%------------------------------------------------------------------------------
% File     : Zenon---0.7.1
% Problem  : SEU165+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_zenon %s %d

% Computer : n032.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 15:59:54 EDT 2022

% Result   : Theorem 0.10s 0.36s
% Output   : Proof 0.10s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : SEU165+2 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.08  % Command  : run_zenon %s %d
% 0.06/0.26  % Computer : n032.cluster.edu
% 0.06/0.26  % Model    : x86_64 x86_64
% 0.06/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26  % Memory   : 8042.1875MB
% 0.06/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26  % CPULimit : 300
% 0.06/0.26  % WCLimit  : 600
% 0.06/0.26  % DateTime : Sun Jun 19 21:33:18 EDT 2022
% 0.06/0.26  % CPUTime  : 
% 0.10/0.36  Zenon warning: unused variable (B : zenon_U) in idempotence_k2_xboole_0
% 0.10/0.36  Zenon warning: unused variable (B : zenon_U) in idempotence_k3_xboole_0
% 0.10/0.36  Zenon warning: unused variable (B : zenon_U) in irreflexivity_r2_xboole_0
% 0.10/0.36  Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski
% 0.10/0.36  (* PROOF-FOUND *)
% 0.10/0.36  % SZS status Theorem
% 0.10/0.36  (* BEGIN-PROOF *)
% 0.10/0.36  % SZS output start Proof
% 0.10/0.36  Theorem t106_zfmisc_1 : (forall A : zenon_U, (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((in (ordered_pair A B) (cartesian_product2 C D))<->((in A C)/\(in B D))))))).
% 0.10/0.36  Proof.
% 0.10/0.36  apply NNPP. intro zenon_G.
% 0.10/0.36  exact (zenon_G l55_zfmisc_1).
% 0.10/0.36  Qed.
% 0.10/0.36  % SZS output end Proof
% 0.10/0.36  (* END-PROOF *)
% 0.10/0.36  nodes searched: 1
% 0.10/0.36  max branch formulas: 75
% 0.10/0.36  proof nodes created: 1
% 0.10/0.36  formulas created: 1137
% 0.10/0.36  
%------------------------------------------------------------------------------