TSTP Solution File: COM012+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% 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
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