%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWC375+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n014.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 22:30:42 EDT 2022 % Result : Theorem 34.06s 34.22s % Output : Proof 34.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.11 % Problem : SWC375+1 : TPTP v8.1.0. Released v2.4.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n014.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 : Sat Jun 11 23:46:08 EDT 2022 % 0.12/0.33 % CPUTime : % 34.06/34.22 (* PROOF-FOUND *) % 34.06/34.22 % SZS status Theorem % 34.06/34.22 (* BEGIN-PROOF *) % 34.06/34.22 % SZS output start Proof % 34.06/34.22 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))\/((~(X = W))\/(forall Y : zenon_U, ((ssItem Y)->(((~(memberP V Y))/\(~(memberP U Y)))\/((memberP V Y)/\(memberP U Y)))))))))))))))). % 34.06/34.22 Proof. % 34.06/34.22 assert (zenon_L1_ : forall (zenon_TV_dv : zenon_U) (zenon_TW_dw : zenon_U) (zenon_TX_dx : zenon_U), (zenon_TX_dx = zenon_TW_dw) -> (zenon_TV_dv = zenon_TX_dx) -> (~(zenon_TW_dw = zenon_TV_dv)) -> False). % 34.06/34.22 do 3 intro. intros zenon_H60 zenon_H61 zenon_H62. % 34.06/34.22 elim (classic (zenon_TV_dv = zenon_TV_dv)); [ zenon_intro zenon_H66 | zenon_intro zenon_H67 ]. % 34.06/34.22 cut ((zenon_TV_dv = zenon_TV_dv) = (zenon_TW_dw = zenon_TV_dv)). % 34.06/34.22 intro zenon_D_pnotp. % 34.06/34.22 apply zenon_H62. % 34.06/34.22 rewrite <- zenon_D_pnotp. % 34.06/34.22 exact zenon_H66. % 34.06/34.22 cut ((zenon_TV_dv = zenon_TV_dv)); [idtac | apply NNPP; zenon_intro zenon_H67]. % 34.06/34.22 cut ((zenon_TV_dv = zenon_TW_dw)); [idtac | apply NNPP; zenon_intro zenon_H68]. % 34.06/34.22 congruence. % 34.06/34.22 cut ((zenon_TX_dx = zenon_TW_dw) = (zenon_TV_dv = zenon_TW_dw)). % 34.06/34.22 intro zenon_D_pnotp. % 34.06/34.22 apply zenon_H68. % 34.06/34.22 rewrite <- zenon_D_pnotp. % 34.06/34.22 exact zenon_H60. % 34.06/34.22 cut ((zenon_TW_dw = zenon_TW_dw)); [idtac | apply NNPP; zenon_intro zenon_H69]. % 34.06/34.22 cut ((zenon_TX_dx = zenon_TV_dv)); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 34.06/34.22 congruence. % 34.06/34.22 elim (classic (zenon_TV_dv = zenon_TV_dv)); [ zenon_intro zenon_H66 | zenon_intro zenon_H67 ]. % 34.06/34.22 cut ((zenon_TV_dv = zenon_TV_dv) = (zenon_TX_dx = zenon_TV_dv)). % 34.06/34.22 intro zenon_D_pnotp. % 34.06/34.22 apply zenon_H6a. % 34.06/34.22 rewrite <- zenon_D_pnotp. % 34.06/34.22 exact zenon_H66. % 34.06/34.22 cut ((zenon_TV_dv = zenon_TV_dv)); [idtac | apply NNPP; zenon_intro zenon_H67]. % 34.06/34.22 cut ((zenon_TV_dv = zenon_TX_dx)); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 34.06/34.22 congruence. % 34.06/34.22 exact (zenon_H6b zenon_H61). % 34.06/34.22 apply zenon_H67. apply refl_equal. % 34.06/34.22 apply zenon_H67. apply refl_equal. % 34.06/34.22 apply zenon_H69. apply refl_equal. % 34.06/34.22 apply zenon_H67. apply refl_equal. % 34.06/34.22 apply zenon_H67. apply refl_equal. % 34.06/34.22 (* end of lemma zenon_L1_ *) % 34.06/34.22 apply NNPP. intro zenon_G. % 34.06/34.22 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))\/((~(X = W))\/(forall Y : zenon_U, ((ssItem