%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU025+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n011.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Tue Jul 19 15:59:04 EDT 2022 % Result : Theorem 3.89s 4.08s % Output : Proof 3.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.14 % Problem : SEU025+1 : TPTP v8.1.0. Released v3.2.0. % 0.04/0.14 % Command : run_zenon %s %d % 0.14/0.36 % Computer : n011.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 600 % 0.14/0.36 % DateTime : Sun Jun 19 16:03:09 EDT 2022 % 0.14/0.36 % CPUTime : % 3.89/4.08 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 3.89/4.08 (* PROOF-FOUND *) % 3.89/4.08 % SZS status Theorem % 3.89/4.08 (* BEGIN-PROOF *) % 3.89/4.08 % SZS output start Proof % 3.89/4.08 Theorem t58_funct_1 : (forall A : zenon_U, (((relation A)/\(function A))->((one_to_one A)->(((relation_dom (relation_composition A (function_inverse A))) = (relation_dom A))/\((relation_rng (relation_composition A (function_inverse A))) = (relation_dom A)))))). % 3.89/4.08 Proof. % 3.89/4.08 assert (zenon_L1_ : forall (zenon_TA_bt : zenon_U), (relation zenon_TA_bt) -> (function zenon_TA_bt) -> (~(relation (function_inverse zenon_TA_bt))) -> False). % 3.89/4.08 do 1 intro. intros zenon_H2a zenon_H2b zenon_H2c. % 3.89/4.08 generalize (dt_k2_funct_1 zenon_TA_bt). zenon_intro zenon_H2e. % 3.89/4.08 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ]. % 3.89/4.08 apply (zenon_notand_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 3.89/4.08 exact (zenon_H32 zenon_H2a). % 3.89/4.08 exact (zenon_H31 zenon_H2b). % 3.89/4.08 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H34. zenon_intro zenon_H33. % 3.89/4.08 exact (zenon_H2c zenon_H34). % 3.89/4.08 (* end of lemma zenon_L1_ *) % 3.89/4.08 assert (zenon_L2_ : forall (zenon_TA_bt : zenon_U), (forall x : zenon_U, (subset x x)) -> (~(subset (relation_dom (function_inverse zenon_TA_bt)) (relation_rng zenon_TA_bt))) -> ((relation_rng zenon_TA_bt) = (relation_dom (function_inverse zenon_TA_bt))) -> False). % 3.89/4.08 do 1 intro. intros zenon_H35 zenon_H36 zenon_H37. % 3.89/4.08 generalize (zenon_H35 (relation_dom (function_inverse zenon_TA_bt))). zenon_intro zenon_H38. % 3.89/4.08 cut ((subset (relation_dom (function_inverse zenon_TA_bt)) (relation_dom (function_inverse zenon_TA_bt))) = (subset (relation_dom (function_inverse zenon_TA_bt)) (relation_rng zenon_TA_bt))). % 3.89/4.08 intro zenon_D_pnotp. % 3.89/4.08 apply zenon_H36. % 3.89/4.08 rewrite <- zenon_D_pnotp. % 3.89/4.08 exact zenon_H38. % 3.89/4.08 cut (((relation_dom (function_inverse zenon_TA_bt)) = (relation_rng zenon_TA_bt))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 3.89/4.08 cut (((relation_dom (function_inverse zenon_TA_bt)) = (relation_dom (function_inverse zenon_TA_bt)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 3.89/4.08 congruence. % 3.89/4.08 apply zenon_H3a. apply refl_equal. % 3.89/4.08 apply zenon_H39. apply sym_equal. exact zenon_H37. % 3.89/4.08 (* end of lemma zenon_L2_ *) % 3.89/4.08 apply NNPP. intro zenon_G. % 3.89/4.08 elim (classic (forall x : zenon_U, (subset x x))); [ zenon_intro zenon_H35 | zenon_intro zenon_H3b ]. % 3.89/4.08 apply (zenon_notallex_s (fun A : zenon_U => (((relation A)/\(function A))->((one_to_one A)->(((relation_dom (relation_composition A (function_inverse A))) = (relation_dom A))/\((relation_rng (relation_composition A (function_inverse A))) = (relation_dom A)))))) zenon_G); [ zenon_intro zenon_H3c; idtac ]. % 3.89/4.08 elim zenon_H3c. zenon_intro zenon_TA_bt. zenon_intro zenon_H3d. % 3.89/4.08 apply (zenon_notimply_s _ _ zenon_H3d). zenon_intro zenon_H3f. zenon_intro zenon_H3e. % 3.89/4.08 apply (zenon_notimply_s _ _ zenon_H3e). zenon_intro zenon_H41. zenon_intro zenon_H40. % 3.89/4.08 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H2a. zenon_intro zenon_H2b. % 3.89/4.08 apply (zenon_notand_s _ _ zenon_H40); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 3.89/4.08 generalize (t46_relat_1 zenon_TA_bt). zenon_intro zenon_H44. % 3.89/4.08 apply (zenon_imply_s _ _ zenon_H44); [ zenon_intro zenon_H32 | zenon_intro zenon_H45 ]. % 3.89/4.08 exact (zenon_H32 zenon_H2a). % 3.89/4.08 generalize (t55_funct_1 zenon_TA_bt). zenon_intro zenon_H46. % 3.89/4.08 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H30 | zenon_intro zenon_H47 ]. % 3.89/4.08 apply (zenon_notand_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 3.89/4.08 exact (zenon_H32 zenon_H2a). % 3.89/4.08 exact (zenon_H31 zenon_H2b). % 3.89/4.08 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ]. % 3.89/4.08 exact (zenon_H49 zenon_H41). % 3.89/4.08 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H37. zenon_intro zenon_H4a. % 3.89/4.08 generalize (zenon_H45 (function_inverse zenon_TA_bt)). zenon_intro zenon_H4b. % 3.89/4.08 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H2c | zenon_intro zenon_H4c ]. % 3.89/4.08 apply (zenon_L1_ zenon_TA_bt); trivial. % 3.89/4.08 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H4e | zenon_intro zenon_H4d ]. % 3.89/4.08 generalize (zenon_H35 (relation_rng zenon_TA_bt)). zenon_intro zenon_H4f. % 3.89/4.08 cut ((subset (relation_rng zenon_TA_bt) (relation_rng zenon_TA_bt)) = (subset (relation_rng zenon_TA_bt) (relation_dom (function_inverse zenon_TA_bt)))). % 3.89/4.08 intro zenon_D_pnotp. % 3.89/4.08 apply zenon_H4e. % 3.89/4.08 rewrite <- zenon_D_pnotp. % 3.89/4.08 exact zenon_H4f. % 3.89/4.08 cut (((relation_rng zenon_TA_bt) = (relation_dom (function_inverse zenon_TA_bt)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 3.89/4.08 cut (((relation_rng zenon_TA_bt) = (relation_rng zenon_TA_bt))); [idtac | apply NNPP; zenon_intro zenon_H51]. % 3.89/4.08 congruence. % 3.89/4.08 apply zenon_H51. apply refl_equal. % 3.89/4.08 exact (zenon_H50 zenon_H37). % 3.89/4.08 exact (zenon_H43 zenon_H4d). % 3.89/4.08 generalize (t47_relat_1 (function_inverse zenon_TA_bt)). zenon_intro zenon_H52. % 3.89/4.08 apply (zenon_imply_s _ _ zenon_H52); [ zenon_intro zenon_H2c | zenon_intro zenon_H53 ]. % 3.89/4.08 apply (zenon_L1_ zenon_TA_bt); trivial. % 3.89/4.08 generalize (t55_funct_1 zenon_TA_bt). zenon_intro zenon_H46. % 3.89/4.08 