%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : NUM571+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n019.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 : Mon Jul 18 15:56:57 EDT 2022 % Result : Theorem 0.52s 0.73s % Output : Proof 0.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM571+3 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.12/0.31 % Computer : n019.cluster.edu % 0.12/0.31 % Model : x86_64 x86_64 % 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.31 % Memory : 8042.1875MB % 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.31 % CPULimit : 300 % 0.12/0.31 % WCLimit : 600 % 0.12/0.31 % DateTime : Wed Jul 6 06:19:08 EDT 2022 % 0.12/0.32 % CPUTime : % 0.52/0.73 (* PROOF-FOUND *) % 0.52/0.73 % SZS status Theorem % 0.52/0.73 (* BEGIN-PROOF *) % 0.52/0.73 % SZS output start Proof % 0.52/0.73 Theorem m__ : ((((aSet0 (sdtlpdtrp0 (xN) (xi)))/\(forall W0 : zenon_U, ((aElementOf0 W0 (sdtlpdtrp0 (xN) (xi)))->(aElementOf0 W0 (szNzAzT0)))))\/(aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0)))/\(isCountable0 (sdtlpdtrp0 (xN) (xi)))). % 0.52/0.73 Proof. % 0.52/0.73 assert (zenon_L1_ : (~((xN) = (xN))) -> False). % 0.52/0.73 do 0 intro. intros zenon_H54. % 0.52/0.73 apply zenon_H54. apply refl_equal. % 0.52/0.73 (* end of lemma zenon_L1_ *) % 0.52/0.73 assert (zenon_L2_ : (~((xS) = (xS))) -> False). % 0.52/0.73 do 0 intro. intros zenon_H55. % 0.52/0.73 apply zenon_H55. apply refl_equal. % 0.52/0.73 (* end of lemma zenon_L2_ *) % 0.52/0.73 assert (zenon_L3_ : ((sdtlpdtrp0 (xN) (sz00)) = (xS)) -> ((xi) = (sz00)) -> (~((xS) = (sdtlpdtrp0 (xN) (xi)))) -> False). % 0.52/0.73 do 0 intro. intros zenon_H56 zenon_H57 zenon_H58. % 0.52/0.73 elim (classic ((sdtlpdtrp0 (xN) (xi)) = (sdtlpdtrp0 (xN) (xi)))); [ zenon_intro zenon_H59 | zenon_intro zenon_H5a ]. % 0.52/0.73 cut (((sdtlpdtrp0 (xN) (xi)) = (sdtlpdtrp0 (xN) (xi))) = ((xS) = (sdtlpdtrp0 (xN) (xi)))). % 0.52/0.73 intro zenon_D_pnotp. % 0.52/0.73 apply zenon_H58. % 0.52/0.73 rewrite <- zenon_D_pnotp. % 0.52/0.73 exact zenon_H59. % 0.52/0.73 cut (((sdtlpdtrp0 (xN) (xi)) = (sdtlpdtrp0 (xN) (xi)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 0.52/0.73 cut (((sdtlpdtrp0 (xN) (xi)) = (xS))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 0.52/0.73 congruence. % 0.52/0.73 cut (((sdtlpdtrp0 (xN) (sz00)) = (xS)) = ((sdtlpdtrp0 (xN) (xi)) = (xS))). % 0.52/0.73 intro zenon_D_pnotp. % 0.52/0.73 apply zenon_H5b. % 0.52/0.73 rewrite <- zenon_D_pnotp. % 0.52/0.73 exact zenon_H56. % 0.52/0.73 cut (((xS) = (xS))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 0.52/0.73 cut (((sdtlpdtrp0 (xN) (sz00)) = (sdtlpdtrp0 (xN) (xi)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 0.52/0.73 congruence. % 0.52/0.73 elim (classic ((sdtlpdtrp0 (xN) (xi)) = (sdtlpdtrp0 (xN) (xi)))); [ zenon_intro zenon_H59 | zenon_intro zenon_H5a ]. % 0.52/0.73 cut (((sdtlpdtrp0 (xN) (xi)) = (sdtlpdtrp0 (xN) (xi))) = ((sdtlpdtrp0 (xN) (sz00)) = (sdtlpdtrp0 (xN) (xi)))). % 0.52/0.73 intro zenon_D_pnotp. % 0.52/0.73 apply zenon_H5c. % 0.52/0.73 rewrite <- zenon_D_pnotp. % 0.52/0.73 exact zenon_H59. % 0.52/0.73 cut (((sdtlpdtrp0 (xN) (xi)) = (sdtlpdtrp0 (xN) (xi)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 0.52/0.73 cut (((sdtlpdtrp0 (xN) (xi)) = (sdtlpdtrp0 (xN) (sz00)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 0.52/0.73 congruence. % 0.52/0.73 cut (((xi) = (sz00))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 0.52/0.73 