%------------------------------------------------------------------------------
% File     : Zenon---0.7.1
% Problem  : SET086+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_zenon %s %d

% Computer : n004.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 06:33:45 EDT 2022

% Result   : Theorem 0.15s 0.48s
% Output   : Proof 0.15s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : SET086+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.02/0.11  % Command  : run_zenon %s %d
% 0.11/0.31  % Computer : n004.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 600
% 0.11/0.31  % DateTime : Sun Jul 10 10:49:52 EDT 2022
% 0.11/0.31  % CPUTime  : 
% 0.15/0.48  (* PROOF-FOUND *)
% 0.15/0.48  % SZS status Theorem
% 0.15/0.48  (* BEGIN-PROOF *)
% 0.15/0.48  % SZS output start Proof
% 0.15/0.48  Theorem member_of_substitution : (forall X : zenon_U, (exists U : zenon_U, (((member U (universal_class))/\(X = (singleton U)))\/((~(exists Y : zenon_U, ((member Y (universal_class))/\(X = (singleton Y)))))/\(U = X))))).
% 0.15/0.48  Proof.
% 0.15/0.48  apply NNPP. intro zenon_G.
% 0.15/0.48  apply (zenon_notallex_s (fun X : zenon_U => (exists U : zenon_U, (((member U (universal_class))/\(X = (singleton U)))\/((~(exists Y : zenon_U, ((member Y (universal_class))/\(X = (singleton Y)))))/\(U = X))))) zenon_G); [ zenon_intro zenon_H2c; idtac ].
% 0.15/0.48  elim zenon_H2c. zenon_intro zenon_TX_bt. zenon_intro zenon_H2e.
% 0.15/0.48  apply zenon_H2e. exists zenon_TX_bt. apply NNPP. zenon_intro zenon_H2f.
% 0.15/0.48  apply (zenon_notor_s _ _ zenon_H2f). zenon_intro zenon_H31. zenon_intro zenon_H30.
% 0.15/0.48  apply (zenon_notand_s _ _ zenon_H30); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 0.15/0.48  apply zenon_H33. zenon_intro zenon_H34.
% 0.15/0.48  elim zenon_H34. zenon_intro zenon_TY_cb. zenon_intro zenon_H36.
% 0.15/0.48  apply zenon_H2e. exists zenon_TY_cb. apply NNPP. zenon_intro zenon_H37.
% 0.15/0.48  apply (zenon_notor_s _ _ zenon_H37). zenon_intro zenon_H39. zenon_intro zenon_H38.
% 0.15/0.48  exact (zenon_H39 zenon_H36).
% 0.15/0.48  apply zenon_H32. apply refl_equal.
% 0.15/0.48  Qed.
% 0.15/0.48  % SZS output end Proof
% 0.15/0.48  (* END-PROOF *)
% 0.15/0.48  nodes searched: 640
% 0.15/0.48  max branch formulas: 556
% 0.15/0.48  proof nodes created: 22
% 0.15/0.48  formulas created: 6395
% 0.15/0.48  
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