%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL674+1.005 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n018.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 01:32:45 PM UTC 2026 % Result : Theorem 0.12s 0.45s % Output : Proof 0.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL674+1.005 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.09/0.35 % Computer : n018.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Sat Sep 5 02:07:33 UTC 2026 % 0.09/0.35 % CPUTime : % 0.12/0.45 (* PROOF-FOUND *) % 0.12/0.45 % SZS status Theorem % 0.12/0.45 (* BEGIN-PROOF *) % 0.12/0.45 % SZS output start Proof % 0.12/0.45 Theorem main : (~(exists X : zenon_U, (~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p6 X))/\((~(p106 X))/\(p105 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p6 X)/\((~(p106 X))/\(p105 X))))))))\/(~((~(p105 Y))/\(p104 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p5 X))/\((~(p105 X))/\(p104 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p5 X)/\((~(p105 X))/\(p104 X))))))))\/(~((~(p104 Y))/\(p103 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p4 X))/\((~(p104 X))/\(p103 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p4 X)/\((~(p104 X))/\(p103 X))))))))\/(~((~(p103 Y))/\(p102 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p3 X))/\((~(p103 X))/\(p102 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p3 X)/\((~(p103 X))/\(p102 X))))))))\/(~((~(p102 Y))/\(p101 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p2 X))/\((~(p102 X))/\(p101 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p2 X)/\((~(p102 X))/\(p101 X))))))))\/(~((~(p101 Y))/\(p100 Y))))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p6 X))\/(~(p105 X)))))\/(p6 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p6 X)\/(~(p105 X)))))\/(~(p6 Y))))\/(~(p105 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p5 X))\/(~(p104 X)))))\/(p5 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p5 X)\/(~(p104 X)))))\/(~(p5 Y))))\/(~(p104 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p4 X))\/(~(p103 X)))))\/(p4 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p4 X)\/(~(p103 X)))))\/(~(p4 Y))))\/(~(p103 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p3 X))\/(~(p102 X)))))\/(p3 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p3 X)\/(~(p102 X)))))\/(~(p3 Y))))\/(~(p102 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p2 X))\/(~(p101 X)))))\/(p2 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p2 X)\/(~(p101 X)))))\/(~(p2 Y))))\/(~(p101 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p1 X))\/(~(p100 X)))))\/(p1 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(p100 X)))))\/(~(p1 Y))))\/(~(p100 Y)))/\(((p105 Y)\/(~(p106 Y)))/\(((p104 Y)\/(~(p105 Y)))/\(((p103 Y)\/(~(p104 Y)))/\(((p102 Y)\/(~(p103 Y)))/\(((p101 Y)\/(~(p102 Y)))/\((p100 Y)\/(~(p101 Y)))))))))))))))))))))/\((~(p101 X))/\(p100 X)))))))). % 0.12/0.45 Proof. % 0.12/0.45 apply NNPP. intro zenon_G. % 0.12/0.45 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z))))))); [ zenon_intro zenon_H3 | zenon_intro zenon_H4 ]. % 0.12/0.45 apply zenon_G. zenon_intro zenon_H5. % 0.12/0.45 elim zenon_H5. zenon_intro zenon_TX_g. zenon_intro zenon_H7. % 0.12/0.45 apply (zenon_notor_s _ _ zenon_H7). zenon_intro zenon_H9. zenon_intro zenon_H8. % 0.12/0.45 apply zenon_H8. zenon_intro zenon_Ha. % 0.12/0.45 apply (zenon_and_s _ _ zenon_Ha). zenon_intro zenon_Hc. zenon_intro