TSTP Solution File: SET693+4 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET693+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n023.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 0.47s 0.64s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET693+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n023.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 : Mon Jul 11 06:14:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.47/0.64 (* PROOF-FOUND *)
% 0.47/0.64 % SZS status Theorem
% 0.47/0.64 (* BEGIN-PROOF *)
% 0.47/0.64 % SZS output start Proof
% 0.47/0.64 Theorem thI20 : (forall A : zenon_U, (forall B : zenon_U, ((equal_set A (union A B))<->(subset B A)))).
% 0.47/0.64 Proof.
% 0.47/0.64 apply NNPP. intro zenon_G.
% 0.47/0.64 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, ((equal_set A (union A B))<->(subset B A)))) zenon_G); [ zenon_intro zenon_Hc; idtac ].
% 0.47/0.64 elim zenon_Hc. zenon_intro zenon_TA_n. zenon_intro zenon_He.
% 0.47/0.64 apply (zenon_notallex_s (fun B : zenon_U => ((equal_set zenon_TA_n (union zenon_TA_n B))<->(subset B zenon_TA_n))) zenon_He); [ zenon_intro zenon_Hf; idtac ].
% 0.47/0.64 elim zenon_Hf. zenon_intro zenon_TB_q. zenon_intro zenon_H11.
% 0.47/0.64 apply (zenon_notequiv_s _ _ zenon_H11); [ zenon_intro zenon_H15; zenon_intro zenon_H14 | zenon_intro zenon_H13; zenon_intro zenon_H12 ].
% 0.47/0.64 generalize (equal_set zenon_TA_n). zenon_intro zenon_H16.
% 0.47/0.64 generalize (zenon_H16 (union zenon_TA_n zenon_TB_q)). zenon_intro zenon_H17.
% 0.47/0.64 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H15; zenon_intro zenon_H19 | zenon_intro zenon_H13; zenon_intro zenon_H18 ].
% 0.47/0.64 generalize (subset zenon_TB_q). zenon_intro zenon_H1a.
% 0.47/0.64 generalize (zenon_H1a zenon_TA_n). zenon_intro zenon_H1b.
% 0.47/0.64 apply (zenon_equiv_s _ _ zenon_H1b); [ zenon_intro zenon_H12; zenon_intro zenon_H1d | zenon_intro zenon_H14; zenon_intro zenon_H1c ].
% 0.47/0.64 exact (zenon_H12 zenon_H14).
% 0.47/0.64 apply (zenon_notand_s _ _ zenon_H19); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ].
% 0.47/0.64 generalize (subset zenon_TA_n). zenon_intro zenon_H20.
% 0.47/0.64 generalize (zenon_H20 (union zenon_TA_n zenon_TB_q)). zenon_intro zenon_H21.
% 0.47/0.64 apply (zenon_equiv_s _ _ zenon_H21); [ zenon_intro zenon_H1f; zenon_intro zenon_H24 | zenon_intro zenon_H23; zenon_intro zenon_H22 ].
% 0.47/0.64 apply (zenon_notallex_s (fun X : zenon_U => ((member X zenon_TA_n)->(member X (union zenon_TA_n zenon_TB_q)))) zenon_H24); [ zenon_intro zenon_H25; idtac ].
% 0.47/0.64 elim zenon_H25. zenon_intro zenon_TX_bm. zenon_intro zenon_H27.
% 0.47/0.64 apply (zenon_notimply_s _ _ zenon_H27). zenon_intro zenon_H29. zenon_intro zenon_H28.
% 0.47/0.64 generalize (union zenon_TX_bm). zenon_intro zenon_H2a.
% 0.47/0.64 generalize (zenon_H2a zenon_TA_n). zenon_intro zenon_H2b.
% 0.47/0.64 generalize (zenon_H2b zenon_TB_q). zenon_intro zenon_H2c.
% 0.47/0.64 apply (zenon_equiv_s _ _ zenon_H2c); [ zenon_intro zenon_H28; zenon_intro zenon_H2f | zenon_intro zenon_H2e; zenon_intro zenon_H2d ].
% 0.47/0.64 apply (zenon_notor_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30.
% 0.47/0.64 exact (zenon_H31 zenon_H29).
% 0.47/0.64 exact (zenon_H28 zenon_H2e).
% 0.47/0.64 exact (zenon_H1f zenon_H23).
% 0.47/0.64 generalize (subset (union zenon_TA_n zenon_TB_q)). zenon_intro zenon_H32.
% 0.47/0.64 generalize (zenon_H32 zenon_TA_n). zenon_intro zenon_H33.
% 0.47/0.64 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H1e; zenon_intro zenon_H36 | zenon_intro zenon_H35; zenon_intro zenon_H34 ].
% 0.47/0.64 apply (zenon_notallex_s (fun X : zenon_U => ((member X (union zenon_TA_n zenon_TB_q))->(member X zenon_TA_n))) zenon_H36); [ zenon_intro zenon_H37; idtac ].
% 0.47/0.64 elim zenon_H37. zenon_intro zenon_TX_ce. zenon_intro zenon_H39.