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H30 | zenon_intro zenon_H47 ]. % 3.89/4.08 apply (zenon_notand_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 3.89/4.08 exact (zenon_H32 zenon_H2a). % 3.89/4.08 exact (zenon_H31 zenon_H2b). % 3.89/4.08 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ]. % 3.89/4.08 exact (zenon_H49 zenon_H41). % 3.89/4.08 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H37. zenon_intro zenon_H4a. % 3.89/4.08 generalize (zenon_H53 zenon_TA_bt). zenon_intro zenon_H54. % 3.89/4.08 apply (zenon_imply_s _ _ zenon_H54); [ zenon_intro zenon_H32 | zenon_intro zenon_H55 ]. % 3.89/4.08 exact (zenon_H32 zenon_H2a). % 3.89/4.08 apply (zenon_imply_s _ _ zenon_H55); [ zenon_intro zenon_H36 | zenon_intro zenon_H56 ]. % 3.89/4.08 apply (zenon_L2_ zenon_TA_bt); trivial. % 3.89/4.08 elim (classic ((relation_dom zenon_TA_bt) = (relation_dom zenon_TA_bt))); [ zenon_intro zenon_H57 | zenon_intro zenon_H58 ]. % 3.89/4.08 cut (((relation_dom zenon_TA_bt) = (relation_dom zenon_TA_bt)) = ((relation_rng (relation_composition zenon_TA_bt (function_inverse zenon_TA_bt))) = (relation_dom zenon_TA_bt))). % 3.89/4.08 intro zenon_D_pnotp. % 3.89/4.08 apply zenon_H42. % 3.89/4.08 rewrite <- zenon_D_pnotp. % 3.89/4.08 exact zenon_H57. % 3.89/4.08 cut (((relation_dom zenon_TA_bt) = (relation_dom zenon_TA_bt))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 3.89/4.08 cut (((relation_dom zenon_TA_bt) = (relation_rng (relation_composition zenon_TA_bt (function_inverse zenon_TA_bt))))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 3.89/4.08 congruence. % 3.89/4.08 cut (((relation_dom zenon_TA_bt) = (relation_rng (function_inverse zenon_TA_bt))) = ((relation_dom zenon_TA_bt) = (relation_rng (relation_composition zenon_TA_bt (function_inverse zenon_TA_bt))))). % 3.89/4.08 intro zenon_D_pnotp. % 3.89/4.08 apply zenon_H59. % 3.89/4.08 rewrite <- zenon_D_pnotp. % 3.89/4.08 exact zenon_H4a. % 3.89/4.08 cut (((relation_rng (function_inverse zenon_TA_bt)) = (relation_rng (relation_composition zenon_TA_bt (function_inverse zenon_TA_bt))))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 3.89/4.08 cut (((relation_dom zenon_TA_bt) = (relation_dom zenon_TA_bt))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 3.89/4.08 congruence. % 3.89/4.08 apply zenon_H58. apply refl_equal. % 3.89/4.08 apply zenon_H5a. apply sym_equal. exact zenon_H56. % 3.89/4.08 apply zenon_H58. apply refl_equal. % 3.89/4.08 apply zenon_H58. apply refl_equal. % 3.89/4.08 apply zenon_H3b. zenon_intro zenon_Tx_dn. apply NNPP. zenon_intro zenon_H5c. % 3.89/4.08 generalize (reflexivity_r1_tarski zenon_Tx_dn). zenon_intro zenon_H0. % 3.89/4.08 generalize (zenon_H0 zenon_E). zenon_intro zenon_H5d. % 3.89/4.08 exact (zenon_H5c zenon_H5d). % 3.89/4.08 Qed. % 3.89/4.08 % SZS output end Proof % 3.89/4.08 (* END-PROOF *) % 3.89/4.08 nodes searched: 94387 % 3.89/4.08 max branch formulas: 3355 % 3.89/4.08 proof nodes created: 5388 % 3.89/4.08 formulas created: 189716 % 3.89/4.08 %------------------------------------------------------------------------------