%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : COM012+3 : TPTP v8.1.0. Released v4.0.0. % 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 : Fri Jul 15 01:52:58 EDT 2022 % Result : Theorem 0.20s 0.52s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : COM012+3 : TPTP v8.1.0. Released v4.0.0. % 0.03/0.13 % 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 : Thu Jun 16 19:36:38 EDT 2022 % 0.13/0.34 % CPUTime : % 0.20/0.52 (* PROOF-FOUND *) % 0.20/0.52 % SZS status Theorem % 0.20/0.52 (* BEGIN-PROOF *) % 0.20/0.52 % SZS output start Proof % 0.20/0.52 Theorem m__ : (((((xx) = (xy))\/(((aReductOfIn0 (xy) (xx) (xR))\/(exists W0 : zenon_U, ((aElement0 W0)/\((aReductOfIn0 W0 (xx) (xR))/\(sdtmndtplgtdt0 W0 (xR) (xy))))))/\(sdtmndtplgtdt0 (xx) (xR) (xy))))/\((sdtmndtasgtdt0 (xx) (xR) (xy))/\((((xy) = (xz))\/(((aReductOfIn0 (xz) (xy) (xR))\/(exists W0 : zenon_U, ((aElement0 W0)/\((aReductOfIn0 W0 (xy) (xR))/\(sdtmndtplgtdt0 W0 (xR) (xz))))))/\(sdtmndtplgtdt0 (xy) (xR) (xz))))/\(sdtmndtasgtdt0 (xy) (xR) (xz)))))->(((xx) = (xz))\/((aReductOfIn0 (xz) (xx) (xR))\/((exists W0 : zenon_U, ((aElement0 W0)/\((aReductOfIn0 W0 (xx) (xR))/\(sdtmndtplgtdt0 W0 (xR) (xz)))))\/((sdtmndtplgtdt0 (xx) (xR) (xz))\/(sdtmndtasgtdt0 (xx) (xR) (xz))))))). % 0.20/0.52 Proof. % 0.20/0.52 assert (zenon_L1_ : (~((xR) = (xR))) -> False). % 0.20/0.52 do 0 intro. intros zenon_Ha. % 0.20/0.52 apply zenon_Ha. apply refl_equal. % 0.20/0.52 (* end of lemma zenon_L1_ *) % 0.20/0.52 assert (zenon_L2_ : (~((xz) = (xz))) -> False). % 0.20/0.52 do 0 intro. intros zenon_Hb. % 0.20/0.52 apply zenon_Hb. apply refl_equal. % 0.20/0.52 (* end of lemma zenon_L2_ *) % 0.20/0.52 assert (zenon_L3_ : (~((xx) = (xx))) -> False). % 0.20/0.52 do 0 intro. intros zenon_Hc. % 0.20/0.52 apply zenon_Hc. apply refl_equal. % 0.20/0.52 (* end of lemma zenon_L3_ *) % 0.20/0.52 apply NNPP. intro zenon_G. % 0.20/0.52 apply (zenon_and_s _ _ m__349). zenon_intro zenon_He. zenon_intro zenon_Hd. % 0.20/0.52 apply (zenon_and_s _ _ zenon_Hd). zenon_intro zenon_H10. zenon_intro zenon_Hf. % 0.20/0.52 apply (zenon_and_s _ _ zenon_Hf). zenon_intro zenon_H12. zenon_intro zenon_H11. % 0.20/0.52 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H14. zenon_intro zenon_H13. % 0.20/0.52 apply (zenon_notor_s _ _ zenon_H13). zenon_intro zenon_H16. zenon_intro zenon_H15. % 0.20/0.52 apply (zenon_notor_s _ _ zenon_H15). zenon_intro zenon_H18. zenon_intro zenon_H17. % 0.20/0.52 apply (zenon_notor_s _ _ zenon_H17). zenon_intro zenon_H1a. zenon_intro zenon_H19. % 0.20/0.52 apply (zenon_notor_s _ _ zenon_H19). zenon_intro zenon_H1c. zenon_intro zenon_H1b. % 0.20/0.52 apply (zenon_and_s _ _ zenon_H14). zenon_intro zenon_H1e. zenon_intro zenon_H1d. % 0.20/0.52 apply (zenon_and_s _ _ zenon_H1d). zenon_intro zenon_H20. zenon_intro zenon_H1f. % 0.20/0.52 apply (zenon_and_s _ _ zenon_H1f). zenon_intro zenon_H22. zenon_intro zenon_H21. % 