zenon_Hb. % 0.12/0.45 apply (zenon_and_s _ _ zenon_Hb). zenon_intro zenon_He. zenon_intro zenon_Hd. % 0.12/0.45 apply zenon_H9. zenon_intro zenon_Hf. % 0.12/0.45 generalize (zenon_Hc zenon_TX_g). zenon_intro zenon_H10. % 0.12/0.45 apply (zenon_or_s _ _ zenon_H10); [ zenon_intro zenon_H12 | zenon_intro zenon_H11 ]. % 0.12/0.45 generalize (reflexivity zenon_TX_g). zenon_intro zenon_H13. % 0.12/0.45 exact (zenon_H12 zenon_H13). % 0.12/0.45 apply (zenon_and_s _ _ zenon_H11). zenon_intro zenon_H15. zenon_intro zenon_H14. % 0.12/0.45 apply (zenon_and_s _ _ zenon_H14). zenon_intro zenon_H17. zenon_intro zenon_H16. % 0.12/0.45 apply (zenon_and_s _ _ zenon_H16). zenon_intro zenon_H19. zenon_intro zenon_H18. % 0.12/0.45 apply (zenon_and_s _ _ zenon_H18). zenon_intro zenon_H1b. zenon_intro zenon_H1a. % 0.12/0.45 apply (zenon_and_s _ _ zenon_H1a). zenon_intro zenon_H1d. zenon_intro zenon_H1c. % 0.12/0.45 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ]. % 0.12/0.45 apply (zenon_and_s _ _ zenon_H1f). zenon_intro zenon_H21. zenon_intro zenon_H20. % 0.12/0.45 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TX_g X))\/(~((~(p2 X))/\((~(p102 X))/\(p101 X)))))) zenon_H21); [ zenon_intro zenon_H22; idtac ]. % 0.12/0.45 elim zenon_H22. zenon_intro zenon_TX_bj. zenon_intro zenon_H24. % 0.12/0.45 apply (zenon_notor_s _ _ zenon_H24). zenon_intro zenon_H26. zenon_intro zenon_H25. % 0.12/0.45 apply zenon_H25. zenon_intro zenon_H27. % 0.12/0.45 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H29. zenon_intro zenon_H28. % 0.12/0.45 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2b. zenon_intro zenon_H2a. % 0.12/0.45 apply zenon_H26. zenon_intro zenon_H2c. % 0.12/0.45 generalize (zenon_Hc zenon_TX_bj). zenon_intro zenon_H2d. % 0.12/0.45 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 0.12/0.45 exact (zenon_H2f zenon_H2c). % 0.12/0.45 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H31. zenon_intro zenon_H30. % 0.12/0.45 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H33. zenon_intro zenon_H32. % 0.12/0.45 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H35. zenon_intro zenon_H34. % 0.12/0.45 apply (zenon_and_s _ _ zenon_H34). zenon_intro zenon_H37. zenon_intro zenon_H36. % 0.12/0.45 apply (zenon_or_s _ _ zenon_H37); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ]. % 0.12/0.45 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H3b. zenon_intro zenon_H3a. % 0.12/0.45 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TX_bj X))\/(~((~(p3 X))/\((~(p103 X))/\(p102 X)))))) zenon_H3b); [ zenon_intro zenon_H3c; idtac ]. % 0.12/0.45 elim zenon_H3c. zenon_intro zenon_TX_cj. zenon_intro zenon_H3e. % 0.12/0.45 apply (zenon_notor_s _ _ zenon_H3e). zenon_intro zenon_H40. zenon_intro zenon_H3f. % 0.12/0.45 apply zenon_H3f. zenon_intro zenon_H41. % 0.12/0.45 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42. % 0.12/0.45 apply zenon_H40. zenon_intro zenon_H44. % 0.12/0.45 generalize (zenon_Hf zenon_TX_cj). zenon_intro zenon_H45. % 0.12/0.45 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.12/0.45 elim (classic ((~(zenon_TX_g = zenon_TX_bj))/\(~(r1 zenon_TX_g zenon_TX_bj)))); [ zenon_intro zenon_H48 | zenon_intro zenon_H49 ]. % 0.12/0.45 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H4a. zenon_intro zenon_H2f. % 0.12/0.45 exact (zenon_H2f zenon_H2c). % 0.12/0.45 cut ((r1 zenon_TX_bj zenon_TX_cj) = (r1 zenon_TX_g zenon_TX_cj)). % 0.12/0.45 intro zenon_D_pnotp. % 