Theorem. (
t36_pboole)
∀esk6_1 : set → set, ∀esk5_0 : set, ∀esk3_0 : set, ∀esk2_0 : set, ∀esk4_0 : set, ∀esk1_0 : set, ∀v1_relat_1 : set → prop, ∀v4_relat_1 : set → set → prop, ∀v1_partfun1 : set → set → prop, ∀v1_funct_1 : set → prop, ∀k2_pboole : set → set → set → set, ∀k3_pboole : set → set → set → set, ∀r6_pboole : set → set → set → prop, (∀X3 X2 X1 X4, (r6_pboole X2 (k2_pboole X2 X1 (k3_pboole X2 X3 X4)) (k3_pboole X2 (k2_pboole X2 X1 X3) (k2_pboole X2 X1 X4)) → False) → v1_relat_1 X4 → v1_relat_1 X3 → v1_relat_1 X1 → v1_funct_1 X4 → v1_funct_1 X3 → v1_funct_1 X1 → v4_relat_1 X4 X2 → v4_relat_1 X3 X2 → v4_relat_1 X1 X2 → v1_partfun1 X4 X2 → v1_partfun1 X3 X2 → v1_partfun1 X1 X2 → False) → (∀X3 X2 X1 X4, (r6_pboole X2 (k2_pboole X2 (k2_pboole X2 X1 X3) X4) (k2_pboole X2 X1 (k2_pboole X2 X3 X4)) → False) → v1_relat_1 X4 → v1_relat_1 X3 → v1_relat_1 X1 → v1_funct_1 X4 → v1_funct_1 X3 → v1_funct_1 X1 → v4_relat_1 X4 X2 → v4_relat_1 X3 X2 → v4_relat_1 X1 X2 → v1_partfun1 X4 X2 → v1_partfun1 X3 X2 → v1_partfun1 X1 X2 → False) → (∀X3 X2 X1 X4, (r6_pboole X2 (k3_pboole X2 (k3_pboole X2 X1 X3) X4) (k3_pboole X2 X1 (k3_pboole X2 X3 X4)) → False) → v1_relat_1 X4 → v1_relat_1 X3 → v1_relat_1 X1 → v1_funct_1 X4 → v1_funct_1 X3 → v1_funct_1 X1 → v4_relat_1 X4 X2 → v4_relat_1 X3 X2 → v4_relat_1 X1 X2 → v1_partfun1 X4 X2 → v1_partfun1 X3 X2 → v1_partfun1 X1 X2 → False) → (∀X1 X2 X3, (r6_pboole X2 (k2_pboole X2 X1 (k3_pboole X2 X1 X3)) X1 → False) → v1_relat_1 X3 → v1_relat_1 X1 → v1_funct_1 X3 → v1_funct_1 X1 → v4_relat_1 X3 X2 → v4_relat_1 X1 X2 → v1_partfun1 X3 X2 → v1_partfun1 X1 X2 → False) → (∀X1 X2 X3, (r6_pboole X2 X3 X1 → False) → v1_relat_1 X3 → v1_relat_1 X1 → v1_funct_1 X3 → v1_funct_1 X1 → v4_relat_1 X3 X2 → v4_relat_1 X1 X2 → v1_partfun1 X3 X2 → v1_partfun1 X1 X2 → r6_pboole X2 X1 X3 → False) → (∀X2 X1 X3, (v1_partfun1 (k2_pboole X1 X2 X3) X1 → False) → v1_relat_1 X3 → v1_relat_1 X2 → v1_funct_1 X3 → v1_funct_1 X2 → v4_relat_1 X3 X1 → v4_relat_1 X2 X1 → v1_partfun1 X3 X1 → v1_partfun1 X2 X1 → False) → (∀X2 X1 X3, (v1_partfun1 (k3_pboole X1 X2 X3) X1 → False) → v1_relat_1 X3 → v1_relat_1 X2 → v1_funct_1 X3 → v1_funct_1 X2 → v4_relat_1 X3 X1 → v4_relat_1 X2 X1 → v1_partfun1 X3 X1 → v1_partfun1 X2 X1 → False) → (∀X2 X1 X3, (v4_relat_1 (k2_pboole X1 X2 X3) X1 → False) → v1_relat_1 X3 → v1_relat_1 X2 → v1_funct_1 X3 → v1_funct_1 X2 → v4_relat_1 X3 X1 → v4_relat_1 X2 X1 → v1_partfun1 X3 X1 → v1_partfun1 X2 X1 → False) → (∀X2 X1 X3, (v4_relat_1 (k3_pboole X1 X2 X3) X1 → False) → v1_relat_1 X3 → v1_relat_1 X2 → v1_funct_1 X3 → v1_funct_1 X2 → v4_relat_1 X3 X1 → v4_relat_1 X2 X1 → v1_partfun1 X3 X1 → v1_partfun1 X2 X1 → False) → (∀X2 X1 X3, (v1_funct_1 (k2_pboole X1 X2 X3) → False) → v1_relat_1 X3 → v1_relat_1 X2 → v1_funct_1 X3 → v1_funct_1 X2 → v4_relat_1 X3 X1 → v4_relat_1 X2 X1 → v1_partfun1 X3 X1 → v1_partfun1 X2 X1 → False) → (∀X2 X1 X3, (v1_funct_1 (k3_pboole X1 X2 X3) → False) → v1_relat_1 X3 → v1_relat_1 X2 → v1_funct_1 X3 → v1_funct_1 X2 → v4_relat_1 X3 X1 → v4_relat_1 