%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : KRS082+1 : TPTP v8.1.0. Released v3.1.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n027.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 : Sun Jul 17 03:39:24 EDT 2022 % Result : Unsatisfiable 1.07s 1.29s % Output : Proof 1.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.12 % Problem : KRS082+1 : TPTP v8.1.0. Released v3.1.0. % 0.09/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n027.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Tue Jun 7 18:38:25 EDT 2022 % 0.12/0.33 % CPUTime : % 1.07/1.29 (* PROOF-FOUND *) % 1.07/1.29 % SZS status Unsatisfiable % 1.07/1.29 (* BEGIN-PROOF *) % 1.07/1.29 % SZS output start Proof % 1.07/1.29 Theorem zenon_thm : False. % 1.07/1.29 Proof. % 1.07/1.29 assert (zenon_L1_ : forall (zenon_TW_o : zenon_U) (zenon_TZ_p : zenon_U) (zenon_TY_q : zenon_U), (rp zenon_TY_q zenon_TZ_p) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((rp x y)->((rp y z)->(rp x z)))))) -> (~(rp zenon_TY_q zenon_TW_o)) -> (rp zenon_TZ_p zenon_TW_o) -> False). % 1.07/1.29 do 3 intro. intros zenon_Ha zenon_Hb zenon_Hc zenon_Hd. % 1.07/1.29 elim (classic ((~(zenon_TY_q = zenon_TZ_p))/\(~(rp zenon_TY_q zenon_TZ_p)))); [ zenon_intro zenon_H11 | zenon_intro zenon_H12 ]. % 1.07/1.29 apply (zenon_and_s _ _ zenon_H11). zenon_intro zenon_H14. zenon_intro zenon_H13. % 1.07/1.29 exact (zenon_H13 zenon_Ha). % 1.07/1.29 cut ((rp zenon_TZ_p zenon_TW_o) = (rp zenon_TY_q zenon_TW_o)). % 1.07/1.29 intro zenon_D_pnotp. % 1.07/1.29 apply zenon_Hc. % 1.07/1.29 rewrite <- zenon_D_pnotp. % 1.07/1.29 exact zenon_Hd. % 1.07/1.29 cut ((zenon_TW_o = zenon_TW_o)); [idtac | apply NNPP; zenon_intro zenon_H15]. % 1.07/1.29 cut ((zenon_TZ_p = zenon_TY_q)); [idtac | apply NNPP; zenon_intro zenon_H16]. % 1.07/1.29 congruence. % 1.07/1.29 apply (zenon_notand_s _ _ zenon_H12); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 1.07/1.29 apply zenon_H18. zenon_intro zenon_H19. % 1.07/1.29 elim (classic (zenon_TY_q = zenon_TY_q)); [ zenon_intro zenon_H1a | zenon_intro zenon_H1b ]. % 1.07/1.29 cut ((zenon_TY_q = zenon_TY_q) = (zenon_TZ_p = zenon_TY_q)). % 1.07/1.29 intro zenon_D_pnotp. % 1.07/1.29 apply zenon_H16. % 1.07/1.29 rewrite <- zenon_D_pnotp. % 1.07/1.29 exact zenon_H1a. % 1.07/1.29 cut ((zenon_TY_q = zenon_TY_q)); [idtac | apply NNPP; zenon_intro zenon_H1b]. % 1.07/1.29 cut ((zenon_TY_q = zenon_TZ_p)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 1.07/1.29 congruence. % 1.07/1.29 exact (zenon_H14 zenon_H19). % 1.07/1.29 apply zenon_H1b. apply refl_equal. % 1.07/1.29 apply zenon_H1b. apply refl_equal. % 1.07/1.29 apply zenon_H17. zenon_intro zenon_Ha. % 1.07/1.29 generalize (zenon_Hb zenon_TY_q). zenon_intro zenon_H1c. % 1.07/1.29 generalize (zenon_H1c zenon_TZ_p). zenon_intro zenon_H1d. % 1.07/1.29 generalize (zenon_H1d