TSTP Solution File: SET692+4 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET692+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n009.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 06:38:01 EDT 2022
% Result : Theorem 0.91s 1.10s
% Output : Proof 0.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET692+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n009.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 : Sun Jul 10 08:54:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.91/1.10 (* PROOF-FOUND *)
% 0.91/1.10 % SZS status Theorem
% 0.91/1.10 (* BEGIN-PROOF *)
% 0.91/1.10 % SZS output start Proof
% 0.91/1.10 Theorem thI19 : (forall A : zenon_U, (forall B : zenon_U, ((equal_set A (intersection A B))<->(subset A B)))).
% 0.91/1.10 Proof.
% 0.91/1.10 assert (zenon_L1_ : forall (zenon_TA_q : zenon_U) (zenon_TB_r : zenon_U) (zenon_TX_s : zenon_U), (~(~(member zenon_TX_s zenon_TB_r))) -> (member zenon_TX_s zenon_TA_q) -> (~(member zenon_TX_s (intersection zenon_TA_q zenon_TB_r))) -> (forall A : zenon_U, (forall B : zenon_U, ((member zenon_TX_s (intersection A B))<->((member zenon_TX_s A)/\(member zenon_TX_s B))))) -> False).
% 0.91/1.10 do 3 intro. intros zenon_Hc zenon_Hd zenon_He zenon_Hf.
% 0.91/1.10 apply zenon_Hc. zenon_intro zenon_H13.
% 0.91/1.10 generalize (zenon_Hf zenon_TA_q). zenon_intro zenon_H14.
% 0.91/1.10 generalize (zenon_H14 zenon_TB_r). zenon_intro zenon_H15.
% 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H15); [ zenon_intro zenon_He; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H16 ].
% 0.91/1.10 apply (zenon_notand_s _ _ zenon_H18); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ].
% 0.91/1.10 exact (zenon_H1a zenon_Hd).
% 0.91/1.10 exact (zenon_H19 zenon_H13).
% 0.91/1.10 exact (zenon_He zenon_H17).
% 0.91/1.10 (* end of lemma zenon_L1_ *)
% 0.91/1.10 assert (zenon_L2_ : forall (zenon_TX_s : zenon_U) (zenon_TB_r : zenon_U) (zenon_TA_q : zenon_U), (forall X : zenon_U, ((member X zenon_TA_q)->(member X zenon_TB_r))) -> (member zenon_TX_s zenon_TA_q) -> (~(member zenon_TX_s zenon_TB_r)) -> False).
% 0.91/1.10 do 3 intro. intros zenon_H1b zenon_Hd zenon_H19.
% 0.91/1.10 generalize (zenon_H1b zenon_TX_s). zenon_intro zenon_H1c.
% 0.91/1.10 apply (zenon_imply_s _ _ zenon_H1c); [ zenon_intro zenon_H1a | zenon_intro zenon_H13 ].
% 0.91/1.10 exact (zenon_H1a zenon_Hd).
% 0.91/1.10 exact (zenon_H19 zenon_H13).
% 0.91/1.10 (* end of lemma zenon_L2_ *)
% 0.91/1.10 assert (zenon_L3_ : forall (zenon_TB_r : zenon_U) (zenon_TA_q : zenon_U) (zenon_TX_bf : zenon_U), ((member zenon_TX_bf zenon_TA_q)/\(member zenon_TX_bf zenon_TB_r)) -> (~(member zenon_TX_bf zenon_TB_r)) -> False).
% 0.91/1.10 do 3 intro. intros zenon_H1d zenon_H1e.
% 0.91/1.10 apply (zenon_and_s _ _ zenon_H1d). zenon_intro zenon_H21. zenon_intro zenon_H20.
% 0.91/1.10 exact (zenon_H1e zenon_H20).
% 0.91/1.10 (* end of lemma zenon_L3_ *)
% 0.91/1.10 apply NNPP. intro zenon_G.
% 0.91/1.10 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, ((equal_set A (intersection A B))<->(subset A B)))) zenon_G); [ zenon_intro zenon_H22; idtac ].
% 0.91/1.10 elim zenon_H22. zenon_intro zenon_TA_q. zenon_intro zenon_H23.
% 0.91/1.10 apply (zenon_notallex_s (fun B : zenon_U => ((equal_set zenon_TA_q (intersection zenon_TA_q B))<->(subset zenon_TA_q B))) zenon_H23); [ zenon_intro zenon_H24; idtac ].
