%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU219+3 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n009.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 16:00:20 EDT 2022 % Result : Theorem 0.84s 1.04s % Output : Proof 0.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SEU219+3 : TPTP v8.1.0. Released v3.2.0. % 0.04/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n009.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sun Jun 19 19:30:22 EDT 2022 % 0.13/0.34 % CPUTime : % 0.84/1.04 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 0.84/1.04 (* PROOF-FOUND *) % 0.84/1.04 % SZS status Theorem % 0.84/1.04 (* BEGIN-PROOF *) % 0.84/1.04 % SZS output start Proof % 0.84/1.04 Theorem t55_funct_1 : (forall A : zenon_U, (((relation A)/\(function A))->((one_to_one A)->(((relation_rng A) = (relation_dom (function_inverse A)))/\((relation_dom A) = (relation_rng (function_inverse A))))))). % 0.84/1.04 Proof. % 0.84/1.04 assert (zenon_L1_ : forall (zenon_TA_bq : zenon_U), (~((relation_rng (relation_inverse (relation_inverse zenon_TA_bq))) = (relation_rng zenon_TA_bq))) -> ((relation_inverse (relation_inverse zenon_TA_bq)) = zenon_TA_bq) -> False). % 0.84/1.04 do 1 intro. intros zenon_H28 zenon_H29. % 0.84/1.04 cut (((relation_inverse (relation_inverse zenon_TA_bq)) = zenon_TA_bq)); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 0.84/1.04 congruence. % 0.84/1.04 exact (zenon_H2b zenon_H29). % 0.84/1.04 (* end of lemma zenon_L1_ *) % 0.84/1.04 apply NNPP. intro zenon_G. % 0.84/1.04 apply (zenon_notallex_s (fun A : zenon_U => (((relation A)/\(function A))->((one_to_one A)->(((relation_rng A) = (relation_dom (function_inverse A)))/\((relation_dom A) = (relation_rng (function_inverse A))))))) zenon_G); [ zenon_intro zenon_H2c; idtac ]. % 0.84/1.04 elim zenon_H2c. zenon_intro zenon_TA_bq. zenon_intro zenon_H2d. % 0.84/1.04 apply (zenon_notimply_s _ _ zenon_H2d). zenon_intro zenon_H2f. zenon_intro zenon_H2e. % 0.84/1.04 apply (zenon_notimply_s _ _ zenon_H2e). zenon_intro zenon_H31. zenon_intro zenon_H30. % 0.84/1.04 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H33. zenon_intro zenon_H32. % 0.84/1.04 apply (zenon_notand_s _ _ zenon_H30); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 0.84/1.04 generalize (involutiveness_k4_relat_1 zenon_TA_bq). zenon_intro zenon_H36. % 0.84/1.04 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_H37 | zenon_intro zenon_H29 ]. % 0.84/1.04 exact (zenon_H37 zenon_H33). % 0.84/1.04 generalize (t37_relat_1 (relation_inverse zenon_TA_bq)). zenon_intro zenon_H38. % 0.84/1.04 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 0.84/1.04 generalize (dt_k4_relat_1 zenon_TA_bq). zenon_intro zenon_H3b. % 0.84/1.04 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H37 | zenon_intro zenon_H3c ]. % 0.84/1.04 exact (zenon_H37 zenon_H33). % 0.84/1.04 exact (zenon_H3a zenon_H3c). % 0.84/1.04 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H3e. zenon_intro zenon_H3d. % 0.84/1.04 elim (classic ((relation_dom (function_inverse zenon_TA_bq)) = (relation_dom (function_inverse zenon_TA_bq)))); [ zenon_intro zenon_H3f | zenon_intro zenon_H40 ]. % 0.84/1.04 cut (((relation_dom (function_inverse zenon_TA_bq)) = (relation_dom (function_inverse zenon_TA_bq))) = ((relation_rng zenon_TA_bq) = (relation_dom (function_inverse zenon_TA_bq)))). % 0.84/1.04 intro zenon_D_pnotp. % 0.84/1.04 apply zenon_H35. % 0.84/1.04 rewrite <- zenon_D_pnotp. % 0.84/1.04 exact zenon_H3f. % 0.84/1.04 cut (((relation_dom (function_inverse zenon_TA_bq)) = (relation_dom (function_inverse zenon_TA_bq)))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 0.84/1.04 cut (((relation_dom (function_inverse zenon_TA_bq)) = (relation_rng zenon_TA_bq))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 0.84/1.04 congruence. % 0.84/1.04 cut (((relation_dom (relation_inverse zenon_TA_bq)) = (relation_rng (relation_inverse (relation_inverse zenon_TA_bq)))) = ((relation_dom (function_inverse zenon_TA_bq)) = (relation_rng zenon_TA_bq))). % 0.84/1.04 intro zenon_D_pnotp. % 