%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU212+3 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n004.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 0.48s 0.70s % Output : Proof 0.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SEU212+3 : TPTP v8.1.0. Released v3.2.0. % 0.10/0.12 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n004.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 15:29:08 EDT 2022 % 0.13/0.34 % CPUTime : % 0.48/0.70 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 0.48/0.70 (* PROOF-FOUND *) % 0.48/0.70 % SZS status Theorem % 0.48/0.70 (* BEGIN-PROOF *) % 0.48/0.70 % SZS output start Proof % 0.48/0.70 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)))))))). % 0.48/0.70 Proof. % 0.48/0.70 assert (zenon_L1_ : forall (zenon_TB_bl : zenon_U) (zenon_TC_bm : zenon_U) (zenon_TA_bn : zenon_U), (~(exists D : zenon_U, (in (ordered_pair zenon_TA_bn D) zenon_TC_bm))) -> (in (ordered_pair zenon_TA_bn zenon_TB_bl) zenon_TC_bm) -> False). % 0.48/0.70 do 3 intro. intros zenon_H23 zenon_H24. % 0.48/0.70 apply zenon_H23. exists zenon_TB_bl. apply NNPP. zenon_intro zenon_H28. % 0.48/0.70 exact (zenon_H28 zenon_H24). % 0.48/0.70 (* end of lemma zenon_L1_ *) % 0.48/0.70 assert (zenon_L2_ : forall (zenon_TB_bl : zenon_U) (zenon_TA_bn : zenon_U) (zenon_TC_bm : zenon_U), (forall B : zenon_U, ((B = (relation_dom zenon_TC_bm))<->(forall C : zenon_U, ((in C B)<->(exists D : zenon_U, (in (ordered_pair C D) zenon_TC_bm)))))) -> (in (ordered_pair zenon_TA_bn zenon_TB_bl) zenon_TC_bm) -> (~(in zenon_TA_bn (relation_dom zenon_TC_bm))) -> False). % 0.48/0.70 do 3 intro. intros zenon_H29 zenon_H24 zenon_H2a. % 0.48/0.70 generalize (zenon_H29 (relation_dom zenon_TC_bm)). zenon_intro zenon_H2b. % 0.48/0.70 apply (zenon_equiv_s _ _ zenon_H2b); [ zenon_intro zenon_H2f; zenon_intro zenon_H2e | zenon_intro zenon_H2d; zenon_intro zenon_H2c ]. % 0.48/0.70 apply zenon_H2f. apply refl_equal. % 0.48/0.70 generalize (zenon_H2c zenon_TA_bn). zenon_intro zenon_H30. % 0.48/0.70 apply (zenon_equiv_s _ _ zenon_H30); [ zenon_intro zenon_H2a; zenon_intro zenon_H23 | zenon_intro zenon_H32; zenon_intro zenon_H31 ]. % 0.48/0.70 apply (zenon_L1_ zenon_TB_bl zenon_TC_bm zenon_TA_bn); trivial. % 0.48/0.70 exact (zenon_H2a zenon_H32). % 0.48/0.70 (* end of lemma zenon_L2_ *) % 0.48/0.70 assert (zenon_L3_ : forall (zenon_TA_bn : zenon_U) (zenon_TC_bm : zenon_U) (zenon_TB_bl : zenon_U), ((zenon_TB_bl = (apply zenon_TC_bm zenon_TA_bn))<->(in (ordered_pair zenon_TA_bn zenon_TB_bl) zenon_TC_bm)) -> (~(zenon_TB_bl = (apply zenon_TC_bm zenon_TA_bn))) -> (in (ordered_pair zenon_TA_bn zenon_TB_bl) zenon_TC_bm) -> False). % 0.48/0.70 do 3 intro. intros zenon_H33 zenon_H34 zenon_H24. % 0.48/0.70 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H34; zenon_intro zenon_H28 | zenon_intro zenon_H35; zenon_intro zenon_H24 ]. % 0.48/0.70 exact (zenon_H28 zenon_H24). % 0.48/0.70 exact (zenon_H34 zenon_H35). % 0.48/0.70 (* end of lemma zenon_L3_ *) % 0.48/0.70 apply NNPP. intro zenon_G. % 0.48/0.70 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_H36; idtac ]. % 0.48/0.70 elim zenon_H36. zenon_intro zenon_TA_bn. zenon_intro zenon_H37. % 0.48/0.70 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((relation C)/\(function C))->((in (ordered_pair zenon_TA_bn B) C)<->((in zenon_TA_bn (relation_dom C))/\(B = (apply