%------------------------------------------------------------------------------
% File     : Zenon---0.7.1
% Problem  : SYN321+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_zenon %s %d

% Computer : n015.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 : Thu Jul 21 13:51:03 EDT 2022

% Result   : Theorem 0.18s 0.48s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYN321+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12  % Command  : run_zenon %s %d
% 0.12/0.33  % Computer : n015.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 : Tue Jul 12 02:40:39 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.48  (* PROOF-FOUND *)
% 0.18/0.48  % SZS status Theorem
% 0.18/0.48  (* BEGIN-PROOF *)
% 0.18/0.48  % SZS output start Proof
% 0.18/0.48  Theorem church_46_3_2 : (exists X : zenon_U, (exists Y : zenon_U, (((exists Z : zenon_U, (big_f X Z))->(forall Z : zenon_U, (big_g X Z)))->((forall Z : zenon_U, ((big_g Z Z)->(big_f Z Y)))->((big_f X Y)<->(forall Z : zenon_U, (big_g X Z))))))).
% 0.18/0.48  Proof.
% 0.18/0.48  assert (zenon_L1_ : (forall Z : zenon_U, (big_g zenon_E Z)) -> (~(big_f zenon_E zenon_E)) -> (forall Z : zenon_U, ((big_g Z Z)->(big_f Z zenon_E))) -> False).
% 0.18/0.48  do 0 intro. intros zenon_H3 zenon_H4 zenon_H5.
% 0.18/0.48  generalize (zenon_H3 zenon_E). zenon_intro zenon_H6.
% 0.18/0.48  generalize (zenon_H5 zenon_E). zenon_intro zenon_H7.
% 0.18/0.48  apply (zenon_imply_s _ _ zenon_H7); [ zenon_intro zenon_H9 | zenon_intro zenon_H8 ].
% 0.18/0.48  exact (zenon_H9 zenon_H6).
% 0.18/0.48  exact (zenon_H4 zenon_H8).
% 0.18/0.48  (* end of lemma zenon_L1_ *)
% 0.18/0.48  apply NNPP. intro zenon_G.
% 0.18/0.48  apply zenon_G. exists zenon_E. apply NNPP. zenon_intro zenon_Ha.
% 0.18/0.48  apply zenon_Ha. exists zenon_E. apply NNPP. zenon_intro zenon_Hb.
% 0.18/0.48  apply (zenon_notimply_s _ _ zenon_Hb). zenon_intro zenon_Hd. zenon_intro zenon_Hc.
% 0.18/0.49  apply (zenon_notimply_s _ _ zenon_Hc). zenon_intro zenon_H5. zenon_intro zenon_He.
% 0.18/0.49  apply (zenon_imply_s _ _ zenon_Hd); [ zenon_intro zenon_Hf | zenon_intro zenon_H3 ].
% 0.18/0.49  apply (zenon_notequiv_s _ _ zenon_He); [ zenon_intro zenon_H4; zenon_intro zenon_H3 | zenon_intro zenon_H8; zenon_intro zenon_H10 ].
% 0.18/0.49  apply (zenon_L1_); trivial.
% 0.18/0.49  apply zenon_Hf. exists zenon_E. apply NNPP. zenon_intro zenon_H4.
% 0.18/0.49  exact (zenon_H4 zenon_H8).
% 0.18/0.49  apply (zenon_notequiv_s _ _ zenon_He); [ zenon_intro zenon_H4; zenon_intro zenon_H3 | zenon_intro zenon_H8; zenon_intro zenon_H10 ].
% 0.18/0.49  apply (zenon_L1_); trivial.
% 0.18/0.49  exact (zenon_H10 zenon_H3).
% 0.18/0.49  Qed.
% 0.18/0.49  % SZS output end Proof
% 0.18/0.49  (* END-PROOF *)
% 0.18/0.49  nodes searched: 109
% 0.18/0.49  max branch formulas: 46
% 0.18/0.49  proof nodes created: 35
% 0.18/0.49  formulas created: 404
% 0.18/0.49  
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