%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWC358+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n005.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 22:30:37 EDT 2022 % Result : Theorem 7.70s 7.93s % Output : Proof 7.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SWC358+1 : TPTP v8.1.0. Released v2.4.0. % 0.12/0.14 % Command : run_zenon %s %d % 0.14/0.35 % Computer : n005.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Sun Jun 12 08:53:24 EDT 2022 % 0.14/0.35 % CPUTime : % 7.70/7.93 (* PROOF-FOUND *) % 7.70/7.93 % SZS status Theorem % 7.70/7.93 (* BEGIN-PROOF *) % 7.70/7.93 % SZS output start Proof % 7.70/7.93 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 V (nil)))\/((segmentP V U)\/(((~((nil) = X))\/(~((nil) = W)))/\((~(neq W (nil)))\/(~(segmentP X W)))))))))))))))). % 7.70/7.93 Proof. % 7.70/7.93 assert (zenon_L1_ : forall (zenon_TW_dw : zenon_U) (zenon_TX_dx : zenon_U) (zenon_TU_dy : zenon_U) (zenon_TV_dz : zenon_U), (~(segmentP zenon_TV_dz zenon_TU_dy)) -> (segmentP zenon_TX_dx zenon_TW_dw) -> (zenon_TU_dy = zenon_TW_dw) -> (zenon_TV_dz = zenon_TX_dx) -> False). % 7.70/7.93 do 4 intro. intros zenon_H60 zenon_H61 zenon_H62 zenon_H63. % 7.70/7.93 cut ((segmentP zenon_TX_dx zenon_TW_dw) = (segmentP zenon_TV_dz zenon_TU_dy)). % 7.70/7.93 intro zenon_D_pnotp. % 7.70/7.93 apply zenon_H60. % 7.70/7.93 rewrite <- zenon_D_pnotp. % 7.70/7.93 exact zenon_H61. % 7.70/7.93 cut ((zenon_TW_dw = zenon_TU_dy)); [idtac | apply NNPP; zenon_intro zenon_H68]. % 7.70/7.93 cut ((zenon_TX_dx = zenon_TV_dz)); [idtac | apply NNPP; zenon_intro zenon_H69]. % 7.70/7.93 congruence. % 7.70/7.93 apply zenon_H69. apply sym_equal. exact zenon_H63. % 7.70/7.93 apply zenon_H68. apply sym_equal. exact zenon_H62. % 7.70/7.93 (* end of lemma zenon_L1_ *) % 7.70/7.93 assert (zenon_L2_ : forall (zenon_TU_dy : zenon_U) (zenon_TV_dz : zenon_U) (zenon_TW_dw : zenon_U) (zenon_TX_dx : zenon_U), (forall V : zenon_U, ((ssList V)->(forall W : zenon_U, ((ssList W)->(((segmentP zenon_TX_dx V)/\(segmentP V W))->(segmentP zenon_TX_dx W)))))) -> (ssList zenon_TW_dw) -> (segmentP zenon_TX_dx (nil)) -> (segmentP (nil) zenon_TW_dw) -> (~(segmentP zenon_TV_dz zenon_TU_dy)) -> (zenon_TU_dy = zenon_TW_dw) -> (zenon_TV_dz = zenon_TX_dx) -> False). % 7.70/7.93 do 4 intro. intros zenon_H6a zenon_H6b zenon_H6c zenon_H6d zenon_H60 zenon_H62 zenon_H63. % 7.70/7.93 generalize (zenon_H6a (nil)). zenon_intro zenon_H6e. % 7.70/7.93 apply (zenon_imply_s _ _ zenon_H6e); [ zenon_intro zenon_H70 | zenon_intro zenon_H6f ]. % 7.70/7.93 exact (zenon_H70 ax17). % 7.70/7.93 generalize (zenon_H6f zenon_TW_dw). zenon_intro zenon_H71. % 7.70/7.93 apply (zenon_imply_s _ _ zenon_H71); [ zenon_intro zenon_H73 | zenon_intro zenon_H72 ]. % 7.70/7.93 exact (zenon_H73 zenon_H6b). % 7.70/7.93 apply (zenon_imply_s _ _ zenon_H72); [ zenon_intro zenon_H74 | zenon_intro zenon_H61 ]. % 7.70/7.93 apply (zenon_notand_s _ _ zenon_H74); [ zenon_intro zenon_H76 | zenon_intro zenon_H75 ]. % 7.70/7.93 exact (zenon_H76 zenon_H6c). % 7.70/7.93 exact (zenon_H75 zenon_H6d). % 7.70/7.93 apply (zenon_L1_ zenon_TW_dw zenon_TX_dx zenon_TU_dy zenon_TV_dz); trivial. % 7.70/7.93 (* end of lemma zenon_L2_ *) % 7.70/7.93 apply NNPP. intro zenon_G. % 7.70/7.93 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 V (nil)))\/((segmentP V U)\/(((~((nil) = X))\/(~((nil) = W)))/\((~(neq W (nil)))\/(~(segmentP X W)))))))))))))))) zenon_G); [ zenon_intro zenon_H77; idtac ]. % 7.70/7.93 elim zenon_H77. zenon_intro zenon_TU_dy. zenon_intro zenon_H78. % 7.70/7.93 apply (zenon_notimply_s _ _ zenon_H78). zenon_intro zenon_H7a. zenon_intro zenon_H79. % 7.70/7.93 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_dy = W))\/((~(neq V (nil)))\/((segmentP V zenon_TU_dy)\/(((~((nil) = X))\/(~((nil) = W)))/\((~(neq W (nil)))\/(~(segmentP X W)))))))))))))) zenon_H79); [ zenon_intro zenon_H7b; idtac ]. % 7.70/7.93 elim