0.84/1.04 apply zenon_H41. % 0.84/1.04 rewrite <- zenon_D_pnotp. % 0.84/1.04 exact zenon_H3d. % 0.84/1.04 cut (((relation_rng (relation_inverse (relation_inverse zenon_TA_bq))) = (relation_rng zenon_TA_bq))); [idtac | apply NNPP; zenon_intro zenon_H28]. % 0.84/1.04 cut (((relation_dom (relation_inverse zenon_TA_bq)) = (relation_dom (function_inverse zenon_TA_bq)))); [idtac | apply NNPP; zenon_intro zenon_H42]. % 0.84/1.04 congruence. % 0.84/1.04 elim (classic ((relation_dom (function_inverse zenon_TA_bq)) = (relation_dom (function_inverse zenon_TA_bq)))); [ zenon_intro zenon_H3f | zenon_intro zenon_H40 ]. % 0.84/1.04 cut (((relation_dom (function_inverse zenon_TA_bq)) = (relation_dom (function_inverse zenon_TA_bq))) = ((relation_dom (relation_inverse zenon_TA_bq)) = (relation_dom (function_inverse zenon_TA_bq)))). % 0.84/1.04 intro zenon_D_pnotp. % 0.84/1.04 apply zenon_H42. % 0.84/1.04 rewrite <- zenon_D_pnotp. % 0.84/1.04 exact zenon_H3f. % 0.84/1.04 cut (((relation_dom (function_inverse zenon_TA_bq)) = (relation_dom (function_inverse zenon_TA_bq)))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 0.84/1.04 cut (((relation_dom (function_inverse zenon_TA_bq)) = (relation_dom (relation_inverse zenon_TA_bq)))); [idtac | apply NNPP; zenon_intro zenon_H43]. % 0.84/1.04 congruence. % 0.84/1.04 cut (((function_inverse zenon_TA_bq) = (relation_inverse zenon_TA_bq))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 0.84/1.04 congruence. % 0.84/1.04 generalize (d9_funct_1 zenon_TA_bq). zenon_intro zenon_H45. % 0.84/1.04 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.84/1.04 apply (zenon_notand_s _ _ zenon_H47); [ zenon_intro zenon_H37 | zenon_intro zenon_H48 ]. % 0.84/1.04 exact (zenon_H37 zenon_H33). % 0.84/1.04 exact (zenon_H48 zenon_H32). % 0.84/1.04 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ]. % 0.84/1.04 exact (zenon_H4a zenon_H31). % 0.84/1.04 exact (zenon_H44 zenon_H49). % 0.84/1.04 apply zenon_H40. apply refl_equal. % 0.84/1.04 apply zenon_H40. apply refl_equal. % 0.84/1.04 apply (zenon_L1_ zenon_TA_bq); trivial. % 0.84/1.04 apply zenon_H40. apply refl_equal. % 0.84/1.04 apply zenon_H40. apply refl_equal. % 0.84/1.04 generalize (t37_relat_1 zenon_TA_bq). zenon_intro zenon_H4b. % 0.84/1.04 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H37 | zenon_intro zenon_H4c ]. % 0.84/1.04 exact (zenon_H37 zenon_H33). % 0.84/1.04 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 0.84/1.04 generalize (d9_funct_1 zenon_TA_bq). zenon_intro zenon_H45. % 0.84/1.04 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.84/1.04 apply (zenon_notand_s _ _ zenon_H47); [ zenon_intro zenon_H37 | zenon_intro zenon_H48 ]. % 0.84/1.04 exact (zenon_H37 zenon_H33). % 0.84/1.04 exact (zenon_H48 zenon_H32). % 0.84/1.04 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ]. % 0.84/1.04 exact (zenon_H4a zenon_H31). % 0.84/1.04 cut (((relation_dom zenon_TA_bq) = (relation_rng (relation_inverse zenon_TA_bq))) = ((relation_dom zenon_TA_bq) = (relation_rng (function_inverse zenon_TA_bq)))). % 0.84/1.04 intro zenon_D_pnotp. % 0.84/1.04 apply zenon_H34. % 0.84/1.04 rewrite <- zenon_D_pnotp. % 0.84/1.04 exact zenon_H4d. % 0.84/1.04 cut (((relation_rng (relation_inverse zenon_TA_bq)) = (relation_rng (function_inverse zenon_TA_bq)))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 0.84/1.04 cut (((relation_dom zenon_TA_bq) = (relation_dom zenon_TA_bq))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 0.84/1.04 congruence. % 0.84/1.04 apply zenon_H50. apply refl_equal. % 0.84/1.04 cut (((relation_inverse zenon_TA_bq) = (function_inverse zenon_TA_bq))); [idtac | apply NNPP; zenon_intro zenon_H51]. % 0.84/1.04 congruence. % 0.84/1.04 apply zenon_H51. apply sym_equal. exact zenon_H49. % 0.84/1.04 Qed. % 0.84/1.04 % SZS output end Proof % 0.84/1.04 (* END-PROOF *) % 0.84/1.04 nodes searched: 8258 % 0.84/1.04 max branch formulas: 2063 % 0.84/1.04 proof nodes created: 566 % 0.84/1.04 formulas created: 30027 % 0.84/1.04 %------------------------------------------------------------------------------