TSTP Solution File: SET015+4 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET015+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n029.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 06:32:26 EDT 2022
% Result : Theorem 0.37s 0.57s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET015+4 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n029.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 : Sun Jul 10 07:28:31 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.37/0.57 (* PROOF-FOUND *)
% 0.37/0.57 % SZS status Theorem
% 0.37/0.57 (* BEGIN-PROOF *)
% 0.37/0.57 % SZS output start Proof
% 0.37/0.57 Theorem thI07 : (forall A : zenon_U, (forall B : zenon_U, (equal_set (union A B) (union B A)))).
% 0.37/0.57 Proof.
% 0.37/0.57 assert (zenon_L1_ : forall (zenon_TA_p : zenon_U) (zenon_TB_q : zenon_U) (zenon_TX_r : zenon_U), (forall B : zenon_U, ((member zenon_TX_r (union zenon_TB_q B))<->((member zenon_TX_r zenon_TB_q)\/(member zenon_TX_r B)))) -> (member zenon_TX_r zenon_TA_p) -> (~(member zenon_TX_r (union zenon_TB_q zenon_TA_p))) -> False).
% 0.37/0.57 do 3 intro. intros zenon_Hc zenon_Hd zenon_He.
% 0.37/0.57 generalize (zenon_Hc zenon_TA_p). zenon_intro zenon_H12.
% 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H12); [ zenon_intro zenon_He; zenon_intro zenon_H15 | zenon_intro zenon_H14; zenon_intro zenon_H13 ].
% 0.37/0.57 apply (zenon_notor_s _ _ zenon_H15). zenon_intro zenon_H17. zenon_intro zenon_H16.
% 0.37/0.57 exact (zenon_H16 zenon_Hd).
% 0.37/0.57 exact (zenon_He zenon_H14).
% 0.37/0.57 (* end of lemma zenon_L1_ *)
% 0.37/0.57 assert (zenon_L2_ : forall (zenon_TB_q : zenon_U) (zenon_TA_p : zenon_U) (zenon_TX_bb : zenon_U), (forall B : zenon_U, ((member zenon_TX_bb (union zenon_TA_p B))<->((member zenon_TX_bb zenon_TA_p)\/(member zenon_TX_bb B)))) -> (member zenon_TX_bb zenon_TB_q) -> (~(member zenon_TX_bb (union zenon_TA_p zenon_TB_q))) -> False).
% 0.37/0.57 do 3 intro. intros zenon_H18 zenon_H19 zenon_H1a.
% 0.37/0.57 generalize (zenon_H18 zenon_TB_q). zenon_intro zenon_H1c.
% 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H1c); [ zenon_intro zenon_H1a; zenon_intro zenon_H1f | zenon_intro zenon_H1e; zenon_intro zenon_H1d ].
% 0.37/0.57 apply (zenon_notor_s _ _ zenon_H1f). zenon_intro zenon_H21. zenon_intro zenon_H20.
% 0.37/0.57 exact (zenon_H20 zenon_H19).
% 0.37/0.57 exact (zenon_H1a zenon_H1e).
% 0.37/0.57 (* end of lemma zenon_L2_ *)
% 0.37/0.57 apply NNPP. intro zenon_G.
% 0.37/0.57 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (equal_set (union A B) (union B A)))) zenon_G); [ zenon_intro zenon_H22; idtac ].
% 0.37/0.57 elim zenon_H22. zenon_intro zenon_TA_p. zenon_intro zenon_H23.
% 0.37/0.57 apply (zenon_notallex_s (fun B : zenon_U => (equal_set (union zenon_TA_p B) (union B zenon_TA_p))) zenon_H23); [ zenon_intro zenon_H24; idtac ].
% 0.37/0.57 elim zenon_H24. zenon_intro zenon_TB_q. zenon_intro zenon_H25.
% 0.37/0.57 generalize (equal_set (union zenon_TA_p zenon_TB_q)). zenon_intro zenon_H26.
% 0.37/0.57 generalize (zenon_H26 (union zenon_TB_q zenon_TA_p)). zenon_intro zenon_H27.
% 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H27); [ zenon_intro zenon_H25; zenon_intro zenon_H2a | zenon_intro zenon_H29; zenon_intro zenon_H28 ].
% 0.37/0.57 apply (zenon_notand_s _ _ zenon_H2a); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ].
% 0.37/0.57 generalize (subset (union zenon_TA_p zenon_TB_q)). zenon_intro zenon_H2d.
% 0.37/0.57 generalize (zenon_H2d (union zenon_TB_q zenon_TA_p)). zenon_intro zenon_H2e.
% 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H2e); [ zenon_intro zenon_H2c; zenon_intro zenon_H31 | zenon_intro zenon_H30; zenon_intro zenon_H2f ].
% 0.37/0.57 apply (zenon_notallex_s (fun X : zenon_U => ((member X (union zenon_TA_p zenon_TB_q))->(member X (union zenon_TB_q zenon_TA_p)))) zenon_H31); [ zenon_intro zenon_H32; idtac ].
% 0.37/0.57 elim zenon_H32. zenon_intro zenon_TX_r. zenon_intro zenon_H33.
% 0.37/0.57 apply (zenon_notimply_s _ _ zenon_H33). zenon_intro zenon_H34. zenon_intro zenon_He.
% 0.37/0.57 generalize (union zenon_TX_r). zenon_intro zenon_H35.
% 0.37/0.57 generalize (zenon_H35 zenon_TA_p). zenon_intro zenon_H36.
% 0.37/0.57 generalize (zenon_H35 zenon_TB_q). zenon_intro zenon_Hc.
