%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU212+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n010.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 16:00:16 EDT 2022 % Result : Theorem 85.84s 86.06s % Output : Proof 85.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU212+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n010.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sun Jun 19 18:49:52 EDT 2022 % 0.12/0.34 % CPUTime : % 85.84/86.06 (* PROOF-FOUND *) % 85.84/86.06 % SZS status Theorem % 85.84/86.06 (* BEGIN-PROOF *) % 85.84/86.06 % SZS output start Proof % 85.84/86.06 Theorem t8_funct_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, (((relation C)/\(function C))->((in (ordered_pair A B) C)<->((in A (relation_dom C))/\(B = (apply C A)))))))). % 85.84/86.06 Proof. % 85.84/86.06 assert (zenon_L1_ : forall (zenon_TB_bf : zenon_U) (zenon_TC_bg : zenon_U) (zenon_TA_bh : zenon_U), (~(exists D : zenon_U, (in (ordered_pair zenon_TA_bh D) zenon_TC_bg))) -> (in (ordered_pair zenon_TA_bh zenon_TB_bf) zenon_TC_bg) -> False). % 85.84/86.06 do 3 intro. intros zenon_H1d zenon_H1e. % 85.84/86.06 apply zenon_H1d. exists zenon_TB_bf. apply NNPP. zenon_intro zenon_H22. % 85.84/86.06 exact (zenon_H22 zenon_H1e). % 85.84/86.06 (* end of lemma zenon_L1_ *) % 85.84/86.06 assert (zenon_L2_ : forall (zenon_TB_bf : zenon_U) (zenon_TA_bh : zenon_U) (zenon_TC_bg : zenon_U), (forall C : zenon_U, ((in C (relation_dom zenon_TC_bg))<->(exists D : zenon_U, (in (ordered_pair C D) zenon_TC_bg)))) -> (in (ordered_pair zenon_TA_bh zenon_TB_bf) zenon_TC_bg) -> (~(in zenon_TA_bh (relation_dom zenon_TC_bg))) -> False). % 85.84/86.06 do 3 intro. intros zenon_H23 zenon_H1e zenon_H24. % 85.84/86.06 generalize (zenon_H23 zenon_TA_bh). zenon_intro zenon_H25. % 85.84/86.06 apply (zenon_equiv_s _ _ zenon_H25); [ zenon_intro zenon_H24; zenon_intro zenon_H1d | zenon_intro zenon_H27; zenon_intro zenon_H26 ]. % 85.84/86.06 apply (zenon_L1_ zenon_TB_bf zenon_TC_bg zenon_TA_bh); trivial. % 85.84/86.06 exact (zenon_H24 zenon_H27). % 85.84/86.06 (* end of lemma zenon_L2_ *) % 85.84/86.06 assert (zenon_L3_ : forall (zenon_TA_bh : zenon_U) (zenon_TC_bg : zenon_U) (zenon_TB_bf : zenon_U), ((zenon_TB_bf = (apply zenon_TC_bg zenon_TA_bh))<->(in (ordered_pair zenon_TA_bh zenon_TB_bf) zenon_TC_bg)) -> (~(zenon_TB_bf = (apply zenon_TC_bg zenon_TA_bh))) -> (in (ordered_pair zenon_TA_bh zenon_TB_bf) zenon_TC_bg) -> False). % 85.84/86.06 do 3 intro. intros zenon_H28 zenon_H29 zenon_H1e. % 85.84/86.06 apply (zenon_equiv_s _ _ zenon_H28); [ zenon_intro zenon_H29; zenon_intro zenon_H22 | zenon_intro zenon_H2a; zenon_intro zenon_H1e ]. % 85.84/86.06 exact (zenon_H22 zenon_H1e). % 85.84/86.06 exact (zenon_H29 zenon_H2a). % 85.84/86.06 (* end of lemma zenon_L3_ *) % 85.84/86.06 apply NNPP. intro zenon_G. % 85.84/86.06 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (forall C : zenon_U, (((relation C)/\(function C))->((in (ordered_pair A B) C)<->((in A (relation_dom C))/\(B = (apply C A)))))))) zenon_G); [ zenon_intro zenon_H2b; idtac ]. % 85.84/86.06 elim zenon_H2b. zenon_intro zenon_TA_bh. zenon_intro zenon_H2c. % 85.84/86.06 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((relation C)/\(function C))->((in (ordered_pair zenon_TA_bh B) C)<->((in zenon_TA_bh (relation_dom C))/\(B = (apply C zenon_TA_bh))))))) zenon_H2c); [ zenon_intro zenon_H2d; idtac ]. % 85.84/86.06 elim zenon_H2d. zenon_intro zenon_TB_bf. zenon_intro zenon_H2e. % 85.84/86.06 apply (zenon_notallex_s (fun C : zenon_U => (((relation C)/\(function C))->((in (ordered_pair zenon_TA_bh zenon_TB_bf) C)<->((in zenon_TA_bh (relation_dom C))/\(zenon_TB_bf = (apply C zenon_TA_bh)))))) zenon_H2e); [ zenon_intro zenon_H2f; idtac ]. % 85.84/86.06 elim zenon_H2f. zenon_intro