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