% 0.37/0.57 generalize (zenon_H36 zenon_TA_p). zenon_intro zenon_H37.
% 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H37); [ zenon_intro zenon_H3b; zenon_intro zenon_H3a | zenon_intro zenon_H39; zenon_intro zenon_H38 ].
% 0.37/0.57 apply (zenon_notor_s _ _ zenon_H3a). zenon_intro zenon_H16. zenon_intro zenon_H16.
% 0.37/0.57 generalize (zenon_Hc zenon_TA_p). zenon_intro zenon_H12.
% 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H12); [ zenon_intro zenon_He; zenon_intro zenon_H15 | zenon_intro zenon_H14; zenon_intro zenon_H13 ].
% 0.37/0.57 apply (zenon_notor_s _ _ zenon_H15). zenon_intro zenon_H17. zenon_intro zenon_H16.
% 0.37/0.57 generalize (zenon_H36 zenon_TB_q). zenon_intro zenon_H3c.
% 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H3c); [ zenon_intro zenon_H3f; zenon_intro zenon_H3e | zenon_intro zenon_H34; zenon_intro zenon_H3d ].
% 0.37/0.57 exact (zenon_H3f zenon_H34).
% 0.37/0.57 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_Hd | zenon_intro zenon_H40 ].
% 0.37/0.57 exact (zenon_H16 zenon_Hd).
% 0.37/0.57 exact (zenon_H17 zenon_H40).
% 0.37/0.57 exact (zenon_He zenon_H14).
% 0.37/0.57 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_Hd | zenon_intro zenon_Hd ].
% 0.37/0.57 apply (zenon_L1_ zenon_TA_p zenon_TB_q zenon_TX_r); trivial.
% 0.37/0.57 apply (zenon_L1_ zenon_TA_p zenon_TB_q zenon_TX_r); trivial.
% 0.37/0.57 exact (zenon_H2c zenon_H30).
% 0.37/0.57 generalize (subset (union zenon_TB_q zenon_TA_p)). zenon_intro zenon_H41.
% 0.37/0.57 generalize (zenon_H41 (union zenon_TA_p zenon_TB_q)). zenon_intro zenon_H42.
% 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H42); [ zenon_intro zenon_H2b; zenon_intro zenon_H45 | zenon_intro zenon_H44; zenon_intro zenon_H43 ].
% 0.37/0.57 apply (zenon_notallex_s (fun X : zenon_U => ((member X (union zenon_TB_q zenon_TA_p))->(member X (union zenon_TA_p zenon_TB_q)))) zenon_H45); [ zenon_intro zenon_H46; idtac ].
% 0.37/0.57 elim zenon_H46. zenon_intro zenon_TX_bb. zenon_intro zenon_H47.
% 0.37/0.57 apply (zenon_notimply_s _ _ zenon_H47). zenon_intro zenon_H48. zenon_intro zenon_H1a.
% 0.37/0.57 generalize (union zenon_TX_bb). zenon_intro zenon_H49.
% 0.37/0.57 generalize (zenon_H49 zenon_TB_q). zenon_intro zenon_H4a.
% 0.37/0.57 generalize (zenon_H49 zenon_TA_p). zenon_intro zenon_H18.
% 0.37/0.57 generalize (zenon_H4a zenon_TB_q). zenon_intro zenon_H4b.
% 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H4b); [ zenon_intro zenon_H4f; zenon_intro zenon_H4e | zenon_intro zenon_H4d; zenon_intro zenon_H4c ].
% 0.37/0.57 apply (zenon_notor_s _ _ zenon_H4e). zenon_intro zenon_H20. zenon_intro zenon_H20.
% 0.37/0.57 generalize (zenon_H18 zenon_TB_q). zenon_intro zenon_H1c.
% 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H1c); [ zenon_intro zenon_H1a; zenon_intro zenon_H1f | zenon_intro zenon_H1e; zenon_intro zenon_H1d ].
% 0.37/0.57 apply (zenon_notor_s _ _ zenon_H1f). zenon_intro zenon_H21. zenon_intro zenon_H20.
% 0.37/0.57 generalize (zenon_H4a zenon_TA_p). zenon_intro zenon_H50.
% 0.37/0.57 apply (zenon_equiv_s _ _ zenon_H50); [ zenon_intro zenon_H53; zenon_intro zenon_H52 | zenon_intro zenon_H48; zenon_intro zenon_H51 ].
% 0.37/0.57 exact (zenon_H53 zenon_H48).
% 0.37/0.57 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H19 | zenon_intro zenon_H54 ].
% 0.37/0.57 exact (zenon_H20 zenon_H19).
% 0.37/0.57 exact (zenon_H21 zenon_H54).
% 0.37/0.57 exact (zenon_H1a zenon_H1e).
% 0.37/0.57 apply (zenon_or_s _ _ zenon_H4c); [ zenon_intro zenon_H19 | zenon_intro zenon_H19 ].
% 0.37/0.57 apply (zenon_L2_ zenon_TB_q zenon_TA_p zenon_TX_bb); trivial.
% 0.37/0.57 apply (zenon_L2_ zenon_TB_q zenon_TA_p zenon_TX_bb); trivial.
% 0.37/0.57 exact (zenon_H2b zenon_H44).
% 0.37/0.57 exact (zenon_H25 zenon_H29).
% 0.37/0.57 Qed.
% 0.37/0.57 % SZS output end Proof
% 0.37/0.57 (* END-PROOF *)
% 0.37/0.57 nodes searched: 2821
% 0.37/0.57 max branch formulas: 800
% 0.37/0.57 proof nodes created: 153
% 0.37/0.57 formulas created: 16259
% 0.37/0.57
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