Theorem. (
t41_procal_1)
∀k6_cqc_lang : set → set → set, ∀esk7_2 : set → set → set, ∀esk6_1 : set → set, ∀esk5_0 : set, ∀esk2_0 : set, ∀esk4_0 : set, ∀esk3_0 : set, ∀esk1_0 : set, ∀k1_zfmisc_1 : set → set, ∀v1_xboole_0 : set → prop, ∀k2_qc_lang2 : set → set → set → set, ∀k3_qc_lang2 : set → set → set → set, ∀k14_qc_lang1 : set → set → set → set, ∀k13_qc_lang1 : set → set → set, ∀m1_subset_1 : set → set → prop, ∀r2_hidden : set → set → prop, ∀k8_cqc_lang : set → set → set → set, ∀k9_cqc_lang : set → set → set → set, ∀k7_cqc_lang : set → set → set → set, ∀k4_cqc_the1 : set → set, ∀k9_qc_lang1 : set → set, ∀k3_cqc_lang : set → set, ∀m2_subset_1 : set → set → set → prop, ∀m1_qc_lang1 : set → prop, (∀X4 X3 X2 X1, (r2_hidden (k8_cqc_lang X1 (k7_cqc_lang X1 (k9_cqc_lang X1 X2 X3) (k9_cqc_lang X1 X4 X3)) (k9_cqc_lang X1 (k7_cqc_lang X1 X2 X4) X3)) (k4_cqc_the1 X1) → False) → m1_qc_lang1 X1 → m2_subset_1 X4 (k9_qc_lang1 X1) (k3_cqc_lang X1) → m2_subset_1 X3 (k9_qc_lang1 X1) (k3_cqc_lang X1) → m2_subset_1 X2 (k9_qc_lang1 X1) (k3_cqc_lang X1) → False) → (∀X2 X3 X1, (r2_hidden (k8_cqc_lang X1 (k7_cqc_lang X1 (k6_cqc_lang X1 X2) (k6_cqc_lang X1 X3)) (k6_cqc_lang X1 (k9_cqc_lang X1 X2 X3))) (k4_cqc_the1 X1) → False) → m1_qc_lang1 X1 → m2_subset_1 X3 (k9_qc_lang1 X1) (k3_cqc_lang X1) → m2_subset_1 X2 (k9_qc_lang1 X1) (k3_cqc_lang X1) → False) → (∀X2 X3 X1, (r2_hidden (k8_cqc_lang X1 (k6_cqc_lang X1 (k7_cqc_lang X1 X2 X3)) (k9_cqc_lang X1 (k6_cqc_lang X1 X2) (k6_cqc_lang X1 X3))) (k4_cqc_the1 X1) → False) → m1_qc_lang1 X1 → m2_subset_1 X3 (k9_qc_lang1 X1) (k3_cqc_lang X1) → m2_subset_1 X2 (k9_qc_lang1 X1) (k3_cqc_lang X1) → False) → (∀X4 X2 X3 X1, (r2_hidden (k8_cqc_lang X1 (k7_cqc_lang X1 X4 X2) (k7_cqc_lang X1 X4 X3)) (k4_cqc_the1 X1) → False) → m1_qc_lang1 X1 → m2_subset_1 X4 (k9_qc_lang1 X1) (k3_cqc_lang X1) → m2_subset_1 X3 (k9_qc_lang1 X1) (k3_cqc_lang X1) → m2_subset_1 X2 (k9_qc_lang1 X1) (k3_cqc_lang X1) → r2_hidden (k8_cqc_lang X1 X2 X3) (k4_cqc_the1 X1) → False) → (∀X4 X2 X3 X1, (r2_hidden (k8_cqc_lang X1 (k9_cqc_lang X1 X2 X4) (k9_cqc_lang X1 X3 X4)) (k4_cqc_the1 X1) → False) → m1_qc_lang1 X1 → m2_subset_1 X4 (k9_qc_lang1 X1) (k3_cqc_lang X1) → m2_subset_1 X3 (k9_qc_lang1 X1) (k3_cqc_lang X1) → m2_subset_1 X2 (k9_qc_lang1 X1) (k3_cqc_lang X1) → r2_hidden (k8_cqc_lang X1 X2 X3) (k4_cqc_the1 X1) → False) → (∀X4 X2 X3 X1, (r2_hidden (k8_cqc_lang X1 (k9_cqc_lang X1 X4 X2) (k9_cqc_lang X1 X4 X3)) (k4_cqc_the1 X1) → False) → m1_qc_lang1 X1 → m2_subset_1 X4 (k9_qc_lang1 X1) (k3_cqc_lang X1) → m2_subset_1 X3 (k9_qc_lang1 X1) (k3_cqc_lang X1) → m2_subset_1 X2 (k9_qc_lang1 X1) (k3_cqc_lang X1) → r2_hidden (k8_cqc_lang X1 X2 X3) (k4_cqc_the1 X1) → False) → (∀X2 X3 X1, (r2_hidden (k8_cqc_lang X1 (k8_cqc_lang X1 (k6_cqc_lang X1 X2) X3) (k8_cqc_lang X1 (k6_cqc_lang X1 X3) X2)) (k4_cqc_the1 X1) → False) → m1_qc_lang1 X1 → m2_subset_1 X3 (k9_qc_lang1 X1) (k3_cqc_lang X1) → m2_subset_1 X2 (k9_qc_lang1 X1) (k3_cqc_lang X1) → False) → (∀X3 X2 X4 X1, (r2_hidden (k8_cqc_lang X1 X2 X4) (k4_cqc_the1 X1) → False) → m1_qc_lang1 X1 → m2_subset_1 X4 (k9_qc_lang1 X1) (k3_cqc_lang X1) → m2_subset_1 X3 (k9_qc_lang1 X1) (k3_cqc_lang X1) → m2_subset_1 X2 (k9_qc_lang1 X1) (k3_cqc_lang X1) → r2_hidden (k8_cqc_lang X1 X3 X4) (k4_cqc_the1 X1) → r2_hidden (k8_cqc_lang X1 X2 X3) (k4_cqc_the1 X1) → False) → (∀X3 X2 X1, (r2_hidden (k8_cqc_lang X1 X3 X2) (k4_cqc_the1 X1) → False) → m1_qc_lang1 X1 → m2_subset_1 X3 (k9_qc_lang1 X1) (k3_cqc_lang X1) → m2_subset_1 X2 (k9_qc_lang1 X1) (k3_cqc_lang X1) → r2_hidden (k8_cqc_lang X1 (k6_cqc_lang X1 X2) (k6_cqc_lang X1 X3)) (k4_cqc_the1 X1) → False) → (∀X3 X2 X1, (r2_hidden (k8_cqc_lang X1 (k6_cqc_lang X1 X3) (k6_cqc_lang X1 X2)) (k4_cqc_the1 X1) → False) → m1_qc_lang1 X1 → m2_subset_1 X3 (k9_qc_lang1 X1) (k3_cqc_lang X1) → m2_subset_1 X2 (k9_qc_lang1 X1) (k3_cqc_lang X1) → r2_hidden (k8_cqc_lang X1 X2 X3) (k4_cqc_the1 X1) → False) → (∀X2 X3 X1, (r2_hidden X3 (k4_cqc_the1 X1) → False) → m1_qc_lang1 X1 → r2_hidden X2 (k4_cqc_the1 X1) → m2_subset_1 X3 (k9_qc_lang1 X1) (k3_cqc_lang X1) → m2_subset_1 X2 (k9_qc_lang1 X1) (k3_cqc_lang X1) → r2_hidden (k8_cqc_lang X1 X2 X3) (k4_cqc_the1 X1) → False) → (∀X2 X1, (r2_hidden (k8_cqc_lang X1 X2 (k6_cqc_lang X1 (k6_cqc_lang X1 X2))) (k4_cqc_the1 X1) → False) → m1_qc_lang1 X1 → m2_subset_1 X2 (k9_qc_lang1 X1) (k3_cqc_lang X1) → False) → (∀X2 X3 X1, ((k13_qc_lang1 X1 (k14_qc_lang1 X1 (k13_qc_lang1 X1 X2) (k13_qc_lang1 X1 X3))) = (k3_qc_lang2 X1 X2 X3) → False) → m1_qc_lang1 X1 → m1_subset_1 X3 (k9_qc_lang1 X1) → m1_subset_1 X2 (k9_qc_lang1 X1) → False) → (∀X2 X3 X1, (m2_subset_1 (k8_cqc_lang X1 X2 X3) (k9_qc_lang1 X1) (k3_cqc_lang X1) → False) → m1_qc_lang1 X1 → m1_subset_1 X3 (k3_cqc_lang X1) → m1_subset_1 X2 (k3_cqc_lang X1) → False) → (∀X2 X3 X1, (m2_subset_1 (k7_cqc_lang X1 X2 X3) (k9_qc_lang1 X1) (k3_cqc_lang X1) → False) → m1_qc_lang1 X1 → m1_subset_1 X3 (k3_cqc_lang X1) → m1_subset_1 X2 (k3_cqc_lang X1) → False) → (∀X2 X3 X1, (m2_subset_1 (k9_cqc_lang X1 X2 X3) (k9_qc_lang1 X1) (k3_cqc_lang X1) → False) → m1_qc_lang1 X1 → m1_subset_1 X3 (k3_cqc_lang