%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL893+1 : TPTP v9.3.1. Released v5.5.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n017.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 01:33:11 PM UTC 2026 % Result : Theorem 28.94s 29.20s % Output : Proof 28.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL893+1 : TPTP v9.3.1. Released v5.5.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.08/0.34 % Computer : n017.cluster.edu % 0.08/0.34 % Model : x86_64 x86_64 % 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.34 % Memory : 8046.5625MB % 0.08/0.34 % OS : Linux 6.8.0-71-generic % 0.08/0.34 % CPULimit : 300 % 0.08/0.34 % WCLimit : 300 % 0.08/0.34 % DateTime : Sun Sep 6 00:21:22 UTC 2026 % 0.08/0.35 % CPUTime : % 28.94/29.20 (* PROOF-FOUND *) % 28.94/29.20 % SZS status Theorem % 28.94/29.20 (* BEGIN-PROOF *) % 28.94/29.20 % SZS output start Proof % 28.94/29.20 Theorem goals_15 : (forall X17 : zenon_U, (((h X17) = X17)->(X17 = (0)))). % 28.94/29.20 Proof. % 28.94/29.20 assert (zenon_L1_ : forall (zenon_TX17_s : zenon_U), ((>= (+ zenon_TX17_s (0)) zenon_TX17_s)<->(>= (0) (==> zenon_TX17_s zenon_TX17_s))) -> (~(>= (0) (==> zenon_TX17_s zenon_TX17_s))) -> ((+ zenon_TX17_s (0)) = zenon_TX17_s) -> False). % 28.94/29.20 do 1 intro. intros zenon_Hf zenon_H10 zenon_H11. % 28.94/29.20 apply (zenon_equiv_s _ _ zenon_Hf); [ zenon_intro zenon_H15; zenon_intro zenon_H10 | zenon_intro zenon_H14; zenon_intro zenon_H13 ]. % 28.94/29.20 generalize (sos_05 (+ zenon_TX17_s (0))). zenon_intro zenon_H16. % 28.94/29.20 cut ((>= (+ zenon_TX17_s (0)) (+ zenon_TX17_s (0))) = (>= (+ zenon_TX17_s (0)) zenon_TX17_s)). % 28.94/29.20 intro zenon_D_pnotp. % 28.94/29.20 apply zenon_H15. % 28.94/29.20 rewrite <- zenon_D_pnotp. % 28.94/29.20 exact zenon_H16. % 28.94/29.20 cut (((+ zenon_TX17_s (0)) = zenon_TX17_s)); [idtac | apply NNPP; zenon_intro zenon_H17]. % 28.94/29.20 cut (((+ zenon_TX17_s (0)) = (+ zenon_TX17_s (0)))); [idtac | apply NNPP; zenon_intro zenon_H18]. % 28.94/29.20 congruence. % 28.94/29.20 apply zenon_H18. apply refl_equal. % 28.94/29.20 exact (zenon_H17 zenon_H11). % 28.94/29.20 exact (zenon_H10 zenon_H13). % 28.94/29.20 (* end of lemma zenon_L1_ *) % 28.94/29.20 assert (zenon_L2_ : (~((0) = (0))) -> False). % 28.94/29.20 do 0 intro. intros zenon_H19. % 28.94/29.20 apply zenon_H19. apply refl_equal. % 28.94/29.20 (* end of lemma zenon_L2_ *) % 28.94/29.20 assert (zenon_L3_ : forall (zenon_TX17_s : zenon_U), (~((==> zenon_TX17_s zenon_TX17_s) = (==> (h zenon_TX17_s) zenon_TX17_s))) -> ((h zenon_TX17_s) = zenon_TX17_s) -> False). % 28.94/29.20 do 1 intro. intros zenon_H1a zenon_H1b. % 28.94/29.20 cut ((zenon_TX17_s = zenon_TX17_s)); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 28.94/29.20 cut ((zenon_TX17_s = (h zenon_TX17_s))); [idtac | apply NNPP; zenon_intro zenon_H1d]. % 28.94/29.20 congruence. % 28.94/29.20 apply zenon_H1d. apply sym_equal. exact zenon_H1b. % 28.94/29.20 apply zenon_H1c. apply refl_equal. % 28.94/29.20 (* end of lemma zenon_L3_ *) % 28.94/29.20 assert (zenon_L4_ : forall (zenon_TX17_s : zenon_U), ((+ zenon_TX17_s (0)) = zenon_TX17_s) -> (~(>= (0) (==> (h zenon_TX17_s) zenon_TX17_s))) -> ((h zenon_TX17_s) = zenon_TX17_s) -> False). % 28.94/29.20 do 1 intro. intros zenon_H11 zenon_H1e zenon_H1b. % 28.94/29.20 generalize (sos_08 zenon_TX17_s). zenon_intro zenon_H1f. % 28.94/29.20 generalize (zenon_H1f (0)). zenon_intro zenon_H20. % 28.94/29.20 generalize (zenon_H20 zenon_TX17_s). zenon_intro zenon_Hf. % 28.94/29.20 apply (zenon_equiv_s _ _ zenon_Hf); [ zenon_intro zenon_H15; zenon_intro zenon_H10 | zenon_intro zenon_H14; zenon_intro zenon_H13 ]. % 28.94/29.20 apply (zenon_L1_ zenon_TX17_s); trivial. % 28.94/29.20 cut ((>= (0) (==> zenon_TX17_s zenon_TX17_s)) = (>= (0) (==> (h zenon_TX17_s) zenon_TX17_s))). % 28.94/29.20 intro zenon_D_pnotp. % 28.94/29.20 apply zenon_H1e. % 28.94/29.20 rewrite <- zenon_D_pnotp. % 28.94/29.20 exact zenon_H13. % 