%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWC134+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n024.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 : Tue Jul 19 22:29:28 EDT 2022 % Result : Theorem 1.00s 1.20s % Output : Proof 1.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWC134+1 : TPTP v8.1.0. Released v2.4.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n024.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Sun Jun 12 22:48:33 EDT 2022 % 0.13/0.33 % CPUTime : % 1.00/1.20 (* PROOF-FOUND *) % 1.00/1.20 % SZS status Theorem % 1.00/1.20 (* BEGIN-PROOF *) % 1.00/1.20 % SZS output start Proof % 1.00/1.20 Theorem co1 : (forall U : zenon_U, ((ssList U)->(forall V : zenon_U, ((ssList V)->(forall W : zenon_U, ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(V = X))\/((~(U = W))\/((neq X (nil))\/(cyclefreeP V)))))))))))). % 1.00/1.20 Proof. % 1.00/1.20 assert (zenon_L1_ : forall (zenon_TX_dv : zenon_U), ((neq zenon_TX_dv (nil))<->(~(zenon_TX_dv = (nil)))) -> (~(neq zenon_TX_dv (nil))) -> (~(zenon_TX_dv = (nil))) -> False). % 1.00/1.20 do 1 intro. intros zenon_H60 zenon_H61 zenon_H62. % 1.00/1.20 apply (zenon_equiv_s _ _ zenon_H60); [ zenon_intro zenon_H61; zenon_intro zenon_H65 | zenon_intro zenon_H64; zenon_intro zenon_H62 ]. % 1.00/1.20 exact (zenon_H65 zenon_H62). % 1.00/1.20 exact (zenon_H61 zenon_H64). % 1.00/1.20 (* end of lemma zenon_L1_ *) % 1.00/1.20 assert (zenon_L2_ : forall (zenon_TX_dv : zenon_U), (ssList zenon_TX_dv) -> (~(neq zenon_TX_dv (nil))) -> (~(zenon_TX_dv = (nil))) -> False). % 1.00/1.20 do 1 intro. intros zenon_H66 zenon_H61 zenon_H62. % 1.00/1.20 generalize (ax15 zenon_TX_dv). zenon_intro zenon_H67. % 1.00/1.20 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H69 | zenon_intro zenon_H68 ]. % 1.00/1.20 exact (zenon_H69 zenon_H66). % 1.00/1.20 generalize (zenon_H68 (nil)). zenon_intro zenon_H6a. % 1.00/1.20 apply (zenon_imply_s _ _ zenon_H6a); [ zenon_intro zenon_H6b | zenon_intro zenon_H60 ]. % 1.00/1.20 exact (zenon_H6b ax17). % 1.00/1.20 apply (zenon_L1_ zenon_TX_dv); trivial. % 1.00/1.20 (* end of lemma zenon_L2_ *) % 1.00/1.20 apply NNPP. intro zenon_G. % 1.00/1.20 apply (zenon_notallex_s (fun U : zenon_U => ((ssList U)->(forall V : zenon_U, ((ssList V)->(forall W : zenon_U, ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(V = X))\/((~(U = W))\/((neq X (nil))\/(cyclefreeP V)))))))))))) zenon_G); [ zenon_intro zenon_H6c; idtac ]. % 1.00/1.20 elim zenon_H6c. zenon_intro zenon_TU_ef. zenon_intro zenon_H6e. % 1.00/1.20 apply (zenon_notimply_s _ _ zenon_H6e). zenon_intro zenon_H70. zenon_intro zenon_H6f. % 1.00/1.20 apply (zenon_notallex_s (fun V : zenon_U => ((ssList V)->(forall W : zenon_U, ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(V = X))\/((~(zenon_TU_ef = W))\/((neq X (nil))\/(cyclefreeP V)))))))))) zenon_H6f); [ zenon_intro zenon_H71; idtac ]. % 1.00/1.20 elim zenon_H71. zenon_intro zenon_TV_ek. zenon_intro