X1) → m1_subset_1 X2 (k3_cqc_lang X1) → False) → (∀X2 X3 X1, (m1_subset_1 (k2_qc_lang2 X1 X2 X3) (k9_qc_lang1 X1) → False) → m1_qc_lang1 X1 → m1_subset_1 X3 (k9_qc_lang1 X1) → m1_subset_1 X2 (k9_qc_lang1 X1) → False) → (∀X2 X3 X1, (m1_subset_1 (k14_qc_lang1 X1 X2 X3) (k9_qc_lang1 X1) → False) → m1_qc_lang1 X1 → m1_subset_1 X3 (k9_qc_lang1 X1) → m1_subset_1 X2 (k9_qc_lang1 X1) → False) → (∀X2 X3 X1, (m1_subset_1 (k3_qc_lang2 X1 X2 X3) (k9_qc_lang1 X1) → False) → m1_qc_lang1 X1 → m1_subset_1 X3 (k9_qc_lang1 X1) → m1_subset_1 X2 (k9_qc_lang1 X1) → False) → (∀X2 X3 X1, ((k2_qc_lang2 X1 X2 X3) = (k8_cqc_lang X1 X2 X3) → False) → m1_qc_lang1 X1 → m1_subset_1 X3 (k3_cqc_lang X1) → m1_subset_1 X2 (k3_cqc_lang X1) → False) → (∀X2 X3 X1, ((k7_cqc_lang X1 X2 X3) = (k14_qc_lang1 X1 X2 X3) → False) → m1_qc_lang1 X1 → m1_subset_1 X3 (k3_cqc_lang X1) → m1_subset_1 X2 (k3_cqc_lang X1) → False) → (∀X2 X3 X1, ((k9_cqc_lang X1 X2 X3) = (k3_qc_lang2 X1 X2 X3) → False) → m1_qc_lang1 X1 → m1_subset_1 X3 (k3_cqc_lang X1) → m1_subset_1 X2 (k3_cqc_lang X1) → 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) → (∀X2 X1, (m2_subset_1 (k6_cqc_lang X1 X2) (k9_qc_lang1 X1) (k3_cqc_lang X1) → False) → m1_qc_lang1 X1 → m1_subset_1 X2 (k3_cqc_lang X1) → 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) → (∀X2 X1, (m1_subset_1 (k13_qc_lang1 X1 X2) (k9_qc_lang1 X1) → False) → m1_qc_lang1 X1 → m1_subset_1 X2 (k9_qc_lang1 X1) → False) → (∀X2 X1, ((k13_qc_lang1 X1 X2) = (k6_cqc_lang X1 X2) → False) → m1_qc_lang1 X1 → m1_subset_1 X2 (k3_cqc_lang X1) → False) → (∀X1, (m1_subset_1 (k4_cqc_the1 X1) (k1_zfmisc_1 (k3_cqc_lang X1)) → False) → m1_qc_lang1 X1 → False) → (∀X1, (m1_subset_1 (k3_cqc_lang X1) (k1_zfmisc_1 (k9_qc_lang1 X1)) → False) → m1_qc_lang1 X1 → False) → (∀X2 X1, r2_hidden X2 X1 → r2_hidden X1 X2 → False) → (∀X1, m1_qc_lang1 X1 → v1_xboole_0 (k3_cqc_lang X1) → False) → (∀X1, m1_qc_lang1 X1 → v1_xboole_0 (k9_qc_lang1 X1) → False) → (r2_hidden (k8_cqc_lang esk1_0 (k7_cqc_lang esk1_0 (k9_cqc_lang esk1_0 esk2_0 esk3_0) esk4_0) (k9_cqc_lang esk1_0 (k7_cqc_lang esk1_0 esk2_0 esk4_0) (k7_cqc_lang esk1_0 esk3_0 esk4_0))) (k4_cqc_the1 esk1_0) → False) → ((m2_subset_1 esk4_0 (k9_qc_lang1 esk1_0) (k3_cqc_lang esk1_0) → False) → False) → ((m2_subset_1 esk3_0 (k9_qc_lang1 esk1_0) (k3_cqc_lang esk1_0) → False) → False) → ((m2_subset_1 esk2_0 (k9_qc_lang1 esk1_0) (k3_cqc_lang esk1_0) → False) → False) → (∀X1, (m1_subset_1 (esk6_1 X1) X1 → False) → False) → ((m1_qc_lang1 esk5_0 → False) → False) → ((m1_qc_lang1 esk1_0 → False) → False) → False