zenon_TW_o). zenon_intro zenon_H1e. % 1.07/1.29 apply (zenon_imply_s _ _ zenon_H1e); [ zenon_intro zenon_H13 | zenon_intro zenon_H1f ]. % 1.07/1.29 exact (zenon_H13 zenon_Ha). % 1.07/1.29 apply (zenon_imply_s _ _ zenon_H1f); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ]. % 1.07/1.29 exact (zenon_H21 zenon_Hd). % 1.07/1.29 exact (zenon_Hc zenon_H20). % 1.07/1.29 apply zenon_H15. apply refl_equal. % 1.07/1.29 (* end of lemma zenon_L1_ *) % 1.07/1.29 assert (zenon_L2_ : forall (zenon_TY_q : zenon_U), (forall W : zenon_U, ((rinvS zenon_TY_q W)->(~(ca W)))) -> (rs (i2003_11_14_17_19_28752) zenon_TY_q) -> False). % 1.07/1.29 do 1 intro. intros zenon_H22 zenon_H23. % 1.07/1.29 generalize (axiom_3 (i2003_11_14_17_19_28752)). zenon_intro zenon_H24. % 1.07/1.29 apply (zenon_imply_s _ _ zenon_H24); [ zenon_intro zenon_H26 | zenon_intro zenon_H25 ]. % 1.07/1.29 exact (zenon_H26 axiom_9). % 1.07/1.29 generalize (zenon_H22 (i2003_11_14_17_19_28752)). zenon_intro zenon_H27. % 1.07/1.29 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ]. % 1.07/1.29 generalize (axiom_7 zenon_TY_q). zenon_intro zenon_H2a. % 1.07/1.29 generalize (zenon_H2a (i2003_11_14_17_19_28752)). zenon_intro zenon_H2b. % 1.07/1.29 apply (zenon_equiv_s _ _ zenon_H2b); [ zenon_intro zenon_H29; zenon_intro zenon_H2d | zenon_intro zenon_H2c; zenon_intro zenon_H23 ]. % 1.07/1.29 exact (zenon_H2d zenon_H23). % 1.07/1.29 exact (zenon_H29 zenon_H2c). % 1.07/1.29 exact (zenon_H28 zenon_H25). % 1.07/1.29 (* end of lemma zenon_L2_ *) % 1.07/1.29 assert (zenon_L3_ : forall (zenon_TZ_p : zenon_U) (zenon_TY_q : zenon_U) (zenon_TW_o : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((rp x y)->((rp y z)->(rp x z)))))) -> (forall Z : zenon_U, ((rinvP zenon_TW_o Z)->(forall W : zenon_U, ((rinvS Z W)->(~(ca W)))))) -> (rp zenon_TY_q zenon_TZ_p) -> (rp zenon_TZ_p zenon_TW_o) -> (rs (i2003_11_14_17_19_28752) zenon_TY_q) -> False). % 1.07/1.29 do 3 intro. intros zenon_Hb zenon_H2e zenon_Ha zenon_Hd zenon_H23. % 1.07/1.29 generalize (zenon_H2e zenon_TY_q). zenon_intro zenon_H2f. % 1.07/1.29 apply (zenon_imply_s _ _ zenon_H2f); [ zenon_intro zenon_H30 | zenon_intro zenon_H22 ]. % 1.07/1.29 generalize (axiom_5 zenon_TW_o). zenon_intro zenon_H31. % 1.07/1.29 generalize (zenon_H31 zenon_TY_q). zenon_intro zenon_H32. % 1.07/1.29 apply (zenon_equiv_s _ _ zenon_H32); [ zenon_intro zenon_H30; zenon_intro zenon_Hc | zenon_intro zenon_H33; zenon_intro zenon_H20 ]. % 1.07/1.29 apply (zenon_L1_ zenon_TW_o zenon_TZ_p zenon_TY_q); trivial. % 1.07/1.29 exact (zenon_H30 zenon_H33). % 1.07/1.29 apply (zenon_L2_ zenon_TY_q); trivial. % 1.07/1.29 (* end of lemma zenon_L3_ *) % 1.07/1.29 assert (zenon_L4_ : forall (zenon_TZ_p : zenon_U) (zenon_TY_q : zenon_U) (zenon_TW_o : zenon_U) (zenon_TW_cc : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((rp x