TSTP Solution File: SET013+4 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET013+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n003.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 06:32:21 EDT 2022
% Result : Theorem 0.55s 0.71s
% Output : Proof 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET013+4 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : run_zenon %s %d
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 9 20:52:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.55/0.71 (* PROOF-FOUND *)
% 0.55/0.71 % SZS status Theorem
% 0.55/0.71 (* BEGIN-PROOF *)
% 0.55/0.71 % SZS output start Proof
% 0.55/0.71 Theorem thI06 : (forall A : zenon_U, (forall B : zenon_U, (equal_set (intersection A B) (intersection B A)))).
% 0.55/0.71 Proof.
% 0.55/0.71 assert (zenon_L1_ : forall (zenon_TB_p : zenon_U) (zenon_TA_q : zenon_U) (zenon_TX_r : zenon_U), (forall B : zenon_U, ((member zenon_TX_r (intersection zenon_TA_q B))<->((member zenon_TX_r zenon_TA_q)/\(member zenon_TX_r B)))) -> (member zenon_TX_r (intersection zenon_TA_q zenon_TB_p)) -> (~(member zenon_TX_r zenon_TB_p)) -> False).
% 0.55/0.71 do 3 intro. intros zenon_Hc zenon_Hd zenon_He.
% 0.55/0.71 generalize (zenon_Hc zenon_TB_p). zenon_intro zenon_H12.
% 0.55/0.71 apply (zenon_equiv_s _ _ zenon_H12); [ zenon_intro zenon_H15; zenon_intro zenon_H14 | zenon_intro zenon_Hd; zenon_intro zenon_H13 ].
% 0.55/0.71 exact (zenon_H15 zenon_Hd).
% 0.55/0.71 apply (zenon_and_s _ _ zenon_H13). zenon_intro zenon_H17. zenon_intro zenon_H16.
% 0.55/0.71 exact (zenon_He zenon_H16).
% 0.55/0.71 (* end of lemma zenon_L1_ *)
% 0.55/0.71 assert (zenon_L2_ : forall (zenon_TA_q : zenon_U) (zenon_TB_p : zenon_U) (zenon_TX_r : zenon_U), (forall A : zenon_U, (forall B : zenon_U, ((member zenon_TX_r (intersection A B))<->((member zenon_TX_r A)/\(member zenon_TX_r B))))) -> (~(member zenon_TX_r (intersection zenon_TB_p zenon_TA_q))) -> (forall B : zenon_U, ((member zenon_TX_r (intersection zenon_TA_q B))<->((member zenon_TX_r zenon_TA_q)/\(member zenon_TX_r B)))) -> (member zenon_TX_r (intersection zenon_TA_q zenon_TB_p)) -> (member zenon_TX_r zenon_TA_q) -> False).
% 0.55/0.71 do 3 intro. intros zenon_H18 zenon_H19 zenon_Hc zenon_Hd zenon_H17.
% 0.55/0.71 generalize (zenon_H18 zenon_TB_p). zenon_intro zenon_H1a.
% 0.55/0.71 generalize (zenon_H1a zenon_TA_q). zenon_intro zenon_H1b.
% 0.55/0.71 apply (zenon_equiv_s _ _ zenon_H1b); [ zenon_intro zenon_H19; zenon_intro zenon_H1e | zenon_intro zenon_H1d; zenon_intro zenon_H1c ].
% 0.55/0.71 apply (zenon_notand_s _ _ zenon_H1e); [ zenon_intro zenon_He | zenon_intro zenon_H1f ].
% 0.55/0.71 apply (zenon_L1_ zenon_TB_p zenon_TA_q zenon_TX_r); trivial.
% 0.55/0.71 exact (zenon_H1f zenon_H17).
% 0.55/0.71 exact (zenon_H19 zenon_H1d).
% 0.55/0.71 (* end of lemma zenon_L2_ *)
% 0.55/0.71 assert (zenon_L3_ : forall (zenon_TA_q : zenon_U) (zenon_TB_p : zenon_U) (zenon_TX_bj : zenon_U), (forall B : zenon_U, ((member zenon_TX_bj (intersection zenon_TB_p B))<->((member zenon_TX_bj zenon_TB_p)/\(member zenon_TX_bj B)))) -> (member zenon_TX_bj (intersection zenon_TB_p zenon_TA_q)) -> (~(member zenon_TX_bj zenon_TA_q)) -> False).