28.94/29.20 cut (((==> zenon_TX17_s zenon_TX17_s) = (==> (h zenon_TX17_s) zenon_TX17_s))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 28.94/29.20 cut (((0) = (0))); [idtac | apply NNPP; zenon_intro zenon_H19]. % 28.94/29.20 congruence. % 28.94/29.20 apply zenon_H19. apply refl_equal. % 28.94/29.20 apply (zenon_L3_ zenon_TX17_s); trivial. % 28.94/29.20 (* end of lemma zenon_L4_ *) % 28.94/29.20 apply NNPP. intro zenon_G. % 28.94/29.20 apply (zenon_notallex_s (fun X17 : zenon_U => (((h X17) = X17)->(X17 = (0)))) zenon_G); [ zenon_intro zenon_H21; idtac ]. % 28.94/29.20 elim zenon_H21. zenon_intro zenon_TX17_s. zenon_intro zenon_H22. % 28.94/29.20 apply (zenon_notimply_s _ _ zenon_H22). zenon_intro zenon_H1b. zenon_intro zenon_H23. % 28.94/29.20 generalize (sos_07 (0)). zenon_intro zenon_H24. % 28.94/29.20 generalize (sos_09 zenon_TX17_s). zenon_intro zenon_H25. % 28.94/29.20 generalize (zenon_H24 zenon_TX17_s). zenon_intro zenon_H26. % 28.94/29.20 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 28.94/29.20 apply (zenon_notand_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 28.94/29.20 elim (classic (>= (0) (h zenon_TX17_s))); [ zenon_intro zenon_H2b | zenon_intro zenon_H2c ]. % 28.94/29.20 cut ((>= (0) (h zenon_TX17_s)) = (>= (0) zenon_TX17_s)). % 28.94/29.20 intro zenon_D_pnotp. % 28.94/29.20 apply zenon_H2a. % 28.94/29.20 rewrite <- zenon_D_pnotp. % 28.94/29.20 exact zenon_H2b. % 28.94/29.20 cut (((h zenon_TX17_s) = zenon_TX17_s)); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 28.94/29.20 cut (((0) = (0))); [idtac | apply NNPP; zenon_intro zenon_H19]. % 28.94/29.20 congruence. % 28.94/29.20 apply zenon_H19. apply refl_equal. % 28.94/29.20 exact (zenon_H2d zenon_H1b). % 28.94/29.20 generalize (sos_14 zenon_TX17_s). zenon_intro zenon_H2e. % 28.94/29.20 elim (classic ((==> (h zenon_TX17_s) zenon_TX17_s) = (h zenon_TX17_s))); [ zenon_intro zenon_H2f | zenon_intro zenon_H30 ]. % 28.94/29.23 elim (classic (>= (0) (==> (h zenon_TX17_s) zenon_TX17_s))); [ zenon_intro zenon_H31 | zenon_intro zenon_H1e ]. % 28.94/29.23 cut ((>= (0) (==> (h zenon_TX17_s) zenon_TX17_s)) = (>= (0) (h zenon_TX17_s))). % 28.94/29.23 intro zenon_D_pnotp. % 28.94/29.23 apply zenon_H2c. % 28.94/29.23 rewrite <- zenon_D_pnotp. % 28.94/29.23 exact zenon_H31. % 28.94/29.23 cut (((==> (h zenon_TX17_s) zenon_TX17_s) = (h zenon_TX17_s))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 28.94/29.23 cut (((0) = (0))); [idtac | apply NNPP; zenon_intro zenon_H19]. % 28.94/29.23 congruence. % 28.94/29.23 apply zenon_H19. apply refl_equal. % 28.94/29.23 exact (zenon_H30 zenon_H2f). % 28.94/29.23 generalize (sos_03 zenon_TX17_s). zenon_intro zenon_H11. % 28.94/29.23 apply (zenon_L4_ zenon_TX17_s); trivial. % 28.94/29.23 elim (classic ((h zenon_TX17_s) = (h zenon_TX17_s))); [ zenon_intro zenon_H32 | zenon_intro zenon_H33 ]. % 28.94/29.23 cut (((h zenon_TX17_s) = (h zenon_TX17_s)) = ((==> (h zenon_TX17_s) zenon_TX17_s) = (h zenon_TX17_s))). % 28.94/29.23 intro zenon_D_pnotp. % 28.94/29.23 apply zenon_H30. % 28.94/29.23 rewrite <- zenon_D_pnotp. % 28.94/29.23 exact zenon_H32. % 28.94/29.23 cut (((h zenon_TX17_s) = (h zenon_TX17_s))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 28.94/29.23 cut (((h zenon_TX17_s) = (==> (h zenon_TX17_s) zenon_TX17_s))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 28.94/29.23 congruence. % 28.94/29.23 exact (zenon_H34 zenon_H2e). % 28.94/29.23 apply zenon_H33. apply refl_equal. % 28.94/29.23 apply zenon_H33. apply refl_equal. % 28.94/29.23 exact (zenon_H29 zenon_H25). % 28.94/29.23 apply zenon_H23. apply sym_equal. exact zenon_H27. % 28.94/29.23 Qed. % 28.94/29.23 % SZS output end Proof % 28.94/29.23 (* END-PROOF *) % 28.94/29.23 nodes searched: 1173125 % 28.94/29.23 max branch formulas: 8785 % 28.94/29.23 proof nodes created: 3299 % 28.94/29.23 formulas created: 228399 % 28.94/29.23 %------------------------------------------------------------------------------