TSTP Solution File: SEU321+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SEU321+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : Tue Jul 19 16:01:12 EDT 2022
% Result : Theorem 1.38s 1.55s
% Output : Proof 1.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU321+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n019.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 06:32:24 EDT 2022
% 0.20/0.34 % CPUTime :
% 1.38/1.55 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski
% 1.38/1.55 (* PROOF-FOUND *)
% 1.38/1.55 % SZS status Theorem
% 1.38/1.55 (* BEGIN-PROOF *)
% 1.38/1.55 % SZS output start Proof
% 1.38/1.55 Theorem l40_tops_1 : (forall A : zenon_U, (((~(empty_carrier A))/\(one_sorted_str A))->(forall B : zenon_U, ((element B (powerset (the_carrier A)))->(forall C : zenon_U, ((element C (the_carrier A))->((in C (subset_complement (the_carrier A) B))<->(~(in C B))))))))).
% 1.38/1.55 Proof.
% 1.38/1.55 assert (zenon_L1_ : forall (zenon_TA_bq : zenon_U), (forall x : zenon_U, (subset x x)) -> (~(subset (the_carrier zenon_TA_bq) (empty_set))) -> ((the_carrier zenon_TA_bq) = (empty_set)) -> False).
% 1.38/1.55 do 1 intro. intros zenon_H27 zenon_H28 zenon_H29.
% 1.38/1.55 generalize (zenon_H27 (the_carrier zenon_TA_bq)). zenon_intro zenon_H2b.
% 1.38/1.55 cut ((subset (the_carrier zenon_TA_bq) (the_carrier zenon_TA_bq)) = (subset (the_carrier zenon_TA_bq) (empty_set))).
% 1.38/1.55 intro zenon_D_pnotp.
% 1.38/1.55 apply zenon_H28.
% 1.38/1.55 rewrite <- zenon_D_pnotp.
% 1.38/1.55 exact zenon_H2b.
% 1.38/1.55 cut (((the_carrier zenon_TA_bq) = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_H2c].
% 1.38/1.55 cut (((the_carrier zenon_TA_bq) = (the_carrier zenon_TA_bq))); [idtac | apply NNPP; zenon_intro zenon_H2d].
% 1.38/1.55 congruence.
% 1.38/1.55 apply zenon_H2d. apply refl_equal.
% 1.38/1.55 exact (zenon_H2c zenon_H29).
% 1.38/1.55 (* end of lemma zenon_L1_ *)
% 1.38/1.55 assert (zenon_L2_ : forall (zenon_TA_bq : zenon_U), (forall x : zenon_U, (subset x x)) -> (~(element (the_carrier zenon_TA_bq) (powerset (empty_set)))) -> ((the_carrier zenon_TA_bq) = (empty_set)) -> False).
% 1.38/1.55 do 1 intro. intros zenon_H27 zenon_H2e zenon_H29.
% 1.38/1.55 generalize (t3_subset (the_carrier zenon_TA_bq)). zenon_intro zenon_H2f.
% 1.38/1.55 generalize (zenon_H2f (empty_set)). zenon_intro zenon_H30.
% 1.38/1.55 apply (zenon_equiv_s _ _ zenon_H30); [ zenon_intro zenon_H2e; zenon_intro zenon_H28 | zenon_intro zenon_H32; zenon_intro zenon_H31 ].
% 1.38/1.55 apply (zenon_L1_ zenon_TA_bq); trivial.
% 1.38/1.55 exact (zenon_H2e zenon_H32).
% 1.38/1.55 (* end of lemma zenon_L2_ *)
% 1.38/1.55 assert (zenon_L3_ : forall (zenon_TC_ce : zenon_U) (zenon_TB_cf : zenon_U) (zenon_TA_bq : zenon_U), (forall B : zenon_U, ((element B (powerset (the_carrier zenon_TA_bq)))->(forall C : zenon_U, ((element C (the_carrier zenon_TA_bq))->((~(in C B))->(in C (subset_complement (the_carrier zenon_TA_bq) B))))))) -> (element zenon_TB_cf (powerset (the_carrier zenon_TA_bq))) -> (element zenon_TC_ce (the_carrier zenon_TA_bq)) -> (~(in zenon_TC_ce zenon_TB_cf)) -> (~(in zenon_TC_ce (subset_complement (the_carrier zenon_TA_bq) zenon_TB_cf))) -> False).