Y)->(((~(memberP V Y))/\(~(memberP U Y)))\/((memberP V Y)/\(memberP U Y)))))))))))))))) zenon_G); [ zenon_intro zenon_H6c; idtac ]. % 34.06/34.22 elim zenon_H6c. zenon_intro zenon_TU_ef. zenon_intro zenon_H6e. % 34.06/34.22 apply (zenon_notimply_s _ _ zenon_H6e). zenon_intro zenon_H70. zenon_intro zenon_H6f. % 34.06/34.22 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))\/((~(X = W))\/(forall Y : zenon_U, ((ssItem Y)->(((~(memberP V Y))/\(~(memberP zenon_TU_ef Y)))\/((memberP V Y)/\(memberP zenon_TU_ef Y)))))))))))))) zenon_H6f); [ zenon_intro zenon_H71; idtac ]. % 34.06/34.22 elim zenon_H71. zenon_intro zenon_TV_dv. zenon_intro zenon_H72. % 34.06/34.22 apply (zenon_notimply_s _ _ zenon_H72). zenon_intro zenon_H74. zenon_intro zenon_H73. % 34.06/34.22 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(zenon_TV_dv = X))\/((~(zenon_TU_ef = W))\/((~(X = W))\/(forall Y : zenon_U, ((ssItem Y)->(((~(memberP zenon_TV_dv Y))/\(~(memberP zenon_TU_ef Y)))\/((memberP zenon_TV_dv Y)/\(memberP zenon_TU_ef Y)))))))))))) zenon_H73); [ zenon_intro zenon_H75; idtac ]. % 34.06/34.22 elim zenon_H75. zenon_intro zenon_TW_dw. zenon_intro zenon_H76. % 34.06/34.22 apply (zenon_notimply_s _ _ zenon_H76). zenon_intro zenon_H78. zenon_intro zenon_H77. % 34.06/34.22 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~(zenon_TV_dv = X))\/((~(zenon_TU_ef = zenon_TW_dw))\/((~(X = zenon_TW_dw))\/(forall Y : zenon_U, ((ssItem Y)->(((~(memberP zenon_TV_dv Y))/\(~(memberP zenon_TU_ef Y)))\/((memberP zenon_TV_dv Y)/\(memberP zenon_TU_ef Y)))))))))) zenon_H77); [ zenon_intro zenon_H79; idtac ]. % 34.06/34.22 elim zenon_H79. zenon_intro zenon_TX_dx. zenon_intro zenon_H7a. % 34.06/34.22 apply (zenon_notimply_s _ _ zenon_H7a). zenon_intro zenon_H7c. zenon_intro zenon_H7b. % 34.06/34.22 apply (zenon_notor_s _ _ zenon_H7b). zenon_intro zenon_H7e. zenon_intro zenon_H7d. % 34.06/34.23 apply (zenon_notor_s _ _ zenon_H7d). zenon_intro zenon_H80. zenon_intro zenon_H7f. % 34.06/34.23 apply (zenon_notor_s _ _ zenon_H7f). zenon_intro zenon_H82. zenon_intro zenon_H81. % 34.06/34.23 apply zenon_H82. zenon_intro zenon_H60. % 34.06/34.23 apply zenon_H80. zenon_intro zenon_H83. % 34.06/34.23 apply zenon_H7e. zenon_intro zenon_H61. % 34.06/34.23 apply (zenon_notallex_s (fun Y : zenon_U => ((ssItem Y)->(((~(memberP zenon_TV_dv Y))/\(~(memberP zenon_TU_ef Y)))\/((memberP zenon_TV_dv Y)/\(memberP zenon_TU_ef Y))))) zenon_H81); [ zenon_intro zenon_H84; idtac ]. % 34.06/34.23 elim zenon_H84. zenon_intro zenon_TY_fd. zenon_intro zenon_H86. % 34.06/34.23 apply (zenon_notimply_s _ _ zenon_H86). zenon_intro zenon_H88. zenon_intro zenon_H87. % 34.06/34.23 apply (zenon_notor_s _ _ zenon_H87). zenon_intro zenon_H8a. zenon_intro zenon_H89. % 34.06/34.23 apply (zenon_notand_s _ _ zenon_H8a); [ zenon_intro zenon_H8c | zenon_intro zenon_H8b ]. % 34.06/34.23 apply zenon_H8c. zenon_intro zenon_H8d. % 34.06/34.23 apply (zenon_notand_s _ _ zenon_H89); [ zenon_intro zenon_H8f | zenon_intro zenon_H8e ]. % 34.06/34.23 exact (zenon_H8f zenon_H8d). % 34.06/34.23 cut ((memberP zenon_TV_dv zenon_TY_fd) = (memberP zenon_TU_ef zenon_TY_fd)). % 34.06/34.23 intro