C zenon_TA_bn))))))) zenon_H37); [ zenon_intro zenon_H38; idtac ]. % 0.48/0.70 elim zenon_H38. zenon_intro zenon_TB_bl. zenon_intro zenon_H39. % 0.48/0.70 apply (zenon_notallex_s (fun C : zenon_U => (((relation C)/\(function C))->((in (ordered_pair zenon_TA_bn zenon_TB_bl) C)<->((in zenon_TA_bn (relation_dom C))/\(zenon_TB_bl = (apply C zenon_TA_bn)))))) zenon_H39); [ zenon_intro zenon_H3a; idtac ]. % 0.48/0.70 elim zenon_H3a. zenon_intro zenon_TC_bm. zenon_intro zenon_H3b. % 0.48/0.70 apply (zenon_notimply_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 0.48/0.70 apply (zenon_and_s _ _ zenon_H3d). zenon_intro zenon_H3f. zenon_intro zenon_H3e. % 0.48/0.70 apply (zenon_notequiv_s _ _ zenon_H3c); [ zenon_intro zenon_H28; zenon_intro zenon_H41 | zenon_intro zenon_H24; zenon_intro zenon_H40 ]. % 0.48/0.70 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H32. zenon_intro zenon_H35. % 0.48/0.70 generalize (d4_funct_1 zenon_TC_bm). zenon_intro zenon_H42. % 0.48/0.70 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 0.48/0.70 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ]. % 0.48/0.70 exact (zenon_H46 zenon_H3f). % 0.48/0.70 exact (zenon_H45 zenon_H3e). % 0.48/0.70 generalize (zenon_H43 zenon_TA_bn). zenon_intro zenon_H47. % 0.48/0.70 generalize (zenon_H47 zenon_TB_bl). zenon_intro zenon_H48. % 0.48/0.70 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 0.48/0.70 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 0.48/0.70 exact (zenon_H2a zenon_H32). % 0.48/0.70 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H34; zenon_intro zenon_H28 | zenon_intro zenon_H35; zenon_intro zenon_H24 ]. % 0.48/0.70 exact (zenon_H34 zenon_H35). % 0.48/0.70 exact (zenon_H28 zenon_H24). % 0.48/0.70 apply (zenon_notand_s _ _ zenon_H40); [ zenon_intro zenon_H2a | zenon_intro zenon_H34 ]. % 0.48/0.70 generalize (d4_relat_1 zenon_TC_bm). zenon_intro zenon_H4b. % 0.48/0.70 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H46 | zenon_intro zenon_H29 ]. % 0.48/0.70 exact (zenon_H46 zenon_H3f). % 0.48/0.70 apply (zenon_L2_ zenon_TB_bl zenon_TA_bn zenon_TC_bm); trivial. % 0.48/0.70 generalize (d4_funct_1 zenon_TC_bm). zenon_intro zenon_H42. % 0.48/0.70 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 0.48/0.70 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ]. % 0.48/0.70 exact (zenon_H46 zenon_H3f). % 0.48/0.70 exact (zenon_H45 zenon_H3e). % 0.48/0.70 generalize (d4_relat_1 zenon_TC_bm). zenon_intro zenon_H4b. % 0.48/0.70 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H46 | zenon_intro zenon_H29 ]. % 0.48/0.70 exact (zenon_H46 zenon_H3f). % 0.48/0.70 generalize (zenon_H43 zenon_TA_bn). zenon_intro zenon_H47. % 0.48/0.70 generalize (zenon_H47 zenon_TB_bl). zenon_intro zenon_H48. % 0.48/0.70 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 0.48/0.70 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H2a | zenon_intro zenon_H33 ]. % 0.48/0.70 apply (zenon_L2_ zenon_TB_bl zenon_TA_bn zenon_TC_bm); trivial. % 0.48/0.70 apply (zenon_L3_ zenon_TA_bn zenon_TC_bm zenon_TB_bl); trivial. % 0.48/0.70 Qed. % 0.48/0.70 % SZS output end Proof % 0.48/0.70 (* END-PROOF *) % 0.48/0.70 nodes searched: 8082 % 0.48/0.70 max branch formulas: 893 % 0.48/0.70 proof nodes created: 906 % 0.48/0.70 formulas created: 25144 % 0.48/0.70 %------------------------------------------------------------------------------