zenon_H73. % 1.00/1.20 apply (zenon_notimply_s _ _ zenon_H73). zenon_intro zenon_H75. zenon_intro zenon_H74. % 1.00/1.20 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(zenon_TV_ek = X))\/((~(zenon_TU_ef = W))\/((neq X (nil))\/(cyclefreeP zenon_TV_ek)))))))) zenon_H74); [ zenon_intro zenon_H76; idtac ]. % 1.00/1.20 elim zenon_H76. zenon_intro zenon_TW_ep. zenon_intro zenon_H78. % 1.00/1.20 apply (zenon_notimply_s _ _ zenon_H78). zenon_intro zenon_H7a. zenon_intro zenon_H79. % 1.00/1.20 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~(zenon_TV_ek = X))\/((~(zenon_TU_ef = zenon_TW_ep))\/((neq X (nil))\/(cyclefreeP zenon_TV_ek)))))) zenon_H79); [ zenon_intro zenon_H7b; idtac ]. % 1.00/1.20 elim zenon_H7b. zenon_intro zenon_TX_dv. zenon_intro zenon_H7c. % 1.00/1.20 apply (zenon_notimply_s _ _ zenon_H7c). zenon_intro zenon_H66. zenon_intro zenon_H7d. % 1.00/1.20 apply (zenon_notor_s _ _ zenon_H7d). zenon_intro zenon_H7f. zenon_intro zenon_H7e. % 1.00/1.20 apply (zenon_notor_s _ _ zenon_H7e). zenon_intro zenon_H81. zenon_intro zenon_H80. % 1.00/1.20 apply (zenon_notor_s _ _ zenon_H80). zenon_intro zenon_H61. zenon_intro zenon_H82. % 1.00/1.20 apply zenon_H7f. zenon_intro zenon_H83. % 1.00/1.20 cut ((cyclefreeP (nil)) = (cyclefreeP zenon_TV_ek)). % 1.00/1.20 intro zenon_D_pnotp. % 1.00/1.20 apply zenon_H82. % 1.00/1.20 rewrite <- zenon_D_pnotp. % 1.00/1.20 exact ax60. % 1.00/1.20 cut (((nil) = zenon_TV_ek)); [idtac | apply NNPP; zenon_intro zenon_H84]. % 1.00/1.20 congruence. % 1.00/1.20 elim (classic (zenon_TV_ek = zenon_TV_ek)); [ zenon_intro zenon_H85 | zenon_intro zenon_H86 ]. % 1.00/1.20 cut ((zenon_TV_ek = zenon_TV_ek) = ((nil) = zenon_TV_ek)). % 1.00/1.20 intro zenon_D_pnotp. % 1.00/1.20 apply zenon_H84. % 1.00/1.20 rewrite <- zenon_D_pnotp. % 1.00/1.20 exact zenon_H85. % 1.00/1.20 cut ((zenon_TV_ek = zenon_TV_ek)); [idtac | apply NNPP; zenon_intro zenon_H86]. % 1.00/1.20 cut ((zenon_TV_ek = (nil))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 1.00/1.20 congruence. % 1.00/1.20 cut ((zenon_TV_ek = zenon_TX_dv) = (zenon_TV_ek = (nil))). % 1.00/1.20 intro zenon_D_pnotp. % 1.00/1.20 apply zenon_H87. % 1.00/1.20 rewrite <- zenon_D_pnotp. % 1.00/1.20 exact zenon_H83. % 1.00/1.20 cut ((zenon_TX_dv = (nil))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 1.00/1.20 cut ((zenon_TV_ek = zenon_TV_ek)); [idtac | apply NNPP; zenon_intro zenon_H86]. % 1.00/1.20 congruence. % 1.00/1.20 apply zenon_H86. apply refl_equal. % 1.00/1.20 apply (zenon_L2_ zenon_TX_dv); trivial. % 1.00/1.20 apply zenon_H86. apply refl_equal. % 1.00/1.20 apply zenon_H86. apply refl_equal. % 1.00/1.20 Qed. % 1.00/1.20 % SZS output end Proof % 1.00/1.20 (* END-PROOF *) % 1.00/1.20 nodes searched: 13172 % 1.00/1.20 max branch formulas: 4972 % 1.00/1.20 proof nodes created: 1179 % 1.00/1.20 formulas created: 84014 % 1.00/1.20 %------------------------------------------------------------------------------