%------------------------------------------------------------------------------
% File     : Zenon---0.7.1
% Problem  : SET148+3 : 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 06:34:25 EDT 2022

% Result   : Theorem 0.20s 0.54s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET148+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13  % Command  : run_zenon %s %d
% 0.13/0.33  % Computer : n023.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % 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 : Sat Jul  9 22:34:55 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.54  (* PROOF-FOUND *)
% 0.20/0.54  % SZS status Theorem
% 0.20/0.54  (* BEGIN-PROOF *)
% 0.20/0.54  % SZS output start Proof
% 0.20/0.54  Theorem prove_idempotency_of_intersection : (forall B : zenon_U, ((intersection B B) = B)).
% 0.20/0.54  Proof.
% 0.20/0.54  apply NNPP. intro zenon_G.
% 0.20/0.54  apply (zenon_notallex_s (fun B : zenon_U => ((intersection B B) = B)) zenon_G); [ zenon_intro zenon_H8; idtac ].
% 0.20/0.54  elim zenon_H8. zenon_intro zenon_TB_j. zenon_intro zenon_Ha.
% 0.20/0.54  generalize (equal_member_defn zenon_TB_j). zenon_intro zenon_Hb.
% 0.20/0.54  generalize (intersection_defn zenon_TB_j). zenon_intro zenon_Hc.
% 0.20/0.54  generalize (zenon_Hc zenon_TB_j). zenon_intro zenon_Hd.
% 0.20/0.54  generalize (zenon_Hb (intersection zenon_TB_j zenon_TB_j)). zenon_intro zenon_He.
% 0.20/0.54  apply (zenon_equiv_s _ _ zenon_He); [ zenon_intro zenon_H12; zenon_intro zenon_H11 | zenon_intro zenon_H10; zenon_intro zenon_Hf ].
% 0.20/0.54  apply (zenon_notallex_s (fun D : zenon_U => ((member D zenon_TB_j)<->(member D (intersection zenon_TB_j zenon_TB_j)))) zenon_H11); [ zenon_intro zenon_H13; idtac ].
% 0.20/0.54  elim zenon_H13. zenon_intro zenon_TD_u. zenon_intro zenon_H15.
% 0.20/0.54  apply (zenon_notequiv_s _ _ zenon_H15); [ zenon_intro zenon_H19; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H16 ].
% 0.20/0.54  generalize (zenon_Hd zenon_TD_u). zenon_intro zenon_H1a.
% 0.20/0.54  apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H16; zenon_intro zenon_H1c | zenon_intro zenon_H18; zenon_intro zenon_H1b ].
% 0.20/0.54  exact (zenon_H16 zenon_H18).
% 0.20/0.54  apply (zenon_and_s _ _ zenon_H1b). zenon_intro zenon_H17. zenon_intro zenon_H17.
% 0.20/0.54  exact (zenon_H19 zenon_H17).
% 0.20/0.54  generalize (zenon_Hd zenon_TD_u). zenon_intro zenon_H1a.
% 0.20/0.54  apply (zenon_equiv_s _ _ zenon_H1a); [ zenon_intro zenon_H16; zenon_intro zenon_H1c | zenon_intro zenon_H18; zenon_intro zenon_H1b ].
% 0.20/0.54  apply (zenon_notand_s _ _ zenon_H1c); [ zenon_intro zenon_H19 | zenon_intro zenon_H19 ].
% 0.20/0.54  exact (zenon_H19 zenon_H17).
% 0.20/0.54  exact (zenon_H19 zenon_H17).
% 0.20/0.54  exact (zenon_H16 zenon_H18).
% 0.20/0.54  apply zenon_Ha. apply sym_equal. exact zenon_H10.
% 0.20/0.54  Qed.
% 0.20/0.54  % SZS output end Proof
% 0.20/0.54  (* END-PROOF *)
% 0.20/0.54  nodes searched: 797
% 0.20/0.54  max branch formulas: 298
% 0.20/0.54  proof nodes created: 87
% 0.20/0.54  formulas created: 3015
% 0.20/0.54  
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