TSTP Solution File: SET588+3 by Zenon---0.7.1

View Problem - Process Solution

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% File     : Zenon---0.7.1
% Problem  : SET588+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_zenon %s %d

% Computer : n021.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 06:37:03 EDT 2022

% Result   : Theorem 0.20s 0.54s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET588+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13  % Command  : run_zenon %s %d
% 0.14/0.34  % Computer : n021.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 : Sat Jul  9 20:55:36 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.20/0.54  (* PROOF-FOUND *)
% 0.20/0.54  % SZS status Theorem
% 0.20/0.54  (* BEGIN-PROOF *)
% 0.20/0.54  % SZS output start Proof
% 0.20/0.54  Theorem prove_difference_subset1 : (forall B : zenon_U, (forall C : zenon_U, (forall D : zenon_U, ((subset B C)->(subset (difference B D) (difference C D)))))).
% 0.20/0.54  Proof.
% 0.20/0.54  apply NNPP. intro zenon_G.
% 0.20/0.54  apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (forall D : zenon_U, ((subset B C)->(subset (difference B D) (difference C D)))))) zenon_G); [ zenon_intro zenon_H4; idtac ].
% 0.20/0.54  elim zenon_H4. zenon_intro zenon_TB_f. zenon_intro zenon_H6.
% 0.20/0.54  apply (zenon_notallex_s (fun C : zenon_U => (forall D : zenon_U, ((subset zenon_TB_f C)->(subset (difference zenon_TB_f D) (difference C D))))) zenon_H6); [ zenon_intro zenon_H7; idtac ].
% 0.20/0.54  elim zenon_H7. zenon_intro zenon_TC_i. zenon_intro zenon_H9.
% 0.20/0.54  apply (zenon_notallex_s (fun D : zenon_U => ((subset zenon_TB_f zenon_TC_i)->(subset (difference zenon_TB_f D) (difference zenon_TC_i D)))) zenon_H9); [ zenon_intro zenon_Ha; idtac ].
% 0.20/0.54  elim zenon_Ha. zenon_intro zenon_TD_l. zenon_intro zenon_Hc.
% 0.20/0.54  apply (zenon_notimply_s _ _ zenon_Hc). zenon_intro zenon_He. zenon_intro zenon_Hd.
% 0.20/0.54  generalize (subset_defn zenon_TB_f). zenon_intro zenon_Hf.
% 0.20/0.54  generalize (zenon_Hf zenon_TC_i). zenon_intro zenon_H10.
% 0.20/0.54  apply (zenon_equiv_s _ _ zenon_H10); [ zenon_intro zenon_H13; zenon_intro zenon_H12 | zenon_intro zenon_He; zenon_intro zenon_H11 ].
% 0.20/0.54  exact (zenon_H13 zenon_He).
% 0.20/0.54  generalize (subset_defn (difference zenon_TB_f zenon_TD_l)). zenon_intro zenon_H14.
% 0.20/0.54  generalize (zenon_H14 (difference zenon_TC_i zenon_TD_l)). zenon_intro zenon_H15.
% 0.20/0.54  apply (zenon_equiv_s _ _ zenon_H15); [ zenon_intro zenon_Hd; zenon_intro zenon_H18 | zenon_intro zenon_H17; zenon_intro zenon_H16 ].
% 0.20/0.54  apply (zenon_notallex_s (fun D : zenon_U => ((member D (difference zenon_TB_f zenon_TD_l))->(member D (difference zenon_TC_i zenon_TD_l)))) zenon_H18); [ zenon_intro zenon_H19; idtac ].
% 0.20/0.54  elim zenon_H19. zenon_intro zenon_TD_ba. zenon_intro zenon_H1b.
% 0.20/0.54  apply (zenon_notimply_s _ _ zenon_H1b). zenon_intro zenon_H1d. zenon_intro zenon_H1c.
% 0.20/0.54  generalize (difference_defn zenon_TC_i). zenon_intro zenon_H1e.
% 0.20/0.54  generalize (zenon_H1e zenon_TD_l). zenon_intro zenon_H1f.
% 0.20/0.54  generalize (zenon_H1f zenon_TD_ba). zenon_intro zenon_H20.
% 0.20/0.54  apply (zenon_equiv_s _ _ zenon_H20); [ zenon_intro zenon_H1c; zenon_intro zenon_H23 | zenon_intro zenon_H22; zenon_intro zenon_H21 ].
% 0.20/0.54  apply (zenon_notand_s _ _ zenon_H23); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ].
% 0.20/0.54  generalize (zenon_H11 zenon_TD_ba). zenon_intro zenon_H26.
% 0.20/0.54  apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ].
% 0.20/0.54  generalize (difference_defn zenon_TB_f). zenon_intro zenon_H29.
% 0.20/0.54  generalize (zenon_H29 zenon_TD_l). zenon_intro zenon_H2a.
% 0.20/0.54  generalize (zenon_H2a zenon_TD_ba). zenon_intro zenon_H2b.
% 0.20/0.54  apply (zenon_equiv_s _ _ zenon_H2b); [ zenon_intro zenon_H2e; zenon_intro zenon_H2d | zenon_intro zenon_H1d; zenon_intro zenon_H2c ].
% 0.20/0.54  exact (zenon_H2e zenon_H1d).
% 0.20/0.54  apply (zenon_and_s _ _ zenon_H2c). zenon_intro zenon_H30. zenon_intro zenon_H2f.
% 0.20/0.54  exact (zenon_H28 zenon_H30).
% 0.20/0.54  exact (zenon_H25 zenon_H27).
% 0.20/0.54  apply zenon_H24. zenon_intro zenon_H31.
% 0.20/0.54  generalize (difference_defn zenon_TB_f). zenon_intro zenon_H29.
% 0.20/0.54  generalize (zenon_H29 zenon_TD_l). zenon_intro zenon_H2a.
% 0.20/0.54  generalize (zenon_H2a zenon_TD_ba). zenon_intro zenon_H2b.
% 0.20/0.54  apply (zenon_equiv_s _ _ zenon_H2b); [ zenon_intro zenon_H2e; zenon_intro zenon_H2d | zenon_intro zenon_H1d; zenon_intro zenon_H2c ].
% 0.20/0.54  exact (zenon_H2e zenon_H1d).
% 0.20/0.54  apply (zenon_and_s _ _ zenon_H2c). zenon_intro zenon_H30. zenon_intro zenon_H2f.
% 0.20/0.54  exact (zenon_H2f zenon_H31).
% 0.20/0.54  exact (zenon_H1c zenon_H22).
% 0.20/0.54  exact (zenon_Hd zenon_H17).
% 0.20/0.54  Qed.
% 0.20/0.54  % SZS output end Proof
% 0.20/0.54  (* END-PROOF *)
% 0.20/0.54  nodes searched: 1470
% 0.20/0.54  max branch formulas: 448
% 0.20/0.54  proof nodes created: 165
% 0.20/0.54  formulas created: 6574
% 0.20/0.54  
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