TSTP Solution File: SET766+4 by Zenon---0.7.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zenon---0.7.1
% Problem  : SET766+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_zenon %s %d

% Computer : n008.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 06:38:26 EDT 2022

% Result   : Theorem 0.19s 0.54s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SET766+4 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13  % Command  : run_zenon %s %d
% 0.12/0.34  % Computer : n008.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jul 10 08:00:23 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.54  (* PROOF-FOUND *)
% 0.19/0.54  % SZS status Theorem
% 0.19/0.54  (* BEGIN-PROOF *)
% 0.19/0.54  % SZS output start Proof
% 0.19/0.54  Theorem thIII02 : (forall E : zenon_U, (forall R : zenon_U, (forall A : zenon_U, (((equivalence R E)/\(member A E))->(member A (equivalence_class A E R)))))).
% 0.19/0.54  Proof.
% 0.19/0.54  apply NNPP. intro zenon_G.
% 0.19/0.54  apply (zenon_notallex_s (fun E : zenon_U => (forall R : zenon_U, (forall A : zenon_U, (((equivalence R E)/\(member A E))->(member A (equivalence_class A E R)))))) zenon_G); [ zenon_intro zenon_H11; idtac ].
% 0.19/0.54  elim zenon_H11. zenon_intro zenon_TE_s. zenon_intro zenon_H13.
% 0.19/0.54  apply (zenon_notallex_s (fun R : zenon_U => (forall A : zenon_U, (((equivalence R zenon_TE_s)/\(member A zenon_TE_s))->(member A (equivalence_class A zenon_TE_s R))))) zenon_H13); [ zenon_intro zenon_H14; idtac ].
% 0.19/0.54  elim zenon_H14. zenon_intro zenon_TR_v. zenon_intro zenon_H16.
% 0.19/0.54  apply (zenon_notallex_s (fun A : zenon_U => (((equivalence zenon_TR_v zenon_TE_s)/\(member A zenon_TE_s))->(member A (equivalence_class A zenon_TE_s zenon_TR_v)))) zenon_H16); [ zenon_intro zenon_H17; idtac ].
% 0.19/0.54  elim zenon_H17. zenon_intro zenon_TA_y. zenon_intro zenon_H19.
% 0.19/0.54  apply (zenon_notimply_s _ _ zenon_H19). zenon_intro zenon_H1b. zenon_intro zenon_H1a.
% 0.19/0.54  apply (zenon_and_s _ _ zenon_H1b). zenon_intro zenon_H1d. zenon_intro zenon_H1c.
% 0.19/0.54  generalize (equivalence zenon_TE_s). zenon_intro zenon_H1e.
% 0.19/0.54  generalize (zenon_H1e zenon_TR_v). zenon_intro zenon_H1f.
% 0.19/0.54  apply (zenon_equiv_s _ _ zenon_H1f); [ zenon_intro zenon_H22; zenon_intro zenon_H21 | zenon_intro zenon_H1d; zenon_intro zenon_H20 ].
% 0.19/0.54  exact (zenon_H22 zenon_H1d).
% 0.19/0.54  apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H24. zenon_intro zenon_H23.
% 0.19/0.54  generalize (equivalence_class zenon_TR_v). zenon_intro zenon_H25.
% 0.19/0.54  generalize (zenon_H25 zenon_TE_s). zenon_intro zenon_H26.
% 0.19/0.54  generalize (zenon_H26 zenon_TA_y). zenon_intro zenon_H27.
% 0.19/0.54  generalize (zenon_H27 zenon_TA_y). zenon_intro zenon_H28.
% 0.19/0.54  apply (zenon_equiv_s _ _ zenon_H28); [ zenon_intro zenon_H1a; zenon_intro zenon_H2b | zenon_intro zenon_H2a; zenon_intro zenon_H29 ].
% 0.19/0.54  apply (zenon_notand_s _ _ zenon_H2b); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ].
% 0.19/0.54  exact (zenon_H2d zenon_H1c).
% 0.19/0.54  generalize (zenon_H24 zenon_TA_y). zenon_intro zenon_H2e.
% 0.19/0.54  apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H2d | zenon_intro zenon_H2f ].
% 0.19/0.54  exact (zenon_H2d zenon_H1c).
% 0.19/0.54  exact (zenon_H2c zenon_H2f).
% 0.19/0.54  exact (zenon_H1a zenon_H2a).
% 0.19/0.54  Qed.
% 0.19/0.54  % SZS output end Proof
% 0.19/0.54  (* END-PROOF *)
% 0.19/0.54  nodes searched: 1118
% 0.19/0.54  max branch formulas: 676
% 0.19/0.54  proof nodes created: 77
% 0.19/0.54  formulas created: 7536
% 0.19/0.54  
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