TSTP Solution File: SWC375+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------