y)->((rp y z)->(rp x z)))))) -> (cc zenon_TW_cc) -> (rr zenon_TW_o zenon_TW_cc) -> (rp zenon_TY_q zenon_TZ_p) -> (rp zenon_TZ_p zenon_TW_o) -> (rs (i2003_11_14_17_19_28752) zenon_TY_q) -> False). % 1.07/1.29 do 4 intro. intros zenon_Hb zenon_H34 zenon_H35 zenon_Ha zenon_Hd zenon_H23. % 1.07/1.29 generalize (axiom_4 zenon_TW_cc). zenon_intro zenon_H37. % 1.07/1.29 apply (zenon_equiv_s _ _ zenon_H37); [ zenon_intro zenon_H3a; zenon_intro zenon_H39 | zenon_intro zenon_H34; zenon_intro zenon_H38 ]. % 1.07/1.29 exact (zenon_H3a zenon_H34). % 1.07/1.29 generalize (zenon_H38 zenon_TW_o). zenon_intro zenon_H3b. % 1.07/1.29 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H3c | zenon_intro zenon_H2e ]. % 1.07/1.29 generalize (axiom_6 zenon_TW_cc). zenon_intro zenon_H3d. % 1.07/1.29 generalize (zenon_H3d zenon_TW_o). zenon_intro zenon_H3e. % 1.07/1.29 apply (zenon_equiv_s _ _ zenon_H3e); [ zenon_intro zenon_H3c; zenon_intro zenon_H40 | zenon_intro zenon_H3f; zenon_intro zenon_H35 ]. % 1.07/1.29 exact (zenon_H40 zenon_H35). % 1.07/1.29 exact (zenon_H3c zenon_H3f). % 1.07/1.29 apply (zenon_L3_ zenon_TZ_p zenon_TY_q zenon_TW_o); trivial. % 1.07/1.29 (* end of lemma zenon_L4_ *) % 1.07/1.29 assert (zenon_L5_ : forall (zenon_TY_q : zenon_U) (zenon_TZ_p : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((rp x y)->((rp y z)->(rp x z)))))) -> (exists W : zenon_U, ((rp zenon_TZ_p W)/\(cowlThing W))) -> (forall Z : zenon_U, ((rp zenon_TY_q Z)->(exists W : zenon_U, ((rr Z W)/\(cowlThing W))))) -> (rp zenon_TY_q zenon_TZ_p) -> (forall Z : zenon_U, ((rp zenon_TY_q Z)->(forall W : zenon_U, ((rr Z W)->(cc W))))) -> (rs (i2003_11_14_17_19_28752) zenon_TY_q) -> False). % 1.07/1.29 do 2 intro. intros zenon_Hb zenon_H41 zenon_H42 zenon_Ha zenon_H43 zenon_H23. % 1.07/1.29 elim zenon_H41. zenon_intro zenon_TW_o. zenon_intro zenon_H44. % 1.07/1.29 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_Hd. zenon_intro zenon_H45. % 1.07/1.29 generalize (zenon_H42 zenon_TW_o). zenon_intro zenon_H46. % 1.07/1.29 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_Hc | zenon_intro zenon_H47 ]. % 1.07/1.29 apply (zenon_L1_ zenon_TW_o zenon_TZ_p zenon_TY_q); trivial. % 1.07/1.29 elim zenon_H47. zenon_intro zenon_TW_cc. zenon_intro zenon_H48. % 1.07/1.29 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H35. zenon_intro zenon_H49. % 1.07/1.29 generalize (zenon_H43 zenon_TW_o). zenon_intro zenon_H4a. % 1.07/1.29 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_Hc | zenon_intro zenon_H4b ]. % 1.07/1.29 apply (zenon_L1_ zenon_TW_o zenon_TZ_p zenon_TY_q); trivial. % 1.07/1.29 generalize (zenon_H4b zenon_TW_cc). zenon_intro zenon_H4c. % 1.07/1.29 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H40 | zenon_intro zenon_H34 ]. % 1.07/1.29 exact (zenon_H40 zenon_H35). % 1.07/1.29 apply (zenon_L4_ zenon_TZ_p zenon_TY_q