0.12/0.45 apply zenon_H47. % 0.12/0.45 rewrite <- zenon_D_pnotp. % 0.12/0.45 exact zenon_H44. % 0.12/0.45 cut ((zenon_TX_cj = zenon_TX_cj)); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 0.12/0.45 cut ((zenon_TX_bj = zenon_TX_g)); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 0.12/0.45 congruence. % 0.12/0.45 apply (zenon_notand_s _ _ zenon_H49); [ zenon_intro zenon_H4d | zenon_intro zenon_H26 ]. % 0.12/0.45 apply zenon_H4d. zenon_intro zenon_H4e. % 0.12/0.45 elim (classic (zenon_TX_g = zenon_TX_g)); [ zenon_intro zenon_H4f | zenon_intro zenon_H50 ]. % 0.12/0.45 cut ((zenon_TX_g = zenon_TX_g) = (zenon_TX_bj = zenon_TX_g)). % 0.12/0.45 intro zenon_D_pnotp. % 0.12/0.45 apply zenon_H4c. % 0.12/0.45 rewrite <- zenon_D_pnotp. % 0.12/0.45 exact zenon_H4f. % 0.12/0.45 cut ((zenon_TX_g = zenon_TX_g)); [idtac | apply NNPP; zenon_intro zenon_H50]. % 0.12/0.45 cut ((zenon_TX_g = zenon_TX_bj)); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 0.12/0.45 congruence. % 0.12/0.45 exact (zenon_H4a zenon_H4e). % 0.12/0.45 apply zenon_H50. apply refl_equal. % 0.12/0.45 apply zenon_H50. apply refl_equal. % 0.12/0.45 apply zenon_H26. zenon_intro zenon_H2c. % 0.12/0.45 generalize (zenon_H3 zenon_TX_g). zenon_intro zenon_H51. % 0.12/0.45 generalize (zenon_H51 zenon_TX_bj). zenon_intro zenon_H52. % 0.12/0.45 generalize (zenon_H52 zenon_TX_cj). zenon_intro zenon_H53. % 0.12/0.45 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H2f | zenon_intro zenon_H54 ]. % 0.12/0.45 exact (zenon_H2f zenon_H2c). % 0.12/0.45 apply (zenon_imply_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 0.12/0.45 exact (zenon_H56 zenon_H44). % 0.12/0.45 exact (zenon_H47 zenon_H55). % 0.12/0.45 apply zenon_H4b. apply refl_equal. % 0.12/0.45 exact (zenon_H43 zenon_H46). % 0.12/0.45 apply (zenon_notand_s _ _ zenon_H38); [ zenon_intro zenon_H58 | zenon_intro zenon_H57 ]. % 0.12/0.45 exact (zenon_H58 zenon_H2b). % 0.12/0.45 exact (zenon_H57 zenon_H2a). % 0.12/0.45 apply (zenon_notand_s _ _ zenon_H1e); [ zenon_intro zenon_H5a | zenon_intro zenon_H59 ]. % 0.12/0.45 exact (zenon_H5a zenon_He). % 0.12/0.45 exact (zenon_H59 zenon_Hd). % 0.12/0.45 apply zenon_H4. zenon_intro zenon_Tx_dn. apply NNPP. zenon_intro zenon_H5c. % 0.12/0.45 apply zenon_H5c. zenon_intro zenon_Ty_dp. apply NNPP. zenon_intro zenon_H5e. % 0.12/0.45 apply zenon_H5e. zenon_intro zenon_Tz_dr. apply NNPP. zenon_intro zenon_H60. % 0.12/0.45 apply (zenon_notimply_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61. % 0.12/0.45 apply (zenon_notimply_s _ _ zenon_H61). zenon_intro zenon_H64. zenon_intro zenon_H63. % 0.12/0.45 generalize (transitivity zenon_Tx_dn). zenon_intro zenon_H65. % 0.12/0.45 generalize (zenon_H65 zenon_Ty_dp). zenon_intro zenon_H66. % 0.12/0.45 generalize (zenon_H66 zenon_Tz_dr). zenon_intro zenon_H67. % 0.12/0.45 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H69 | zenon_intro zenon_H68 ]. % 0.12/0.45 apply (zenon_notand_s _ _ zenon_H69); [ zenon_intro zenon_H6b | zenon_intro zenon_H6a ]. % 0.12/0.45 exact (zenon_H6b zenon_H62). % 0.12/0.45 exact (zenon_H6a zenon_H64). % 0.12/0.45 exact (zenon_H63 zenon_H68). % 0.12/0.45 Qed. % 0.12/0.45 % SZS output end Proof % 0.12/0.45 (* END-PROOF *) % 0.12/0.45 nodes searched: 460 % 0.12/0.45 max branch formulas: 407 % 0.12/0.45 proof nodes created: 88 % 0.12/0.45 formulas created: 3369 % 0.12/0.45 %------------------------------------------------------------------------------