TSTP Solution File: SEU189+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SEU189+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n021.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 16:00:06 EDT 2022
% Result : Theorem 0.20s 0.52s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU189+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 20 11:14:18 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.52 (* PROOF-FOUND *)
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52 (* BEGIN-PROOF *)
% 0.20/0.52 % SZS output start Proof
% 0.20/0.52 Theorem t65_relat_1 : (forall A : zenon_U, ((relation A)->(((relation_dom A) = (empty_set))<->((relation_rng A) = (empty_set))))).
% 0.20/0.52 Proof.
% 0.20/0.52 assert (zenon_L1_ : (~((empty_set) = (empty_set))) -> False).
% 0.20/0.52 do 0 intro. intros zenon_H16.
% 0.20/0.52 apply zenon_H16. apply refl_equal.
% 0.20/0.52 (* end of lemma zenon_L1_ *)
% 0.20/0.52 apply NNPP. intro zenon_G.
% 0.20/0.52 apply (zenon_notallex_s (fun A : zenon_U => ((relation A)->(((relation_dom A) = (empty_set))<->((relation_rng A) = (empty_set))))) zenon_G); [ zenon_intro zenon_H17; idtac ].
% 0.20/0.52 elim zenon_H17. zenon_intro zenon_TA_y. zenon_intro zenon_H19.
% 0.20/0.52 apply (zenon_notimply_s _ _ zenon_H19). zenon_intro zenon_H1b. zenon_intro zenon_H1a.
% 0.20/0.52 apply (zenon_and_s _ _ t60_relat_1). zenon_intro zenon_H1d. zenon_intro zenon_H1c.
% 0.20/0.52 apply (zenon_notequiv_s _ _ zenon_H1a); [ zenon_intro zenon_H21; zenon_intro zenon_H20 | zenon_intro zenon_H1f; zenon_intro zenon_H1e ].
% 0.20/0.52 cut (((relation_dom (empty_set)) = (empty_set)) = ((relation_dom zenon_TA_y) = (empty_set))).
% 0.20/0.52 intro zenon_D_pnotp.
% 0.20/0.52 apply zenon_H21.
% 0.20/0.52 rewrite <- zenon_D_pnotp.
% 0.20/0.52 exact zenon_H1d.
% 0.20/0.52 cut (((empty_set) = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_H16].
% 0.20/0.52 cut (((relation_dom (empty_set)) = (relation_dom zenon_TA_y))); [idtac | apply NNPP; zenon_intro zenon_H22].
% 0.20/0.52 congruence.
% 0.20/0.52 elim (classic ((relation_dom zenon_TA_y) = (relation_dom zenon_TA_y))); [ zenon_intro zenon_H23 | zenon_intro zenon_H24 ].
% 0.20/0.52 cut (((relation_dom zenon_TA_y) = (relation_dom zenon_TA_y)) = ((relation_dom (empty_set)) = (relation_dom zenon_TA_y))).
% 0.20/0.52 intro zenon_D_pnotp.
% 0.20/0.52 apply zenon_H22.
% 0.20/0.52 rewrite <- zenon_D_pnotp.
% 0.20/0.52 exact zenon_H23.
% 0.20/0.52 cut (((relation_dom zenon_TA_y) = (relation_dom zenon_TA_y))); [idtac | apply NNPP; zenon_intro zenon_H24].
% 0.20/0.52 cut (((relation_dom zenon_TA_y) = (relation_dom (empty_set)))); [idtac | apply NNPP; zenon_intro zenon_H25].
% 0.20/0.52 congruence.
% 0.20/0.52 cut ((zenon_TA_y = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_H26].
% 0.20/0.52 congruence.
% 0.20/0.52 generalize (t64_relat_1 zenon_TA_y). zenon_intro zenon_H27.
% 0.20/0.52 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ].
% 0.20/0.52 exact (zenon_H29 zenon_H1b).
% 0.20/0.52 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ].
% 0.20/0.52 apply (zenon_notor_s _ _ zenon_H2b). zenon_intro zenon_H21. zenon_intro zenon_H1e.
% 0.20/0.52 exact (zenon_H1e zenon_H20).
% 0.20/0.52 exact (zenon_H26 zenon_H2a).
% 0.20/0.52 apply zenon_H24. apply refl_equal.
% 0.20/0.52 apply zenon_H24. apply refl_equal.
% 0.20/0.52 apply zenon_H16. apply refl_equal.
% 0.20/0.52 cut (((relation_rng (empty_set)) = (empty_set)) = ((relation_rng zenon_TA_y) = (empty_set))).
% 0.20/0.52 intro zenon_D_pnotp.
% 0.20/0.52 apply zenon_H1e.
% 0.20/0.52 rewrite <- zenon_D_pnotp.
% 0.20/0.52 exact zenon_H1c.
% 0.20/0.52 cut (((empty_set) = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_H16].
% 0.20/0.52 cut (((relation_rng (empty_set)) = (relation_rng zenon_TA_y))); [idtac | apply NNPP; zenon_intro zenon_H2c].
% 0.20/0.52 congruence.
% 0.20/0.52 elim (classic ((relation_rng zenon_TA_y) = (relation_rng zenon_TA_y))); [ zenon_intro zenon_H2d | zenon_intro zenon_H2e ].
% 0.20/0.52 cut (((relation_rng zenon_TA_y) = (relation_rng zenon_TA_y)) = ((relation_rng (empty_set)) = (relation_rng zenon_TA_y))).
% 0.20/0.52 intro zenon_D_pnotp.
% 0.20/0.52 apply zenon_H2c.
% 0.20/0.52 rewrite <- zenon_D_pnotp.
% 0.20/0.52 exact zenon_H2d.
% 0.20/0.52 cut (((relation_rng zenon_TA_y) = (relation_rng zenon_TA_y))); [idtac | apply NNPP; zenon_intro zenon_H2e].
% 0.20/0.52 cut (((relation_rng zenon_TA_y) = (relation_rng (empty_set)))); [idtac | apply NNPP; zenon_intro zenon_H2f].
% 0.20/0.52 congruence.
% 0.20/0.52 cut ((zenon_TA_y = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_H26].
% 0.20/0.52 congruence.
% 0.20/0.52 generalize (t64_relat_1 zenon_TA_y). zenon_intro zenon_H27.
% 0.20/0.52 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ].
% 0.20/0.52 exact (zenon_H29 zenon_H1b).
% 0.20/0.52 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ].
% 0.20/0.52 apply (zenon_notor_s _ _ zenon_H2b). zenon_intro zenon_H21. zenon_intro zenon_H1e.
% 0.20/0.52 exact (zenon_H21 zenon_H1f).
% 0.20/0.52 exact (zenon_H26 zenon_H2a).
% 0.20/0.52 apply zenon_H2e. apply refl_equal.
% 0.20/0.52 apply zenon_H2e. apply refl_equal.
% 0.20/0.52 apply zenon_H16. apply refl_equal.
% 0.20/0.52 Qed.
% 0.20/0.52 % SZS output end Proof
% 0.20/0.52 (* END-PROOF *)
% 0.20/0.52 nodes searched: 167
% 0.20/0.52 max branch formulas: 111
% 0.20/0.52 proof nodes created: 21
% 0.20/0.52 formulas created: 828
% 0.20/0.52
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