%------------------------------------------------------------------------------
% File     : Zenon---0.7.1
% Problem  : SYN078+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_zenon %s %d

% Computer : n014.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 13:49:28 EDT 2022

% Result   : Theorem 0.21s 0.51s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN078+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13  % Command  : run_zenon %s %d
% 0.14/0.34  % Computer : n014.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Mon Jul 11 12:14:49 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.21/0.51  (* PROOF-FOUND *)
% 0.21/0.51  % SZS status Theorem
% 0.21/0.51  (* BEGIN-PROOF *)
% 0.21/0.51  % SZS output start Proof
% 0.21/0.51  Theorem pel56 : ((forall X : zenon_U, ((exists Y : zenon_U, ((big_p Y)/\(X = (f Y))))->(big_p X)))<->(forall U : zenon_U, ((big_p U)->(big_p (f U))))).
% 0.21/0.51  Proof.
% 0.21/0.51  apply NNPP. intro zenon_G.
% 0.21/0.51  apply (zenon_notequiv_s _ _ zenon_G); [ zenon_intro zenon_H4; zenon_intro zenon_H3 | zenon_intro zenon_H2; zenon_intro zenon_H1 ].
% 0.21/0.51  apply (zenon_notallex_s (fun X : zenon_U => ((exists Y : zenon_U, ((big_p Y)/\(X = (f Y))))->(big_p X))) zenon_H4); [ zenon_intro zenon_H5; idtac ].
% 0.21/0.51  elim zenon_H5. zenon_intro zenon_TX_g. zenon_intro zenon_H7.
% 0.21/0.51  apply (zenon_notimply_s _ _ zenon_H7). zenon_intro zenon_H9. zenon_intro zenon_H8.
% 0.21/0.51  elim zenon_H9. zenon_intro zenon_TY_k. zenon_intro zenon_Hb.
% 0.21/0.51  apply (zenon_and_s _ _ zenon_Hb). zenon_intro zenon_Hd. zenon_intro zenon_Hc.
% 0.21/0.51  generalize (zenon_H3 zenon_TY_k). zenon_intro zenon_He.
% 0.21/0.51  apply (zenon_imply_s _ _ zenon_He); [ zenon_intro zenon_H10 | zenon_intro zenon_Hf ].
% 0.21/0.51  exact (zenon_H10 zenon_Hd).
% 0.21/0.51  cut ((big_p (f zenon_TY_k)) = (big_p zenon_TX_g)).
% 0.21/0.51  intro zenon_D_pnotp.
% 0.21/0.51  apply zenon_H8.
% 0.21/0.51  rewrite <- zenon_D_pnotp.
% 0.21/0.51  exact zenon_Hf.
% 0.21/0.51  cut (((f zenon_TY_k) = zenon_TX_g)); [idtac | apply NNPP; zenon_intro zenon_H11].
% 0.21/0.51  congruence.
% 0.21/0.51  apply zenon_H11. apply sym_equal. exact zenon_Hc.
% 0.21/0.51  apply (zenon_notallex_s (fun U : zenon_U => ((big_p U)->(big_p (f U)))) zenon_H1); [ zenon_intro zenon_H12; idtac ].
% 0.21/0.51  elim zenon_H12. zenon_intro zenon_TU_t. zenon_intro zenon_H14.
% 0.21/0.51  apply (zenon_notimply_s _ _ zenon_H14). zenon_intro zenon_H16. zenon_intro zenon_H15.
% 0.21/0.51  generalize (zenon_H2 (f zenon_TU_t)). zenon_intro zenon_H17.
% 0.21/0.51  apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ].
% 0.21/0.51  apply zenon_H19. exists zenon_TU_t. apply NNPP. zenon_intro zenon_H1a.
% 0.21/0.51  apply (zenon_notand_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ].
% 0.21/0.51  exact (zenon_H1c zenon_H16).
% 0.21/0.51  apply zenon_H1b. apply refl_equal.
% 0.21/0.51  exact (zenon_H15 zenon_H18).
% 0.21/0.51  Qed.
% 0.21/0.51  % SZS output end Proof
% 0.21/0.51  (* END-PROOF *)
% 0.21/0.51  nodes searched: 39
% 0.21/0.51  max branch formulas: 20
% 0.21/0.51  proof nodes created: 19
% 0.21/0.51  formulas created: 205
% 0.21/0.51  
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