Theorem. (t35_quatern3)
∀v1_xboole_0 : set → prop, ∀m1_subset_1 : set → set → prop, ∀k1_zfmisc_1 : set → set, ∀k2_zfmisc_1 : set → set → set, ∀m1_funct_2 : set → set → set → prop, ∀m2_funct_2 : set → set → set → set → prop, ∀a_0_0_quaterni : set, ∀r2_hidden : set → set → prop, ∀k6_numbers : set, ∀k1_seq_1 : set → set → set, ∀np__2 : set, ∀k1_numbers : set, ∀k9_funct_2 : set → set → set, ∀np__4 : set, ∀np__3 : set, ∀m2_subset_1 : set → set → set → prop, ∀v1_xreal_0 : set → prop, ∀r1_xxreal_0 : set → set → prop, ∀k2_xcmplx_0 : set → set → set, ∀v1_xcmplx_0 : set → prop, ∀k3_xcmplx_0 : set → set → set, ∀v2_xxreal_0 : set → prop, ∀r1_tarski : set → set → prop, ∀v5_membered : set → prop, ∀k2_xboole_0 : set → set → set, ∀v3_membered : set → prop, ∀v1_membered : set → prop, ∀k7_quaterni : set → set → set, ∀v7_ordinal1 : set → prop, ∀v1_rat_1 : set → prop, ∀k1_funct_2 : set → set → set, ∀k2_numbers : set, ∀k6_square_1 : set → set, ∀np__1 : set, ∀k13_quaterni : set → set, ∀k15_quaterni : set → set, ∀v7_membered : set → prop, ∀esk3_0 : set, ∀esk2_0 : set, ∀esk1_0 : set, ∀np__0 : set, ∀esk11_0 : set, ∀k4_ordinal1 : set, ∀esk10_0 : set, ∀esk5_1 : set → set, ∀esk4_2 : set → set → set, ∀esk9_0 : set, ∀esk12_0 : set, ∀k1_xboole_0 : set, ∀k16_quaterni : set → set, ∀k14_quaterni : set → set, ∀k3_quatern2 : set → set, ∀k3_square_1 : set → set, ∀k5_numbers : set, ∀v1_int_1 : set → prop, ∀k6_subset_1 : set → set → set, ∀v1_xxreal_0 : set → prop, ∀v6_membered : set → prop, ∀v2_membered : set → prop, ∀v4_membered : set → prop, ∀k1_quaterni : set, ∀k9_real_1 : set → set → set, ∀k4_xcmplx_0 : set → set, ∀esk13_2 : set → set → set, ∀esk7_2 : set → set → set, ∀k6_xcmplx_0 : set → set → set, ∀k26_quaterni : set → set → set, ∀esk8_1 : set → set, ∀esk6_3 : set → set → set → set, ∀v1_funct_1 : set → prop, ∀v1_funct_2 : set → set → set → prop, ∀k32_quaterni : set → set, ∀k5_square_1 : set → set, ∀k20_quaterni : set → set, ∀k19_quaterni : set → set, ∀k18_quaterni : set → set, ∀k17_quaterni : set → set, ∀k7_real_1 : set → set → set, ∀k7_square_1 : set → set, ∀v1_quaterni : set → prop, (∀X1, ((k7_square_1 (k7_real_1 (k7_real_1 (k7_real_1 (k5_square_1 (k17_quaterni X1)) (k5_square_1 (k18_quaterni X1))) (k5_square_1 (k19_quaterni X1))) (k5_square_1 (k20_quaterni X1)))) = (k32_quaterni X1) → False) → v1_quaterni X1 → False) → (∀X1 X2 X4 X3, (v1_xboole_0 X3 → False) → (m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → m1_funct_2 X4 X2 X3 → m2_funct_2 X1 X2 X3 X4 → False) → (∀X1 X2 X4 X3, (v1_xboole_0 X3 → False) → (v1_funct_2 X1 X2 X3 → False) → m1_funct_2 X4 X2 X3 → m2_funct_2 X1 X2 X3 X4 → False) → (∀X4 X1 X2 X3, (v1_xboole_0 X3 → False) → (m1_subset_1 X1 X4 → False) → m1_funct_2 X4 X2 X3 → m2_funct_2 X1 X2 X3 X4 → False) → (∀X1 X2 X4 X3, (v1_xboole_0 X3 → False) → (v1_funct_1 X1 → False) → m1_funct_2 X4 X2 X3 → m2_funct_2 X1 X2 X3 X4 → False) → (∀X1 X2, (r2_hidden X2 a_0_0_quaterni → False) → X1 = X2 → (k1_seq_1 X1 np__2) = k6_numbers → (k1_seq_1 X1 np__3) = k6_numbers → m2_funct_2 X1 np__4 k1_numbers (k9_funct_2 np__4 k1_numbers) → False) → (∀X3 X2 X1, (v1_xboole_0 X1 → False) → (m2_funct_2 (esk6_3 X3 X1 X2) X3 X1 X2 → False) → m1_funct_2 X2 X3 X1 → False) → (∀X2 X1 X3 X4, (v1_xboole_0 X4 → False) → (m2_funct_2 X1 X3 X4 X2 → False) → m1_subset_1 X1 X2 → m1_funct_2 X2 X3 X4 → False) → (∀X1, (m2_funct_2 (esk8_1 X1) np__4 k1_numbers (k9_funct_2 np__4 k1_numbers) → False) → r2_hidden X1 a_0_0_quaterni → False) → (∀X1 X3 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m1_subset_1 X3 X1 → False) → m2_subset_1 X3 X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1 X3, (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (m1_subset_1 X1 X3 → False) → m2_subset_1 X1 X2 X3 → m1_subset_1 X3 (k1_zfmisc_1 X2) → False) → (∀X3 X1 X2 X4, (r1_xxreal_0 (k2_xcmplx_0 X1 X3) (k2_xcmplx_0 X2 X4) → False) → v1_xreal_0 X4 → v1_xreal_0 X3 → v1_xreal_0 X2 → v1_xreal_0 X1 → r1_xxreal_0 X3 X4 → r1_xxreal_0 X1 X2 → False) → (∀X2 X1, (r1_xxreal_0 (k32_quaterni (k26_quaterni X1 X2)) (k2_xcmplx_0 (k32_quaterni X1) (k32_quaterni X2)) → False) → v1_quaterni X2 → v1_quaterni X1 → False) → (∀X1 X2 X3, ((k2_xcmplx_0 (k3_xcmplx_0 X1 X3) (k3_xcmplx_0 X2 X3)) = (k3_xcmplx_0 (k2_xcmplx_0 X1 X2) X3) → False) → v1_xcmplx_0 X3 → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X2 X1 X3, (r1_xxreal_0 (k6_xcmplx_0 X1 X2) X3 → False) → v1_xreal_0 X3 → v1_xreal_0 X2 → v1_xreal_0 X1 → r1_xxreal_0 X1 (k2_xcmplx_0 X2 X3) → False) → (∀X2 X1 X3, (r1_xxreal_0 (k2_xcmplx_0 X1 X3) X2 → False) → v1_xreal_0 X3 → v1_xreal_0 X2 → v1_xreal_0 X1 → r1_xxreal_0 X1 (k6_xcmplx_0 X2 X3) → False) → (∀X2 X1 X3, (r1_xxreal_0 X1 (k6_xcmplx_0 X3 X2) → False) → v1_xreal_0 X3 → v1_xreal_0 X2 → v1_xreal_0 X1 → r1_xxreal_0 (k2_xcmplx_0 X1 X2) X3 → False) → (∀X2 X1 X3, (r1_xxreal_0 X1 (k2_xcmplx_0 X2 X3) → False) → v1_xreal_0 X3 → v1_xreal_0 X2 → v1_xreal_0 X1 → r1_xxreal_0 (k6_xcmplx_0 X1 X2) X3 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m2_subset_1 (esk7_2 X1 X2) X1 X2 → False) → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1 X3, (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (m2_subset_1 X1 X3 X2 → False) → m1_subset_1 X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X1 X3 X2, r2_hidden X3 X2 → r2_hidden X1 X2 → r2_hidden X1 (esk13_2 X3 X2) → False) → (∀X1 X2 X3, ((k3_xcmplx_0 (k3_xcmplx_0 X1 X2) X3) = (k3_xcmplx_0 X1 (k3_xcmplx_0 X2 X3)) → False) → v1_xcmplx_0 X3 → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X1 X2 X3, ((k2_xcmplx_0 (k2_xcmplx_0 X1 X2) X3) = (k2_xcmplx_0 X1 (k2_xcmplx_0 X2 X3)) → False) → v1_xcmplx_0 X3 → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X1 X2 X3, ((k26_quaterni (k26_quaterni X1 X2) X3) = (k26_quaterni X1 (k26_quaterni X2 X3)) → False) → v1_quaterni X3 → v1_quaterni X2 → v1_quaterni X1 → False) → (∀X3 X2 X1, v1_xboole_0 X1 → m1_funct_2 X1 X2 X3 → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (m1_funct_2 (k9_funct_2 X2 X1) X2 X1 → False) → False) → (∀X2 X1, ((k2_xcmplx_0 (k4_xcmplx_0 X1) (k4_xcmplx_0 X2)) = (k4_xcmplx_0 (k2_xcmplx_0 X1 X2)) → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X2 X1 X3, (m1_subset_1 X1 X3 → False) → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X2 X1, (m1_subset_1 (k9_real_1 X1 X2) k1_numbers → False) → v1_xreal_0 X2 → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, (m1_subset_1 (k7_real_1 X1 X2) k1_numbers → False) → v1_xreal_0 X2 → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, (r2_hidden (esk13_2 X1 X2) X2 → False) → r2_hidden X1 X2 → False) → (∀X2 X1 X3, v1_xboole_0 X3 → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X2 X1, ((k9_real_1 X1 X2) = (k6_xcmplx_0 X1 X2) → False) → v1_xreal_0 X2 → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, ((k7_real_1 X1 X2) = (k2_xcmplx_0 X1 X2) → False) → v1_xreal_0 X2 → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, ((k7_real_1 X1 X2) = (k7_real_1 X2 X1) → False) → v1_xreal_0 X2 → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, ((k6_xcmplx_0 (k4_xcmplx_0 X1) (k4_xcmplx_0 X2)) = (k6_xcmplx_0 X2 X1) → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X2 X1, (m1_subset_1 (k26_quaterni X1 X2) k1_quaterni → False) → v1_quaterni X2 → v1_quaterni X1 → False) → (∀X1 X2, (v2_xxreal_0 X2 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v2_xxreal_0 X1 → r1_xxreal_0 X1 X2 → False) → (∀X1 X2, (v2_xxreal_0 X2 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v2_xxreal_0 X1 → r1_xxreal_0 X1 X2 → False) → (∀X2 X1, ((k2_xcmplx_0 X1 (k4_xcmplx_0 X2)) = (k6_xcmplx_0 X1 X2) → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X2 X1, ((k2_xcmplx_0 X1 (k4_xcmplx_0 X2)) = (k6_xcmplx_0 X1 X2) → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X2 X1, r2_hidden X2 X1 → r2_hidden X1 X2 → False) → (∀X2 X1, (v5_membered (k2_xboole_0 X1 X2) → False) → v5_membered X2 → v5_membered X1 → False) → (∀X2 X1, (v4_membered (k2_xboole_0 X1 X2) → False) → v4_membered X2 → v4_membered X1 → False) → (∀X2 X1, (v3_membered (k2_xboole_0 X1 X2) → False) → v3_membered X2 → v3_membered X1 → False) → (∀X2 X1, (v2_membered (k2_xboole_0 X1 X2) → False) → v2_membered X2 → v2_membered X1 → False) → (∀X2 X1, (v1_membered (k2_xboole_0 X1 X2) → False) → v1_membered X2 → v1_membered X1 → False) → (∀X2 X1, (v6_membered (k2_xboole_0 X1 X2) → False) → v6_membered X2 → v6_membered X1 → False) → (∀X2 X1, (v1_quaterni (k7_quaterni X1 X2) → False) → v1_quaterni X2 → v1_quaterni X1 → False) → (∀X1 X2, (v5_membered X2 → False) → v5_membered X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v4_membered X2 → False) → v4_membered X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v3_membered X2 → False) → v3_membered X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v2_membered X2 → False) → v2_membered X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v1_membered X2 → False) → v1_membered X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v6_membered X2 → False) → v6_membered X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1, (r1_xxreal_0 X2 X1 → False) → (r1_xxreal_0 X1 X2 → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X2 X1, (m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → r1_tarski X1 X2 → False) → (∀X2 X1, ((k7_quaterni X1 X2) = (k7_quaterni X2 X1) → False) → v1_quaterni X2 → v1_quaterni X1 → False) → (∀X2 X1, ((k7_quaterni X1 X2) = (k26_quaterni X1 X2) → False) → v1_quaterni X2 → v1_quaterni X1 → False) → (∀X2 X1, ((k3_xcmplx_0 X1 X2) = (k3_xcmplx_0 X2 X1) → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X2 X1, ((k2_xcmplx_0 X1 X2) = (k2_xcmplx_0 X2 X1) → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X2 X1, ((k26_quaterni X1 X2) = (k26_quaterni X2 X1) → False) → v1_quaterni X2 → v1_quaterni X1 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (r2_hidden X1 X2 → False) → m1_subset_1 X1 X2 → False) → (∀X1, (m1_subset_1 (k7_square_1 X1) k1_numbers → False) → m1_subset_1 X1 k1_numbers → False) → (∀X1, (m1_subset_1 (k5_square_1 X1) k1_numbers → False) → m1_subset_1 X1 k1_numbers → False) → (∀X1, ((k1_seq_1 (esk8_1 X1) np__3) = k6_numbers → False) → r2_hidden X1 a_0_0_quaterni → False) → (∀X1, ((k1_seq_1 (esk8_1 X1) np__2) = k6_numbers → False) → r2_hidden X1 a_0_0_quaterni → False) → (∀X2 X1, (v5_membered (k6_subset_1 X1 X2) → False) → v5_membered X1 → False) → (∀X2 X1, (v4_membered (k6_subset_1 X1 X2) → False) → v4_membered X1 → False) → (∀X2 X1, (v3_membered (k6_subset_1 X1 X2) → False) → v3_membered X1 → False) → (∀X2 X1, (v2_membered (k6_subset_1 X1 X2) → False) → v2_membered X1 → False) → (∀X2 X1, (v1_membered (k6_subset_1 X1 X2) → False) → v1_membered X1 → False) → (∀X2 X1, (v6_membered (k6_subset_1 X1 X2) → False) → v6_membered X1 → False) → (∀X2 X1, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → False) → (∀X1 X2, (v7_ordinal1 X2 → False) → v6_membered X1 → m1_subset_1 X2 X1 → False) → (∀X1 X2, (v1_int_1 X2 → False) → v5_membered X1 → m1_subset_1 X2 X1 → False) → (∀X1 X2, (v1_rat_1 X2 → False) → v4_membered X1 → m1_subset_1 X2 X1 → False) → (∀X1 X2, (v1_xreal_0 X2 → False) → v3_membered X1 → m1_subset_1 X2 X1 → False) → (∀X1 X2, (v1_xxreal_0 X2 → False) → v2_membered X1 → m1_subset_1 X2 X1 → False) → (∀X1 X2, (v1_xcmplx_0 X2 → False) → v1_membered X1 → m1_subset_1 X2 X1 → False) → (∀X2 X1, ((k1_funct_2 X2 X1) = (k9_funct_2 X2 X1) → False) → (v1_xboole_0 X1 → False) → False) → (∀X1, (v3_membered X1 → False) → m1_subset_1 X1 (k1_zfmisc_1 k1_numbers) → False) → (∀X1, (v1_membered X1 → False) → m1_subset_1 X1 (k1_zfmisc_1 k2_numbers) → False) → (∀X1, (v6_membered X1 → False) → m1_subset_1 X1 (k1_zfmisc_1 k5_numbers) → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X2 X1, (r1_xxreal_0 X1 X1 → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X1, ((k7_square_1 X1) = (k6_square_1 X1) → False) → m1_subset_1 X1 k1_numbers → False) → (∀X1, ((k5_square_1 X1) = (k3_square_1 X1) → False) → m1_subset_1 X1 k1_numbers → False) → (∀X1, ((k3_xcmplx_0 X1 (k4_xcmplx_0 np__1)) = (k4_xcmplx_0 X1) → False) → v1_xcmplx_0 X1 → False) → (∀X1, (m1_subset_1 (k20_quaterni X1) k1_numbers → False) → v1_quaterni X1 → False) → (∀X1, (m1_subset_1 (k19_quaterni X1) k1_numbers → False) → v1_quaterni X1 → False) → (∀X1, (m1_subset_1 (k18_quaterni X1) k1_numbers → False) → v1_quaterni X1 → False) → (∀X1, (m1_subset_1 (k17_quaterni X1) k1_numbers → False) → v1_quaterni X1 → False) → (∀X1, (m1_subset_1 (k3_quatern2 X1) k1_numbers → False) → v1_quaterni X1 → False) → (∀X1, ((esk8_1 X1) = X1 → False) → r2_hidden X1 a_0_0_quaterni → False) → (∀X1, ((k3_xcmplx_0 