zenon_TC_bg. zenon_intro zenon_H30. % 85.84/86.06 apply (zenon_notimply_s _ _ zenon_H30). zenon_intro zenon_H32. zenon_intro zenon_H31. % 85.84/86.06 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H34. zenon_intro zenon_H33. % 85.84/86.06 apply (zenon_notequiv_s _ _ zenon_H31); [ zenon_intro zenon_H22; zenon_intro zenon_H36 | zenon_intro zenon_H1e; zenon_intro zenon_H35 ]. % 85.84/86.06 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H27. zenon_intro zenon_H2a. % 85.84/86.06 generalize (d4_funct_1 zenon_TC_bg). zenon_intro zenon_H37. % 85.84/86.06 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ]. % 85.84/86.06 apply (zenon_notand_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ]. % 85.84/86.06 exact (zenon_H3b zenon_H34). % 85.84/86.06 exact (zenon_H3a zenon_H33). % 85.84/86.06 generalize (zenon_H38 zenon_TA_bh). zenon_intro zenon_H3c. % 85.84/86.06 generalize (zenon_H3c zenon_TB_bf). zenon_intro zenon_H3d. % 85.84/86.06 apply (zenon_and_s _ _ zenon_H3d). zenon_intro zenon_H3f. zenon_intro zenon_H3e. % 85.84/86.06 apply (zenon_imply_s _ _ zenon_H3f); [ zenon_intro zenon_H24 | zenon_intro zenon_H28 ]. % 85.84/86.06 exact (zenon_H24 zenon_H27). % 85.84/86.06 apply (zenon_equiv_s _ _ zenon_H28); [ zenon_intro zenon_H29; zenon_intro zenon_H22 | zenon_intro zenon_H2a; zenon_intro zenon_H1e ]. % 85.84/86.06 exact (zenon_H29 zenon_H2a). % 85.84/86.07 exact (zenon_H22 zenon_H1e). % 85.84/86.07 apply (zenon_notand_s _ _ zenon_H35); [ zenon_intro zenon_H24 | zenon_intro zenon_H29 ]. % 85.84/86.07 generalize (d4_relat_1 zenon_TC_bg). zenon_intro zenon_H40. % 85.84/86.07 apply (zenon_imply_s _ _ zenon_H40); [ zenon_intro zenon_H3b | zenon_intro zenon_H41 ]. % 85.84/86.07 exact (zenon_H3b zenon_H34). % 85.84/86.07 generalize (zenon_H41 (relation_dom zenon_TC_bg)). zenon_intro zenon_H42. % 85.84/86.07 apply (zenon_equiv_s _ _ zenon_H42); [ zenon_intro zenon_H45; zenon_intro zenon_H44 | zenon_intro zenon_H43; zenon_intro zenon_H23 ]. % 85.84/86.07 apply zenon_H45. apply refl_equal. % 85.84/86.07 apply (zenon_L2_ zenon_TB_bf zenon_TA_bh zenon_TC_bg); trivial. % 85.84/86.07 generalize (d4_funct_1 zenon_TC_bg). zenon_intro zenon_H37. % 85.84/86.07 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ]. % 85.84/86.07 apply (zenon_notand_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ]. % 85.84/86.07 exact (zenon_H3b zenon_H34). % 85.84/86.07 exact (zenon_H3a zenon_H33). % 85.84/86.07 generalize (d4_relat_1 zenon_TC_bg). zenon_intro zenon_H40. % 85.84/86.07 apply (zenon_imply_s _ _ zenon_H40); [ zenon_intro zenon_H3b | zenon_intro zenon_H41 ]. % 85.84/86.07 exact (zenon_H3b zenon_H34). % 85.84/86.07 generalize (zenon_H38 zenon_TA_bh). zenon_intro zenon_H3c. % 85.84/86.07 generalize (zenon_H41 (relation_dom zenon_TC_bg)). zenon_intro zenon_H42. % 85.84/86.07 apply (zenon_equiv_s _ _ zenon_H42); [ zenon_intro zenon_H45; zenon_intro zenon_H44 | zenon_intro zenon_H43; zenon_intro zenon_H23 ]. % 85.84/86.07 apply zenon_H45. apply refl_equal. % 85.84/86.07 generalize (zenon_H3c zenon_TB_bf). zenon_intro zenon_H3d. % 85.84/86.07 apply (zenon_and_s _ _ zenon_H3d). zenon_intro zenon_H3f. zenon_intro zenon_H3e. % 85.84/86.07 apply (zenon_imply_s _ _ zenon_H3f); [ zenon_intro zenon_H24 | zenon_intro zenon_H28 ]. % 85.84/86.07 apply (zenon_L2_ zenon_TB_bf zenon_TA_bh zenon_TC_bg); trivial. % 85.84/86.07 apply (zenon_L3_ zenon_TA_bh zenon_TC_bg zenon_TB_bf); trivial. % 85.84/86.07 Qed. % 85.84/86.07 % SZS output end Proof % 85.84/86.07 (* END-PROOF *) % 85.84/86.07 nodes searched: 1694523 % 85.84/86.07 max branch formulas: 28447 % 85.84/86.07 proof nodes created: 139335 % 85.84/86.07 formulas created: 8903554 % 85.84/86.07 %------------------------------------------------------------------------------