%------------------------------------------------------------------------------
% File     : Zenon---0.7.1
% Problem  : SET146+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_zenon %s %d

% Computer : n014.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 06:34:24 EDT 2022

% Result   : Theorem 0.46s 0.64s
% Output   : Proof 0.46s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET146+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12  % Command  : run_zenon %s %d
% 0.12/0.33  % Computer : n014.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 00:48:05 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.46/0.64  (* PROOF-FOUND *)
% 0.46/0.64  % SZS status Theorem
% 0.46/0.64  (* BEGIN-PROOF *)
% 0.46/0.64  % SZS output start Proof
% 0.46/0.64  Theorem prove_th61 : (forall B : zenon_U, ((intersection B (empty_set)) = (empty_set))).
% 0.46/0.64  Proof.
% 0.46/0.64  assert (zenon_L1_ : forall (zenon_TD_k : zenon_U), (member zenon_TD_k (empty_set)) -> False).
% 0.46/0.64  do 1 intro. intros zenon_H9.
% 0.46/0.64  generalize (empty_set_defn zenon_TD_k). zenon_intro zenon_Hb.
% 0.46/0.64  exact (zenon_Hb zenon_H9).
% 0.46/0.64  (* end of lemma zenon_L1_ *)
% 0.46/0.64  apply NNPP. intro zenon_G.
% 0.46/0.64  apply (zenon_notallex_s (fun B : zenon_U => ((intersection B (empty_set)) = (empty_set))) zenon_G); [ zenon_intro zenon_Hc; idtac ].
% 0.46/0.64  elim zenon_Hc. zenon_intro zenon_TB_n. zenon_intro zenon_He.
% 0.46/0.64  generalize (equal_member_defn (empty_set)). zenon_intro zenon_Hf.
% 0.46/0.64  generalize (zenon_Hf (intersection zenon_TB_n (empty_set))). zenon_intro zenon_H10.
% 0.46/0.64  apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_H14; zenon_intro zenon_H13 | zenon_intro zenon_H12; zenon_intro zenon_H11 ].
% 0.46/0.64  apply (zenon_notallex_s (fun D : zenon_U => ((member D (empty_set))<->(member D (intersection zenon_TB_n (empty_set))))) zenon_H13); [ zenon_intro zenon_H15; idtac ].
% 0.46/0.64  elim zenon_H15. zenon_intro zenon_TD_k. zenon_intro zenon_H16.
% 0.46/0.64  apply (zenon_notequiv_s _ _ zenon_H16); [ zenon_intro zenon_Hb; zenon_intro zenon_H18 | zenon_intro zenon_H9; zenon_intro zenon_H17 ].
% 0.46/0.64  generalize (intersection_defn zenon_TB_n). zenon_intro zenon_H19.
% 0.46/0.64  generalize (zenon_H19 (empty_set)). zenon_intro zenon_H1a.
% 0.46/0.64  generalize (zenon_H1a zenon_TD_k). zenon_intro zenon_H1b.
% 0.46/0.64  apply (zenon_equiv_s _ _ zenon_H1b); [ zenon_intro zenon_H17; zenon_intro zenon_H1d | zenon_intro zenon_H18; zenon_intro zenon_H1c ].
% 0.46/0.64  exact (zenon_H17 zenon_H18).
% 0.46/0.64  apply (zenon_and_s _ _ zenon_H1c). zenon_intro zenon_H1e. zenon_intro zenon_H9.
% 0.46/0.64  exact (zenon_Hb zenon_H9).
% 0.46/0.64  apply (zenon_L1_ zenon_TD_k); trivial.
% 0.46/0.64  apply zenon_He. apply sym_equal. exact zenon_H12.
% 0.46/0.64  Qed.
% 0.46/0.64  % SZS output end Proof
% 0.46/0.64  (* END-PROOF *)
% 0.46/0.64  nodes searched: 6410
% 0.46/0.64  max branch formulas: 798
% 0.46/0.64  proof nodes created: 411
% 0.46/0.64  formulas created: 15401
% 0.46/0.64  
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