% 1.38/1.55 do 3 intro. intros zenon_H33 zenon_H34 zenon_H35 zenon_H36 zenon_H37.
% 1.38/1.55 generalize (zenon_H33 zenon_TB_cf). zenon_intro zenon_H3a.
% 1.38/1.55 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ].
% 1.38/1.55 exact (zenon_H3c zenon_H34).
% 1.38/1.55 generalize (zenon_H3b zenon_TC_ce). zenon_intro zenon_H3d.
% 1.38/1.55 apply (zenon_imply_s _ _ zenon_H3d); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ].
% 1.38/1.55 exact (zenon_H3f zenon_H35).
% 1.38/1.55 apply (zenon_imply_s _ _ zenon_H3e); [ zenon_intro zenon_H41 | zenon_intro zenon_H40 ].
% 1.38/1.55 exact (zenon_H41 zenon_H36).
% 1.38/1.55 exact (zenon_H37 zenon_H40).
% 1.38/1.55 (* end of lemma zenon_L3_ *)
% 1.38/1.55 apply NNPP. intro zenon_G.
% 1.38/1.55 elim (classic (forall x : zenon_U, (subset x x))); [ zenon_intro zenon_H27 | zenon_intro zenon_H42 ].
% 1.38/1.55 apply (zenon_and_s _ _ fc6_membered). zenon_intro zenon_H44. zenon_intro zenon_H43.
% 1.38/1.55 apply (zenon_notallex_s (fun A : zenon_U => (((~(empty_carrier A))/\(one_sorted_str A))->(forall B : zenon_U, ((element B (powerset (the_carrier A)))->(forall C : zenon_U, ((element C (the_carrier A))->((in C (subset_complement (the_carrier A) B))<->(~(in C B))))))))) zenon_G); [ zenon_intro zenon_H45; idtac ].
% 1.38/1.55 elim zenon_H45. zenon_intro zenon_TA_bq. zenon_intro zenon_H46.
% 1.38/1.55 apply (zenon_notimply_s _ _ zenon_H46). zenon_intro zenon_H48. zenon_intro zenon_H47.
% 1.38/1.55 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H4a. zenon_intro zenon_H49.
% 1.38/1.55 apply (zenon_notallex_s (fun B : zenon_U => ((element B (powerset (the_carrier zenon_TA_bq)))->(forall C : zenon_U, ((element C (the_carrier zenon_TA_bq))->((in C (subset_complement (the_carrier zenon_TA_bq) B))<->(~(in C B))))))) zenon_H47); [ zenon_intro zenon_H4b; idtac ].
% 1.38/1.55 elim zenon_H4b. zenon_intro zenon_TB_cf. zenon_intro zenon_H4c.
% 1.38/1.55 apply (zenon_notimply_s _ _ zenon_H4c). zenon_intro zenon_H34. zenon_intro zenon_H4d.
% 1.38/1.55 apply (zenon_notallex_s (fun C : zenon_U => ((element C (the_carrier zenon_TA_bq))->((in C (subset_complement (the_carrier zenon_TA_bq) zenon_TB_cf))<->(~(in C zenon_TB_cf))))) zenon_H4d); [ zenon_intro zenon_H4e; idtac ].
% 1.38/1.55 elim zenon_H4e. zenon_intro zenon_TC_ce. zenon_intro zenon_H4f.
% 1.38/1.55 apply (zenon_notimply_s _ _ zenon_H4f). zenon_intro zenon_H35. zenon_intro zenon_H50.
% 1.38/1.55 apply (zenon_notequiv_s _ _ zenon_H50); [ zenon_intro zenon_H37; zenon_intro zenon_H36 | zenon_intro zenon_H40; zenon_intro zenon_H41 ].
