%------------------------------------------------------------------------------
% File     : Zenon---0.7.1
% Problem  : GRA010+2 : TPTP v8.1.0. Bugfixed 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 : Sat Jul 16 07:24:30 EDT 2022

% Result   : Theorem 0.21s 0.52s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GRA010+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.07/0.13  % Command  : run_zenon %s %d
% 0.14/0.35  % Computer : n018.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Mon May 30 22:44:57 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.21/0.52  (* PROOF-FOUND *)
% 0.21/0.52  % SZS status Theorem
% 0.21/0.52  (* BEGIN-PROOF *)
% 0.21/0.52  % SZS output start Proof
% 0.21/0.52  Theorem complete_means_sequential_pairs_and_triangles : ((complete)->(forall P : zenon_U, (forall V1 : zenon_U, (forall V2 : zenon_U, (((path V1 V2 P)/\(forall E1 : zenon_U, (forall E2 : zenon_U, (((on_path E1 P)/\((on_path E2 P)/\(sequential E1 E2)))->(exists E3 : zenon_U, (triangle E1 E2 E3))))))->((number_of_in (sequential_pairs) P) = (number_of_in (triangles) P))))))).
% 0.21/0.52  Proof.
% 0.21/0.52  apply NNPP. intro zenon_G.
% 0.21/0.52  apply (zenon_notimply_s _ _ zenon_G). zenon_intro zenon_H14. zenon_intro zenon_H13.
% 0.21/0.52  exact (zenon_H13 sequential_pairs_and_triangles).
% 0.21/0.52  Qed.
% 0.21/0.52  % SZS output end Proof
% 0.21/0.52  (* END-PROOF *)
% 0.21/0.52  nodes searched: 9
% 0.21/0.52  max branch formulas: 27
% 0.21/0.52  proof nodes created: 2
% 0.21/0.52  formulas created: 491
% 0.21/0.52  
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