X1 X1) = (k3_square_1 X1) → False) → v1_xcmplx_0 X1 → False) → (∀X1, (v6_membered X1 → False) → m1_subset_1 X1 k5_numbers → False) → (∀X1, (v1_quaterni X1 → False) → m1_subset_1 X1 k1_quaterni → False) → (∀X1, ((k3_xcmplx_0 np__1 X1) = X1 → False) → v1_xcmplx_0 X1 → False) → (∀X1, ((k6_xcmplx_0 X1 k6_numbers) = X1 → False) → v1_xcmplx_0 X1 → False) → (∀X1, ((k2_xcmplx_0 X1 k6_numbers) = X1 → False) → v1_xcmplx_0 X1 → False) → (∀X1, ((k3_xcmplx_0 X1 k6_numbers) = k6_numbers → False) → v1_xcmplx_0 X1 → False) → (∀X1, ((k4_xcmplx_0 (k4_xcmplx_0 X1)) = X1 → False) → v1_xcmplx_0 X1 → False) → (∀X1, (v1_xreal_0 (k14_quaterni X1) → False) → v1_quaterni X1 → False) → (∀X1, (v1_xreal_0 (k13_quaterni X1) → False) → v1_quaterni X1 → False) → (∀X1, (v1_xreal_0 (k16_quaterni X1) → False) → v1_quaterni X1 → False) → (∀X1, (v1_xreal_0 (k15_quaterni X1) → False) → v1_quaterni X1 → False) → (∀X1, (v1_xreal_0 (k6_square_1 X1) → False) → v1_xreal_0 X1 → False) → (∀X1, (v1_xreal_0 (k32_quaterni X1) → False) → v1_quaterni X1 → False) → (∀X1, (v1_xcmplx_0 (k4_xcmplx_0 X1) → False) → v1_xcmplx_0 X1 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, ((k18_quaterni X1) = (k14_quaterni X1) → False) → v1_quaterni X1 → False) → (∀X1, ((k17_quaterni X1) = (k13_quaterni X1) → False) → v1_quaterni X1 → False) → (∀X1, ((k20_quaterni X1) = (k16_quaterni X1) → False) → v1_quaterni X1 → False) → (∀X1, ((k19_quaterni X1) = (k15_quaterni X1) → False) → v1_quaterni X1 → False) → (∀X1, ((k3_quatern2 X1) = (k32_quaterni X1) → False) → v1_quaterni X1 → False) → (∀X1, (v7_membered X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v5_membered X1 → False) → v6_membered X1 → False) → (∀X1, (v4_membered X1 → False) → v5_membered X1 → False) → (∀X1, (v3_membered X1 → False) → v4_membered X1 → False) → (∀X1, (v2_membered X1 → False) → v3_membered X1 → False) → (∀X1, (v1_membered X1 → False) → v3_membered X1 → False) → (∀X1, (v6_membered X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (r1_xxreal_0 (k3_quatern2 (k26_quaterni (k26_quaterni esk1_0 esk2_0) esk3_0)) (k7_real_1 (k7_real_1 (k3_quatern2 esk1_0) (k3_quatern2 esk2_0)) (k3_quatern2 esk3_0)) → False) → (r1_xxreal_0 np__1 (k4_xcmplx_0 np__1) → False) → (r1_xxreal_0 np__0 (k4_xcmplx_0 np__1) → False) → (r1_xxreal_0 np__1 np__0 → False) → (r1_xxreal_0 np__3 np__1 → False) → (r1_xxreal_0 np__3 np__0 → False) → (r1_xxreal_0 np__3 np__2 → False) → (r1_xxreal_0 np__2 np__1 → False) → (r1_xxreal_0 np__2 np__0 → False) → (r1_xxreal_0 np__4 np__1 → False) → (r1_xxreal_0 np__4 np__0 → False) → (r1_xxreal_0 np__4 np__3 → False) → (r1_xxreal_0 np__4 np__2 → False) → (v1_xboole_0 esk12_0 → False) → (v1_xboole_0 esk11_0 → False) → (v1_xboole_0 esk9_0 → False) → (v1_xboole_0 np__1 → False) → (v1_xboole_0 np__3 → False) → (v1_xboole_0 np__2 → False) → (v1_xboole_0 np__4 → False) → (v1_xboole_0 k1_quaterni → False) → (∀X2 X1, (m1_funct_2 (esk4_2 X1 X2) X1 X2 → False) → False) → (((k2_xboole_0 (k6_subset_1 (k9_funct_2 np__4 k1_numbers) a_0_0_quaterni) k2_numbers) = k1_quaterni → False) → False) → ((m2_subset_1 np__1 k1_numbers k5_numbers → False) → False) → ((m2_subset_1 np__0 k1_numbers k5_numbers → False) → False) → ((m2_subset_1 np__3 k1_numbers k5_numbers → False) → False) → ((m2_subset_1 np__2 k1_numbers k5_numbers → False) → False) → ((m2_subset_1 k6_numbers k1_numbers k5_numbers → False) → False) → ((m2_subset_1 np__4 k1_numbers k5_numbers → False) → False) → (∀X1 X2, (m1_subset_1 (k6_subset_1 X1 X2) (k1_zfmisc_1 X1) → False) → False) → (∀X2 X1, ((k2_xboole_0 X1 X2) = (k2_xboole_0 X2 X1) → False) → False) → (((k6_xcmplx_0 (k4_xcmplx_0 np__3) (k4_xcmplx_0 np__1)) = (k4_xcmplx_0 np__2) → False) → False) → (((k6_xcmplx_0 (k4_xcmplx_0 np__2) (k4_xcmplx_0 np__1)) = (k4_xcmplx_0 np__1) → False) → False) → (((k6_xcmplx_0 (k4_xcmplx_0 np__4) (k4_xcmplx_0 np__2)) = (k4_xcmplx_0 np__2) → False) → False) → (((k2_xcmplx_0 (k4_xcmplx_0 np__1) (k4_xcmplx_0 np__1)) = (k4_xcmplx_0 np__2) → False) → False) → ((r1_xxreal_0 (k4_xcmplx_0 np__1) (k4_xcmplx_0 np__1) → False) → False) → (((k6_xcmplx_0 (k4_xcmplx_0 np__1) (k4_xcmplx_0 np__1)) = np__0 → False) → False) → (((k6_xcmplx_0 (k4_xcmplx_0 np__1) (k4_xcmplx_0 np__3)) = np__2 → False) → False) → (((k6_xcmplx_0 (k4_xcmplx_0 np__1) (k4_xcmplx_0 np__2)) = np__1 → False) → False) → (((k6_xcmplx_0 (k4_xcmplx_0 np__1) (k4_xcmplx_0 np__4)) = np__3 → False) → False) → (((k6_xcmplx_0 (k4_xcmplx_0 np__3) (k4_xcmplx_0 np__3)) = np__0 → False) → False) → (((k6_xcmplx_0 (k4_xcmplx_0 np__3) (k4_xcmplx_0 np__4)) = np__1 → False) → False) → (((k6_xcmplx_0 (k4_xcmplx_0 np__2) (k4_xcmplx_0 np__3)) = np__1 → False) → False) → (((k6_xcmplx_0 (k4_xcmplx_0 np__2) (k4_xcmplx_0 np__2)) = np__0 → False) → False) → (((k6_xcmplx_0 (k4_xcmplx_0 np__2) (k4_xcmplx_0 np__4)) = np__2 → False) → False) → (((k6_xcmplx_0 (k4_xcmplx_0 np__4) (k4_xcmplx_0 np__4)) = np__0 → False) → False) → (((k3_xcmplx_0 (k4_xcmplx_0 np__2) (k4_xcmplx_0 np__2)) = np__4 → False) → False) → (∀X1, (m1_subset_1 (esk5_1 X1) X1 → False) → False) → (((k6_xcmplx_0 (k4_xcmplx_0 np__1) np__1) = (k4_xcmplx_0 np__2) → False) → False) → (((k6_xcmplx_0 (k4_xcmplx_0 np__1) np__0) = (k4_xcmplx_0 np__1) → False) → False) → (((k6_xcmplx_0 (k4_xcmplx_0 np__1) np__2) = (k4_xcmplx_0 np__3) → False) → False) → (((k6_xcmplx_0 (k4_xcmplx_0 np__2) np__1) = (k4_xcmplx_0 np__3) → False) → False) → (((k6_xcmplx_0 (k4_xcmplx_0 np__2) np__2) = (k4_xcmplx_0 np__4) → False) → False) → (((k3_xcmplx_0 (k4_xcmplx_0 np__2) np__1) = (k4_xcmplx_0 np__2) → False) → False) → (((k3_xcmplx_0 (k4_xcmplx_0 np__4) np__1) = (k4_xcmplx_0 np__4) → False) → False) → (((k2_xcmplx_0 (k4_xcmplx_0 np__1) np__0) = (k4_xcmplx_0 np__1) → False) → False) → (((k3_xcmplx_0 np__1 (k4_xcmplx_0 np__2)) = (k4_xcmplx_0 np__2) → False) → False) → (((k3_xcmplx_0 np__2 (k4_xcmplx_0 np__2)) = (k4_xcmplx_0 np__4) → False) → False) → (((k2_xcmplx_0 np__1 (k4_xcmplx_0 np__2)) = (k4_xcmplx_0 np__1) → False) → False) → (((k2_xcmplx_0 np__0 (k4_xcmplx_0 np__1)) = (k4_xcmplx_0 np__1) → False) → False) → ((r1_xxreal_0 (k4_xcmplx_0 np__1) np__1 → False) → False) → ((r1_xxreal_0 (k4_xcmplx_0 np__1) np__0 → False) → False) → ((m1_subset_1 k5_numbers (k1_zfmisc_1 k1_numbers) → False) → False) → (((k2_xcmplx_0 (k4_xcmplx_0 np__1) np__1) = np__0 → False) → False) → (((k2_xcmplx_0 (k4_xcmplx_0 np__1) np__2) = np__1 → False) → False) → (((k2_xcmplx_0 (k4_xcmplx_0 np__2) np__2) = np__0 → False) → False) → (((k6_xcmplx_0 np__1 (k4_xcmplx_0 np__1)) = np__2 → False) → False) → (((k6_xcmplx_0 np__1 (k4_xcmplx_0 np__2)) = np__3 → False) → False) → (((k6_xcmplx_0 np__0 (k4_xcmplx_0 np__1)) = np__1 → False) → False) → (((k6_xcmplx_0 np__2 (k4_xcmplx_0 np__1)) = np__3 → False) → False) → (((k6_xcmplx_0 np__2 (k4_xcmplx_0 np__2)) = np__4 → False) → False) → (((k2_xcmplx_0 np__1 (k4_xcmplx_0 np__1)) = np__0 → False) → False) → (((k2_xcmplx_0 np__2 (k4_xcmplx_0 np__2)) = np__0 → False) → False) → (∀X1, ((k2_xboole_0 X1 X1) = X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → (((k6_xcmplx_0 np__1 np__3) = (k4_xcmplx_0 np__2) → False) → False) → (((k6_xcmplx_0 np__1 np__2) = (k4_xcmplx_0 np__1) → False) → False) → (((k6_xcmplx_0 np__1 np__4) = (k4_xcmplx_0 np__3) → False) → False) → (((k6_xcmplx_0 np__0 np__1) = (k4_xcmplx_0 np__1) → False) → False) → (((k6_xcmplx_0 np__0 np__3) = (k4_xcmplx_0 np__3) → False) → False) → (((k6_xcmplx_0 np__0 np__2) = (k4_xcmplx_0 np__2) → False) → False) → (((k6_xcmplx_0 np__0 np__4) = (k4_xcmplx_0 np__4) → False) → False) → (((k6_xcmplx_0 np__3 np__4) = (k4_xcmplx_0 np__1) → False) → False) → (((k6_xcmplx_0 np__2 np__3) = (k4_xcmplx_0 np__1) → False) → False) → (((k6_xcmplx_0 np__2 np__4) = (k4_xcmplx_0 np__2) → False) → False) → (∀X1, ((k6_subset_1 X1 k1_xboole_0) = X1 → False) → False) → (∀X1, ((k2_xboole_0 X1 k1_xboole_0) = X1 → False) → False) → (∀X1, ((k6_subset_1 k1_xboole_0 X1) = k1_xboole_0 → False) → False) → ((m1_subset_1 np__1 k1_numbers → False) → False) → ((m1_subset_1 np__1 k5_numbers → False) → False) → ((m1_subset_1 np__0 k1_numbers → False) → False) → ((m1_subset_1 np__0 k5_numbers → False) → False) → ((m1_subset_1 k1_xboole_0 k4_ordinal1 → False) → False) → ((m1_subset_1 np__3 k1_numbers → False) → False) → ((m1_subset_1 np__3 k5_numbers → False) → False) → ((m1_subset_1 np__2 k1_numbers → False) → False) → ((m1_subset_1 np__2 k5_numbers → False) → False) → ((m1_subset_1 np__4 k1_numbers → False) → False) → ((m1_subset_1 np__4 k5_numbers → False) → False) → ((r1_xxreal_0 np__1 np__1 → False) → False) → ((r1_xxreal_0 np__1 np__3 → False) → False) → ((r1_xxreal_0 np__1 np__2 → False) → False) → ((r1_xxreal_0 np__1 np__4 → False) → False) → ((r1_xxreal_0 np__0 np__1 → False) → False) → ((r1_xxreal_0 np__0 np__0 → False) → False) → ((r1_xxreal_0 np__0 np__3 → False) → False) → ((r1_xxreal_0 np__0 np__2 → False) → False) → ((r1_xxreal_0 np__0 np__4 → False) → False) → ((r1_xxreal_0 np__3 np__3 → False) → False) → ((r1_xxreal_0 np__3 np__4 → False) → False) → ((r1_xxreal_0 np__2 np__3 → False) → False) → ((r1_xxreal_0 np__2 np__2 → False) → False) → ((r1_xxreal_0 np__2 np__4 → False) → False) → ((r1_xxreal_0 np__4 np__4 → False) → False) → (((k6_xcmplx_0 np__1 np__1) = np__0 → False) → False) → (((k6_xcmplx_0 np__1 np__0) = np__1 → False) → False) → (((k6_xcmplx_0 np__3 np__1) = np__2 → False) → False) → (((k6_xcmplx_0 