% 1.38/1.55 generalize (t2_subset zenon_TC_ce). zenon_intro zenon_H51.
% 1.38/1.55 generalize (t5_subset zenon_TC_ce). zenon_intro zenon_H52.
% 1.38/1.55 generalize (t50_subset_1 (the_carrier zenon_TA_bq)). zenon_intro zenon_H53.
% 1.38/1.55 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H54 | zenon_intro zenon_H33 ].
% 1.38/1.55 apply zenon_H54. zenon_intro zenon_H29.
% 1.38/1.55 generalize (fc1_struct_0 zenon_TA_bq). zenon_intro zenon_H55.
% 1.38/1.55 apply (zenon_imply_s _ _ zenon_H55); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ].
% 1.38/1.55 apply (zenon_notand_s _ _ zenon_H57); [ zenon_intro zenon_H59 | zenon_intro zenon_H58 ].
% 1.38/1.55 exact (zenon_H59 zenon_H4a).
% 1.38/1.55 exact (zenon_H58 zenon_H49).
% 1.38/1.55 generalize (zenon_H51 (the_carrier zenon_TA_bq)). zenon_intro zenon_H5a.
% 1.38/1.55 apply (zenon_imply_s _ _ zenon_H5a); [ zenon_intro zenon_H3f | zenon_intro zenon_H5b ].
% 1.38/1.55 exact (zenon_H3f zenon_H35).
% 1.38/1.55 apply (zenon_or_s _ _ zenon_H5b); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ].
% 1.38/1.55 exact (zenon_H56 zenon_H5d).
% 1.38/1.55 generalize (zenon_H52 (the_carrier zenon_TA_bq)). zenon_intro zenon_H5e.
% 1.38/1.55 generalize (zenon_H5e (empty_set)). zenon_intro zenon_H5f.
% 1.38/1.55 apply (zenon_notand_s _ _ zenon_H5f); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ].
% 1.38/1.55 exact (zenon_H61 zenon_H5c).
% 1.38/1.55 apply (zenon_notand_s _ _ zenon_H60); [ zenon_intro zenon_H2e | zenon_intro zenon_H62 ].
% 1.38/1.55 apply (zenon_L2_ zenon_TA_bq); trivial.
% 1.38/1.55 exact (zenon_H62 zenon_H44).
% 1.38/1.55 apply (zenon_L3_ zenon_TC_ce zenon_TB_cf zenon_TA_bq); trivial.
% 1.38/1.55 apply zenon_H41. zenon_intro zenon_H63.
% 1.38/1.55 generalize (t54_subset_1 (the_carrier zenon_TA_bq)). zenon_intro zenon_H64.
% 1.38/1.55 generalize (zenon_H64 zenon_TC_ce). zenon_intro zenon_H65.
% 1.38/1.55 generalize (zenon_H65 zenon_TB_cf). zenon_intro zenon_H66.
% 1.38/1.55 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_H3c | zenon_intro zenon_H67 ].
% 1.38/1.55 exact (zenon_H3c zenon_H34).
% 1.38/1.55 apply (zenon_notand_s _ _ zenon_H67); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ].
% 1.38/1.55 exact (zenon_H37 zenon_H40).
% 1.38/1.55 exact (zenon_H36 zenon_H63).
% 1.38/1.55 apply zenon_H42. zenon_intro zenon_Tx_ea. apply NNPP. zenon_intro zenon_H69.
% 1.38/1.55 generalize (reflexivity_r1_tarski zenon_Tx_ea). zenon_intro zenon_H0.
% 1.38/1.55 generalize (zenon_H0 zenon_E). zenon_intro zenon_H6a.
% 1.38/1.55 exact (zenon_H69 zenon_H6a).
% 1.38/1.55 Qed.
% 1.38/1.55 % SZS output end Proof
% 1.38/1.55 (* END-PROOF *)
% 1.38/1.55 nodes searched: 34311
% 1.38/1.55 max branch formulas: 2685
% 1.38/1.55 proof nodes created: 2376
% 1.38/1.55 formulas created: 84365
% 1.38/1.55
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