cut (((xN) = (xN))); [idtac | apply NNPP; zenon_intro zenon_H54]. % 0.52/0.73 congruence. % 0.52/0.73 apply zenon_H54. apply refl_equal. % 0.52/0.73 exact (zenon_H5e zenon_H57). % 0.52/0.73 apply zenon_H5a. apply refl_equal. % 0.52/0.73 apply zenon_H5a. apply refl_equal. % 0.52/0.73 apply zenon_H55. apply refl_equal. % 0.52/0.73 apply zenon_H5a. apply refl_equal. % 0.52/0.73 apply zenon_H5a. apply refl_equal. % 0.52/0.73 (* end of lemma zenon_L3_ *) % 0.52/0.73 assert (zenon_L4_ : (~((szNzAzT0) = (szNzAzT0))) -> False). % 0.52/0.73 do 0 intro. intros zenon_H5f. % 0.52/0.73 apply zenon_H5f. apply refl_equal. % 0.52/0.73 (* end of lemma zenon_L4_ *) % 0.52/0.73 apply NNPP. intro zenon_G. % 0.52/0.73 apply (zenon_and_s _ _ m__3435). zenon_intro zenon_H61. zenon_intro zenon_H60. % 0.52/0.73 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H63. zenon_intro zenon_H62. % 0.52/0.73 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H65. zenon_intro zenon_H64. % 0.52/0.73 apply (zenon_and_s _ _ m__3623). zenon_intro zenon_H67. zenon_intro zenon_H66. % 0.52/0.73 apply (zenon_and_s _ _ zenon_H66). zenon_intro zenon_H69. zenon_intro zenon_H68. % 0.52/0.73 apply (zenon_and_s _ _ zenon_H68). zenon_intro zenon_H56. zenon_intro zenon_H6a. % 0.52/0.73 apply (zenon_imply_s _ _ m__3702_02); [ zenon_intro zenon_H6c | zenon_intro zenon_H6b ]. % 0.52/0.73 apply zenon_H6c. zenon_intro zenon_H57. % 0.52/0.73 apply (zenon_notand_s _ _ zenon_G); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 0.52/0.73 apply (zenon_notor_s _ _ zenon_H6e). zenon_intro zenon_H70. zenon_intro zenon_H6f. % 0.52/0.73 cut ((aSubsetOf0 (xS) (szNzAzT0)) = (aSubsetOf0 (sdtlpdtrp0 (xN) (xi)) (szNzAzT0))). % 0.52/0.73 intro zenon_D_pnotp. % 0.52/0.73 apply zenon_H6f. % 0.52/0.73 rewrite <- zenon_D_pnotp. % 0.52/0.73 exact zenon_H65. % 0.52/0.73 cut (((szNzAzT0) = (szNzAzT0))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 0.52/0.73 cut (((xS) = (sdtlpdtrp0 (xN) (xi)))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 0.52/0.73 congruence. % 0.52/0.73 apply (zenon_L3_); trivial. % 0.52/0.73 apply zenon_H5f. apply refl_equal. % 0.52/0.73 cut ((isCountable0 (xS)) = (isCountable0 (sdtlpdtrp0 (xN) (xi)))). % 0.52/0.73 intro zenon_D_pnotp. % 0.52/0.73 apply zenon_H6d. % 0.52/0.73 rewrite <- zenon_D_pnotp. % 0.52/0.73 exact zenon_H64. % 0.52/0.73 cut (((xS) = (sdtlpdtrp0 (xN) (xi)))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 0.52/0.73 congruence. % 0.52/0.73 apply (zenon_L3_); trivial. % 0.52/0.73 apply (zenon_and_s _ _ zenon_H6b). zenon_intro zenon_H72. zenon_intro zenon_H71. % 0.52/0.73 apply (zenon_and_s _ _ zenon_H71). zenon_intro zenon_H74. zenon_intro zenon_H73. % 0.52/0.73 apply (zenon_and_s _ _ zenon_H73). zenon_intro zenon_H76. zenon_intro zenon_H75. % 0.52/0.73 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_H78. zenon_intro zenon_H77. % 0.52/0.73 apply (zenon_notand_s _ _ zenon_G); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 0.52/0.73 apply (zenon_notor_s _ _ zenon_H6e). zenon_intro zenon_H70. zenon_intro zenon_H6f. % 0.52/0.73 exact (zenon_H6f zenon_H78). % 0.52/0.73 exact (zenon_H6d zenon_H77). % 0.52/0.73 Qed. % 0.52/0.73 % SZS output end Proof % 0.52/0.73 (* END-PROOF *) % 0.52/0.73 nodes searched: 4189 % 0.52/0.73 max branch formulas: 1883 % 0.52/0.73 proof nodes created: 66 % 0.52/0.73 formulas created: 36527 % 0.52/0.73 %------------------------------------------------------------------------------