%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWV077+1 : TPTP v8.1.0. Bugfixed v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n032.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 : Wed Jul 20 23:02:53 EDT 2022 % Result : Theorem 0.13s 0.40s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : SWV077+1 : TPTP v8.1.0. Bugfixed v3.3.0. % 0.00/0.09 % Command : run_zenon %s %d % 0.09/0.29 % Computer : n032.cluster.edu % 0.09/0.29 % Model : x86_64 x86_64 % 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.29 % Memory : 8042.1875MB % 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.29 % CPULimit : 300 % 0.09/0.29 % WCLimit : 600 % 0.09/0.29 % DateTime : Wed Jun 15 15:41:29 EDT 2022 % 0.09/0.29 % CPUTime : % 0.13/0.40 (* PROOF-FOUND *) % 0.13/0.40 % SZS status Theorem % 0.13/0.40 (* BEGIN-PROOF *) % 0.13/0.40 % SZS output start Proof % 0.13/0.40 Theorem cl5_nebula_array_0018 : (((leq (n0) (pv31))/\(leq (pv31) (minus (n5) (n1))))->((leq (n0) (pv31))/\((leq (pv31) (minus (n5) (n1)))/\(((~((n0) = (pv40)))->((leq (n0) (pv31))/\(leq (pv31) (minus (n5) (n1)))))/\(((n0) = (pv40))->(true)))))). % 0.13/0.40 Proof. % 0.13/0.40 assert (zenon_L1_ : (gt (succ (pv31)) (n0)) -> (~(leq (n0) (pv31))) -> False). % 0.13/0.40 do 0 intro. intros zenon_H55 zenon_H56. % 0.13/0.40 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H57. % 0.13/0.40 generalize (zenon_H57 (pv31)). zenon_intro zenon_H58. % 0.13/0.40 apply (zenon_equiv_s _ _ zenon_H58); [ zenon_intro zenon_H56; zenon_intro zenon_H5a | zenon_intro zenon_H59; zenon_intro zenon_H55 ]. % 0.13/0.40 exact (zenon_H5a zenon_H55). % 0.13/0.40 exact (zenon_H56 zenon_H59). % 0.13/0.40 (* end of lemma zenon_L1_ *) % 0.13/0.40 assert (zenon_L2_ : (gt (succ (minus (n5) (n1))) (pv31)) -> (~(leq (pv31) (minus (n5) (n1)))) -> False). % 0.13/0.40 do 0 intro. intros zenon_H5b zenon_H5c. % 0.13/0.40 generalize (leq_succ_gt_equiv (pv31)). zenon_intro zenon_H5d. % 0.13/0.40 generalize (zenon_H5d (minus (n5) (n1))). zenon_intro zenon_H5e. % 0.13/0.40 apply (zenon_equiv_s _ _ zenon_H5e); [ zenon_intro zenon_H5c; zenon_intro zenon_H60 | zenon_intro zenon_H5f; zenon_intro zenon_H5b ]. % 0.13/0.40 exact (zenon_H60 zenon_H5b). % 0.13/0.40 exact (zenon_H5c zenon_H5f). % 0.13/0.40 (* end of lemma zenon_L2_ *) % 0.13/0.40 apply NNPP. intro zenon_G. % 0.13/0.40 apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H62. zenon_intro zenon_H61. % 0.13/0.40 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H59. zenon_intro zenon_H5f. % 0.13/0.40 generalize (leq_succ_gt_equiv (n0)). zenon_intro zenon_H57. % 0.13/0.40 generalize (zenon_H57 (pv31)). zenon_intro zenon_H58. % 0.13/0.40 apply (zenon_equiv_s _ _ zenon_H58); [ zenon_intro zenon_H56; zenon_intro zenon_H5a | zenon_intro zenon_H59; zenon_intro zenon_H55 ]. % 0.13/0.40 exact (zenon_H56 zenon_H59). % 0.13/0.40 generalize (leq_succ_gt_equiv (pv31)). zenon_intro zenon_H5d. % 0.13/0.40 generalize (zenon_H5d (minus (n5) (n1))). zenon_intro zenon_H5e. % 0.13/0.40 apply (zenon_equiv_s _ _ zenon_H5e); [ zenon_intro zenon_H5c; zenon_intro zenon_H60 | zenon_intro zenon_H5f; zenon_intro zenon_H5b ]. % 0.13/0.40 exact (zenon_H5c zenon_H5f). % 0.13/0.40 apply (zenon_notand_s _ _ zenon_H61); [ zenon_intro zenon_H56 | zenon_intro zenon_H63 ]. % 0.13/0.40 apply (zenon_L1_); trivial. % 0.13/0.40 apply (zenon_notand_s _ _ zenon_H63); [ zenon_intro zenon_H5c | zenon_intro zenon_H64 ]. % 0.13/0.40 apply (zenon_L2_); trivial. % 0.13/0.40 apply (zenon_notand_s _ _ zenon_H64); [ zenon_intro zenon_H66 | zenon_intro zenon_H65 ]. % 0.13/0.40 apply (zenon_notimply_s _ _ zenon_H66). zenon_intro zenon_H68. zenon_intro zenon_H67. % 0.13/0.40 apply (zenon_notand_s _ _ zenon_H67); [ zenon_intro zenon_H56 | zenon_intro zenon_H5c ]. % 0.13/0.40 apply (zenon_L1_); trivial. % 0.13/0.40 apply (zenon_L2_); trivial. % 0.13/0.40 apply (zenon_notimply_s _ _ zenon_H65). zenon_intro zenon_H6a. zenon_intro zenon_H69. % 0.13/0.40 exact (zenon_H69 ttrue). % 0.13/0.40 Qed. % 0.13/0.40 % SZS output end Proof % 0.13/0.40 (* END-PROOF *) % 0.13/0.40 nodes searched: 12 % 0.13/0.40 max branch formulas: 88 % 0.13/0.40 proof nodes created: 12 % 0.13/0.40 formulas created: 1350 % 0.13/0.40 %------------------------------------------------------------------------------