np__3 np__3) = np__0 → False) → False) → (((k6_xcmplx_0 np__3 np__2) = np__1 → False) → False) → (((k6_xcmplx_0 np__2 np__1) = np__1 → False) → False) → (((k6_xcmplx_0 np__2 np__0) = np__2 → False) → False) → (((k6_xcmplx_0 np__2 np__2) = np__0 → False) → False) → (((k6_xcmplx_0 np__4 np__1) = np__3 → False) → False) → (((k6_xcmplx_0 np__4 np__0) = np__4 → False) → False) → (((k6_xcmplx_0 np__4 np__3) = np__1 → False) → False) → (((k6_xcmplx_0 np__4 np__2) = np__2 → False) → False) → (((k6_xcmplx_0 np__4 np__4) = np__0 → False) → False) → (((k3_xcmplx_0 np__1 np__1) = np__1 → False) → False) → (((k3_xcmplx_0 np__1 np__0) = np__0 → False) → False) → (((k3_xcmplx_0 np__1 np__3) = np__3 → False) → False) → (((k3_xcmplx_0 np__1 np__2) = np__2 → False) → False) → (((k3_xcmplx_0 np__1 np__4) = np__4 → False) → False) → (((k3_xcmplx_0 np__0 np__1) = np__0 → False) → False) → (((k3_xcmplx_0 np__0 np__0) = np__0 → False) → False) → (((k3_xcmplx_0 np__0 np__2) = np__0 → False) → False) → (((k3_xcmplx_0 np__3 np__1) = np__3 → False) → False) → (((k3_xcmplx_0 np__2 np__1) = np__2 → False) → False) → (((k3_xcmplx_0 np__2 np__0) = np__0 → False) → False) → (((k3_xcmplx_0 np__2 np__2) = np__4 → False) → False) → (((k3_xcmplx_0 np__4 np__1) = np__4 → False) → False) → (((k2_xcmplx_0 np__1 np__1) = np__2 → False) → False) → (((k2_xcmplx_0 np__1 np__0) = np__1 → False) → False) → (((k2_xcmplx_0 np__1 np__3) = np__4 → False) → False) → (((k2_xcmplx_0 np__1 np__2) = np__3 → False) → False) → (((k2_xcmplx_0 np__0 np__1) = np__1 → False) → False) → (((k2_xcmplx_0 np__0 np__0) = np__0 → False) → False) → (((k2_xcmplx_0 np__3 np__1) = np__4 → False) → False) → (((k2_xcmplx_0 np__2 np__1) = np__3 → False) → False) → (((k2_xcmplx_0 np__2 np__2) = np__4 → False) → False) → (((k4_xcmplx_0 (k4_xcmplx_0 np__1)) = np__1 → False) → False) → (((k4_xcmplx_0 (k4_xcmplx_0 np__3)) = np__3 → False) → False) → (((k4_xcmplx_0 (k4_xcmplx_0 np__2)) = np__2 → False) → False) → (((k4_xcmplx_0 (k4_xcmplx_0 np__4)) = np__4 → False) → False) → ((v2_xxreal_0 np__1 → False) → False) → ((v2_xxreal_0 np__3 → False) → False) → ((v2_xxreal_0 np__2 → False) → False) → ((v2_xxreal_0 np__4 → False) → False) → ((v7_membered esk12_0 → False) → False) → ((v7_membered k4_ordinal1 → False) → False) → ((v7_membered k1_numbers → False) → False) → ((v7_membered k2_numbers → False) → False) → ((v1_xboole_0 np__0 → False) → False) → ((v3_membered k1_numbers → False) → False) → ((v1_membered k2_numbers → False) → False) → ((v6_membered esk12_0 → False) → False) → ((v6_membered esk11_0 → False) → False) → ((v6_membered esk9_0 → False) → False) → ((v6_membered k4_ordinal1 → False) → False) → ((v1_quaterni esk10_0 → False) → False) → ((v1_quaterni esk3_0 → False) → False) → ((v1_quaterni esk2_0 → False) → False) → ((v1_quaterni esk1_0 → False) → False) → (((k4_xcmplx_0 np__0) = np__0 → False) → False) → ((k6_numbers = k1_xboole_0 → False) → False) → ((k4_ordinal1 = k5_numbers → False) → False) → False
In Proofgold the corresponding term root is eed02b... and proposition id is 23b98a...
Proof:
The rest of the proof is missing.