% 0.55/0.71 do 3 intro. intros zenon_H20 zenon_H21 zenon_H22.
% 0.55/0.71 generalize (zenon_H20 zenon_TA_q). zenon_intro zenon_H24.
% 0.55/0.71 apply (zenon_equiv_s _ _ zenon_H24); [ zenon_intro zenon_H27; zenon_intro zenon_H26 | zenon_intro zenon_H21; zenon_intro zenon_H25 ].
% 0.55/0.71 exact (zenon_H27 zenon_H21).
% 0.55/0.71 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H29. zenon_intro zenon_H28.
% 0.55/0.71 exact (zenon_H22 zenon_H28).
% 0.55/0.71 (* end of lemma zenon_L3_ *)
% 0.55/0.71 assert (zenon_L4_ : forall (zenon_TB_p : zenon_U) (zenon_TA_q : zenon_U) (zenon_TX_bj : zenon_U), (forall A : zenon_U, (forall B : zenon_U, ((member zenon_TX_bj (intersection A B))<->((member zenon_TX_bj A)/\(member zenon_TX_bj B))))) -> (~(member zenon_TX_bj (intersection zenon_TA_q zenon_TB_p))) -> (forall B : zenon_U, ((member zenon_TX_bj (intersection zenon_TB_p B))<->((member zenon_TX_bj zenon_TB_p)/\(member zenon_TX_bj B)))) -> (member zenon_TX_bj (intersection zenon_TB_p zenon_TA_q)) -> (member zenon_TX_bj zenon_TB_p) -> False).
% 0.55/0.71 do 3 intro. intros zenon_H2a zenon_H2b zenon_H20 zenon_H21 zenon_H29.
% 0.55/0.71 generalize (zenon_H2a zenon_TA_q). zenon_intro zenon_H2c.
% 0.55/0.71 generalize (zenon_H2c zenon_TB_p). zenon_intro zenon_H2d.
% 0.55/0.71 apply (zenon_equiv_s _ _ zenon_H2d); [ zenon_intro zenon_H2b; zenon_intro zenon_H30 | zenon_intro zenon_H2f; zenon_intro zenon_H2e ].
% 0.55/0.71 apply (zenon_notand_s _ _ zenon_H30); [ zenon_intro zenon_H22 | zenon_intro zenon_H31 ].
% 0.55/0.71 apply (zenon_L3_ zenon_TA_q zenon_TB_p zenon_TX_bj); trivial.
% 0.55/0.71 exact (zenon_H31 zenon_H29).
% 0.55/0.71 exact (zenon_H2b zenon_H2f).
% 0.55/0.71 (* end of lemma zenon_L4_ *)
% 0.55/0.71 apply NNPP. intro zenon_G.
% 0.55/0.71 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (equal_set (intersection A B) (intersection B A)))) zenon_G); [ zenon_intro zenon_H32; idtac ].
% 0.55/0.71 elim zenon_H32. zenon_intro zenon_TA_q. zenon_intro zenon_H33.
% 0.55/0.71 apply (zenon_notallex_s (fun B : zenon_U => (equal_set (intersection zenon_TA_q B) (intersection B zenon_TA_q))) zenon_H33); [ zenon_intro zenon_H34; idtac ].
% 0.55/0.71 elim zenon_H34. zenon_intro zenon_TB_p. zenon_intro zenon_H35.
% 0.55/0.71 generalize (equal_set (intersection zenon_TA_q zenon_TB_p)). zenon_intro zenon_H36.
% 0.55/0.71 generalize (zenon_H36 (intersection zenon_TB_p zenon_TA_q)). zenon_intro zenon_H37.
% 0.55/0.71 apply (zenon_equiv_s _ _ zenon_H37); [ zenon_intro zenon_H35; zenon_intro zenon_H3a | zenon_intro zenon_H39; zenon_intro zenon_H38 ].
% 0.55/0.71 apply (zenon_notand_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ].
% 0.55/0.71 generalize (subset (intersection zenon_TA_q zenon_TB_p)). zenon_intro zenon_H3d.