0.20/0.52 apply (zenon_or_s _ _ zenon_H1e); [ zenon_intro zenon_H24 | zenon_intro zenon_H23 ]. % 0.20/0.52 cut ((sdtmndtasgtdt0 (xy) (xR) (xz)) = (sdtmndtasgtdt0 (xx) (xR) (xz))). % 0.20/0.52 intro zenon_D_pnotp. % 0.20/0.52 apply zenon_H1b. % 0.20/0.52 rewrite <- zenon_D_pnotp. % 0.20/0.52 exact zenon_H21. % 0.20/0.52 cut (((xz) = (xz))); [idtac | apply NNPP; zenon_intro zenon_Hb]. % 0.20/0.52 cut (((xR) = (xR))); [idtac | apply NNPP; zenon_intro zenon_Ha]. % 0.20/0.52 cut (((xy) = (xx))); [idtac | apply NNPP; zenon_intro zenon_H25]. % 0.20/0.52 congruence. % 0.20/0.52 apply zenon_H25. apply sym_equal. exact zenon_H24. % 0.20/0.52 apply zenon_Ha. apply refl_equal. % 0.20/0.52 apply zenon_Hb. apply refl_equal. % 0.20/0.52 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H27. zenon_intro zenon_H26. % 0.20/0.52 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 0.20/0.52 cut ((sdtmndtasgtdt0 (xx) (xR) (xy)) = (sdtmndtasgtdt0 (xx) (xR) (xz))). % 0.20/0.52 intro zenon_D_pnotp. % 0.20/0.52 apply zenon_H1b. % 0.20/0.52 rewrite <- zenon_D_pnotp. % 0.20/0.52 exact zenon_H20. % 0.20/0.52 cut (((xy) = (xz))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 0.20/0.52 cut (((xR) = (xR))); [idtac | apply NNPP; zenon_intro zenon_Ha]. % 0.20/0.52 cut (((xx) = (xx))); [idtac | apply NNPP; zenon_intro zenon_Hc]. % 0.20/0.52 congruence. % 0.20/0.52 apply zenon_Hc. apply refl_equal. % 0.20/0.52 apply zenon_Ha. apply refl_equal. % 0.20/0.52 exact (zenon_H2a zenon_H29). % 0.20/0.52 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2c. zenon_intro zenon_H2b. % 0.20/0.52 generalize (mTCTrans (xx)). zenon_intro zenon_H2d. % 0.20/0.52 generalize (zenon_H2d (xR)). zenon_intro zenon_H2e. % 0.20/0.52 generalize (zenon_H2e (xy)). zenon_intro zenon_H2f. % 0.20/0.52 generalize (zenon_H2f (xz)). zenon_intro zenon_H30. % 0.20/0.52 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 0.20/0.52 apply (zenon_notand_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 0.20/0.52 exact (zenon_H34 zenon_He). % 0.20/0.52 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ]. % 0.20/0.52 exact (zenon_H36 zenon_H10). % 0.20/0.52 apply (zenon_notand_s _ _ zenon_H35); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ]. % 0.20/0.52 exact (zenon_H38 zenon_H12). % 0.20/0.52 exact (zenon_H37 zenon_H11). % 0.20/0.52 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 0.20/0.52 apply (zenon_notand_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ]. % 0.20/0.52 exact (zenon_H3c zenon_H26). % 0.20/0.52 exact (zenon_H3b zenon_H2b). % 0.20/0.52 exact (zenon_H1c zenon_H39). % 0.20/0.52 Qed. % 0.20/0.52 % SZS output end Proof % 0.20/0.52 (* END-PROOF *) % 0.20/0.52 nodes searched: 554 % 0.20/0.52 max branch formulas: 219 % 0.20/0.52 proof nodes created: 37 % 0.20/0.52 formulas created: 1859 % 0.20/0.52 %------------------------------------------------------------------------------