zenon_H7b. zenon_intro zenon_TV_dz. zenon_intro zenon_H7c. % 7.70/7.93 apply (zenon_notimply_s _ _ zenon_H7c). zenon_intro zenon_H7e. zenon_intro zenon_H7d. % 7.70/7.93 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(zenon_TV_dz = X))\/((~(zenon_TU_dy = W))\/((~(neq zenon_TV_dz (nil)))\/((segmentP zenon_TV_dz zenon_TU_dy)\/(((~((nil) = X))\/(~((nil) = W)))/\((~(neq W (nil)))\/(~(segmentP X W)))))))))))) zenon_H7d); [ zenon_intro zenon_H7f; idtac ]. % 7.70/7.93 elim zenon_H7f. zenon_intro zenon_TW_dw. zenon_intro zenon_H80. % 7.70/7.93 apply (zenon_notimply_s _ _ zenon_H80). zenon_intro zenon_H6b. zenon_intro zenon_H81. % 7.70/7.93 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~(zenon_TV_dz = X))\/((~(zenon_TU_dy = zenon_TW_dw))\/((~(neq zenon_TV_dz (nil)))\/((segmentP zenon_TV_dz zenon_TU_dy)\/(((~((nil) = X))\/(~((nil) = zenon_TW_dw)))/\((~(neq zenon_TW_dw (nil)))\/(~(segmentP X zenon_TW_dw)))))))))) zenon_H81); [ zenon_intro zenon_H82; idtac ]. % 7.70/7.93 elim zenon_H82. zenon_intro zenon_TX_dx. zenon_intro zenon_H83. % 7.70/7.93 apply (zenon_notimply_s _ _ zenon_H83). zenon_intro zenon_H85. zenon_intro zenon_H84. % 7.70/7.93 apply (zenon_notor_s _ _ zenon_H84). zenon_intro zenon_H87. zenon_intro zenon_H86. % 7.70/7.93 apply (zenon_notor_s _ _ zenon_H86). zenon_intro zenon_H89. zenon_intro zenon_H88. % 7.70/7.93 apply (zenon_notor_s _ _ zenon_H88). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 7.70/7.93 apply (zenon_notor_s _ _ zenon_H8a). zenon_intro zenon_H60. zenon_intro zenon_H8c. % 7.70/7.93 apply zenon_H89. zenon_intro zenon_H62. % 7.70/7.93 apply zenon_H87. zenon_intro zenon_H63. % 7.70/7.93 apply (zenon_notand_s _ _ zenon_H8c); [ zenon_intro zenon_H8e | zenon_intro zenon_H8d ]. % 7.70/7.93 apply (zenon_notor_s _ _ zenon_H8e). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 7.70/7.93 apply zenon_H8f. zenon_intro zenon_H91. % 7.70/7.93 generalize (ax58 zenon_TW_dw). zenon_intro zenon_H92. % 7.70/7.93 apply (zenon_imply_s _ _ zenon_H92); [ zenon_intro zenon_H73 | zenon_intro zenon_H93 ]. % 7.70/7.93 exact (zenon_H73 zenon_H6b). % 7.70/7.93 apply (zenon_equiv_s _ _ zenon_H93); [ zenon_intro zenon_H75; zenon_intro zenon_H94 | zenon_intro zenon_H6d; zenon_intro zenon_H91 ]. % 7.70/7.93 exact (zenon_H94 zenon_H91). % 7.70/7.93 generalize (ax7 zenon_TX_dx). zenon_intro zenon_H95. % 7.70/7.93 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H97 | zenon_intro zenon_H96 ]. % 7.70/7.93 exact (zenon_H97 zenon_H85). % 7.70/7.93 generalize (ax53 zenon_TX_dx). zenon_intro zenon_H98. % 7.70/7.93 apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H97 | zenon_intro zenon_H6a ]. % 7.70/7.93 exact (zenon_H97 zenon_H85). % 7.70/7.93 generalize (zenon_H96 (nil)). zenon_intro zenon_H99. % 7.70/7.93 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H70 | zenon_intro zenon_H9a ]. % 7.70/7.93 exact (zenon_H70 ax17). % 7.70/7.93 apply (zenon_equiv_s _ _ zenon_H9a); [ zenon_intro zenon_H76; zenon_intro zenon_H9c | zenon_intro zenon_H6c; zenon_intro zenon_H9b ]. % 7.70/7.93 generalize (ax57 zenon_TX_dx). zenon_intro zenon_H9d. % 7.70/7.93 apply (zenon_imply_s _ _ zenon_H9d); [ zenon_intro zenon_H97 | zenon_intro zenon_H6c ]. % 7.70/7.93 exact (zenon_H97 zenon_H85). % 7.70/7.93 exact (zenon_H76 zenon_H6c). % 7.70/7.93 apply (zenon_L2_ zenon_TU_dy zenon_TV_dz zenon_TW_dw zenon_TX_dx); trivial. % 7.70/7.93 apply (zenon_notor_s _ _ zenon_H8d). zenon_intro zenon_H9f. zenon_intro zenon_H9e. % 7.70/7.93 apply zenon_H9e. zenon_intro zenon_H61. % 7.70/7.93 apply (zenon_L1_ zenon_TW_dw zenon_TX_dx zenon_TU_dy zenon_TV_dz); trivial. % 7.70/7.93 Qed. % 7.70/7.93 % SZS output end Proof % 7.70/7.93 (* END-PROOF *) % 7.70/7.93 nodes searched: 101183 % 7.70/7.93 max branch formulas: 9836 % 7.70/7.93 proof nodes created: 7619 % 7.70/7.93 formulas created: 470656 % 7.70/7.93 %------------------------------------------------------------------------------