcmplx_0__r2_rm2, rqRealDiff__k6_xcmplx_0__r1_rm1_r2, rqRealMult__k3_xcmplx_0__r2_r1_r2, rqRealDiff__k6_xcmplx_0__r2_r2_r0]), [interesting(np__0.65), file(diff_4, e13_6_1__diff_4), [file(diff_4, e13_6_1__diff_4)]]). thf(t78_xcmplx_1, theorem, (! [A: $i] : ( (v1_xcmplx_0 @ A) => (! [B: $i] : ( (v1_xcmplx_0 @ B) => (! [C: $i] : ( (v1_xcmplx_0 @ C) => ( (= @ ( (k7_xcmplx_0 @ A) @ ( (k3_xcmplx_0 @ B) @ C) ) ) @ ( (k7_xcmplx_0 @ ( (k7_xcmplx_0 @ A) @ B) ) @ C) ) ) ) ) ) ) ) , file(xcmplx_1, t78_xcmplx_1), [interesting(np__0.9), axiom, file(xcmplx_1, t78_xcmplx_1)]). thf(e14_6_1__diff_4, plain, ( (= @ (k10_complex1 @ ( (k13_complex1 @ ( (k13_complex1 @ ( (k9_real_1 @ (k5_square_1 @ (k21_sin_cos @ c2_6__diff_4) ) ) @ (k5_square_1 @ (k21_sin_cos @ c1_6__diff_4) ) ) ) @ (k5_square_1 @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ c2_6__diff_4) ) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) ) @ (k10_complex1 @ ( (k13_complex1 @ ( (k9_real_1 @ (k5_square_1 @ (k21_sin_cos @ c2_6__diff_4) ) ) @ (k5_square_1 @ (k21_sin_cos @ c1_6__diff_4) ) ) ) @ ( (k8_real_1 @ (k5_square_1 @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ c2_6__diff_4) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) ) ) , inference(mizar_by, [status(thm), assumptions([dt_c1_6__diff_4, dt_c2_6__diff_4])], [fc40_valued_2, fc41_valued_2, fc42_valued_2, fc43_valued_2, cc10_valued_2, cc15_valued_2, cc16_valued_2, cc21_valued_2, cc25_valued_2, cc26_valued_2, cc28_valued_2, cc29_valued_2, cc7_valued_2, cc8_valued_2, cc9_valued_2, fc14_valued_2, fc15_valued_2, fc16_valued_2, fc17_valued_2, fc44_valued_2, cc11_valued_2, cc17_valued_2, cc23_valued_0, cc24_valued_0, cc24_valued_2, cc2_seq_2, cc30_valued_2, cc4_valued_2, cc5_valued_2, fc18_valued_2, fc45_valued_2, rc3_valued_0, dt_k3_numbers, dt_k4_numbers, cc10_membered, cc10_valued_0, cc11_valued_0, cc12_valued_2, cc13_valued_0, cc14_valued_0, cc15_membered, cc18_valued_2, cc19_valued_0, cc1_funct_2, cc1_int_1, cc1_seq_2, cc22_membered, cc22_valued_0, cc23_valued_2, cc28_valued_0, cc2_valued_0, cc30_valued_0, cc31_valued_0, cc31_valued_2, cc3_membered, cc3_valued_0, cc3_valued_2, cc4_seq_2, cc4_valued_0, cc5_relat_1, cc6_funct_1, cc6_relat_1, cc7_relat_1, cc8_relat_1, cc9_membered, fc17_funct_1, fc19_valued_2, fc3_numbers, fc46_valued_2, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc61_valued_0, fc62_valued_0, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc88_valued_0, rc1_funct_2, rc1_partfun1, rc1_relset_1, rc1_seq_2, rc2_valued_0, rc2_valued_1, rc3_ordinal1, rc3_partfun1, rc3_relat_1, rc3_valued_1, rc4_valued_0, rc5_valued_1, rc6_funct_1, rc6_valued_0, rc9_funct_1, reflexivity_r1_tarski, dt_k1_funct_1, dt_k2_zfmisc_1, dt_o_0_0_xboole_0, cc12_valued_0, cc13_membered, cc13_valued_2, cc15_valued_0, cc16_membered, cc16_valued_0, cc17_valued_0, cc18_valued_0, cc19_valued_2, cc1_partfun1, cc1_relset_1, cc1_rfunct_1, cc1_valued_0, cc20_membered, cc20_valued_0, cc21_valued_0, cc22_valued_2, cc23_membered, cc2_funct_2, cc2_membered, cc2_ordinal1, cc2_partfun1, cc2_relset_1, cc2_valued_2, cc32_valued_2, cc33_valued_2, cc3_funct_2, cc3_int_1, cc3_relset_1, cc3_seq_2, cc4_funct_2, cc4_relset_1, cc5_funct_1, cc5_valued_0, cc6_valued_0, cc7_valued_0, cc8_funct_2, cc8_valued_0, fc19_funct_1, fc1_int_1, fc20_valued_2, fc21_valued_2, fc2_int_1, fc3_int_1, fc47_valued_2, fc4_int_1, fc63_valued_0, fc66_valued_0, fc6_relat_1, fc85_valued_0, fc86_valued_0, fc87_valued_0, fc89_valued_0, fc90_valued_0, rc1_int_1, rc1_valued_0, rc2_funct_1, rc2_int_1, rc2_ordinal1, rc2_relat_1, rc2_valued_2, rc3_funct_1, rc4_funct_1, rc5_funct_1, antisymmetry_r2_hidden, redefinition_k1_seq_1, dt_k16_sin_cos, dt_k19_sin_cos, dt_k1_seq_1, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k4_ordinal1, cc10_ordinal1, cc11_membered, cc12_membered, cc14_membered, cc14_valued_2, cc17_membered, cc19_membered, cc1_membered, cc1_ordinal1, cc1_valued_2, cc20_valued_2, cc21_membered, cc24_membered, cc27_valued_2, cc2_funct_1, cc2_int_1, cc2_relat_1, cc2_xcmplx_0, cc2_xreal_0, cc2_xxreal_0, cc3_funct_1, cc3_relat_1, cc3_xxreal_0, cc4_funct_1, cc4_membered, cc4_relat_1, cc4_xxreal_0, cc5_membered, cc5_ordinal1, cc5_xxreal_0, cc6_membered, cc6_ordinal1, cc6_xxreal_0, cc7_xxreal_0, cc8_funct_1, cc8_membered, cc8_ordinal1, cc8_xxreal_0, cc9_funct_1, cc9_valued_0, fc11_xreal_0, fc12_xreal_0, fc13_xreal_0, fc14_xreal_0, fc16_xreal_0, fc17_xreal_0, fc18_xreal_0, fc1_xboole_0, fc21_xreal_0, fc22_xreal_0, fc23_xreal_0, fc24_xreal_0, fc26_xreal_0, fc29_xreal_0, fc30_xreal_0, fc31_xreal_0, fc32_xreal_0, fc33_xreal_0, fc59_membered, fc6_membered, fc6_ordinal1, fc6_sin_cos, fc7_sin_cos, fc9_xreal_0, rc1_funct_1, rc1_membered, rc1_ordinal1, rc1_relat_1, rc1_valued_2, rc1_xxreal_0, rc2_membered, rc2_xreal_0, rc2_xxreal_0, rc3_membered, rc3_xreal_0, rc3_xxreal_0, rc4_ordinal1, rc4_xreal_0, rc4_xxreal_0, rc5_ordinal1, rc7_funct_1, t1_numerals, t1_subset, t3_subset, t4_subset, t5_subset, d2_xboole_0, commutativity_k2_xcmplx_0, involutiveness_k5_xcmplx_0, existence_m1_subset_1, existence_m2_subset_1, redefinition_k5_numbers, redefinition_m2_subset_1, dt_k17_sin_cos, dt_k1_numbers, dt_k20_sin_cos, dt_k2_numbers, dt_k2_xcmplx_0, dt_k3_square_1, dt_k5_numbers, dt_k5_xcmplx_0, dt_m1_subset_1, dt_m2_subset_1, cc18_membered, cc1_funct_1, cc1_relat_1, cc1_xcmplx_0, cc1_xreal_0, cc25_membered, cc26_membered, cc3_ordinal1, cc3_xcmplx_0, cc3_xreal_0, cc4_ordinal1, cc4_xreal_0, cc6_valued_2, cc7_funct_1, cc7_ordinal1, cc9_ordinal1, fc10_xreal_0, fc15_xreal_0, fc19_xreal_0, fc1_membered, fc1_numbers, fc1_square_1, fc20_xreal_0, fc25_xreal_0, fc27_xreal_0, fc28_xreal_0, fc2_numbers, fc2_square_1, fc2_xcmplx_0, fc34_xreal_0, fc3_membered, fc3_sin_cos, fc3_xreal_0, fc4_sin_cos, fc4_xreal_0, fc55_membered, fc56_membered, fc5_xreal_0, fc6_xcmplx_0, fc6_xreal_0, fc7_xcmplx_0, fc7_xreal_0, fc8_numbers, fc8_xcmplx_0, fc8_xreal_0, fc9_numbers, fc9_xcmplx_0, rc1_xboole_0, rc1_xreal_0, rc2_xboole_0, rc2_xcmplx_0, rqRealAdd__k2_xcmplx_0__r0_r0_r0, rqRealAdd__k2_xcmplx_0__r0_r1_r1, rqRealAdd__k2_xcmplx_0__r0_r2_r2, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__r1_r0_r1, rqRealAdd__k2_xcmplx_0__r1_r1_r2, rqRealAdd__k2_xcmplx_0__r1_rm1_r0, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r2_r0_r2, rqRealAdd__k2_xcmplx_0__r2_rm1_r1, rqRealAdd__k2_xcmplx_0__r2_rm2_r0, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, rqRealAdd__k2_xcmplx_0__rm1_r1_r0, rqRealAdd__k2_xcmplx_0__rm1_r2_r1, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, rqRealAdd__k2_xcmplx_0__rm2_r2_r0, rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, spc10_arithm, spc11_arithm, spc12_arithm, spc1_arithm, spc3_arithm, spc5_arithm, spc6_arithm, spc8_arithm, t2_subset, t6_boole, t7_boole, t8_boole, d17_sin_cos, d