%------------------------------------------------------------------------------
% File     : Zenon---0.7.1
% Problem  : SET891+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_zenon %s %d

% Computer : n018.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 06:39:26 EDT 2022

% Result   : Theorem 1.20s 1.42s
% Output   : Proof 1.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET891+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command  : run_zenon %s %d
% 0.12/0.34  % Computer : n018.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 : Sun Jul 10 15:58:28 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.20/1.42  Zenon warning: unused variable (B : zenon_U) in idempotence_k2_xboole_0
% 1.20/1.42  (* PROOF-FOUND *)
% 1.20/1.42  % SZS status Theorem
% 1.20/1.42  (* BEGIN-PROOF *)
% 1.20/1.42  % SZS output start Proof
% 1.20/1.42  Theorem t32_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, ((union (unordered_pair (singleton A) (singleton B))) = (unordered_pair A B)))).
% 1.20/1.42  Proof.
% 1.20/1.42  apply NNPP. intro zenon_G.
% 1.20/1.42  apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, ((union (unordered_pair (singleton A) (singleton B))) = (unordered_pair A B)))) zenon_G); [ zenon_intro zenon_Ha; idtac ].
% 1.20/1.42  elim zenon_Ha. zenon_intro zenon_TA_l. zenon_intro zenon_Hc.
% 1.20/1.42  apply (zenon_notallex_s (fun B : zenon_U => ((union (unordered_pair (singleton zenon_TA_l) (singleton B))) = (unordered_pair zenon_TA_l B))) zenon_Hc); [ zenon_intro zenon_Hd; idtac ].
% 1.20/1.42  elim zenon_Hd. zenon_intro zenon_TB_o. zenon_intro zenon_Hf.
% 1.20/1.42  generalize (t41_enumset1 zenon_TA_l). zenon_intro zenon_H10.
% 1.20/1.42  generalize (zenon_H10 zenon_TB_o). zenon_intro zenon_H11.
% 1.20/1.42  apply (zenon_congruence_lr_s _ (fun zenon_Vg : _ => (~((union (unordered_pair (singleton zenon_TA_l) (singleton zenon_TB_o))) = zenon_Vg))) _ _ zenon_Hf zenon_H11). zenon_intro zenon_H12.
% 1.20/1.42  generalize (l52_zfmisc_1 (singleton zenon_TA_l)). zenon_intro zenon_H13.
% 1.20/1.42  generalize (zenon_H13 (singleton zenon_TB_o)). zenon_intro zenon_H14.
% 1.20/1.42  exact (zenon_H12 zenon_H14).
% 1.20/1.42  Qed.
% 1.20/1.42  % SZS output end Proof
% 1.20/1.42  (* END-PROOF *)
% 1.20/1.42  nodes searched: 6161
% 1.20/1.42  max branch formulas: 791
% 1.20/1.42  proof nodes created: 217
% 1.20/1.42  formulas created: 29184
% 1.20/1.42  
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