zenon_TW_o zenon_TW_cc); trivial. % 1.07/1.29 (* end of lemma zenon_L5_ *) % 1.07/1.29 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((rp x y)->((rp y z)->(rp x z))))))); [ zenon_intro zenon_Hb | zenon_intro zenon_H4d ]. % 1.07/1.29 generalize (axiom_2 (i2003_11_14_17_19_28752)). zenon_intro zenon_H4e. % 1.07/1.29 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H26 | zenon_intro zenon_H4f ]. % 1.07/1.29 exact (zenon_H26 axiom_9). % 1.07/1.29 elim zenon_H4f. zenon_intro zenon_TY_q. zenon_intro zenon_H50. % 1.07/1.29 apply (zenon_and_s _ _ zenon_H50). zenon_intro zenon_H23. zenon_intro zenon_H51. % 1.07/1.29 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H53. zenon_intro zenon_H52. % 1.07/1.29 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H55. zenon_intro zenon_H54. % 1.07/1.29 apply (zenon_and_s _ _ zenon_H54). zenon_intro zenon_H42. zenon_intro zenon_H56. % 1.07/1.29 apply (zenon_and_s _ _ zenon_H56). zenon_intro zenon_H58. zenon_intro zenon_H57. % 1.07/1.29 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H43. zenon_intro zenon_H59. % 1.07/1.29 elim zenon_H53. zenon_intro zenon_TZ_p. zenon_intro zenon_H5a. % 1.07/1.29 apply (zenon_and_s _ _ zenon_H5a). zenon_intro zenon_Ha. zenon_intro zenon_H5b. % 1.07/1.29 generalize (zenon_H58 zenon_TZ_p). zenon_intro zenon_H5c. % 1.07/1.29 apply (zenon_imply_s _ _ zenon_H5c); [ zenon_intro zenon_H13 | zenon_intro zenon_H41 ]. % 1.07/1.29 exact (zenon_H13 zenon_Ha). % 1.07/1.29 apply (zenon_L5_ zenon_TY_q zenon_TZ_p); trivial. % 1.07/1.29 apply zenon_H4d. zenon_intro zenon_Tx_dp. apply NNPP. zenon_intro zenon_H5e. % 1.07/1.29 apply zenon_H5e. zenon_intro zenon_Ty_dr. apply NNPP. zenon_intro zenon_H60. % 1.07/1.29 apply zenon_H60. zenon_intro zenon_Tz_dt. apply NNPP. zenon_intro zenon_H62. % 1.07/1.29 apply (zenon_notimply_s _ _ zenon_H62). zenon_intro zenon_H64. zenon_intro zenon_H63. % 1.07/1.29 apply (zenon_notimply_s _ _ zenon_H63). zenon_intro zenon_H66. zenon_intro zenon_H65. % 1.07/1.29 generalize (axiom_8 zenon_Tx_dp). zenon_intro zenon_H67. % 1.07/1.29 generalize (zenon_H67 zenon_Ty_dr). zenon_intro zenon_H68. % 1.07/1.29 generalize (zenon_H68 zenon_Tz_dt). zenon_intro zenon_H69. % 1.07/1.29 apply (zenon_imply_s _ _ zenon_H69); [ zenon_intro zenon_H6b | zenon_intro zenon_H6a ]. % 1.07/1.29 apply (zenon_notand_s _ _ zenon_H6b); [ zenon_intro zenon_H6d | zenon_intro zenon_H6c ]. % 1.07/1.29 exact (zenon_H6d zenon_H64). % 1.07/1.29 exact (zenon_H6c zenon_H66). % 1.07/1.29 exact (zenon_H65 zenon_H6a). % 1.07/1.29 Qed. % 1.07/1.29 % SZS output end Proof % 1.07/1.29 (* END-PROOF *) % 1.07/1.29 nodes searched: 34986 % 1.07/1.29 max branch formulas: 2724 % 1.07/1.29 proof nodes created: 545 % 1.07/1.29 formulas created: 67825 % 1.07/1.29 %------------------------------------------------------------------------------