%------------------------------------------------------------------------------
% File     : Zenon---0.7.1
% Problem  : SET194+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_zenon %s %d

% Computer : n005.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 06:34:48 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET194+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12  % Command  : run_zenon %s %d
% 0.12/0.33  % Computer : n005.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 13:22:22 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.51  (* PROOF-FOUND *)
% 0.19/0.51  % SZS status Theorem
% 0.19/0.51  (* BEGIN-PROOF *)
% 0.19/0.51  % SZS output start Proof
% 0.19/0.51  Theorem prove_subset_of_union : (forall B : zenon_U, (forall C : zenon_U, (subset B (union B C)))).
% 0.19/0.51  Proof.
% 0.19/0.51  apply NNPP. intro zenon_G.
% 0.19/0.51  apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (subset B (union B C)))) zenon_G); [ zenon_intro zenon_H6; idtac ].
% 0.19/0.51  elim zenon_H6. zenon_intro zenon_TB_h. zenon_intro zenon_H8.
% 0.19/0.51  apply (zenon_notallex_s (fun C : zenon_U => (subset zenon_TB_h (union zenon_TB_h C))) zenon_H8); [ zenon_intro zenon_H9; idtac ].
% 0.19/0.51  elim zenon_H9. zenon_intro zenon_TC_k. zenon_intro zenon_Hb.
% 0.19/0.51  generalize (subset_defn zenon_TB_h). zenon_intro zenon_Hc.
% 0.19/0.51  generalize (zenon_Hc (union zenon_TB_h zenon_TC_k)). zenon_intro zenon_Hd.
% 0.19/0.51  apply (zenon_equiv_s _ _ zenon_Hd); [ zenon_intro zenon_Hb; zenon_intro zenon_H10 | zenon_intro zenon_Hf; zenon_intro zenon_He ].
% 0.19/0.51  apply (zenon_notallex_s (fun D : zenon_U => ((member D zenon_TB_h)->(member D (union zenon_TB_h zenon_TC_k)))) zenon_H10); [ zenon_intro zenon_H11; idtac ].
% 0.19/0.51  elim zenon_H11. zenon_intro zenon_TD_s. zenon_intro zenon_H13.
% 0.19/0.51  apply (zenon_notimply_s _ _ zenon_H13). zenon_intro zenon_H15. zenon_intro zenon_H14.
% 0.19/0.51  generalize (union_defn zenon_TB_h). zenon_intro zenon_H16.
% 0.19/0.51  generalize (zenon_H16 zenon_TC_k). zenon_intro zenon_H17.
% 0.19/0.51  generalize (zenon_H17 zenon_TD_s). zenon_intro zenon_H18.
% 0.19/0.51  apply (zenon_equiv_s _ _ zenon_H18); [ zenon_intro zenon_H14; zenon_intro zenon_H1b | zenon_intro zenon_H1a; zenon_intro zenon_H19 ].
% 0.19/0.51  apply (zenon_notor_s _ _ zenon_H1b). zenon_intro zenon_H1d. zenon_intro zenon_H1c.
% 0.19/0.51  exact (zenon_H1d zenon_H15).
% 0.19/0.51  exact (zenon_H14 zenon_H1a).
% 0.19/0.51  exact (zenon_Hb zenon_Hf).
% 0.19/0.51  Qed.
% 0.19/0.51  % SZS output end Proof
% 0.19/0.51  (* END-PROOF *)
% 0.19/0.51  nodes searched: 360
% 0.19/0.51  max branch formulas: 196
% 0.19/0.51  proof nodes created: 40
% 0.19/0.51  formulas created: 1755
% 0.19/0.51  
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