TSTP Solution File: SET626+3 by Zenon---0.7.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zenon---0.7.1
% Problem  : SET626+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_zenon %s %d

% Computer : n027.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 06:37:31 EDT 2022

% Result   : Theorem 19.53s 19.71s
% Output   : Proof 19.53s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET626+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13  % Command  : run_zenon %s %d
% 0.14/0.34  % Computer : n027.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 09:05:18 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 19.53/19.71  (* PROOF-FOUND *)
% 19.53/19.71  % SZS status Theorem
% 19.53/19.71  (* BEGIN-PROOF *)
% 19.53/19.71  % SZS output start Proof
% 19.53/19.71  Theorem prove_th102 : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((intersect B (intersection C D))->(intersect B C))))).
% 19.53/19.71  Proof.
% 19.53/19.71  assert (zenon_L1_ : forall (zenon_TD_j : zenon_U) (zenon_TC_k : zenon_U) (zenon_TB_l : zenon_U), (~(exists D : zenon_U, ((member D zenon_TB_l)/\(member D zenon_TC_k)))) -> (member zenon_TD_j zenon_TB_l) -> (member zenon_TD_j zenon_TC_k) -> False).
% 19.53/19.71  do 3 intro. intros zenon_H6 zenon_H7 zenon_H8.
% 19.53/19.71  apply zenon_H6. exists zenon_TD_j. apply NNPP. zenon_intro zenon_Hc.
% 19.53/19.71  apply (zenon_notand_s _ _ zenon_Hc); [ zenon_intro zenon_He | zenon_intro zenon_Hd ].
% 19.53/19.71  exact (zenon_He zenon_H7).
% 19.53/19.71  exact (zenon_Hd zenon_H8).
% 19.53/19.71  (* end of lemma zenon_L1_ *)
% 19.53/19.71  apply NNPP. intro zenon_G.
% 19.53/19.71  apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, ((intersect B (intersection C D))->(intersect B C))))) zenon_G); [ zenon_intro zenon_Hf; idtac ].
% 19.53/19.71  elim zenon_Hf. zenon_intro zenon_TB_l. zenon_intro zenon_H10.
% 19.53/19.71  apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, ((intersect zenon_TB_l (intersection C D))->(intersect zenon_TB_l C)))) zenon_H10); [ zenon_intro zenon_H11; idtac ].
% 19.53/19.71  elim zenon_H11. zenon_intro zenon_TC_k. zenon_intro zenon_H12.
% 19.53/19.71  apply (zenon_notallex_s (fun D : zenon_U => ((intersect zenon_TB_l (intersection zenon_TC_k D))->(intersect zenon_TB_l zenon_TC_k))) zenon_H12); [ zenon_intro zenon_H13; idtac ].
% 19.53/19.71  elim zenon_H13. zenon_intro zenon_TD_u. zenon_intro zenon_H15.
% 19.53/19.71  apply (zenon_notimply_s _ _ zenon_H15). zenon_intro zenon_H17. zenon_intro zenon_H16.
% 19.53/19.71  generalize (intersect_defn zenon_TB_l). zenon_intro zenon_H18.
% 19.53/19.71  generalize (zenon_H18 (intersection zenon_TC_k zenon_TD_u)). zenon_intro zenon_H19.
% 19.53/19.71  apply (zenon_equiv_s _ _ zenon_H19); [ zenon_intro zenon_H1c; zenon_intro zenon_H1b | zenon_intro zenon_H17; zenon_intro zenon_H1a ].
% 19.53/19.71  exact (zenon_H1c zenon_H17).
% 19.53/19.71  elim zenon_H1a. zenon_intro zenon_TD_j. zenon_intro zenon_H1d.
% 19.53/19.71  apply (zenon_and_s _ _ zenon_H1d). zenon_intro zenon_H7. zenon_intro zenon_H1e.
% 19.53/19.71  generalize (intersect_defn zenon_TB_l). zenon_intro zenon_H18.
% 19.53/19.71  generalize (zenon_H18 zenon_TC_k). zenon_intro zenon_H1f.
% 19.53/19.71  apply (zenon_equiv_s _ _ zenon_H1f); [ zenon_intro zenon_H16; zenon_intro zenon_H6 | zenon_intro zenon_H21; zenon_intro zenon_H20 ].
% 19.53/19.71  generalize (intersection_defn zenon_TC_k). zenon_intro zenon_H22.
% 19.53/19.71  generalize (zenon_H22 zenon_TB_l). zenon_intro zenon_H23.
% 19.53/19.71  generalize (zenon_H23 zenon_TD_j). zenon_intro zenon_H24.
% 19.53/19.71  apply (zenon_equiv_s _ _ zenon_H24); [ zenon_intro zenon_H28; zenon_intro zenon_H27 | zenon_intro zenon_H26; zenon_intro zenon_H25 ].
% 19.53/19.71  apply (zenon_notand_s _ _ zenon_H27); [ zenon_intro zenon_Hd | zenon_intro zenon_He ].
% 19.53/19.71  generalize (zenon_H22 zenon_TD_u). zenon_intro zenon_H29.
% 19.53/19.71  generalize (zenon_H29 zenon_TD_j). zenon_intro zenon_H2a.
% 19.53/19.71  apply (zenon_equiv_s _ _ zenon_H2a); [ zenon_intro zenon_H2d; zenon_intro zenon_H2c | zenon_intro zenon_H1e; zenon_intro zenon_H2b ].
% 19.53/19.71  exact (zenon_H2d zenon_H1e).
% 19.53/19.71  apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H8. zenon_intro zenon_H2e.
% 19.53/19.71  exact (zenon_Hd zenon_H8).
% 19.53/19.71  exact (zenon_He zenon_H7).
% 19.53/19.71  apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H8. zenon_intro zenon_H7.
% 19.53/19.71  apply (zenon_L1_ zenon_TD_j zenon_TC_k zenon_TB_l); trivial.
% 19.53/19.71  exact (zenon_H16 zenon_H21).
% 19.53/19.71  Qed.
% 19.53/19.71  % SZS output end Proof
% 19.53/19.71  (* END-PROOF *)
% 19.53/19.71  nodes searched: 620721
% 19.53/19.71  max branch formulas: 13462
% 19.53/19.71  proof nodes created: 20174
% 19.53/19.71  formulas created: 780137
% 19.53/19.71  
%------------------------------------------------------------------------------