% 0.91/1.10 elim zenon_H24. zenon_intro zenon_TB_r. zenon_intro zenon_H25.
% 0.91/1.10 apply (zenon_notequiv_s _ _ zenon_H25); [ zenon_intro zenon_H29; zenon_intro zenon_H28 | zenon_intro zenon_H27; zenon_intro zenon_H26 ].
% 0.91/1.10 generalize (equal_set zenon_TA_q). zenon_intro zenon_H2a.
% 0.91/1.10 generalize (zenon_H2a (intersection zenon_TA_q zenon_TB_r)). zenon_intro zenon_H2b.
% 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H2b); [ zenon_intro zenon_H29; zenon_intro zenon_H2d | zenon_intro zenon_H27; zenon_intro zenon_H2c ].
% 0.91/1.10 generalize (subset zenon_TA_q). zenon_intro zenon_H2e.
% 0.91/1.10 generalize (zenon_H2e zenon_TB_r). zenon_intro zenon_H2f.
% 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H2f); [ zenon_intro zenon_H26; zenon_intro zenon_H30 | zenon_intro zenon_H28; zenon_intro zenon_H1b ].
% 0.91/1.10 exact (zenon_H26 zenon_H28).
% 0.91/1.10 apply (zenon_notand_s _ _ zenon_H2d); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ].
% 0.91/1.10 generalize (subset zenon_TA_q). zenon_intro zenon_H2e.
% 0.91/1.10 generalize (zenon_H2e (intersection zenon_TA_q zenon_TB_r)). zenon_intro zenon_H33.
% 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H32; zenon_intro zenon_H36 | zenon_intro zenon_H35; zenon_intro zenon_H34 ].
% 0.91/1.10 apply (zenon_notallex_s (fun X : zenon_U => ((member X zenon_TA_q)->(member X (intersection zenon_TA_q zenon_TB_r)))) zenon_H36); [ zenon_intro zenon_H37; idtac ].
% 0.91/1.10 elim zenon_H37. zenon_intro zenon_TX_s. zenon_intro zenon_H38.
% 0.91/1.10 apply (zenon_notimply_s _ _ zenon_H38). zenon_intro zenon_Hd. zenon_intro zenon_He.
% 0.91/1.10 generalize (difference zenon_TX_s). zenon_intro zenon_H39.
% 0.91/1.10 generalize (intersection zenon_TX_s). zenon_intro zenon_Hf.
% 0.91/1.10 generalize (zenon_H39 zenon_TB_r). zenon_intro zenon_H3a.
% 0.91/1.10 generalize (zenon_H3a zenon_TA_q). zenon_intro zenon_H3b.
% 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H3b); [ zenon_intro zenon_H3f; zenon_intro zenon_H3e | zenon_intro zenon_H3d; zenon_intro zenon_H3c ].
% 0.91/1.10 apply (zenon_notand_s _ _ zenon_H3e); [ zenon_intro zenon_H1a | zenon_intro zenon_Hc ].
% 0.91/1.10 exact (zenon_H1a zenon_Hd).
% 0.91/1.10 apply (zenon_L1_ zenon_TA_q zenon_TB_r zenon_TX_s); trivial.
% 0.91/1.10 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_Hd. zenon_intro zenon_H19.
% 0.91/1.10 apply (zenon_L2_ zenon_TX_s zenon_TB_r zenon_TA_q); trivial.
% 0.91/1.10 exact (zenon_H32 zenon_H35).
% 0.91/1.10 generalize (subset (intersection zenon_TA_q zenon_TB_r)). zenon_intro zenon_H40.
% 0.91/1.10 generalize (zenon_H40 zenon_TA_q). zenon_intro zenon_H41.
% 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H41); [ zenon_intro zenon_H31; zenon_intro zenon_H44 | zenon_intro zenon_H43; zenon_intro zenon_H42 ].
% 0.91/1.10 apply (zenon_notallex_s (fun X : zenon_U => ((member X (intersection zenon_TA_q zenon_TB_r))->(member X zenon_TA_q))) zenon_H44); [ zenon_intro zenon_H45; idtac ].
% 0.91/1.10 elim zenon_H45. zenon_intro zenon_TX_cs. zenon_intro zenon_H47.
% 0.91/1.10 apply (zenon_notimply_s _ _ zenon_H47). zenon_intro zenon_H49. zenon_intro zenon_H48.