% 0.47/0.64 apply (zenon_notimply_s _ _ zenon_H39). zenon_intro zenon_H3b. zenon_intro zenon_H3a.
% 0.47/0.64 generalize (union zenon_TX_ce). zenon_intro zenon_H3c.
% 0.47/0.64 generalize (zenon_H1c zenon_TX_ce). zenon_intro zenon_H3d.
% 0.47/0.64 apply (zenon_imply_s _ _ zenon_H3d); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ].
% 0.47/0.64 generalize (zenon_H3c zenon_TA_n). zenon_intro zenon_H40.
% 0.47/0.64 generalize (zenon_H40 zenon_TB_q). zenon_intro zenon_H41.
% 0.47/0.64 apply (zenon_equiv_s _ _ zenon_H41); [ zenon_intro zenon_H44; zenon_intro zenon_H43 | zenon_intro zenon_H3b; zenon_intro zenon_H42 ].
% 0.47/0.64 exact (zenon_H44 zenon_H3b).
% 0.47/0.64 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H3e | zenon_intro zenon_H45 ].
% 0.47/0.64 exact (zenon_H3a zenon_H3e).
% 0.47/0.64 exact (zenon_H3f zenon_H45).
% 0.47/0.64 exact (zenon_H3a zenon_H3e).
% 0.47/0.64 exact (zenon_H1e zenon_H35).
% 0.47/0.64 exact (zenon_H15 zenon_H13).
% 0.47/0.64 generalize (equal_set zenon_TA_n). zenon_intro zenon_H16.
% 0.47/0.64 generalize (zenon_H16 (union zenon_TA_n zenon_TB_q)). zenon_intro zenon_H17.
% 0.47/0.64 apply (zenon_equiv_s _ _ zenon_H17); [ zenon_intro zenon_H15; zenon_intro zenon_H19 | zenon_intro zenon_H13; zenon_intro zenon_H18 ].
% 0.47/0.64 exact (zenon_H15 zenon_H13).
% 0.47/0.64 apply (zenon_and_s _ _ zenon_H18). zenon_intro zenon_H23. zenon_intro zenon_H35.
% 0.47/0.64 generalize (subset (union zenon_TA_n zenon_TB_q)). zenon_intro zenon_H32.
% 0.47/0.64 generalize (zenon_H32 zenon_TA_n). zenon_intro zenon_H33.
% 0.47/0.64 apply (zenon_equiv_s _ _ zenon_H33); [ zenon_intro zenon_H1e; zenon_intro zenon_H36 | zenon_intro zenon_H35; zenon_intro zenon_H34 ].
% 0.47/0.64 exact (zenon_H1e zenon_H35).
% 0.47/0.64 generalize (subset zenon_TB_q). zenon_intro zenon_H1a.
% 0.47/0.64 generalize (zenon_H1a zenon_TA_n). zenon_intro zenon_H1b.
% 0.47/0.64 apply (zenon_equiv_s _ _ zenon_H1b); [ zenon_intro zenon_H12; zenon_intro zenon_H1d | zenon_intro zenon_H14; zenon_intro zenon_H1c ].
% 0.47/0.64 apply (zenon_notallex_s (fun X : zenon_U => ((member X zenon_TB_q)->(member X zenon_TA_n))) zenon_H1d); [ zenon_intro zenon_H46; idtac ].
% 0.47/0.64 elim zenon_H46. zenon_intro zenon_TX_ct. zenon_intro zenon_H48.
% 0.47/0.64 apply (zenon_notimply_s _ _ zenon_H48). zenon_intro zenon_H4a. zenon_intro zenon_H49.
% 0.47/0.64 generalize (zenon_H34 zenon_TX_ct). zenon_intro zenon_H4b.
% 0.47/0.64 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H4d | zenon_intro zenon_H4c ].
% 0.47/0.64 generalize (union zenon_TX_ct). zenon_intro zenon_H4e.
% 0.47/0.64 generalize (zenon_H4e zenon_TA_n). zenon_intro zenon_H4f.
% 0.47/0.64 generalize (zenon_H4f zenon_TB_q). zenon_intro zenon_H50.
% 0.47/0.64 apply (zenon_equiv_s _ _ zenon_H50); [ zenon_intro zenon_H4d; zenon_intro zenon_H53 | zenon_intro zenon_H52; zenon_intro zenon_H51 ].
% 0.47/0.64 apply (zenon_notor_s _ _ zenon_H53). zenon_intro zenon_H49. zenon_intro zenon_H54.
% 0.47/0.64 exact (zenon_H54 zenon_H4a).
% 0.47/0.64 exact (zenon_H4d zenon_H52).
% 0.47/0.64 exact (zenon_H49 zenon_H4c).
% 0.47/0.64 exact (zenon_H12 zenon_H14).
% 0.47/0.64 Qed.
% 0.47/0.64 % SZS output end Proof
% 0.47/0.64 (* END-PROOF *)
% 0.47/0.64 nodes searched: 6764
% 0.47/0.64 max branch formulas: 1000
% 0.47/0.64 proof nodes created: 308
% 0.47/0.64 formulas created: 35672
% 0.47/0.64
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