19_sin_cos, d1_square_1, involutiveness_k10_complex1, commutativity_k3_xcmplx_0, involutiveness_k4_xcmplx_0, commutativity_k8_real_1, redefinition_k10_complex1, redefinition_k13_complex1, redefinition_k18_sin_cos, redefinition_k21_sin_cos, redefinition_k5_square_1, redefinition_k8_real_1, redefinition_k9_real_1, dt_k10_complex1, dt_k13_complex1, dt_k18_sin_cos, dt_k21_sin_cos, dt_k3_xcmplx_0, dt_k4_xcmplx_0, dt_k5_square_1, dt_k6_xcmplx_0, dt_k7_xcmplx_0, dt_k8_real_1, dt_k9_real_1, dt_c1_6__diff_4, dt_c2_6__diff_4, fc3_xcmplx_0, fc4_xcmplx_0, fc5_xcmplx_0, rc1_xcmplx_0, rqRealDiff__k6_xcmplx_0__r0_r0_r0, rqRealDiff__k6_xcmplx_0__r0_r1_rm1, rqRealDiff__k6_xcmplx_0__r0_r2_rm2, rqRealDiff__k6_xcmplx_0__r0_rm1_r1, rqRealDiff__k6_xcmplx_0__r0_rm2_r2, rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r1_r0_r1, rqRealDiff__k6_xcmplx_0__r1_r2_rm1, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r2_r0_r2, rqRealDiff__k6_xcmplx_0__r2_r1_r1, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, rqRealDiv__k7_xcmplx_0__r1_r1_r1, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, rqRealDiv__k7_xcmplx_0__r2_r1_r2, rqRealDiv__k7_xcmplx_0__r2_r2_r1, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__r0_r0_r0, rqRealMult__k3_xcmplx_0__r0_r1_r0, rqRealMult__k3_xcmplx_0__r0_r2_r0, rqRealMult__k3_xcmplx_0__r0_rm2_r0, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, rqRealMult__k3_xcmplx_0__r1_r0_r0, rqRealMult__k3_xcmplx_0__r1_r2_r2, rqRealMult__k3_xcmplx_0__r1_rm2_rm2, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r2_r0_r0, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_r0_r0, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, rqRealNeg__k4_xcmplx_0__r0_r0, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, spc2_arithm, spc4_arithm, spc7_arithm, spc9_arithm, t3_arithm, t6_arithm, d8_xcmplx_0, d9_xcmplx_0, spc0_numerals, spc1_numerals, spc2_numerals, spc0_boole, spc1_boole, spc2_boole, t78_xcmplx_1, rqRealNeg__k4_xcmplx_0__r1_rm1, rqRealMult__k3_xcmplx_0__r1_r1_r1, rqRealNeg__k4_xcmplx_0__rm1_r1, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, rqRealMult__k3_xcmplx_0__rm2_r1_rm2, rqRealNeg__k4_xcmplx_0__rm2_r2, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, rqRealNeg__k4_xcmplx_0__r2_rm2, rqRealDiff__k6_xcmplx_0__r1_rm1_r2, rqRealDiff__k6_xcmplx_0__r1_r1_r0, rqRealMult__k3_xcmplx_0__r2_r1_r2, rqRealDiff__k6_xcmplx_0__r2_r2_r0]), [interesting(np__0.65), file(diff_4, e14_6_1__diff_4), [file(diff_4, e14_6_1__diff_4)]]). thf(e3_6__diff_4, plain, ( (= @ ( ( (k9_diff_1 @ ( ( ( ( (k20_valued_1 @ k1_numbers) @ k1_numbers) @ k1_numbers) @ k30_sin_cos) @ k30_sin_cos) ) @ c1_6__diff_4) @ c2_6__diff_4) ) @ (k10_complex1 @ ( (k13_complex1 @ ( (k9_real_1 @ (k5_square_1 @ (k21_sin_cos @ c2_6__diff_4) ) ) @ (k5_square_1 @ (k21_sin_cos @ c1_6__diff_4) ) ) ) @ ( (k8_real_1 @ (k5_square_1 @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ c2_6__diff_4) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) ) ) , inference(iterative_eq, [status(thm), assumptions([e1_6__diff_4, dt_c1_6__diff_4, dt_c2_6__diff_4])], [cc10_valued_2, cc15_valued_2, cc16_valued_2, cc21_valued_2, cc28_valued_2, cc29_valued_2, cc7_valued_2, cc8_valued_2, cc9_valued_2, fc14_valued_2, fc15_valued_2, fc16_valued_2, fc17_valued_2, fc40_valued_2, fc41_valued_2, fc42_valued_2, fc43_valued_2, cc11_valued_2, cc17_valued_2, cc25_valued_2, cc26_valued_2, cc30_valued_2, cc4_valued_2, cc5_valued_2, fc18_valued_2, fc44_valued_2, cc12_valued_2, cc15_membered, cc18_valued_2, cc19_valued_0, cc22_membered, cc23_valued_0, cc24_valued_0, cc24_valued_2, cc2_seq_2, cc31_valued_2, cc3_membered, cc3_valued_2, fc19_valued_2, fc40_valued_1, fc45_valued_2, fc88_valued_0, dt_k3_numbers, dt_k4_numbers, cc10_membered, cc13_valued_0, cc13_valued_2, cc14_valued_0, cc16_membered, cc19_valued_2, cc1_int_1, cc1_seq_2, cc20_valued_0, cc22_valued_0, cc23_membered, cc23_valued_2, cc2_membered, cc2_ordinal1, cc2_valued_0, cc2_valued_2, cc32_valued_2, cc3_int_1, cc3_valued_0, cc3_xxreal_0, cc4_valued_0, cc4_xxreal_0, cc5_xxreal_0, cc6_funct_1, cc6_xxreal_0, cc8_xxreal_0, cc9_membered, fc10_xreal_0, fc11_xreal_0, fc12_xreal_0, fc13_xreal_0, fc14_xreal_0, fc15_xreal_0, fc16_xreal_0, fc17_rfunct_1, fc17_xreal_0, fc18_xreal_0, fc19_xreal_0, fc1_int_1, fc20_valued_2, fc20_xreal_0, fc21_xreal_0, fc22_xreal_0, fc23_xreal_0, fc24_xreal_0, fc25_xreal_0, fc26_xreal_0, fc27_xreal_0, fc28_xreal_0, fc29_xreal_0, fc2_int_1, fc30_xreal_0, fc31_xreal_0, fc32_xreal_0, fc33_xreal_0, fc34_xreal_0, fc35_valued_1, fc36_valued_1, fc3_int_1, fc3_numbers, fc41_valued_1, fc46_valued_2, fc4_int_1, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc89_valued_0, fc9_xreal_0, rc1_int_1, rc2_int_1, rc2_ordinal1, rc2_valued_0, rc2_xreal_0, rc2_xxreal_0, rc3_xreal_0, rc3_xxreal_0, rc5_valued_1, cc10_ordinal1, cc10_valued_0, cc11_valued_0, cc12_membered, cc13_membered, cc14_valued_2, cc15_valued_0, cc16_valued_0, cc17_membered, cc17_valued_0, cc19_membered, cc1_funct_2, cc1_membered, cc1_ordinal1, cc1_rfunct_1, cc1_valued_0, cc1_valued_2, cc20_membered, cc20_valued_2, cc21_valued_0, cc22_valued_2, cc24_membered, cc28_valued_0, cc2_int_1, cc2_xcmplx_0, cc2_xreal_0, cc2_xxreal_0, cc30_valued_0, cc33_valued_2, cc5_funct_1, cc5_ordinal1, cc5_relat_1, cc6_ordinal1, cc6_relat_1, cc7_relat_1, cc7_valued_0, cc7_xxreal_0, cc8_funct_1, cc8_relat_1, cc8_valued_0, cc9_funct_1, fc127_valued_1, fc131_valued_1, fc17_funct_1, fc19_funct_1, fc20_rfunct_1, fc21_valued_2, fc33_valued_1, fc37_valued_1, fc38_valued_1, fc42_valued_1, fc47_valued_2, fc61_valued_0, fc62_valued_0, fc66_valued_0, fc85_valued_0, fc86_valued_0, fc90_valued_0, rc1_funct_2, rc1_membered, rc1_ordinal1, rc1_partfun1, rc1_relset_1, rc1_valued_0, rc1_valued_2, rc1_xxreal_0, rc2_funct_1, rc2_membered, rc2_relat_1, rc2_valued_2, rc3_funct_1, rc3_membered, rc3_ordinal1, rc3_partfun1, rc3_relat_1, rc4_funct_1, rc4_ordinal1, rc4_xreal_0, rc4_xxreal_0, rc5_funct_1, rc5_ordinal1, rc6_funct_1, rc6_valued_0, rc7_funct_1, rc9_funct_1, commutativity_k18_valued_1, commutativity_k2_xcmplx_0, commutativity_k3_xcmplx_0, involutiveness_k4_xcmplx_0, involutiveness_k5_xcmplx_0, dt_k17_sin_cos, dt_k18_valued_1, dt_k1_funct_1, dt_k1_zfmisc_1, dt_k20_sin_cos, dt_k2_numbers, dt_k2_xcmplx_0, dt_k2_zfmisc_1, dt_k3_square_1, dt_k3_xcmplx_0, dt_k4_xcmplx_0, dt_k5_xcmplx_0, dt_k6_xcmplx_0, dt_k7_xcmplx_0, dt_m1_subset_1, cc12_valued_0, cc14_membered, cc18_membered, cc18_valued_0, cc1_funct_1, cc1_partfun1, cc1_relat_1, cc1_relset_1, cc1_xcmplx_0, cc1_xreal_0, cc21_membered, cc26_membered, cc27_valued_2, cc2_funct_1, cc2_funct_2, cc2_partfun1, cc2_relat_1, cc2_relset_1, cc3_funct_1, cc3_funct_2, cc3_ordinal1, cc3_relat_1, cc3_relset_1, cc3_xcmplx_0, cc3_xreal_0, cc4_funct_1, cc4_funct_2, cc4_membered, cc4_ordinal1, cc4_relat_1, cc4_relset_1, cc4_xreal_0, cc5_membered, cc5_valued_0, cc6_membered, cc6_valued_0, cc6_valued_2, cc7_funct_1, cc7_ordinal1, cc8_funct_2, cc8_membered, cc9_ordinal1, cc9_valued_0, fc1_membered, fc1_square_1, fc2_numbers, fc2_square_1, fc2_xcmplx_0, fc34_valued_1, fc39_valued_1, fc3_sin_cos, fc3_xcmplx_0, fc3_xreal_0, fc4_sin_cos, fc4_xcmplx_0, fc4_xreal_0, fc55_membered, fc5_xcmplx_0, fc5_xreal_0, fc63_valued_0, fc6_relat_1, fc6_xcmplx_0, fc6_xreal_0, fc7_xcmplx_0, fc7_xreal_0, fc87_valued_0, fc8_xcmplx_0, fc8_xreal_0, fc9_numbers, fc9_xcmplx_0, rc1_funct_1, rc1_relat_1, rc1_xboole_0, rc1_xcmplx_0, rc1_xreal_0, rc2_xboole_0, rc2_xcmplx_0, involutiveness_k10_complex1, involutiveness_k1_real_1, commutativity_k20_valued_1, involutiveness_k2_real_1, commutativity_k4_real_1, commutativity_k7_real_1, commutativity_k8_real_1, commutativity_k9_complex1, redefinition_k10_complex1, redefinition_k13_complex1, redefinition_k18_sin_cos, redefinition_k1_real_1, redefinition_k1_seq_1, redefinition_k20_valued_1, redefinition_k21_sin_cos, redefinition_k2_real_1, redefinition_k3_funct_2, redefinition_k4_real_1, redefinition_k5_square_1, redefinition_k7_real_1, redefinition_k8_real_1, redefinition_k9_complex1, redefinition_k9_real_1, dt_k10_complex1, dt_k13_complex1, dt_k16_sin_cos, dt_k18_sin_cos, dt_k19_sin_cos, dt_k1_numbers, dt_k1_real_1, dt_k1_seq_1, dt_k20_valued_1, dt_k21_sin_cos, dt_k2_real_1, dt_k2_sin_cos4, dt_k30_sin_cos, dt_k3_funct_2, dt_k4_real_1, dt_k5_square_1, dt_k7_real_1, dt_k8_real_1, dt_k9_complex1, dt_k9_diff_1, dt_k9_real_1, dt_c1_6__diff_4, dt_c2_6__diff_4, fc1_numbers, fc3_membered, fc56_membered, fc6_sin_cos, fc7_sin_cos, fc8_numbers, e1_6_1__diff_4, e2_6_1__diff_4, e3_6_1__diff_4, e4_6_1__diff_4, e5_6_1__diff_4, e6_6_1__diff_4, e7_6_1__diff_4, e8_6_1__diff_4, e9_6_1__diff_4, e10_6_1__diff_4, e11_6_1__diff_4, e12_6_1__diff_4, e13_6_1__diff_4, e14_6_1__diff_4]), [interesting(np__0.8), file(diff_4, e3_6__diff_4), [file(diff_4, e3_6__diff_4)]]). thf(e4_6__diff_4, plain, ( (= @ ( ( (k9_diff_1 @ ( ( ( ( (k20_valued_1 @ k1_numbers) @ k1_numbers) @ k1_numbers) @ k30_sin_cos) @ k30_sin_cos) ) @ c1_6__diff_4) @ c2_6__diff_4) ) @ (k10_complex1 @ ( (k13_complex1 @ ( (k9_real_1 @ (k5_square_1 @ (k21_sin_cos @ c2_6__diff_4) ) ) @ (k5_square_1 @ (k21_sin_cos @ c1_6__diff_4) ) ) ) @ ( (k8_real_1 @ (k5_square_1 @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ c2_6__diff_4) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) ) ) , inference(mizar_by, [status(thm), assumptions([e1_6__diff_4, dt_c1_6__diff_4, dt_c2_6__diff_4])], [cc10_valued_2, cc15_valued_2, cc16_valued_2, cc21_valued_2, cc28_valued_2, cc29_valued_2, cc7_valued_2, cc8_valued_2, cc9_valued_2, fc14_valued_2, fc15_valued_2, fc16_valued_2, fc17_valued_2, fc40_valued_2, fc41_valued_2, fc42_valued_2, fc43_valued_2, cc11_valued_2, cc17_valued_2, cc25_valued_2, cc26_valued_2, cc30_valued_2, cc4_valued_2, cc5_valued_2, fc18_valued_2, fc44_valued_2, cc12_valued_2, cc15_membered, cc18_valued_2, cc19_valued_0, cc22_membered, cc23_valued_0, cc24_valued_0, cc24_valued_2, cc2_seq_2, cc31_valued_2, cc3_membered, cc3_valued_2, fc19_valued_2, fc40_valued_1, fc45_valued_2, fc88_valued_0, dt_k3_numbers, dt_k4_numbers, dt_o_0_0_xboole_0, cc10_membered, cc13_valued_0, cc13_valued_2, cc14_valued_0, cc16_membered, cc19_valued_2, cc1_int_1, cc1_seq_2, cc20_valued_0, cc22_valued_0, cc23_membered, cc23_valued_2, cc2_membered, cc2_ordinal1, cc2_valued_0, cc2_valued_2, cc32_valued_2, cc3_int_1, cc3_valued_0, cc3_xxreal_0, cc4_valued_0, cc4_xxreal_0, cc5_xxreal_0, cc6_funct_1, cc6_xxreal_0, cc8_xxreal_0, cc9_membered, fc10_xreal_0, fc11_xreal_0, fc12_xreal_0, fc13_xreal_0, fc14_xreal_0, fc15_xreal_0, fc16_xreal_0, fc17_rfunct_1, fc17_xreal_0, fc18_xreal_0, fc19_xreal_0, fc1_int_1, fc20_valued_2, fc20_xreal_0, fc21_xreal_0, fc22_xreal_0, fc23_xreal_0, fc24_xreal_0, fc25_xreal_0, fc26_xreal_0, fc27_xreal_0, fc28_xreal_0, fc29_xreal_0, fc2_int_1, fc30_xreal_0, fc31_xreal_0, fc32_xreal_0, fc33_xreal_0, fc34_xreal_0, fc35_valued_1, fc36_valued_1, fc3_int_1, fc3_numbers, fc41_valued_1, fc46_valued_2, fc4_int_1, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc89_valued_0, fc9_xreal_0, rc1_int_1, rc2_int_1, rc2_ordinal1, rc2_valued_0, rc2_xreal_0, rc2_xxreal_0, rc3_xreal_0, rc3_xxreal_0, rc5_valued_1, commutativity_k2_xcmplx_0, involutiveness_k5_xcmplx_0, reflexivity_r1_tarski, antisymmetry_r2_hidden, dt_k1_funct_1, dt_k1_rfunct_1, dt_k1_xboole_0, dt_k2_xcmplx_0, dt_k5_xcmplx_0, cc10_ordinal1, cc10_valued_0, cc11_valued_0, cc12_membered, cc13_membered, cc14_valued_2, cc15_valued_0, cc16_valued_0, cc17_membered, cc17_valued_0, cc19_membered, cc1_funct_2, cc1_membered, cc1_ordinal1, cc1_rfunct_1, cc1_valued_0, cc1_valued_2, cc20_membered, cc20_valued_2, cc21_valued_0, cc22_valued_2, cc24_membered, cc28_valued_0, cc2_funct_2, cc2_int_1, cc2_xcmplx_0, cc2_xreal_0, cc2_xxreal_0, cc30_valued_0, cc33_valued_2, cc3_funct_2, cc4_funct_2, cc5_funct_1, cc5_ordinal1, cc5_relat_1, cc6_ordinal1, cc6_relat_1, cc7_relat_1, cc7_valued_0, cc7_xxreal_0, cc8_funct_1, cc8_funct_2, cc8_relat_1, cc8_valued_0, cc9_funct_1, fc127_valued_1, fc131_valued_1, fc17_funct_1, fc19_funct_1, fc1_rfunct_1, fc1_xboole_0, fc20_rfunct_1, fc21_valued_2, fc2_rfunct_1, fc2_xcmplx_0, fc33_valued_1, fc37_valued_1, fc38_valued_1, fc39_valued_1, fc42_valued_1, fc47_valued_2, fc4_xreal_0, fc5_xreal_0, fc61_valued_0, fc62_valued_0, fc63_valued_0, fc66_valued_0, fc7_xcmplx_0, fc85_valued_0, fc86_valued_0, fc90_valued_0, rc1_funct_2, rc1_membered, rc1_ordinal1, rc1_partfun1, rc1_relset_1, rc1_valued_0, rc1_valued_2, rc1_xxreal_0, rc2_funct_1, rc2_membered, rc2_relat_1, rc2_valued_2, rc3_funct_1, rc3_membered, rc3_ordinal1, rc3_partfun1, rc3_relat_1, rc4_funct_1, rc4_ordinal1, rc4_xreal_0, rc4_xxreal_0, rc5_funct_1, rc5_ordinal1, rc6_funct_1, rc6_valued_0, rc7_funct_1, rc9_funct_1, spc10_arithm, spc11_arithm, spc12_arithm, spc1_arithm, spc5_arithm, spc6_arithm, spc8_arithm, t1_subset, t4_subset, t5_subset, d2_xboole_0, commutativity_k18_valued_1, commutativity_k3_xcmplx_0, involutiveness_k4_xcmplx_0, existence_m1_subset_1, redefinition_k10_real_1, redefinition_k1_seq_1, redefinition_k3_rfunct_1, dt_k10_real_1, dt_k16_sin_cos, dt_k17_sin_cos, dt_k18_valued_1, dt_k19_sin_cos, dt_k1_seq_1, dt_k1_zfmisc_1, dt_k20_sin_cos, dt_k2_numbers, dt_k2_zfmisc_1, dt_k3_rfunct_1, dt_k3_square_1, dt_k3_xcmplx_0, dt_k4_xcmplx_0, dt_k6_xcmplx_0, dt_k7_xcmplx_0, dt_m1_subset_1, cc12_valued_0, cc14_membered, cc18_membered, cc18_valued_0, cc1_funct_1, cc1_partfun1, cc1_relat_1, cc1_relset_1, cc1_xcmplx_0, cc1_xreal_0, cc21_membered, cc26_membered, cc27_valued_2, cc2_funct_1, cc2_partfun1, cc2_relat_1, cc2_relset_1, cc3_funct_1, cc3_ordinal1, cc3_relat_1, cc3_relset_1, cc3_xcmplx_0, cc3_xreal_0, cc4_funct_1, cc4_membered, cc4_ordinal1, cc4_relat_1, cc4_relset_1, cc4_xreal_0, cc5_membered, cc5_valued_0, cc6_membered, cc6_valued_0, cc6_valued_2, cc7_funct_1, cc7_ordinal1, cc8_membered, cc9_ordinal1, cc9_valued_0, fc1_membered, fc1_square_1, fc2_numbers, fc2_square_1, fc34_valued_1, fc3_sin_cos, fc3_xcmplx_0, fc3_xreal_0, fc4_sin_cos, fc4_xcmplx_0, fc55_membered, fc5_xcmplx_0, fc6_relat_1, fc6_sin_cos, fc6_xcmplx_0, fc6_xreal_0, fc7_sin_cos, fc7_xreal_0, fc87_valued_0, fc8_xcmplx_0, fc8_xreal_0, fc9_numbers, fc9_xcmplx_0, rc1_funct_1, rc1_relat_1, rc1_xboole_0, rc1_xcmplx_0, rc1_xreal_0, rc2_xboole_0, rc2_xcmplx_0, spc4_arithm, spc7_arithm, spc9_arithm, t2_subset, t3_subset, t6_boole, t7_boole, t8_boole, d17_sin_cos, d19_sin_cos, d1_square_1, d8_xcmplx_0, d9_xcmplx_0, involutiveness_k10_complex1, commutativity_k20_valued_1, commutativity_k8_real_1, redefinition_k10_complex1, redefinition_k13_complex1, redefinition_k18_sin_cos, redefinition_k20_valued_1, redefinition_k21_sin_cos, redefinition_k5_square_1, redefinition_k8_real_1, redefinition_k9_real_1, dt_k10_complex1, dt_k13_complex1, dt_k18_sin_cos, dt_k1_numbers, dt_k20_valued_1, dt_k21_sin_cos, dt_k30_sin_cos, dt_k5_square_1, dt_k8_real_1, dt_k9_diff_1, dt_k9_real_1, dt_c1_6__diff_4, dt_c2_6__diff_4, fc1_numbers, fc3_membered, fc56_membered, fc8_numbers, d27_sin_cos, d9_diff_1, e3_6__diff_4]), [interesting(np__0.8), file(diff_4, e4_6__diff_4), [file(diff_4, e4_6__diff_4)]]). thf(i4_6__diff_4, plain, $true, introduced(tautology, [file(diff_4, i4_6__diff_4)]), [interesting(np__0.8), trivial, file(diff_4, i4_6__diff_4)]). thf(i3_6__diff_4, plain, ( (= @ ( ( (k9_diff_1 @ ( ( ( ( (k20_valued_1 @ k1_numbers) @ k1_numbers) @ k1_numbers) @ k30_sin_cos) @ k30_sin_cos) ) @ c1_6__diff_4) @ c2_6__diff_4) ) @ (k10_complex1 @ ( (k13_complex1 @ ( (k9_real_1 @ (k5_square_1 @ (k21_sin_cos @ c2_6__diff_4) ) ) @ (k5_square_1 @ (k21_sin_cos @ c1_6__diff_4) ) ) ) @ ( (k8_real_1 @ (k5_square_1 @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ c2_6__diff_4) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) ) ) , inference(conclusion, [status(thm), assumptions([e1_6__diff_4, dt_c1_6__diff_4, dt_c2_6__diff_4])], [e4_6__diff_4, i4_6__diff_4]), [interesting(np__0.8), file(diff_4, i3_6__diff_4), [file(diff_4, i3_6__diff_4)]]). thf(i2_6__diff_4, plain, ( ( ( (r2_hidden @ c1_6__diff_4) @ ( (k1_relset_1 @ k1_numbers) @ k30_sin_cos) ) & ( (r2_hidden @ c2_6__diff_4) @ ( (k1_relset_1 @ k1_numbers) @ k30_sin_cos) ) ) => ( (= @ ( ( (k9_diff_1 @ ( ( ( ( (k20_valued_1 @ k1_numbers) @ k1_numbers) @ k1_numbers) @ k30_sin_cos) @ k30_sin_cos) ) @ c1_6__diff_4) @ c2_6__diff_4) ) @ (k10_complex1 @ ( (k13_complex1 @ ( (k9_real_1 @ (k5_square_1 @ (k21_sin_cos @ c2_6__diff_4) ) ) @ (k5_square_1 @ (k21_sin_cos @ c1_6__diff_4) ) ) ) @ ( (k8_real_1 @ (k5_square_1 @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ c2_6__diff_4) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) ) ) ) , inference(discharge_asm, [status(thm), assumptions([dt_c1_6__diff_4, dt_c2_6__diff_4]), discharge_asm(discharge, [e1_6__diff_4])], [e1_6__diff_4, i3_6__diff_4]), [interesting(np__0.8), file(diff_4, i2_6__diff_4), [file(diff_4, i2_6__diff_4)]]). thf(i2_6_tmp__diff_4, plain, ( ( (m1_subset_1 @ c2_6__diff_4) @ k1_numbers) => ( ( ( (r2_hidden @ c1_6__diff_4) @ ( (k1_relset_1 @ k1_numbers) @ k30_sin_cos) ) & ( (r2_hidden @ c2_6__diff_4) @ ( (k1_relset_1 @ k1_numbers) @ k30_sin_cos) ) ) => ( (= @ ( ( (k9_diff_1 @ ( ( ( ( (k20_valued_1 @ k1_numbers) @ k1_numbers) @ k1_numbers) @ k30_sin_cos) @ k30_sin_cos) ) @ c1_6__diff_4) @ c2_6__diff_4) ) @ (k10_complex1 @ ( (k13_complex1 @ ( (k9_real_1 @ (k5_square_1 @ (k21_sin_cos @ c2_6__diff_4) ) ) @ (k5_square_1 @ (k21_sin_cos @ c1_6__diff_4) ) ) ) @ ( (k8_real_1 @ (k5_square_1 @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ c2_6__diff_4) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ c2_6__diff_4) ) ) ) ) ) ) , inference(discharge_asm, [status(thm), assumptions([dt_c1_6__diff_4]), discharge_asm(discharge, [dt_c2_6__diff_4])], [dt_c2_6__diff_4, i2_6__diff_4]), [interesting(np__0.8), i1_6__diff_4]). thf(i1_6__diff_4, plain, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => ( ( ( (r2_hidden @ c1_6__diff_4) @ ( (k1_relset_1 @ k1_numbers) @ k30_sin_cos) ) & ( (r2_hidden @ A) @ ( (k1_relset_1 @ k1_numbers) @ k30_sin_cos) ) ) => ( (= @ ( ( (k9_diff_1 @ ( ( ( ( (k20_valued_1 @ k1_numbers) @ k1_numbers) @ k1_numbers) @ k30_sin_cos) @ k30_sin_cos) ) @ c1_6__diff_4) @ A) ) @ (k10_complex1 @ ( (k13_complex1 @ ( (k9_real_1 @ (k5_square_1 @ (k21_sin_cos @ A) ) ) @ (k5_square_1 @ (k21_sin_cos @ c1_6__diff_4) ) ) ) @ ( (k8_real_1 @ (k5_square_1 @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ A) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ A) ) ) ) ) ) ) ) , inference(let, [status(thm), assumptions([dt_c1_6__diff_4])], [i2_6_tmp__diff_4, dh_c2_6__diff_4]), [interesting(np__0.8), file(diff_4, i1_6__diff_4), [file(diff_4, i1_6__diff_4)]]). thf(i1_6_tmp__diff_4, plain, ( ( (m1_subset_1 @ c1_6__diff_4) @ k1_numbers) => (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => ( ( ( (r2_hidden @ c1_6__diff_4) @ ( (k1_relset_1 @ k1_numbers) @ k30_sin_cos) ) & ( (r2_hidden @ A) @ ( (k1_relset_1 @ k1_numbers) @ k30_sin_cos) ) ) => ( (= @ ( ( (k9_diff_1 @ ( ( ( ( (k20_valued_1 @ k1_numbers) @ k1_numbers) @ k1_numbers) @ k30_sin_cos) @ k30_sin_cos) ) @ c1_6__diff_4) @ A) ) @ (k10_complex1 @ ( (k13_complex1 @ ( (k9_real_1 @ (k5_square_1 @ (k21_sin_cos @ A) ) ) @ (k5_square_1 @ (k21_sin_cos @ c1_6__diff_4) ) ) ) @ ( (k8_real_1 @ (k5_square_1 @ ( (k8_real_1 @ (k18_sin_cos @ c1_6__diff_4) ) @ (k18_sin_cos @ A) ) ) ) @ ( (k9_real_1 @ c1_6__diff_4) @ A) ) ) ) ) ) ) ) ) , inference(discharge_asm, [status(thm), assumptions([]), discharge_asm(discharge, [dt_c1_6__diff_4])], [dt_c1_6__diff_4, i1_6__diff_4]), [interesting(np__1), t6_diff_4]). thf(t6_diff_4, theorem, (! [A: $i] : ( ( (m1_subset_1 @ A) @ k1_numbers) => (! [B: $i] : ( ( (m1_subset_1 @ B) @ k1_numbers) => ( ( ( (r2_hidden @ A) @ ( (k1_relset_1 @ k1_numbers) @ k30_sin_cos) ) & ( (r2_hidden @ B) @ ( (k1_relset_1 @ k1_numbers) @ k30_sin_cos) ) ) => ( (= @ ( ( (k9_diff_1 @ ( ( ( ( (k20_valued_1 @ k1_numbers) @ k1_numbers) @ k1_numbers) @ k30_sin_cos) @ k30_sin_cos) ) @ A) @ B) ) @ (k10_complex1 @ ( (k13_complex1 @ ( (k9_real_1 @ (k5_square_1 @ (k21_sin_cos @ B) ) ) @ (k5_square_1 @ (k21_sin_cos @ A) ) ) ) @ ( (k8_real_1 @ (k5_square_1 @ ( (k8_real_1 @ (k18_sin_cos @ A) ) @ (k18_sin_cos @ B) ) ) ) @ ( (k9_real_1 @ A) @ B) ) ) ) ) ) ) ) ) ) , inference(let, [status(thm), assumptions([])], [i1_6_tmp__diff_4, dh_c1_6__diff_4]), [interesting(np__1), file(diff_4, t6_diff_4), [file(diff_4, t6_diff_4)]]).