%------------------------------------------------------------------------------
% File     : Zenon---0.7.1
% Problem  : KLE001+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_zenon %s %d

% Computer : n029.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 : Sun Jul 17 02:37:09 EDT 2022

% Result   : Theorem 0.20s 0.50s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE001+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12  % Command  : run_zenon %s %d
% 0.12/0.33  % Computer : n029.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 : Thu Jun 16 14:53:42 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.20/0.50  (* PROOF-FOUND *)
% 0.20/0.50  % SZS status Theorem
% 0.20/0.50  (* BEGIN-PROOF *)
% 0.20/0.50  % SZS output start Proof
% 0.20/0.50  Theorem goals : (forall X0 : zenon_U, (forall X1 : zenon_U, (forall X2 : zenon_U, ((leq X0 X1)->(leq (addition X0 X2) (addition X0 X2)))))).
% 0.20/0.50  Proof.
% 0.20/0.50  apply NNPP. intro zenon_G.
% 0.20/0.50  apply (zenon_notallex_s (fun X0 : zenon_U => (forall X1 : zenon_U, (forall X2 : zenon_U, ((leq X0 X1)->(leq (addition X0 X2) (addition X0 X2)))))) zenon_G); [ zenon_intro zenon_Hd; idtac ].
% 0.20/0.50  elim zenon_Hd. zenon_intro zenon_TX0_o. zenon_intro zenon_Hf.
% 0.20/0.50  apply (zenon_notallex_s (fun X1 : zenon_U => (forall X2 : zenon_U, ((leq zenon_TX0_o X1)->(leq (addition zenon_TX0_o X2) (addition zenon_TX0_o X2))))) zenon_Hf); [ zenon_intro zenon_H10; idtac ].
% 0.20/0.50  elim zenon_H10. zenon_intro zenon_TX1_r. zenon_intro zenon_H12.
% 0.20/0.50  apply (zenon_notallex_s (fun X2 : zenon_U => ((leq zenon_TX0_o zenon_TX1_r)->(leq (addition zenon_TX0_o X2) (addition zenon_TX0_o X2)))) zenon_H12); [ zenon_intro zenon_H13; idtac ].
% 0.20/0.50  elim zenon_H13. zenon_intro zenon_TX2_u. zenon_intro zenon_H15.
% 0.20/0.50  apply (zenon_notimply_s _ _ zenon_H15). zenon_intro zenon_H17. zenon_intro zenon_H16.
% 0.20/0.50  generalize (order (addition zenon_TX0_o zenon_TX2_u)). zenon_intro zenon_H18.
% 0.20/0.50  generalize (zenon_H18 (addition zenon_TX0_o zenon_TX2_u)). zenon_intro zenon_H19.
% 0.20/0.50  apply (zenon_equiv_s _ _ zenon_H19); [ zenon_intro zenon_H16; zenon_intro zenon_H1c | zenon_intro zenon_H1b; zenon_intro zenon_H1a ].
% 0.20/0.50  generalize (additive_idempotence (addition zenon_TX0_o zenon_TX2_u)). zenon_intro zenon_H1a.
% 0.20/0.50  exact (zenon_H1c zenon_H1a).
% 0.20/0.50  exact (zenon_H16 zenon_H1b).
% 0.20/0.50  Qed.
% 0.20/0.50  % SZS output end Proof
% 0.20/0.50  (* END-PROOF *)
% 0.20/0.50  nodes searched: 153
% 0.20/0.50  max branch formulas: 103
% 0.20/0.50  proof nodes created: 11
% 0.20/0.50  formulas created: 1517
% 0.20/0.50  
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