zenon_D_pnotp. % 34.06/34.23 apply zenon_H8e. % 34.06/34.23 rewrite <- zenon_D_pnotp. % 34.06/34.23 exact zenon_H8d. % 34.06/34.23 cut ((zenon_TY_fd = zenon_TY_fd)); [idtac | apply NNPP; zenon_intro zenon_H90]. % 34.06/34.23 cut ((zenon_TV_dv = zenon_TU_ef)); [idtac | apply NNPP; zenon_intro zenon_H91]. % 34.06/34.23 congruence. % 34.06/34.23 elim (classic (zenon_TU_ef = zenon_TU_ef)); [ zenon_intro zenon_H92 | zenon_intro zenon_H93 ]. % 34.06/34.23 cut ((zenon_TU_ef = zenon_TU_ef) = (zenon_TV_dv = zenon_TU_ef)). % 34.06/34.23 intro zenon_D_pnotp. % 34.06/34.23 apply zenon_H91. % 34.06/34.23 rewrite <- zenon_D_pnotp. % 34.06/34.23 exact zenon_H92. % 34.06/34.23 cut ((zenon_TU_ef = zenon_TU_ef)); [idtac | apply NNPP; zenon_intro zenon_H93]. % 34.06/34.23 cut ((zenon_TU_ef = zenon_TV_dv)); [idtac | apply NNPP; zenon_intro zenon_H94]. % 34.06/34.23 congruence. % 34.06/34.23 cut ((zenon_TU_ef = zenon_TW_dw) = (zenon_TU_ef = zenon_TV_dv)). % 34.06/34.23 intro zenon_D_pnotp. % 34.06/34.23 apply zenon_H94. % 34.06/34.23 rewrite <- zenon_D_pnotp. % 34.06/34.23 exact zenon_H83. % 34.06/34.23 cut ((zenon_TW_dw = zenon_TV_dv)); [idtac | apply NNPP; zenon_intro zenon_H62]. % 34.06/34.23 cut ((zenon_TU_ef = zenon_TU_ef)); [idtac | apply NNPP; zenon_intro zenon_H93]. % 34.06/34.23 congruence. % 34.06/34.23 apply zenon_H93. apply refl_equal. % 34.06/34.23 apply (zenon_L1_ zenon_TV_dv zenon_TW_dw zenon_TX_dx); trivial. % 34.06/34.23 apply zenon_H93. apply refl_equal. % 34.06/34.23 apply zenon_H93. apply refl_equal. % 34.06/34.23 apply zenon_H90. apply refl_equal. % 34.06/34.23 apply zenon_H8b. zenon_intro zenon_H95. % 34.06/34.23 apply (zenon_notand_s _ _ zenon_H89); [ zenon_intro zenon_H8f | zenon_intro zenon_H8e ]. % 34.06/34.23 cut ((memberP zenon_TU_ef zenon_TY_fd) = (memberP zenon_TV_dv zenon_TY_fd)). % 34.06/34.23 intro zenon_D_pnotp. % 34.06/34.23 apply zenon_H8f. % 34.06/34.23 rewrite <- zenon_D_pnotp. % 34.06/34.23 exact zenon_H95. % 34.06/34.23 cut ((zenon_TY_fd = zenon_TY_fd)); [idtac | apply NNPP; zenon_intro zenon_H90]. % 34.06/34.23 cut ((zenon_TU_ef = zenon_TV_dv)); [idtac | apply NNPP; zenon_intro zenon_H94]. % 34.06/34.23 congruence. % 34.06/34.23 cut ((zenon_TU_ef = zenon_TW_dw) = (zenon_TU_ef = zenon_TV_dv)). % 34.06/34.23 intro zenon_D_pnotp. % 34.06/34.23 apply zenon_H94. % 34.06/34.23 rewrite <- zenon_D_pnotp. % 34.06/34.23 exact zenon_H83. % 34.06/34.23 cut ((zenon_TW_dw = zenon_TV_dv)); [idtac | apply NNPP; zenon_intro zenon_H62]. % 34.06/34.23 cut ((zenon_TU_ef = zenon_TU_ef)); [idtac | apply NNPP; zenon_intro zenon_H93]. % 34.06/34.23 congruence. % 34.06/34.23 apply zenon_H93. apply refl_equal. % 34.06/34.23 apply (zenon_L1_ zenon_TV_dv zenon_TW_dw zenon_TX_dx); trivial. % 34.06/34.23 apply zenon_H90. apply refl_equal. % 34.06/34.23 exact (zenon_H8e zenon_H95). % 34.06/34.23 Qed. % 34.06/34.23 % SZS output end Proof % 34.06/34.23 (* END-PROOF *) % 34.06/34.23 nodes searched: 353329 % 34.06/34.23 max branch formulas: 18317 % 34.06/34.23 proof nodes created: 28962 % 34.06/34.23 formulas created: 1647988 % 34.06/34.23 %------------------------------------------------------------------------------