% 0.55/0.71 generalize (zenon_H3d (intersection zenon_TB_p zenon_TA_q)). zenon_intro zenon_H3e.
% 0.55/0.71 apply (zenon_equiv_s _ _ zenon_H3e); [ zenon_intro zenon_H3c; zenon_intro zenon_H41 | zenon_intro zenon_H40; zenon_intro zenon_H3f ].
% 0.55/0.71 apply (zenon_notallex_s (fun X : zenon_U => ((member X (intersection zenon_TA_q zenon_TB_p))->(member X (intersection zenon_TB_p zenon_TA_q)))) zenon_H41); [ zenon_intro zenon_H42; idtac ].
% 0.55/0.71 elim zenon_H42. zenon_intro zenon_TX_r. zenon_intro zenon_H43.
% 0.55/0.71 apply (zenon_notimply_s _ _ zenon_H43). zenon_intro zenon_Hd. zenon_intro zenon_H19.
% 0.55/0.71 generalize (intersection zenon_TX_r). zenon_intro zenon_H18.
% 0.55/0.71 generalize (zenon_H18 zenon_TA_q). zenon_intro zenon_Hc.
% 0.55/0.71 generalize (zenon_Hc zenon_TB_p). zenon_intro zenon_H12.
% 0.55/0.71 apply (zenon_equiv_s _ _ zenon_H12); [ zenon_intro zenon_H15; zenon_intro zenon_H14 | zenon_intro zenon_Hd; zenon_intro zenon_H13 ].
% 0.55/0.71 exact (zenon_H15 zenon_Hd).
% 0.55/0.71 apply (zenon_and_s _ _ zenon_H13). zenon_intro zenon_H17. zenon_intro zenon_H16.
% 0.55/0.71 apply (zenon_L2_ zenon_TA_q zenon_TB_p zenon_TX_r); trivial.
% 0.55/0.71 exact (zenon_H3c zenon_H40).
% 0.55/0.71 generalize (subset (intersection zenon_TB_p zenon_TA_q)). zenon_intro zenon_H44.
% 0.55/0.71 generalize (zenon_H44 (intersection zenon_TA_q zenon_TB_p)). zenon_intro zenon_H45.
% 0.55/0.71 apply (zenon_equiv_s _ _ zenon_H45); [ zenon_intro zenon_H3b; zenon_intro zenon_H48 | zenon_intro zenon_H47; zenon_intro zenon_H46 ].
% 0.55/0.71 apply (zenon_notallex_s (fun X : zenon_U => ((member X (intersection zenon_TB_p zenon_TA_q))->(member X (intersection zenon_TA_q zenon_TB_p)))) zenon_H48); [ zenon_intro zenon_H49; idtac ].
% 0.55/0.71 elim zenon_H49. zenon_intro zenon_TX_bj. zenon_intro zenon_H4a.
% 0.55/0.71 apply (zenon_notimply_s _ _ zenon_H4a). zenon_intro zenon_H21. zenon_intro zenon_H2b.
% 0.55/0.71 generalize (intersection zenon_TX_bj). zenon_intro zenon_H2a.
% 0.55/0.71 generalize (zenon_H2a zenon_TB_p). zenon_intro zenon_H20.
% 0.55/0.71 generalize (zenon_H20 zenon_TA_q). zenon_intro zenon_H24.
% 0.55/0.71 apply (zenon_equiv_s _ _ zenon_H24); [ zenon_intro zenon_H27; zenon_intro zenon_H26 | zenon_intro zenon_H21; zenon_intro zenon_H25 ].
% 0.55/0.71 exact (zenon_H27 zenon_H21).
% 0.55/0.71 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H29. zenon_intro zenon_H28.
% 0.55/0.71 apply (zenon_L4_ zenon_TB_p zenon_TA_q zenon_TX_bj); trivial.
% 0.55/0.71 exact (zenon_H3b zenon_H47).
% 0.55/0.71 exact (zenon_H35 zenon_H39).
% 0.55/0.71 Qed.
% 0.55/0.71 % SZS output end Proof
% 0.55/0.71 (* END-PROOF *)
% 0.55/0.71 nodes searched: 10543
% 0.55/0.71 max branch formulas: 957
% 0.55/0.71 proof nodes created: 373
% 0.55/0.71 formulas created: 45608
% 0.55/0.71
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