% 0.91/1.10 generalize (intersection zenon_TX_cs). zenon_intro zenon_H4a.
% 0.91/1.10 generalize (zenon_H4a zenon_TA_q). zenon_intro zenon_H4b.
% 0.91/1.10 generalize (zenon_H4b zenon_TB_r). zenon_intro zenon_H4c.
% 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H4f; zenon_intro zenon_H4e | zenon_intro zenon_H49; zenon_intro zenon_H4d ].
% 0.91/1.10 exact (zenon_H4f zenon_H49).
% 0.91/1.10 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H51. zenon_intro zenon_H50.
% 0.91/1.10 exact (zenon_H48 zenon_H51).
% 0.91/1.10 exact (zenon_H31 zenon_H43).
% 0.91/1.10 exact (zenon_H29 zenon_H27).
% 0.91/1.10 generalize (equal_set zenon_TA_q). zenon_intro zenon_H2a.
% 0.91/1.10 generalize (zenon_H2a (intersection zenon_TA_q zenon_TB_r)). zenon_intro zenon_H2b.
% 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H2b); [ zenon_intro zenon_H29; zenon_intro zenon_H2d | zenon_intro zenon_H27; zenon_intro zenon_H2c ].
% 0.91/1.10 exact (zenon_H29 zenon_H27).
% 0.91/1.10 apply (zenon_and_s _ _ zenon_H2c). zenon_intro zenon_H35. zenon_intro zenon_H43.
% 0.91/1.10 generalize (subset zenon_TA_q). zenon_intro zenon_H2e.
% 0.91/1.10 generalize (zenon_H2e (intersection zenon_TA_q zenon_TB_r)). zenon_intro zenon_H33.
% 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H32; zenon_intro zenon_H36 | zenon_intro zenon_H35; zenon_intro zenon_H34 ].
% 0.91/1.10 exact (zenon_H32 zenon_H35).
% 0.91/1.10 generalize (subset zenon_TA_q). zenon_intro zenon_H2e.
% 0.91/1.10 generalize (zenon_H2e zenon_TB_r). zenon_intro zenon_H2f.
% 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H2f); [ zenon_intro zenon_H26; zenon_intro zenon_H30 | zenon_intro zenon_H28; zenon_intro zenon_H1b ].
% 0.91/1.10 apply (zenon_notallex_s (fun X : zenon_U => ((member X zenon_TA_q)->(member X zenon_TB_r))) zenon_H30); [ zenon_intro zenon_H52; idtac ].
% 0.91/1.10 elim zenon_H52. zenon_intro zenon_TX_bf. zenon_intro zenon_H53.
% 0.91/1.10 apply (zenon_notimply_s _ _ zenon_H53). zenon_intro zenon_H21. zenon_intro zenon_H1e.
% 0.91/1.10 generalize (intersection zenon_TX_bf). zenon_intro zenon_H54.
% 0.91/1.10 generalize (zenon_H54 zenon_TA_q). zenon_intro zenon_H55.
% 0.91/1.10 generalize (zenon_H55 zenon_TB_r). zenon_intro zenon_H56.
% 0.91/1.10 apply (zenon_equiv_s _ _ zenon_H56); [ zenon_intro zenon_H59; zenon_intro zenon_H58 | zenon_intro zenon_H57; zenon_intro zenon_H1d ].
% 0.91/1.10 generalize (zenon_H34 zenon_TX_bf). zenon_intro zenon_H5a.
% 0.91/1.10 apply (zenon_imply_s _ _ zenon_H5a); [ zenon_intro zenon_H5b | zenon_intro zenon_H57 ].
% 0.91/1.10 exact (zenon_H5b zenon_H21).
% 0.91/1.10 exact (zenon_H59 zenon_H57).
% 0.91/1.10 apply (zenon_L3_ zenon_TB_r zenon_TA_q zenon_TX_bf); trivial.
% 0.91/1.10 exact (zenon_H26 zenon_H28).
% 0.91/1.10 Qed.
% 0.91/1.10 % SZS output end Proof
% 0.91/1.10 (* END-PROOF *)
% 0.91/1.10 nodes searched: 26774
% 0.91/1.10 max branch formulas: 5616
% 0.91/1.10 proof nodes created: 881
% 0.91/1.10 formulas created: 163249
% 0.91/1.10
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