X2 X1 → v1_partfun1 X3 X1 → v1_partfun1 X2 X1 → False) → (∀X2 X1 X3, (v1_relat_1 (k2_pboole X1 X2 X3) → False) → v1_relat_1 X3 → v1_relat_1 X2 → v1_funct_1 X3 → v1_funct_1 X2 → v4_relat_1 X3 X1 → v4_relat_1 X2 X1 → v1_partfun1 X3 X1 → v1_partfun1 X2 X1 → False) → (∀X2 X1 X3, (v1_relat_1 (k3_pboole X1 X2 X3) → False) → v1_relat_1 X3 → v1_relat_1 X2 → v1_funct_1 X3 → v1_funct_1 X2 → v4_relat_1 X3 X1 → v4_relat_1 X2 X1 → v1_partfun1 X3 X1 → v1_partfun1 X2 X1 → False) → (∀X1 X2 X3, ((k2_pboole X2 X1 X3) = (k2_pboole X2 X3 X1) → False) → v1_relat_1 X3 → v1_relat_1 X1 → v1_funct_1 X3 → v1_funct_1 X1 → v4_relat_1 X3 X2 → v4_relat_1 X1 X2 → v1_partfun1 X3 X2 → v1_partfun1 X1 X2 → False) → (∀X1 X2 X3, ((k3_pboole X2 X1 X3) = (k3_pboole X2 X3 X1) → False) → v1_relat_1 X3 → v1_relat_1 X1 → v1_funct_1 X3 → v1_funct_1 X1 → v4_relat_1 X3 X2 → v4_relat_1 X1 X2 → v1_partfun1 X3 X2 → v1_partfun1 X1 X2 → False) → (∀X1 X2 X3, (X2 = X3 → False) → v1_relat_1 X3 → v1_relat_1 X2 → v1_funct_1 X3 → v1_funct_1 X2 → v4_relat_1 X3 X1 → v4_relat_1 X2 X1 → v1_partfun1 X3 X1 → v1_partfun1 X2 X1 → r6_pboole X1 X2 X3 → False) → (∀X3 X1 X2, (r6_pboole X3 X1 X2 → False) → X1 = X2 → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → v4_relat_1 X2 X3 → v4_relat_1 X1 X3 → v1_partfun1 X2 X3 → v1_partfun1 X1 X3 → False) → (∀X3 X2 X1, ((k2_pboole X2 X1 X1) = X1 → False) → v1_relat_1 X3 → v1_relat_1 X1 → v1_funct_1 X3 → v1_funct_1 X1 → v4_relat_1 X3 X2 → v4_relat_1 X1 X2 → v1_partfun1 X3 X2 → v1_partfun1 X1 X2 → False) → (∀X3 X2 X1, ((k3_pboole X2 X1 X1) = X1 → False) → v1_relat_1 X3 → v1_relat_1 X1 → v1_funct_1 X3 → v1_funct_1 X1 → v4_relat_1 X3 X2 → v4_relat_1 X1 X2 → v1_partfun1 X3 X2 → v1_partfun1 X1 X2 → False) → (∀X3 X2 X1, (r6_pboole X2 X1 X1 → False) → v1_relat_1 X3 → v1_relat_1 X1 → v1_funct_1 X3 → v1_funct_1 X1 → v4_relat_1 X3 X2 → v4_relat_1 X1 X2 → v1_partfun1 X3 X2 → v1_partfun1 X1 X2 → False) → (r6_pboole esk1_0 (k2_pboole esk1_0 (k2_pboole esk1_0 (k3_pboole esk1_0 esk2_0 esk3_0) (k3_pboole esk1_0 esk3_0 esk4_0)) (k3_pboole esk1_0 esk4_0 esk2_0)) (k3_pboole esk1_0 (k3_pboole esk1_0 (k2_pboole esk1_0 esk2_0 esk3_0) (k2_pboole esk1_0 esk3_0 esk4_0)) (k2_pboole esk1_0 esk4_0 esk2_0)) → False) → (∀X1, (v1_partfun1 (esk6_1 X1) X1 → False) → False) → (∀X1, (v4_relat_1 (esk6_1 X1) X1 → False) → False) → ((v1_partfun1 esk4_0 esk1_0 → False) → False) → ((v1_partfun1 esk3_0 esk1_0 → False) → False) → ((v1_partfun1 esk2_0 esk1_0 → False) → False) → ((v4_relat_1 esk4_0 esk1_0 → False) → False) → ((v4_relat_1 esk3_0 esk1_0 → False) → False) → ((v4_relat_1 esk2_0 esk1_0 → False) → False) → (∀X1, (v1_funct_1 (esk6_1 X1) → False) → False) → (∀X1, (v1_relat_1 (esk6_1 X1) → False) → False) → ((v1_funct_1 esk5_0 → False) → False) → ((v1_funct_1 esk4_0 → False) → False) → ((v1_funct_1 esk3_0 → False) → False) → ((v1_funct_1 esk2_0 → False) → False) → ((v1_relat_1 esk5_0 → False) → False) → ((v1_relat_1 esk4_0 → False) → False) → ((v1_relat_1 esk3_0 → False) → False) → ((v1_relat_1 esk2_0 → False) → False) → False